Fluidized Bed Heat Exchangers to Prevent Fouling in Ice ...

Fluidized Bed Heat Exchangers to Prevent Fouling

in

Ice Slurry Systems and Industrial Crystallizers

Proefschrift

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft

op gezag van de Rector Magnificus profdrirJTFokkema

voorzitter van het College voor Promoties

in het openbaar te verdedigen op maandag 25 september 2006 om 1530 uur

door Pepijn PRONK

werktuigkundig ingenieur

geboren te Haarlem

Dit proefschrift is goedgekeurd door de promotor Prof dr GJ Witkamp

Toegevoegd promotor Drir CA Infante Ferreira

Samenstelling promotiecommissie Rector Magnificus voorzitter Profdr GJ Witkamp Technische Universiteit Delft promotor Drir CA Infante Ferreira Technische Universiteit Delft toegevoegd promotor Profdrdr-inghabil H Muumlller-Steinhagen Universitaumlt Stuttgart Profdr-ing M Kauffeld Karlsruhe University of Applied Sciences Profdrir PJAM Kerkhof Technische Universiteit Eindhoven Profir H van der Ree Technische Universiteit Delft drir JS van der Meer Bronswerk Heat Transfer BV

Dit onderzoek is gedeeltelijk gefinancierd door Novem in het kader van het BSE-NECST programma

ISBN 90-9020923-9

Copyright copy 2006 by P Pronk

All rights reserved

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Contents

Summary ix

Samenvatting xiii

1 Introduction 1 11 Recent Developments in Refrigeration 1

111 Reduction of Synthetic Refrigerants 1 112 Revival of Natural Refrigerants 1 113 Advance of Indirect Refrigeration Systems 2

12 Ice Slurry 4 121 Ice Slurry Properties 4 122 Ice Slurry Systems 6 123 Applications of Ice Slurry 7

13 Fluidized Bed Heat Exchanger 8 131 Working Principle and Current Applications 8 132 Fluidized Bed Ice Slurry Generator 9 133 Promising New Applications 11

14 Objectives 12 15 Thesis Outline 12 Nomenclature 14 Abbreviations 14 References 14

2 Influence of Solute Type and Concentration on Ice Scaling 19 21 Introduction 19 22 Experimental Method 19 23 Experimental Results 22 24 Discussion 24

241 Crystal Growth Kinetics 24 242 Influence of Solute Concentration on Ice Scaling 25 243 Influence of Solute Type 26 244 Prediction Model for Ice Scaling 28 245 Application of Model for Other Crystallizers 30 246 Application of Surfactants to Prevent Ice Scaling 30

25 Conclusions 31 Nomenclature 32 Abbreviations 32 References 33

3 Influence of Fluidized Bed Parameters on Ice Scaling Part I Impact Measurements and Analysis 35

31 Introduction 35 32 Experimental Set-up 35

321 Single-tube Fluidized Bed Heat Exchanger 35 322 Measurement of Particle Collisions 36 323 Experimental Conditions 39

33 Results 40 331 Analysis of a Single Experiment 40

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332 Stationary Fluidized Beds 41 333 Circulating Fluidized Beds 43

34 Discussion 49 341 Stationary Fluidized Beds 49 342 Circulating fluidized beds 51 343 Expectations for Fouling Removal 56


4 Influence of Fluidized Bed Parameters on Ice Scaling Part II Coupling of Impacts and Ice Scaling 61


421 Single-tube Fluidized Bed Heat Exchanger 61 422 Experimental Conditions 63

43 Experimental Results 64 431 Determination of Transition Temperature Difference 64 432 Ice Scaling Prevention in Stationary Fluidized Beds 65 433 Ice Scaling Prevention in Circulating Fluidized Beds 66 434 Heat Transfer Coefficients 66

44 Model for Removal of Ice Scaling 67 441 Determination of Removal Rate 68 442 Removal Rate in Stationary Fluidized Beds 68 443 Removal Rate in Circulating Fluidized Beds 71

45 Discussion 73 451 Stationary Fluidized Beds 73 452 Circulating Fluidized Beds 74 453 Best Fluidized Bed Configuration for Fouling Removal 75


5 Fluidized Bed Heat Exchangers for Other Industrial Crystallization Processes 81

51 Introduction 81 52 Perspectives of Fluidized Bed Heat Exchangers for Other Industrial Crystallization

Processes 81 521 Introduction 81 522 Crystallization from the Melt 82 523 Crystallization from Solution 83 524 Eutectic Freeze Crystallization 86 525 Choice of Processes for Experimental Study 90

53 Experimental Set-up 90 54 Cooling Crystallization from Solution 91

541 Operating Conditions 92 542 Experimental Results 92 543 Discussion 94

55 Eutectic Freeze Crystallization from Binary Solutions 95

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551 Operating Conditions 95 552 Expectations based on Previous Experiments 96 553 Experimental Results 96 554 Discussion 98

56 Eutectic Freeze Crystallization from Ternary and Quaternary Solutions 100 561 Operating Conditions 100 562 Experimental Results for Ternary Solutions 101 563 Experimental Results for Quaternary Solutions 103 564 Discussion 104 565 Perspectives of Fluidized Bed Heat Exchangers for EFC 105


6 Comparison between Fluidized Bed and Scraped Surface Ice Slurry Generators111 61 Introduction 111 62 Scraped Surface Ice Slurry Generators 112

621 Ice Slurry Generators with Scraper Blades 112 622 Ice Slurry Generators with Orbital Rods 114

63 Prevention of Ice Scaling 115 631 Introduction 115 632 Experimental Scraped Surface Heat Exchanger and Conditions 116 633 Experimental Results on Ice Scaling Prevention 117 634 Comparison of Ice Scaling Prevention 120

64 Heat Transfer Performance 122 641 Influence of Operating Conditions 122 642 Influence of Thermophysical Properties 124 643 Influence of Ice Crystallization 125

65 Investment and Maintenance Costs 126 651 Investment Costs 126 652 Maintenance Costs 128

66 Energy Consumption 129 661 Additional Power Consumption of Ice Slurry Generators 129 662 Compressor Power Consumption of Ice Slurry Generators 131 663 Total Power Consumption of Ice Slurry Generators 132 664 Total Annual Costs of Ice Slurry Generators 132

67 Conclusions 133 Nomenclature 134 References 134

7 Long-term Ice Slurry Storage 139 71 Introduction 139 72 Recrystallization Mechanisms 141

721 Attrition 141 722 Agglomeration 142 723 Ostwald Ripening 142 724 Conclusions 146

73 Experiments on Ice Slurry Storage 146 731 Experimental Set-up 147

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732 Experimental Procedure 147 733 Results 148 734 Comparison of Results with Results from Literature 151 735 Discussion 153 736 Conclusions 158

74 Dynamic Modeling of Ostwald Ripening 158 741 Model Development 158 742 Validation Conditions 161 743 Validation Results 162 744 Discussion 164 745 Conclusions 166


8 Melting of Ice Slurry in Heat Exchangers 171 81 Introduction 171 82 Literature Review on Ice Slurry Melting in Heat Exchangers 171

821 Flow Patterns 171 822 Rheology 172 823 Pressure Drop 172 824 Heat Transfer Coefficients 173 825 Superheating 174 826 Outlook for Experiments 175

83 Experimental Method 175 831 Experimental Set-up 175 832 Experimental Conditions 176 833 Data Reduction 177

84 Results and Discussion on Superheating 178 841 Analysis of a Single Experiment 178 842 Influence of Ice Fraction and Ice Slurry Velocity 183 843 Influence of Heat Flux 184 844 Influence of Crystal Size 184 845 Influence of Solute Concentration 184 846 Discussion 185 847 Conclusions 190

85 Results and Discussion on Heat Transfer Coefficients 190 851 Influence of Ice Fraction and Ice Slurry Velocity 190 852 Influence of Heat Flux and Ice Crystal Size 192 853 Influence of Solute Concentration 192 854 Conclusions 193

86 Results and Discussion on Pressure Drop 193 861 Influence of Ice Fraction and Ice Slurry Velocity 193 862 Influence of Heat Flux Ice Crystal Size and Solute Concentration 194 863 Conclusions 196


9 Conclusions 201

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Appendix A Properties of Aqueous Solutions 205 A1 Model Description 205

A11 Phase Equilibrium Data 205 A12 Density Specific Heat and Thermal Conductivity 206 A13 Dynamic Viscosity 206 A14 Enthalpy 206 A15 Diffusion Coefficient 208

A2 Organic Aqueous Solutions 209 A21 D-glucose (C6H12O6) 209 A22 Ethanol (C2H6O) 211 A23 Ethylene Glycol (C2H6O2) 213 A24 Propylene Glycol (C3H8O2) 215

A3 Inorganic Aqueous Solutions 217 A31 Magnesium Sulfate (MgSO4) 217 A32 Potassium Chloride (KCl) 219 A33 Potassium Formate (KCOOH or KFo) 221 A34 Potassium Nitrate (KNO3) 223 A35 Sodium Chloride (NaCl) 225

Nomenclature 227 References 227

Appendix B Properties of Ice and Ice Slurries 229 B1 Properties of Ice 229

B11 Density 229 B12 Thermal Conductivity 229 B13 Enthalpy 229 B14 Specific Heat 229

B2 Properties of Ice Slurries 229 B21 Density 229 B22 Thermal Conductivity 230 B23 Enthalpy 230 B24 Specific Heat 230 B25 Dynamic Viscosity 231


Appendix C Calibration of Heat Exchangers 233 C1 Small Fluidized Bed Heat Exchanger 233

C11 Dimensions 233 C12 Determination of Heat Uptake from Surroundings 234 C13 Validation of Heat Transfer Model for Annulus 235

C2 Large Fluidized Bed Heat Exchanger 238 C21 Dimensions 238 C22 Determination of Heat Uptake from the Surroundings 238 C23 Validation of Heat Transfer Model for the Annulus 239

C3 Melting Heat Exchanger 241 C31 Dimensions 241 C32 Determination of Heat Uptake from the Surroundings 241 C33 Formulation of Heat Transfer Expressions 242 C34 Formulation of Pressure Drop Expressions for the Inner Tube 247

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C4 Scraped Surface Heat Exchanger 249 C41 Dimensions 249 C42 Determination of Heat Uptake from the Surroundings 249 C43 Formulation of Heat Transfer Expressions 250


Appendix D Accuracy of Heat Exchanger Measurements 255 D1 Fluidized Bed Heat Exchangers 255

D11 Accuracy of Sensors 255 D12 Overall Heat Transfer Coefficient 255 D13 Fluidized Bed Heat Transfer Coefficient 256 D14 Difference between Wall and Equilibrium Temperature 256 D15 Bed Voidage 257 D16 Average Upward Particle Velocity 257

D2 Melting Heat Exchanger 258 D21 Accuracy of Sensors 258 D22 Overall Heat Transfer Coefficient 258 D23 Wall-to-liquid Heat Transfer Coefficient at Ice Slurry Side 258 D24 Degree of Superheating 259 D25 Pressure Drop 259

D3 Scraped Surface Heat Exchanger 259 D31 Accuracy of Sensors 259 D32 Overall Heat Transfer Coefficient 260 D33 Scraped Surface Heat Transfer Coefficient 260 D34 Difference between Wall and Equilibrium Temperature 260

D4 Summary 261 Nomenclature 262

Dankwoord xvii

Curriculum Vitae xix Publications xix

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Summary

Fluidized Bed Heat Exchangers to Prevent Fouling in Ice Slurry Systems and Industrial Crystallizers

Pepijn Pronk

The phase out of CFC and HCFC refrigerants and the restrictions to HFC refrigerants have led to a revival of natural refrigerants like ammonia and hydrocarbons in refrigeration systems Since most natural refrigerants are toxic or flammable indirect refrigeration systems are more frequently applied nowadays The primary cycle of these indirect systems containing the hazardous refrigerant is safely located in a machine room The cold energy is distributed by a secondary refrigerant usually an aqueous solution to the locations where cooling is required Ice slurry is an interesting secondary refrigerant for indirect systems mainly because of its high heat capacity enabling cold thermal storage A difficulty of ice slurry is however the marked tendency of ice crystals to adhere to cold heat exchanger walls also referred to as ice scaling which requires a mechanism to remove the ice crystals from the walls In most ice slurry systems scraped surface heat exchangers are applied for ice slurry production The investment costs of these apparatuses are relatively high and therefore application of ice slurry as secondary refrigerant has been limited up to now A new type of ice slurry generator using a liquid-solid fluidized bed may reduce the costs of ice slurry systems which may lead to more widespread use of ice slurry as secondary refrigerant

The main objective of this research is to study the capabilities of fluidized bed heat exchangers for ice slurry production in indirect refrigeration systems The main focus is on the ability of liquid-solid fluidized bed to prevent ice scaling and on the physical mechanisms behind this phenomenon Other objectives are to compare the fluidized bed ice slurry generator with competitive equipment and to investigate promising new industrial crystallization applications for the fluidized bed heat exchanger concept A final objective is to study the behavior of produced ice crystals in other components of an ice slurry system namely storage tanks and melting heat exchangers

It is generally known that the ice scaling prevention ability of ice slurry generators is influenced by the solute of the aqueous solution However quantitative data on the role of solutes on ice scaling are lacking in literature and the physical mechanisms behind this phenomenon are not understood yet Chapter 2 presents experiments with a single-tube fluidized bed heat exchanger in which ice crystals were produced from aqueous solutions of various solutes with various concentrations The fluidized bed tube had a diameter of 427 mm and a height of 488 m while a stationary fluidized bed consisting of stainless steel cylinders of 4 mm was operated at a constant bed voidage of 81 The results reveal that ice scaling is only prevented when a certain temperature difference between the wall and the solution is not exceeded This so-called transition temperature difference is approximately proportional with the solute concentration and is higher in aqueous solutions with low diffusion coefficients The explanation for the observed phenomena is that ice scaling is only prevented when the mass transfer controlled growth rate of ice crystals on the wall does not exceed the scale removal rate induced by the fluidized steel particles

Besides the solute the ice scaling prevention ability of fluidized bed ice slurry generators is also influenced by the frequency and force of particle impacts on the wall These impact

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characteristics vary with fluidized bed conditions such as the particle size the bed voidage and the fluidization mode Chapter 3 presents fluidized bed experiments in which a piezoelectric sensor was used to measure the impacts on the wall of both stationary and circulating fluidized beds Impacts were measured for various fluidized bed conditions with particle sizes of 2 3 or 4 mm and with bed voidages ranging from 69 to 96 An analysis of the results shows two different types of impacts namely collisions of particles on the sensor and impacts by liquid pressure fronts induced by particle-particle collisions close to the sensor The impact measurements are used to formulate expressions for the frequency and the forces of both impact types These expressions are subsequently used to analyze the total impulse and energy exerted by impacts on the wall for various fluidized beds In stationary fluidized beds both impulse and energy increase with increasing particle size and decreasing bed voidage The impulse and energy exerted by particles on the wall of circulating fluidized beds increases as the circulation rate increases

In Chapter 4 the influence of fluidized bed conditions such as fluidization mode particle size and bed voidage on ice scaling and heat transfer coefficients during ice crystallization is experimentally studied The single-tube fluidized bed heat exchanger was used to produce ice crystals from an aqueous 77 wt sodium chloride solution Both stationary and circulating fluidized beds were applied with various particle sizes varying from 2 to 4 mm and bed voidages ranging from 72 to 94 The experimental results show that the ice scaling prevention ability of stationary fluidized beds increases with decreasing bed voidage and increasing particle size Furthermore the prevention of ice scaling appears to be more effective in circulating fluidized beds especially at high circulation rates A coupling of the results on ice scaling prevention and the impact characteristics shows that the prevention of ice scaling is realized by both particle-wall collisions and pressure fronts induced by particle-particle collisions The comparison reveals furthermore that the removal rate of ice crystals from the wall is proportional to the total impulse exerted by the impacts on the wall

Besides the application of ice slurry production fluidized bed heat exchangers may also be attractive for other industrial crystallization processes as is discussed in Chapter 5 From several industrial processes that suffer from severe crystallization fouling two processes have been selected for an experimental study First experiments were performed on cooling crystallization of KNO3 and MgSO47H2O from their aqueous solutions showing that fluidized beds are able to prevent salt crystallization fouling Next eutectic freeze concentration experiments were performed from binary aqueous solutions of KNO3 and MgSO4 in which both salt and ice simultaneously crystallized The experiments reveal that crystallization fouling during eutectic freeze crystallization is more severe than during separate salt or ice crystallization from the same solution The explanation for this phenomenon is that the salt crystallization process eliminates the mass transfer limitation for ice growth resulting in an increased ice growth rate and more severe ice scaling The addition of a non-crystallizing component strongly reduces crystallization fouling during eutectic freeze crystallization and enables to perform this process in fluidized bed heat exchangers at reasonable heat fluxes

The performance of fluidized bed ice slurry generators is compared with the performance of scraped surface ice slurry generators in Chapter 6 The latter apparatuses use rotating scraper blades or orbital rods to remove ice crystals from the walls and are the most frequently applied ice slurry generator types in practice Experiments on ice crystallization from KNO3 solutions were performed with a scraped surface heat exchanger showing transition temperature differences for ice scaling that are a factor of 75 higher than in fluidized bed ice slurry generators Heat transfer coefficients in both ice slurry generators are comparable The

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investment costs per square meter are considerably lower for fluidized bed heat exchangers than for scraped surface heat exchangers Due to the low ice scaling prevention ability at temperatures close to 0degC fluidized bed ice slurry generators should be operated at ice slurry temperatures of about ndash5degC with a heat flux of approximately 10 kWm2 Commercial scraped surface ice slurry generators are often operated with an ice slurry temperature of ndash2degC and a heat flux of 20 kWm2 A comparison between these two systems for cooling capacities of 100 kW and larger shows that the investment costs of fluidized bed ice slurry generators are about 30 tot 60 lower than of scraped surface ice slurry generators Furthermore the energy consumption of ice slurry generators with fluidized bed is about 5 to 21 lower It can therefore be concluded that the fluidized bed ice slurry generator is an attractive ice crystallizer concerning both investment costs and energy consumption

One of the main advantages of ice slurry as secondary refrigerant is the possibility of thermal storage which enables load shifting and peak shaving During storage ice crystals are subject to recrystallization mechanisms as attrition agglomeration and Ostwald ripening Storage experiments with ice crystals in various aqueous solutions are presented in Chapter 7 showing that Ostwald ripening is the most important mechanism inducing an increase in the average crystal size The rate of Ostwald ripening strongly decreases as the solute concentration increases and the solute type and the mixing regime also play an important role From these results is concluded that crystal growth and dissolution during Ostwald ripening are mainly limited by mass transfer especially at higher solute concentrations The obtained results are used to develop a computer-based dynamic model of Ostwald ripening in ice suspensions Validation of this model with the experimental results shows that the model is able to predict the development of the average crystal size in time

Another major component of ice slurry systems is the melting heat exchanger where ice slurry absorbs heat and provides cooling to products or processes Several researchers have measured heat transfer coefficients and pressure drop values in melting heat exchangers but relatively little is known about superheating Superheating is the phenomenon that the liquid temperature of ice slurry is higher than its equilibrium temperature which can lead to serious limitations in the capacity of melting heat exchangers Chapter 8 presents melting experiments with a tube-in-tube heat transfer coil in which ice slurry flows through the inner tube and is heated by an aqueous ethylene glycol solution flowing through the annulus The results show superheating values ranging from 05 to 50 K depending on parameters such as velocity average crystal size solute concentration ice fraction and heat flux The various influences are explained by considering the melting process as a two-stage process The first stage is the heat transfer process between the wall and the liquid while the second stage consists of the combined heat and mass transfer process between the crystals and the liquid Parameters like ice crystal size and solute concentration strongly influence the rate of the second stage and therefore also affect superheating Measured trends for wall-to-liquid heat transfer coefficients and pressure drop are in accordance with trends described in literature

Finally it can be concluded that fluidized bed heat exchangers are attractive for ice slurry production Fluidized beds prevent ice scaling when its removal rate exceeds the growth rate of ice crystals attached to the wall The removal rate is proportional to the impulse exerted by particles-wall collisions and by liquid pressure fronts induced by particle-particle collisions The ice growth rate is limited by mass transfer and is therefore low in solutions with high solute concentrations and with low diffusion coefficients Fluidized bed heat exchangers are also attractive for other industrial crystallization processes that suffer from crystallization fouling such as cooling crystallization and eutectic freeze crystallization The investment costs of fluidized bed heat exchangers are low compared to scraped surface heat exchangers

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despite the fact that they must be operated at lower heat fluxes due to their limited scaling prevention ability The average ice crystal size increases during storage due to Ostwald ripening and the capacity of melting heat exchangers can seriously be reduced by superheating Both the rate of Ostwald ripening and the degree of superheating can be explained by ice crystallization kinetics which are mainly dominated by mass transfer

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Samenvatting

Wervelbed-warmtewisselaars ter voorkoming van ijsaankorsting in ijsslurriesystemen en industrieumlle kristallisatoren

Pepijn Pronk

Het uitbannen van CFK and HCFK koudemiddelen en de beperkingen voor HFK koudemiddelen hebben geleid tot een opleving van natuurlijke koudemiddelen zoals ammoniak en koolwaterstoffen in koel- en vriessystemen Omdat deze natuurlijke koudemiddelen giftig of brandbaar zijn worden indirecte koelsystemen tegenwoordig steeds vaker toegepast De primaire kringloop van dergelijke indirecte systemen die het gevaarlijke koudemiddel bevat bevindt zich in een veilig afgesloten machinekamer De koude wordt met behulp van een koudedrager meestal een waterige oplossing gedistribueerd naar plaatsen waar koeling nodig is IJsslurrie een suspensie van een waterige oplossing en ijskristallen is een interessante koudedrager voor indirecte systemen Het grote voordeel van ijsslurrie is de grote koudecapaciteit waardoor energieopslag economisch aantrekkelijk is Een praktisch probleem van ijsslurrie is echter de sterke neiging van ijskristallen om aan de gekoelde wand van de warmtewisselaar te hechten hetgeen ook wel ijsaankorsting wordt genoemd Om dichtvriezen van de warmtewisselaar te voorkomen is een mechanisme nodig dat de ijskristallen van de warmtewisselaarwand verwijdert In de meeste ijsslurriesystemen worden hiervoor geschraapte warmtewisselaars gebruikt De investeringskosten van deze apparaten zijn relatief hoog en daarom wordt ijsslurrie tot nu toe slechts op beperkte schaal toegepast als koudedrager Een nieuw type ijsslurriegenerator die gebruik maakt van een vloeistof-vast wervelbed kan de kosten van ijsslurriesystemen beperken en kan daarom leiden tot bredere toepassing van ijsslurrie als koudedrager

Het hoofddoel van dit onderzoek is het bestuderen van wervelbed-warmtewisselaars voor de productie van ijsslurrie voor indirecte koelsystemen De focus is hierbij vooral gericht op de mogelijkheid van vloeistof-vast wervelbedden om ijsaankorsting aan de wanden van warmtewisselaars te voorkomen en de fysische mechanismen hierachter Andere doelen zijn het vergelijken van wervelbed-ijsslurriegeneratoren met concurrerende apparaten en het onderzoeken van veelbelovende nieuwe toepassingen voor wervelbed-warmtewisselaars op het gebied industrieumlle kristallisatie Een laatste doel is het onderzoeken van het gedrag van geproduceerde ijskristallen in andere componenten van een ijsslurriesysteem zoals buffertanks en smeltwarmtewisselaars

Het is algemeen bekend dat de mate van ijsaankorsting in ijsslurriegeneratoren wordt beiumlnvloedt door de in het water opgeloste stof Kwantitatieve gegevens over deze invloed ontbreken echter in de literatuur en de fysische mechanismen hierachter zijn tot nu toe niet achterhaald Hoofdstuk 2 beschrijft experimenten met een enkelpijps wervelbed-warmtewisselaar waarin ijskristallen zijn geproduceerd in waterige oplossingen van diverse stoffen met verschillende concentraties De buis waarin het wervelbed zich bevond had een diameter van 427 mm en een hoogte van 488 m Het stationaire wervelbed in de buis bestond uit RVS cilinders van 4 mm en de porositeit van het wervelbed was 81 De resultaten van deze experimenten laten zien dat ijsaankorsting alleen voorkomen kan worden door het wervelbed als een bepaald temperatuurverschil tussen de wand en de vloeistof niet wordt overschreden Dit zogenaamde transitie temperatuurverschil is ongeveer proportioneel met de concentratie opgeloste stof en is groter in waterige oplossingen met een lage

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diffusiecoeumlfficieumlnt De verklaring voor deze resultaten is dat ijsaankorsting alleen wordt voorkomen als de groeisnelheid van ijskristallen aan de wand die wordt bepaald door stoftransport niet groter is dan de verwijderingssnelheid die wordt bepaald door de deeltjes van het wervelbed

Naast de invloed van de opgeloste stof wordt de mogelijkheid van wervelbed-deeltjes om ijsaankorsting te voorkomen ook sterk beiumlnvloed door de frequentie en sterkte van de deeltjesinslagen tegen de wand Deze inslagparameters worden bepaald door wervelbedcondities zoals de deeltjesgrootte de bedporositeit en de wijze van fluiumldiseren Hoofdstuk 3 beschrijft experimenten met de enkelpijps wervelbed-warmtewisselaar waarin een pieumlzo-elektrische sensor is gebruikt om inslagen van deeltjes op de wand te meten in zowel stationaire als circulerende wervelbedden De inslagen zijn gemeten bij verschillende wervelbedcondities met RVS deeltjes van 2 3 en 4 mm en met verschillende bedporositeiten varieumlrend van 69 tot 96 De analyse van de resultaten laat twee verschillende soorten inslagen zien namelijk botsingen van deeltjes op de sensor en inslagen door drukgolven als gevolg van botsingen tussen twee deeltjes vlakbij de sensor De meetresultaten zijn gebruikt om empirische formules op te stellen voor de frequentie en de sterkte van de twee soorten inslagen Deze formules zijn vervolgens gebruikt voor het analyseren van de totale impuls en de totale energie die door de inslagen worden uitgeoefend op de wand door verschillende wervelbedden In stationaire wervelbedden blijken zowel de impuls als de energie toe te nemen als grotere deeltjes worden gebruikt of als een lagere bedporositeit wordt toegepast De impuls en de energie uitgeoefend door de deeltjes op de wand van circulerende wervelbedden nemen toe als de circulatiesnelheid toeneemt

In Hoofdstuk 4 worden de invloeden van wervelbedcondities zoals de fluiumldisatie modus de deeltjesgrootte en de bedporositeit op ijsaankorsting en warmteoverdracht tijdens ijskristallisatie experimenteel onderzocht De experimentele enkelpijps wervelbed-warmtewisselaar is in dit kader gebruikt voor het produceren van ijskristallen in een waterige keukenzoutoplossing van 77 wt Voor deze experimenten zijn zowel stationaire als circulerende wervelbedden toegepast met deeltjesgroottes varieumlrend van 2 tot 4 mm en met bedporositeiten tussen 72 en 92 De resultaten van de experimenten laten zien dat de mogelijkheid om ijsaankorsting te voorkomen in stationaire wervelbedden toeneemt als de bedporositeit afneemt of de deeltjesgrootte toeneemt Verder is de verwijdering aan ijsaankorsting effectiever in circulerende wervelbedden vooral bij hoge circulatiesnelheden Een koppeling van de resultaten over ijsaankorsting en de inslagkarakteristieken laat zien dat het voorkomen van ijsaankorsting wordt gerealiseerd door zowel de botsingen van deeltjes op de wand als ook door de drukgolven veroorzaakt door botsingen tussen deeltjes De vergelijking laat verder zien dat de verwijderingsnelheid van ijskristallen van de wand evenredig is met de impuls die uitgeoefend wordt op deze wand

Naast de productie van ijsslurrie zijn wervelbed-warmtewisselaars ook aantrekkelijk voor andere industrieumlle kristallisatieprocessen zoals is beschreven in Hoofdstuk 5 Uit een reeks van industrieumlle processen waarbij afzetting van kristallijn materiaal op warmtewisselende oppervlakken een probleem is zijn twee processen geselecteerd voor een experimenteel onderzoek Allereerst zijn koelkristallisatie experimenten verricht waarbij KNO3 en MgSO47H2O zijn gekristalliseerd uit hun waterige oplossingen De resultaten van deze experimenten tonen aan dat wervelbedden ook in staat zijn om zoutaankorsting te voorkomen Vervolgens zijn eutectische vrieskristallisatie experimenten uitgevoerd met binaire oplossingen van KNO3 en MgSO4 waarbij tegelijkertijd zout- en ijskristallen werden gevormd De experimentele resultaten laten zien dat aankorsting van kristallijn materiaal tijdens eutectische vrieskristallisatie lastiger te verwijderen is dan gedurende individuele zout-

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of ijskristallisatie vanuit dezelfde oplossing De verklaring voor dit verschijnsel is dat zoutkristallisatie in de buurt van het ijsoppervlak de stofoverdrachtsweerstand voor ijsgroei opheft waardoor de groeisnelheid van ijskristallen op de wand toeneemt en ijsaankorsting zeer moeilijk is te voorkomen Het toevoegen van een niet-kristalliserende stof verkleint de neiging tot ijsaankorsting tijdens eutectische vrieskristallisatie aanzienlijk en maakt het mogelijk om dit proces uit te voeren met wervelbed-warmtewisselaars

De prestaties van wervelbed-ijsslurriegeneratoren worden in Hoofdstuk 6 vergeleken met de prestaties van geschraapte ijsslurriegeneratoren De laatstgenoemde apparaten gebruiken schrapers of roterende staven voor het verwijderen van ijskristallen van de wand en zijn momenteel de meest toegepaste ijsslurriegeneratoren Experimenten met waterige KNO3 oplossingen laten zien dat het maximale temperatuurverschil voor het voorkomen van ijsaankorsting in geschraapte warmtewisselaars 75 maal groter is dan in wervelbed-ijsslurriegeneratoren De warmteoverdrachtscoeumlfficieumlnt tussen wand en ijsslurrie is vergelijkbaar voor beide ijsslurriegeneratoren terwijl de investeringskosten per vierkante meter aanzienlijk lager zijn voor wervelbed-warmtewisselaars Door de geringe mogelijkheid om ijsaankorsting te voorkomen bij waterige oplossingen met vriespunten dichtbij 0degC kunnen wervelbed-ijsslurriegeneratoren het best worden bedreven met ijsslurrie temperaturen rond ndash5degC en warmtestroomdichtheden van ongeveer 10 kWm2 Commercieel verkrijgbare geschraapte ijsslurriegeneratoren worden vaak bedreven met een ijsslurrie temperatuur van ndash2degC en een warmtestroomdichtheid van 20 kWm2 Een vergelijking van deze beide systemen voor koelcapaciteiten van 100 kW en groter laat zien dat de investeringskosten van wervelbed-ijsslurriegeneratoren ongeveer 30 tot 60 lager zijn ten opzichte van geschraapte ijsslurriegeneratoren Daarnaast is het energiegebruik van ijsslurriegeneratoren met wervelbed zorsquon 5 tot 21 lager Samenvattend kan worden geconcludeerd dat de wervelbed-ijsslurriegenerator een aantrekkelijke alternatief is zowel wat betreft investeringskosten als energiegebruik

Eeacuten van de grote voordelen van het gebruik van ijsslurrie als koudedrager is de mogelijkheid van koudeopslag waardoor de koudeproductie kan worden verplaatst naar de nacht of pieken in de koudevraag over de gehele dag kunnen worden verdeeld Tijdens opslag in buffervaten zijn ijskristallen onderhevig aan rekristallisatie mechanismen zoals attritie agglomeratie en Ostwald rijpen Hoofdstuk 7 beschrijft experimenten waarbij ijskristallen in diverse waterige oplossingen isotherm zijn opgeslagen De resultaten laten zien dat Ostwald rijpen het belangrijkste mechanisme is dat zorgt voor een toename van de gemiddelde kristalgrootte De snelheid van het Ostwald rijpen neemt sterk af met toenemende concentratie opgeloste stof Daarnaast spelen de soort opgeloste stof en de mate van roeren een belangrijke rol Uit de resultaten kan worden geconcludeerd dat het groeien en oplossen van kristallen tijdens Ostwald rijpen vooral wordt bepaald door stoftransport vooral bij hoger concentraties opgeloste stof De verkregen resultaten zijn gebruikt voor het opstellen van een dynamische model van Ostwald rijpen in ijsslurries De validatie van dit model aan de hand van experimentele resultaten laat zien dat het model in staat is om het verloop van de gemiddelde kristalgrootte in de tijd te voorspellen

Een andere hoofdcomponent van ijsslurrie systemen is de smeltwarmtewisselaar waarin ijsslurrie warmte opneemt en daardoor producten of processen koelt Diverse onderzoekers hebben metingen verricht om de warmteoverdrachtscoeumlfficieumlnt en de drukval van ijsslurrie in deze warmtewisselaars te bepalen maar relatief weinig is bekend over het fenomeen oververhitting Bij oververhitting van ijsslurries is de vloeistoftemperatuur hoger dan de evenwichtstemperatuur hetgeen kan leiden tot een sterke reductie van de capaciteit van smeltwarmtewisselaars Hoofdstuk 8 beschrijft smeltexperimenten met een spiraalvormige

xvi

warmtewisselaar waarin ijsslurrie door de binnenste buis stroomde en werd verhit door een waterige ethyleenglycol oplossing De resultaten van deze experimenten laten een oververhitting zien die varieert tussen 05 en 50 K en afhangt van parameters zoals de snelheid de gemiddelde kristalgrootte de concentratie opgeloste stof de ijsfractie en de warmtestroomdichtheid De invloed van de diverse parameters wordt verklaard aan de hand van het smeltproces dat kan worden beschouwd als een tweestaps proces De eerste stap is het overdragen van warmte van de wand naar de vloeistof de tweede stap bestaat uit het gecombineerde proces van stof- en warmteoverdracht tussen de ijskristallen en de vloeistof Parameters als de kristalgrootte en de concentratie opgeloste stof hebben een sterke invloed op de tweede stap en daarmee ook op de mate van oververhitting De gemeten trends voor de warmteoverdrachtscoeumlfficieumlnt tussen wand en vloeistof en voor de drukval zijn in overeenstemming met de trends die worden beschreven in de literatuur

Tot slot kan worden geconcludeerd dat wervelbed-warmtewisselaars aantrekkelijk zijn voor de productie van ijsslurrie Wervelbedden zijn in staat om ijsaankorsting te voorkomen zolang de verwijderingsnelheid hoger is dan de groeisnelheid van ijskristallen aan de wand De verwijderingsnelheid van het wervelbed is evenredig met de impuls die wordt uitgeoefend door botsingen van deeltjes op de wand en door drukgolven veroorzaakt door botsingen van deeltjes onderling De ijsgroeisnelheid wordt bepaald door stofoverdracht en is daarom laag in oplossingen met hoge concentraties opgeloste stof of met lage diffusiecoeumlfficieumlnten Wervelbed-warmtewisselaars zijn ook aantrekkelijk voor andere industrieumlle kristallisatie-processen waarbij de afzetting van kristallijn materiaal op warmtewisselende oppervlakken optreedt zoals koelkristallisatie en eutectische vrieskristallisatie De investeringskosten van wervelbed-warmtewisselaars zijn laag vergeleken met geschraapte warmtewisselaars ondanks het feit dat lagere warmtestroomdichtheden kunnen worden toegepast Tijdens de opslag van ijsslurrie neemt de gemiddelde kristalgrootte toe als gevolg van Ostwald rijpen en de capaciteit van smeltwarmtewisselaars kan ernstig worden verlaagd door oververhitting Zowel de snelheid van Ostwald rijpen als de mate van oververhitting kunnen worden verklaard aan de hand van de kristallisatie kinetiek van ijskristallen die vooral wordt bepaald door stofoverdracht

1

1 Introduction

11 Recent Developments in Refrigeration

111 Reduction of Synthetic Refrigerants

In 1974 Molina and Rowland (1974) discovered that the emission of chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) into the atmosphere leads to the destruction of the ozone layer which protects life on earth against too much ultraviolet solar radiation From their introduction in the 1930s up to then CFCs and HCFCs had been applied on a large-scale in refrigeration and air conditioning equipment The findings of Molina and Rowland were confirmed by other researchers some years later and refrigerant producers began to search for alternatives (Powell 2002) After the discovery of the lsquoozone holersquo by Farman et al (1985) governments agreed upon the Montreal Protocol in 1987 which prescribes the world-wide phase out of CFCs and HCFCs (UNEP 2003 IIR 2005a)

As alternative to CFCs and HCFCs refrigerants without chlorine called hydrofluorocarbons (HFCs) were developed and successfully introduced in many different types of refrigeration equipment in the 1990s Although some of these HFCs show good thermodynamic properties and are nonflammable and nontoxic they appeared to be also strong greenhouse gases just like CFCs and HCFCs The emission of greenhouse gases into the atmosphere is believed to cause global warming and changes of local climates The most important greenhouse gas in this respect is carbon dioxide (CO2) but also other greenhouse gases such as HFCs are believed to have a significant influence Although the worldwide emissions of HFCs are relatively low compared to CO2 emissions their contributions to global warming per unit of mass are considerably higher In order to reduce global warming in the present century governments drew up the Kyoto Protocol in 1997 In this agreement industrialized countries agreed upon restrictions to greenhouse gas emissions by an average of 52 over the period from 2008 to 2012 compared to the period from 1995 to 2000 For the European Union the total reduction of greenhouse gases was set at 8 with respect to the emission level of 1990 (IIR 2005a IPCC 2005 UNFCC 2005)

112 Revival of Natural Refrigerants

Because of the described international agreements concerning ozone layer depletion and global warming refrigeration industries and research institutes are looking for more sustainable refrigerants with negligible direct effects on the environment At this moment research focuses on refrigerants that were used before synthetic refrigerants such as CFCs HCFCs and HFCs were developed The most important natural refrigerants in this respect are ammonia carbon dioxide hydrocarbons like propane and iso-butane water and air (Lorentzen 1995) From all these refrigerants hydrocarbons and especially ammonia show the best energetic performances in standard vapor compression cycles These performances are in case of ammonia even better than of commonly used HFC refrigerants (see Figure 11)

Chapter 1

2

-250

-200

-150

-100

-50

00

50

-350 -300 -250 -200 -150 -100 -50 00 50Evaporation temperature (degC)

Ammonia

R407C

R404A

R134a

PropaneR

elat

ive

diff

eren

ce in

CO

P co

mpa

red

to a

mm

onia

Figure 11 Comparison of COPs of propane ammonia and some HFCs in a vapor compression system with 70 isentropic compressor efficiency and a condensation

temperature of 40degC

Besides the high energetic efficiencies the application of ammonia as refrigerant shows additional advantages such as high volumetric refrigeration capacities excellent heat transfer performance and the applicability in a wide temperature range (Lorentzen 1988) Despite these advantages ammonia is not widely applied nowadays and its application is limited to installations in industrial environments such as food and beverage industry (Taylor et al 2004) The main reasons for the limited use of ammonia are its toxicity and flammability Ammonia gets toxic in air at concentrations of about 500 ppm However its smell is already noticeable at concentrations of 5 ppm and is intolerable at 50 ppm Due to its distinctive smell small leakages will be detected before dangerous situations will occur Furthermore ammonia gas is much lighter than air and is therefore easily vented away Ammonia gets flammable in air at concentrations between 17 and 29 vol which is high compared to other flammable gases These concentrations are not likely to occur in well-ventilated machine rooms and ammonia explosions are therefore unlikely

The most promising hydrocarbons for refrigeration purposes are propane and iso-butane (Granryd 2001) Their only important disadvantage is the fact that they are combustible The lower flammable limits of propane and iso-butane are only 21 and 13 vol respectively which means that relatively low amounts of hydrocarbon are sufficient to cause dangerous situations Because of this threat the application of hydrocarbons as refrigerant has been restricted to systems with low refrigerant charge or to systems located in well-ventilated machine rooms For example household refrigerators charged with iso-butane or propane are generally accepted by the public in many European countries (Radermacher and Kim 1996) in northern Europe the market is even dominated by these systems For commercial installations however the market share of hydrocarbons has been very small up to now (Granryd 2001)

113 Advance of Indirect Refrigeration Systems

An upcoming technique to safely use hazardous refrigerants like ammonia or hydrocarbons in large installations is the application of indirect refrigeration systems (see Figure 12) In these systems the primary refrigeration cycle with hazardous refrigerant is located in a well-

Introduction

3

ventilated machine room from where a secondary refrigerant distributes the cold energy to the applications where refrigeration is needed The required primary refrigerant charge to operate the system is relatively small which also enhances the safety of the system The secondary refrigerant is a safe and environmentally friendly fluid for example an aqueous solution of potassium formate

Figure 12 Schematic layout of indirect refrigeration system

An additional advantage of a secondary cycle is the possibility to store cold energy which enables to shift electricity loads towards periods of the day with lower electricity tariffs Another possibility of cold storage is peak shaving which results in a reduction of the required installed refrigeration capacity

In principle the extra heat transfer step in indirect systems reduces the energy efficiency compared to direct refrigeration systems However indirect systems can be operated with an energetic favorable refrigerant such as ammonia in the primary loop as a result of which the total system efficiency can be higher compared to a direct system with a synthetic refrigerant The mentioned replacement for refrigeration of display cabinets in supermarkets is described by Presotto and Suumlffert (2001) and Horton and Groll (2003) According to these studies both design calculations and measurements in practice show that indirect systems with ammonia use about 15 less energy compared to direct expansion systems using R22 as refrigerant Furthermore both studies report that the investment costs of indirect systems are comparable with direct expansion systems for cooling capacities of about 300 kW

Apart from supermarkets indirect refrigeration systems can also be applied in numerous other applications The most widespread application is probably air conditioning in medium and large-sized buildings where chilled water is applied as secondary refrigerant Similarly secondary cycles can be applied for district cooling such as in large warehouses for fresh foods Other applications are found in industrial environments for example in food and beverage industries

The most commonly used secondary refrigerant is water either pure or mixed with freezing point depressant In applications where the temperature of the secondary refrigerant is always above 0degC such as air conditioning systems water is most frequently applied In traditional indirect refrigeration systems with lower temperatures such as for cooling and freezing purposes water is mixed with freezing point depressant to avoid the formation of ice in the secondary cycle Frequently applied freezing point depressants in this respect are ethanol

Chapter 1

4

ethylene glycol propylene glycol and more recently potassium formate and betaine (Aittomaumlki and Lahti 1997 Jokinen and Willems 2004 Melinder 1997) The freezing temperature of these aqueous solutions depends on the type and concentration of freezing point depressant An overview of freezing temperatures and thermophysical properties of several aqueous solutions is given in Appendix A

In case of traditional liquid secondary refrigerants only the sensible heat capacity is used and as a result relatively large amounts of liquid need to be circulated to provide enough cooling at the applications The main disadvantages of these high circulation rates are the large pipe diameters and the high required pumping power Moreover large storage tanks are required to benefit from cold storage In order to reduce these disadvantages secondary refrigerants with phase change and therefore higher heat capacities have recently been investigated The most important examples of these secondary refrigerants with phase change are carbon dioxide (CO2) and ice slurry

In case of CO2 liquid refrigerant is pumped from the storage tank to the applications where it evaporates and takes up heat Subsequently the vapor flows to the evaporator of the primary cycle where it is cooled by the primary refrigerant and condensates Finally the condensate flows back to the storage tank Indirect refrigeration systems with CO2 as secondary refrigerant have successfully been applied in supermarkets (Riessen 2004 Verhoef 2004) Disadvantages of CO2 as secondary refrigerant are the high pressures in the secondary cycle especially at higher temperature levels Application of CO2 in secondary cycles seems therefore more beneficial for freezing than for cooling purposes

Ice slurry systems use the phase change of ice into water to take up heat from applications (Kauffeld et al 2005) The heat capacity of ice slurry is therefore substantially higher than of liquid secondary refrigerants which brings about energetic and economic advantages A detailed description of the properties and possibilities of ice slurry is discussed in the next section

12 Ice Slurry

121 Ice Slurry Properties

Ice slurry consists of a water-based liquid in which small ice crystals of about 001 to 05 mm in size are present (see Figure 13) The liquid can be pure water or a mixture of water and a freezing point depressant These freezing point depressants can either be an organic substance like ethanol or ethylene glycol or an inorganic substance like sodium chloride or potassium formate Generally ice fractions vary from 0 up to 40 wt Even at high ice fractions ice slurry remains pumpable and can therefore be circulated through the secondary cycle by standard centrifugal pumps

Introduction

5

Figure 13 Microscopic picture of ice crystals

The temperature at which ice slurry can be applied ranges from 0degC down to approximately -30degC (Meewisse 2004) The initial freezing temperature the temperature at which the original solution is in equilibrium with ice depends on the type and concentration of freezing point depressant used (see Figure 14) Since produced ice crystals contain almost only water molecules the concentration of solute increases as the ice fraction increases As a result the equilibrium temperature of ice slurry decreases as the ice fraction increases (see also Appendix B) Due to this phenomenon ice slurries with low solute concentrations and initial freezing temperature close to 0degC show higher apparent heat capacities than ice slurries with higher solute concentrations Therefore ice slurries are most promising for temperatures between 0 and -10degC

-200

-150

-100

-50

00

00 50 100 150 200 250 300 350 400Solute concentration (wt)

Free

zing

tem

pera

ture

(degC

)

EthanolPotassium formate

Sodium chloride Ethylene glycol

Figure 14 Freezing temperature as function of solute concentration

The high heat capacity of ice slurry is based on the latent heat of fusion of water which is 3335 kJkg at 0degC An ice slurry with an ice fraction of 20 wt represents therefore a heat capacity of approximately 667 kJkg when the sensible heat capacity is neglected A comparable liquid secondary refrigerant for example an aqueous ethylene glycol solution has a specific heat capacity of 36 kJkg K This specific heat capacity results in a heat capacity of 180 kJkg when a temperature glide of 5 K is considered A comparison of both heat capacities shows that ice slurry with 20 wt ice can take up about four times more heat than a traditional secondary refrigerant while the temperature remains practically unchanged

Chapter 1

6

Next to the heat capacity also other thermophysical properties change as the ice fraction increases as shown in Figure 15 (Meewisse 2004) The most important property in this respect is the dynamic viscosity of the ice slurry which increases by a factor of more than three as the ice fraction increases from 0 tot 25 wt The density of ice slurry slightly decreases with increasing ice fraction while the thermal conductivity increases More information on the thermophysical properties of ice slurries can be found in Appendix B

0

50

100

150

200

250

300

350

00 50 100 150 200 250Ice fraction (wt)

Rel

ativ

e pr

oper

ty c

hang

e

Density

Viscosity

Apparent heat capacity

Thermal conductivity

Figure 15 Relative change of thermophysical properties at increasing ice fraction for ice

slurry produced from a 92 wt NaCl solution (Meewisse 2004)

122 Ice Slurry Systems

Indirect refrigeration systems with ice slurry as secondary refrigerant as shown in Figure 16 look very similar to systems with traditional secondary refrigerants Ice slurry is produced in an ice slurry generator which is cooled by the evaporating primary refrigerant The produced ice slurry flows to the storage tank from where it is pumped to the application heat exchangers Here the ice slurry melts and takes up heat from products or processes

Figure 16 Indirect refrigeration system with ice slurry as secondary refrigerant

The ice slurry generator is one of the key components of an ice slurry system Ice crystals have a strong tendency to adhere to cooled heat exchanger walls where they can form an insulating layer that decreases the capacity dramatically The most frequently applied

Introduction

7

technique to prevent this is the application of scraped surface heat exchangers in which rotating scraper blades or orbital rods continuously remove the ice crystals from the walls (Stamatiou et al 2005) Both investment and maintenance costs of these heat exchangers are relatively high It is even generally believed that these high costs are one of the major factors that have limited a widespread application of ice slurry systems up to now In this thesis a new type of ice slurry generator is studied which is based on a liquid-solid fluidized bed and has considerably lower investment costs especially at larger scales The next section describes this fluidized bed ice slurry generator in detail

After production ice slurry is stored in a tank which gives the opportunity to apply load shifting or peak shaving In case of load shifting ice slurry is produced during nighttime when electricity tariffs and outside temperatures are low resulting in economic and energetic efficient ice slurry production In daytime stored ice slurry is used in the application heat exchangers In case of peak shaving a constant amount of ice slurry is produced per unit of time while peaks in heat load are cooled by ice slurry from the storage tank The main advantage of this control strategy is the possibility to install less primary refrigeration capacity than for the case without thermal storage The best control strategy strongly depends on the load profile of the specific application but also on external aspects as electricity tariff structures and local climate conditions (Meewisse 2004)

The latent heat of ice slurry is exploited in applications where the ice crystals melt In most applications ice slurry flows through heat exchangers but it is also possible that the ice crystals melt in direct-contact with the products that need cooling The heat transfer process taking place in melting heat exchangers can strongly differ from single-phase heat transfer processes in terms of heat transfer coefficients and pressure drop (Ayel et al 2003) Furthermore the melting process can operate far from equilibrium resulting in superheated ice slurry at the outlet of the heat exchangers (Frei and Boyman 2003)

123 Applications of Ice Slurry

Up to now ice slurry systems have been applied for several applications in comfort cooling and in food processing and preservation (Bellas and Tassou 2005)

Some typical examples of realized comfort cooling projects can be found in Japan such as the air conditioning systems of the Kyoto station building complex and the Herbis Osaka building in Osaka (Wang and Kusumoto 2001) In South Africa ice slurry has been applied for cooling of gold mines with depths of more than 3000 meters where temperatures normally exceed 50degC (Ophir and Koren 1999) Drawback for air conditioning applications is the maximum temperature of 0degC at which ice slurry can be applied Evaporation temperatures in the primary cycle are therefore around ndash5degC which is considerably lower than in standard air conditioning systems operated with water as secondary refrigerant where the evaporation temperature is normally about 2degC The lower evaporation temperature induces higher energy consumptions for ice slurry systems

In food processing ice slurry has mainly been applied for rapid cooling of fresh fish milk or cheese These products are typically cooled in batches resulting in high peak loads for refrigeration equipment The utilization of ice slurry enables to shave these peak loads and as a result reduced refrigeration capacity is installed In case of fish cooling ice slurry is sprayed over the fish that has just been caught The ice crystals melt by the direct contact with the fish which results in high cooling rates and high product quality (Losada et al 2005) Typical applications of ice slurry for food preservation have been realized in several supermarkets

Chapter 1

8

(Crielaard 2001 IIR 2005b) Refrigerating equipment accounts for approximately 40 to 70 of the total power consumption of supermarkets and daytime use of slurry produced at night generates considerable savings Besides the mentioned applications ice slurry might also be applied for several other applications such as fire fighting instrument cooling and medical uses in the future (Davies 2005)

13 Fluidized Bed Heat Exchanger

The development of an efficient and inexpensive ice slurry generator is one of the key factors to make ice slurry technology more economically feasible A promising ice slurry generator in this respect is the fluidized bed heat exchanger in which inert fluidized particles remove ice crystals from the heat exchanger walls

131 Working Principle and Current Applications

The concept of a liquid-solid fluidized bed heat exchanger was proposed by Klaren (1975) for sea water desalination in the early 1970s The proposed heat exchanger consists of one or more vertical tubes in which an upward flowing fouling liquid fluidizes inert particles (see Figure 17) The fluidized particles continuously impact on the heat exchanger walls and remove therefore possible deposits from these walls (see Figure 18) Moreover the fluidized particles disturb the thermal boundary layer and increase therefore heat transfer coefficients The overall result of the fluidized bed is that heat transfer rates are high and remain high and that periodical cleanings are not necessary

Fluidized bed

Inlet fouling liquid

Outlet fouling liquid

Hot or cold fluid

Thermal boundary

layer

Fluidized bed

Inert particle

Hot or cold fluid

Deposit

Heat exchanger

wall

Figure 17 Stationary fluidized bed heat exchanger

Figure 18 Working principle of deposit removal and heat transfer enhancement

The inert particles used are usually made of stainless steel or glass but also other materials like aluminum oxide or silica sand can be used (Kollbach et al 1987) In case of stainless steel particles are generally made of wire and are therefore cylindrically shaped glass particles are mostly spherical

Introduction

9

The heat exchanger in Figure 17 is a so-called stationary fluidized bed heat exchanger since the particles stay inside the tubes during operation In the 1980s a new fluidized bed concept was developed in which the particles are dragged out of the heat exchanger and are returned to its bottom via a downcomer (Klaren 2000) This concept is schematically represented in Figure 19 and is a so-called circulating fluidized bed heat exchanger

Downcomer

Fluidized bed

Particle separation



Hot or cold fluid

Figure 19 Circulating fluidized bed heat exchanger

The main advantage of the circulating mode is the higher design flexibility since there is more freedom in choosing the velocity of the fouling liquid Furthermore the higher particle velocity may lead to a more efficient cleaning of the walls and higher heat transfer coefficients Possible disadvantages are the higher required pumping power and the occurrence of wear in connections and curves induced by flowing particles

Most installed liquid-solid fluidized bed heat exchangers in industry are operated in circulating mode (Klaren 2000 Rautenbach and Katz 1996) In most cases fluidized beds are used for liquids that cause particulate fouling which is the adherence of suspended particles to the heat exchanger wall Typical examples of these liquids are oil emulsions in petrochemical industry fruit juices in food industry and waste waters in several branches In other applications fluidized bed heat exchangers are used to prevent crystallization fouling also referred to as scaling which is the deposition of dissolved species on the heat transfer surface forming a crystalline layer Typical examples are evaporation and cooling processes for example in desalination of seawater and cooling of geothermal brines respectively

132 Fluidized Bed Ice Slurry Generator

In the early 1990s Klaren and Meer (1991) proposed to use fluidized bed heat exchangers for ice slurry production First experiments proved that the fluidized particles were indeed able to remove ice crystals from the heat exchanger walls

The research on fluidized bed ice slurry generation was subsequently continued at the Delft University of Technology (Meewisse 2004) An experimental set-up consisting of a single-tube fluidized bed heat exchanger was used to study ice slurry production (see Appendix C2)

Chapter 1

10

Most experiments were performed with a stationary fluidized bed which had a diameter of 548 mm and consisted of stainless steel cylinders of 2 3 or 4 mm in both diameter and height The fluidized bed was cooled by a liquid coolant which flowed countercurrently through an annulus around the fluidized bed tube During the ice slurry production experiments overall heat transfer coefficients were determined from the coolant flow rate and temperatures measured at the inlets and outlets Subsequently the fluidized bed heat transfer coefficients were determined from this overall heat transfer coefficient and a model for the coolant heat transfer coefficient

The ice crystals produced in the fluidized bed heat exchanger appeared to be similar to those produced by other ice slurry generation techniques Besides the experiments showed that fluidized bed heat transfer coefficients just before and during ice formation are almost equal From this observation was concluded that the heat transfer process near the wall is hardly influenced by ice formation

Initially fluidized bed heat transfer coefficients between 2500 and 4000 Wm2K were determined (Meewisse and Infante Ferreira 2003) However during calibration experiments came to light that the tube sizes used were slightly different from what was stated in the drawings Consequently initially determined experimental fluidized bed heat transfer coefficients were up to 40 too low The application of the correct dimensions to the measurements showed fluidized bed heat transfer coefficients between 3500 and 8000 Wm2K (see also Pronk et al 2005) An empirical heat transfer model proposed by Haid (1997) predicts heat transfer coefficients in a fluidized bed ice slurry generator reasonably well

0 75 0 63h h0 0734 Nu Re Pr= (11)

Haidrsquos heat transfer model overestimates measured heat transfer coefficients during ice generation with an average error of 94

The ice slurry production experiments also revealed that there exists a maximum allowable temperature difference for each set of fluidized bed parameters below which ice slurry can be stably produced At higher temperature differences the fluidized particles do not remove enough ice from the walls and as a result an insulating ice layer builds up This phenomenon is often referred to as ice scaling The maximum allowable temperature difference increases linearly with the solute concentration but this linearity is different for various solutes The observed phenomena are ascribed to mass transfer phenomena but the physical mechanisms behind these phenomena are not fully understood yet

Most experiments described by Meewisse (2004) were performed with a stationary fluidized bed of 4 mm particles at a bed voidage of 80 but experiments were also performed at other fluidized bed conditions Preliminary circulating fluidized bed experiments revealed that ice slurry production is possible with this operating mode although the allowable maximum temperature differences were lower compared to the stationary mode Next some experiments were performed with stationary fluidized beds with varying bed voidage and particle size Since the number of these experiments was small it is hard to draw conclusions from them The influences of fluidized bed parameters must be identified to optimize the fluidized bed ice slurry generator and therefore systematic experimental research on this topic is essential

An energetic and economic evaluation of the fluidized bed ice slurry generator demonstrates that it performs well in relatively large applications The limited maximum allowable

Introduction

11

temperature difference does not prevent its application at relatively high temperature applications such as air conditioning systems (Meewisse 2004)

133 Promising New Applications

The fact that ice slurry production is feasible with a fluidized bed heat exchanger stimulates to inventory other applications where this apparatus might be successful

A first promising application is freeze concentration in which aqueous solutions such as beverages and wastewaters are concentrated by means of ice crystallization (Deshpande et al 1984 Holt 1999 Verschuur et al 2002) Main advantages of freeze concentration over concentration processes based on evaporation are the reduced energy consumption and the preservation of aromas and flavors Up to now the number of freeze concentration plants has been limited mainly because of the relatively high investment costs of the applied scraped surface heat exchangers The introduction of fluidized bed heat exchangers may reduce these costs and makes this technology economically feasible for more applications

A second interesting application for fluidized bed crystallizers is cooling crystallization of salts (Klaren 2000) In this process salt is crystallized from its aqueous solution by cooling the solution below its solubility temperature (see Figure 110) A typical application in this respect is the crystallization of sodium sulfate (Na2SO4) from its aqueous solution Conventional heat exchangers in which sodium sulfate is crystallized are cleaned every 16 hours to remove the scale layer from the walls Substitution of these heat exchangers by fluidized bed heat exchangers might make these costly maintenance stops redundant

Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point

Salt + aqueous solution

aqueous solution

Ice + salt

Ice line

Salt solubility line

0degC

T eut

0 w eut

Salt

crystallization

crystallization

Ice

crystallizationEutectic freezeIce +

Figure 110 Typical salt-water phase diagram with different crystallization processes

A third and final interesting process for the application of fluidized bed heat exchangers is eutectic freeze crystallization (Vaessen 2003) During eutectic freeze crystallization an aqueous salt solution is cooled down to its eutectic temperature at which both ice and salt simultaneously crystallize (see Figure 110) This process has proven to produce ice and salt crystals of high purities with relatively low energy consumption However the investment costs of the applied scraped surface heat exchangers is a major disadvantage of this crystallization technique The possibility to use fluidized bed heat exchangers may reduce the investments costs of this technique but its applicability should therefore be investigated first

Chapter 1

12

14 Objectives

The first objective of this research is to unravel the mechanisms of ice scaling prevention in fluidized bed ice slurry generators Previous work showed that ice scaling is prevented for certain conditions but the key factors for successful ice scaling prevention are not understood yet The first aim of this research is therefore to reveal the influence of liquid parameters such solute type and concentration on ice scaling prevention in fluidized bed heat exchangers A second aim is to clarify the influence of fluidized bed parameters such as stationary or circulating operation bed voidage and particle size For both purposes ice crystallization experiments are performed with a single-tube fluidized bed heat exchanger An analysis of the experimental results is used to develop models to predict ice scaling in fluidized bed heat exchangers and to distinguish the most effective fluidized bed configuration for ice scaling prevention A separate set of experiments using a piezoelectric sensor is performed to measure and analyze the collisions of fluidized particles on the wall to explain different ice scaling prevention characteristics for different operating conditions

A second objective of this thesis is to compare the most efficient fluidized bed configuration with competitive ice slurry generators An extensive comparison of this configuration in terms of ice scaling prevention heat transfer investment costs and energy consumption is made with the most commonly applied ice slurry generator type in practice the scraped surface heat exchanger Furthermore promising new industrial applications for the fluidized bed heat exchanger concept are selected and investigated Some of these promising applications namely cooling crystallization and eutectic freeze crystallization are tested in the experimental fluidized bed heat exchanger

A final objective of this research is to study the behavior of produced ice crystals in other major components of an ice slurry system Although an ice slurry system consists of a number of separate components the processes taking place in these components strongly interfere with each other In this respect this research focuses on recrystallization mechanisms taking place in storage tanks and on melting processes in heat exchangers For both topics experiments are used to construct models that predict the development of the crystal size distribution during the storage or melting process

15 Thesis Outline

Chapter 2 studies the role of the solute type and concentration on the ice scaling prevention ability of a fluidized bed ice slurry generator For this study ice slurry was produced in a experimental fluidized bed heat exchanger from six different types of aqueous solutions at various concentrations while the fluidized bed conditions were constant The results are analyzed and used to develop a model that predicts ice scaling for different aqueous solutions in fluidized bed heat exchangers

Chapters 3 and 4 focus on the influence of fluidized bed parameters on the prevention of ice scaling in fluidized bed ice slurry generators Chapter 3 describes experiments with a piezoelectric sensor to measure forces and frequencies of particle-wall collisions for both stationary and circulating fluidized beds at different conditions In Chapter 4 ice crystallization experiments are performed at various fluidized bed conditions The experimental results for ice crystallization fouling prevention are compared with the particle-wall collision characteristics obtained with the piezoelectric sensor

Introduction

13

The perspectives of fluidized bed heat exchangers for other industrial crystallization processes are studied in Chapter 5 The focus of this chapter is on cooling crystallization of salts and eutectic freeze crystallization Both types of processes are tested in the experimental fluidized bed heat exchanger and results are compared to the findings of Chapter 2

Chapter 6 compares the fluidized bed ice slurry generator with the most frequently applied ice slurry generator namely the scraped surface heat exchanger The comparison focuses on subjects as ice scaling heat transfer investment costs and energy consumption For comparison on ice scaling ice crystallization experiments are performed with an experimental scraped surface heat exchanger

Chapter 7 describes recrystallization mechanisms that occur during long-term storage of ice slurry On the basis of storage experiments with a 1-liter stirred tank crystallizer a dynamic model is developed that predicts the evolution of ice crystal size distributions during adiabatic storage of ice slurry

The melting of ice slurry in application heat exchangers is thoroughly studied in Chapter 8 Pressure drop heat transfer coefficients and superheating are measured during ice slurry melting experiments in a tube-in-tube heat transfer coil Subsequently a model is developed to understand and predict superheating during melting of ice slurry in heat exchangers

Finally Chapter 9 summarizes the conclusions from the different chapters and gives the integral conclusions from the entire thesis

Chapter 1

14

Nomenclature

cp Specific heat (Jkg K) Greek D Diameter (m) α Heat transfer coefficient (Wm2K) Nuh Hydraulic Nusselt number ε Bed voidage α Dp ε(λliq (1-ε)) λ Thermal conductivity liquid (Wm K) Pr Prandtl number cpliq λliqmicroliq micro Dynamic viscosity (Pa s) ampQ Heat (W) ρ Density (kgm3)

Reh Hydraulic Reynolds number ρliq us Dp(microliq (1-ε)) Subscripts T Temperature (degC) eut Eutectic us Superficial velocity (ms) liq Liquid w Weight fraction solute p Particle

Abbreviations

CFC Chlorofluorocarbon NaCl Sodium chloride CO2 Carbon dioxide R134a 1112-tetrafluoroethane COP Coefficient of Performance R22 Chlorodifluoromethane HCFC Hydrochlorofluorocarbon R404A HFC refrigerant blend HFC Hydrofluorocarbon R407C HFC refrigerant blend Na2SO4 Sodium sulfate

References

Aittomaumlki A Lahti A 1997 Potassium formate as a secondary refrigerant International Journal of Refrigeration vol20 pp276-282

Ayel V Lottin O Peerhossaini H 2003 Rheology flow behaviour and heat transfer of ice slurries a review of the state of the art International Journal of Refrigeration vol26 pp95-107

Bellas I Tassou SA 2005 Present and future applications of ice slurries International Journal of Refrigeration vol28 pp115-121

Crielaard GA 2001 IJsslurry bespaart energie (Ice slurry saves energy) Energietechniek vol79 no3 2001

Davies TW 2005 Slurry ice as a heat transfer fluid with a large number of application domains International Journal of Refrigeration vol28 pp108-114

Deshpande SS Cheryan M Sathe SK Salunkhe DK 1984 Freeze concentration of fruit juices CRC Critical Reviews in Food Science and Nutrition vol20 pp173-247

Farman JC Gardiner BG Shanklin JD 1985 Large losses of total ozone in Antarctica reveal seasonal ClOxNOx interaction Nature vol315 pp207-210

Introduction

15

Frei B Boyman T 2003 Plate heat exchanger operating with ice slurry In Proceedings of the 1st International Conference and Business Forum on Phase Change Materials and Phase Change Slurries 23-26 April 2003 Yverdon-les-Bains (Switzerland)

Granryd E 2001 Hydrocarbons as refrigerants - an overview International Journal of Refrigeration vol24 pp15-24

Haid M 1997 Correlations for the prediction of heat transfer to liquid-solid fluidized beds Chemical Engineering and Processing vol36 pp143-147

Horton WT Groll EA 2003 Secondary loop refrigeration in supermarket applications a case study In Proceedings of the 21st IIR International Congress of Refrigeration 17-23 August 2003 Washington DC (USA) Paris International Institute of Refrigeration

Holt S 1999 The role of freeze concentration in waste water disposal Filtration amp Separation vol36 pp34-35

IIR 2005a Website of the International Institute of Refrigeration (IIR) httpwwwiifiirorg

IIR 2005b French supermarkets turn to ice slurries IIR Newsletter no21 Paris International Institute of Refrigeration

IPCC 2005 Website of the Intergovernmental Panel on Climate Change (IPCC) httpwwwipccch

Jokinen J Willems B 2004 Betaine based heat transfer fluids as a natural solution for environmental toxicity and corrosion problems in heating and cooling systems In Proceedings of the 6th IIR Gustav Lorentzen Conference on Natural Working Fluids 29 August-1 September 2004 Glasgow (UK) Paris International Institute of Refrigeration

Kauffeld M Kawaji M Egolf PW 2005 Handbook on Ice Slurries Fundamentals and Engineering Paris International Institute of Refrigeration

Klaren DG 1975 Development of a vertical flash evaporator PhD Thesis Delft University of Technology (The Netherlands)

Klaren DG 2000 Self-cleaning heat exchangers In Muumlller-Steinhagen H (Ed) Handbook Heat Exchanger Fouling Mitigation and Cleaning Technologies Rugby Institution of Chemical Engineers pp186-198

Klaren DG Meer JS van der 1991 A fluidized bed chiller A new approach in making slush-ice In 1991 Industrial Energy Technology Conference Houston (USA)

Kollbach JS Dahm W Rautenbach R 1987 Continuous cleaning of heat exchanger with recirculating fluidized bed Heat Transfer Engineering vol8 pp26-32

Lorentzen G 1988 Ammonia an excellent alternative International Journal of Refrigeration vol11 pp248-252

Lorentzen G 1995 The use of natural refrigerants a complete solution to the CFCHCFC predicament International Journal of Refrigeration vol18 pp190-197

Chapter 1

16

Losada V Pintildeeiro C Barros-Velaacutezquez J Aubourg SP 2005 Inhibition of chemical changes related to freshness loss during storage of horse mackerel (Trachurus trachurus) in slurry ice Food Chemistry vol93 pp619-625

Meewisse JW 2004 Fluidized Bed Ice Slurry Generator for Enhanced Secondary Cooling Systems PhD Thesis Delft University of Technology (The Netherlands)

Meewisse JW Infante Ferreira CA 2003 Validation of the use of heat transfer models in liquidsolid fluidized beds for ice slurry generation International Journal of Heat and Mass Transfer vol46 pp3683-3695

Melinder Ǻ 1997 Thermophysical Properties of Liquid Secondary Refrigerants Charts and Tables Paris International Institute of Refrigeration

Molina MJ Rowland FS 1974 Stratospheric sink for chlorofluoromethanes chlorine atom catalysed destruction of ozone Nature vol249 pp810-812

Ophir A Koren A 1999 Vacuum freezing vapor compression process (VFVC) for mine cooling In Proceedings of the 20th IIR International Congress of Refrigeration Sydney (Australia) Paris International Institute of Refrigeration

Powell RL 2002 CFC phase-out have we met the challenge Journal of Fluorine Chemistry vol114 pp237-250

Presotto A Suumlffert CG 2001 Ammonia refrigeration in supermarkets ASHRAE Journal vol43 pp25-30

Pronk P Meewisse JW Infante Ferreira CA 2005 Erratum to Validation of the use of heat transfer models in liquidsolid fluidized beds for ice slurry generation [International Journal of Heat and Mass Transfer 46 (2003) 3683-3695] International Journal of Heat and Mass Transfer vol48 pp3478-3483

Radermacher R Kim K 1996 Domestic refrigerators recent developments International Journal of Refrigeration vol19 pp61-69 1996

Rautenbach R Katz T 1996 Survey of long time behavior and costs of industrial fluidized bed heat exchangers Desalination vol108 pp335-344

Riessen GJ van 2004 Ammoniacarbon dioxide supermarket refrigeration system with carbon dioxide in the cooling and freezing system Proceedings of the 6th IIR Gustav Lorentzen Conference on Natural Working Fluids 29 August-1 September 2004 Glasgow (UK) Paris International Institute of Refrigeration

Stamatiou E Meewisse JW Kawaji M 2005 Ice slurry generation involving moving parts International Journal of Refrigeration vol28 pp60-72

Taylor C Horn N Welch J 2004 Ammonia refrigerant in a large world class facility In Proceedings of the 6th IIR Gustav Lorentzen Conference on Natural Working Fluids 29 August-1 September 2004 Glasgow (UK) Paris International Institute of Refrigeration

Introduction

17

UNEP 2003 Handbook for the International Treaties for the Protection of the Ozone Layer 6th edition Ozone Secretariat of the United Nations Environment Programme httpwwwuneporgozone

UNFCC 2005 Website of the United Nations Framework Convention on Climate Change (UNFCC) httpwwwunfccorg

Vaessen RJC 2003 Development of Scraped Eutectic Crystallizers PhD thesis Delft University of Technology (The Netherlands)

Verhoef PJ 2004 Opportunities for carbon dioxide in supermarket refrigeration In Proceedings of the 6th IIR Gustav Lorentzen Conference on Natural Working Fluids 29 August-1 September 2004 Glasgow (UK) Paris International Institute of Refrigeration

Verschuur RJ Scholz R Nistelrooij M van Schreurs B 2002 Innovations in freeze concentration technology In Proceedings of the 15th International Symposium on Industrial Crystallization Sorrento (Italy) pp1035-1040

Wang MJ Kusumoto N 2001 Ice slurry based thermal storage in multifunctional buildings Heat and Mass Transfer vol37 pp597-604

Chapter 1

18

19

2 Influence of Solute Type and Concentration on Ice Scaling

21 Introduction

Previous experiments have shown that fluidized bed heat exchangers as described in Section 13 are able to prevent ice scaling during ice crystallization from aqueous sodium chloride solutions (Meewisse and Infante Ferreira 2003 Meewisse 2004 Pronk et al 2005) However during these experiments ice scaling was only prevented when the temperature difference between cooled wall and solution did not exceed a certain maximum This transition temperature difference ∆Ttrans appeared to increase approximately proportionally to the sodium chloride concentration A similar reduction of ice scaling with increasing solute concentration was also observed by Vaessen et al (2002) for scraped surface heat exchangers According to Stamatiou et al (2005) solutes are generally applied to avoid ice scaling in this type of ice crystallizers Despite the experimental results and the application of this phenomenon in practice little is still known about the physical mechanisms that cause or prevent ice scaling in ice crystallizers and about the role of solutes on these mechanisms

The aim of this chapter is therefore to identify the influence of solution properties such as solute type and concentration on ice scaling in ice crystallizers For this purpose ice crystallization experiments were performed with several aqueous solutions in a liquid-solid fluidized bed heat exchanger The experimental results are analyzed in order to unravel the physical mechanisms of ice scaling and to formulate a model that predicts the transition temperature difference

22 Experimental Method

A single-tube fluidized bed heat exchanger as shown in Figure 21 was used for ice crystallization experiments The heat exchanger was made of two stainless steel tube-in-tube heat exchangers connected by a transparent section The fluidized bed consisted of cylindrical stainless steel particles 4 mm in diameter and height located in the inner tubes The inner tubes had an inside diameter of 427 mm and the heat exchanger had a total length of 488 m The fluidized bed was cooled by a 34 wt potassium formate solution (see Appendix A33) which flowed countercurrently through the annuli of the heat exchangers The temperatures at inlets and outlets of the heat exchangers were measured by PT-100 elements which had an accuracy of 001 K Pressures were measured at the top and bottom of the heat exchanger to determine the bed voidage in the fluidized bed The bed voidage was deduced from the measured pressure drop in the fluidized bed which consists of a hydrostatic term a term for the liquid-wall friction and a term for the particle-wall friction (Garić-Grulović et al 2004)

( )( )liq p frliq-w1p gh pερ ε ρ∆ = + minus + ∆ (21)

The pressure drop by friction between the liquid and the wall was determined from experiments without particles Parts of this chapter have been published in Chemical Engineering Science vol61 pp4354-4362

Chapter 2

20

Figure 21 Experimental single-tube fluidized bed heat exchanger

The total heat flux in the heat exchanger was determined from the coolant flow rate and the coolant temperatures at the inlet and outlet of the heat exchanger This total heat flux was used to calculate the overall heat transfer coefficient Uo

o o lnQ U A T= ∆amp (22)

The overall heat transfer resistance (1Uo) consists of the annular side heat transfer resistance the heat transfer resistance of the tube wall and the fluidized bed heat transfer resistance

oinner oinner oinner

o o w iinner i iinner

1 1 1ln2

D D DU D Dα λ α

= + +

(23)

From Equation 22 the fluidized bed heat transfer coefficient could be determined since a validated heat transfer model was available for the annular heat transfer coefficient (see Appendix C1) Subsequently the ratio of heat transfer coefficients the suspension temperature and the coolant temperature were used to determine the local wall temperature at the inside of the inner tube

( )( )

sl wl oinnero

i iinnersl cooll

T T DUDT T α

minus=

minus (24)

Measurement accuracies of the physical parameters obtained with the experimental fluidized bed heat exchanger are given in Appendix D1

During an experiment the aqueous solution in the fluidized bed was cooled below its freezing temperature by the coolant whose inlet temperature was constant and controlled within 01 K

Influence of Solute Type and Concentration on Ice Scaling

21

As the aqueous solution reached a certain degree of supercooling ice crystals spontaneously nucleated and an ice suspension was formed During ice formation the heater in the ice suspension tank was applied to keep ice fractions in the set-up below 5 wt

Ice crystals were produced from aqueous solutions of different solutes namely D-glucose ethylene glycol potassium chloride (KCl) potassium nitrate (KNO3) magnesium sulfate (MgSO4) and sodium chloride (NaCl) For each solute type the maximum temperature difference for ice crystallization without ice scaling was experimentally determined for different concentrations as listed in Table 21 Solution properties are listed in Appendix A

Table 21 Experimental parameters Solute Solute mass

fraction (wt)

Solute mol fraction (mol)

Freezing temperature

(degC)

Mol fraction diss species

(mol)

Superficial velocity

(ms) D-glucose 90 098 -102 098 037 169 200 -209 200 034 232 294 -310 294 032 Ethylene glycol 33 097 -100 096 037 62 189 -198 189 037 90 279 -298 283 036 116 368 -401 377 035 KCl 42 105 -194 185 037 81 210 -386 364 037 137 368 -685 631 037 KNO3 30 055 -094 090 039 63 119 -190 181 039 MgSO4 63 091 -095 091 035 115 186 -200 191 033 175 312 -361 341 029 NaCl 26 080 -151 144 038 33 104 -196 187 038

50 160 -304 288 037 64 206 -396 372 037 76 247 -480 449 036

The mol fraction of dissolved species both ions and molecules y is also shown in the table and is derived from the freezing temperature of the solution (Smith et al 1996)

2

f H O

100 100expR 27315 27315

h M TyT

∆ = minus sdot +

(25)

The mol fraction of dissolved species approximately equals the solute mol fraction for ethylene glycol and D-glucose solutions Due to the dissociation into ions the mol fractions of dissolved species in the salt solutions are almost twice as high as the solute mol fractions except for MgSO4 which only slightly dissociates into ions During the ice crystallization experiments the solubility limit of the solute was never exceeded and therefore nucleation of solute crystals was avoided

The experiments presented in this chapter were all performed with a stationary fluidized bed with a bed voidage between 80 and 82 In order to achieve this bed voidage the superficial liquid velocity was adjusted for each experiment resulting in lower superficial velocities for

Chapter 2

22

the more viscous solutions (see Table 21) For all experiments reported in this chapter the fluidized bed exhibited a homogeneous fluidization pattern

23 Experimental Results

For all aqueous solutions listed in Table 21 the coolant inlet temperature was varied to determine for which temperature differences between wall and solution ice scaling was prevented by the fluidized bed Since the formation of an ice layer could not be observed directly measured fluidized bed heat transfer coefficients were used to detect ice scaling Figure 22 shows fluidized bed heat transfer coefficients during two experiments for which ice crystallization started at t=0 s During the one experiment ice scaling was prevented and heat transfer coefficients were constant for at least 30 minutes after the first nucleation of ice crystals The other experiment shows decreasing heat transfer coefficients after the onset of crystallization indicating that an insulating ice layer built up on the walls

0

1000

2000

3000

4000

5000

6000

-300 0 300 600 900 1200 1500 1800 2100Time (s)

-60

-50

-40

-30

-20

-10

00

No ice scaling

Ice scaling

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Nucleation

Susp

ensi

on o

utle

t tem

pera

ture

(degC

)

Figure 22 Fluidized bed heat transfer coefficients during ice crystallization from a 50 wt

sodium chloride solution with (Tcoolin= -64degC) and without ice scaling (Tcoolin= -63degC)

During the experiments without ice scaling fluidized bed heat transfer coefficients were slightly smaller after the onset of crystallization A plausible cause for this phenomenon is that a thin layer of ice attaches to the wall An analysis of the reductions in heat transfer coefficient shows that this ice layer is approximately 20 microm on average (Meewisse 2004)

The next section demonstrates that the difference between the wall temperature and equilibrium temperature of the solution determines whether ice scaling occurs The highest value for this parameter was at the top of the heat exchanger for each experiment The wall temperature at this location was calculated by using the coolant inlet temperature and the suspension outlet temperature in Equation 24 Since the ice suspension at the outlet was slightly supercooled its equilibrium temperature was deduced from the heat balance and the assumption that the suspension entering the heat exchanger was in equilibrium The supercooling at the outlet was 01 K at most


23

For all tested aqueous solutions ice scaling was only observed above a certain temperature difference which is shown for sodium chloride solutions in Figure 23 Temperature differences below this transition value resulted in ice crystallization without ice scaling The results in the figure are in accordance with previous experimental results (Meewisse and Infante Ferreira 2003 Pronk et al 2005) which were obtained from a fluidized bed with a slightly larger diameter of 548 mm but with equal particles and bed voidage

00

05

10

15

20

00 10 20 30 40 50Mol fraction of dissolved species (mol)

No ice scalingIce scalingLinear trendline

Diff

eren

ce b

etw

een

wal

l and

eq

uilib

rium

tem

pera

ture

T -T

w (K

)

Figure 23 Differences between wall and equilibrium temperatures for ice crystallization

experiments from sodium chloride solutions with and without ice scaling

The transition temperature difference shows a roughly linear relationship with the mol fraction of dissolved species which is also obtained for the other aqueous solutions as shown in Figure 24 This figure also reveals that the proportionality varies significantly between different solutes

00

05

10

15

20

25

30

00 10 20 30 40 50 60 70

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)

70Mol fraction of dissolved species (mol)

Freezing point depression (K)00 10 20 30 40 50 60 70

D-glucoseEthylene glycolKClKNO3

MgSO4

NaCl

Figure 24 Measured transition temperature differences for ice scaling for several aqueous

solutions with fitted linear trendlines

Chapter 2

24

24 Discussion

The results described in the previous section are explained by the hypothesis that the fluidized bed only prevents ice scaling when the removal rate induced by the stainless steel particles is higher than the growth rate of ice crystals attached to the wall (Foumlrster et al 1999)

R Ggt (26)

The removal rate is determined by fluidized bed parameters such as the bed voidage the particle properties and the superficial velocity Since these parameters were reasonably constant for all experiments (see Table 21) the removal rate is initially assumed constant

241 Crystal Growth Kinetics

The ice growth on the inner wall of the fluidized bed heat exchanger is considered as planar growth This assumption is vindicated by microscopic observations of the produced ice crystals which were solid smooth disks with diameters ranging from 01 to 03 mm for all different solutions (see also Meewisse and Infante Ferreira 2003)

The growth rate of the ice crystals on the wall is determined by heat transfer mass transfer and surface integration kinetics The heat transfer resistance is conductive because the heat of crystallization is transported through the ice layer to the wall

( )iceint w

ice ice f

G T Th

λρ δ

= minus∆

(27)

According to Huige and Thijssen (1972) the surface integration kinetics of ice crystals can be described by

( )1553 int int27 10 ( )G T x Tminus= sdot minus (28)

The mass transfer resistance of ice growth in aqueous solutions is modeled as a transport process through a semi-permeable wall (Mersmann et al 2001)

( )2H Oliq

int bb ice liq

MkG x xx M

ρρ

= minus (29)

For relatively small concentration differences the driving force based on the concentration difference can be translated into a driving force based on a difference in equilibrium temperature

( )2

H Oliq

int bb ice liq b

( ) ( )Mk dxG T x T x

x M dTρρ

asymp minus

(210)


25

The total growth rate of ice crystals on the wall is obtained by combining Equations 27 28 and 210 (Goede and Rosmalen 1990)

2

155

liq3 b ice ice ice fb

liq H O iceb

27 10 ( ) w

Mx hdTG T x T Gk M dx

ρ ρ δρ λ

minus ∆ = sdot minus + minus

(211)

Once the total growth rate is implicitly solved from Equation 211 the contributions of the separate resistances to the total growth resistance can be determined from Equations 27 28 and 210 An analysis of these separate resistances is performed for sodium chloride solutions with a temperature difference of 10 K between wall and equilibrium The thickness of the ice layer at the wall is assumed to be 20 microm and a mass transfer correlation proposed by Schmidt et al (1999) is applied (see Equation 218) The results in Figure 25 demonstrate that the resistance to growth for the experimental conditions of this paper is mainly determined by mass transfer and that heat resistance and surface integration kinetics can be neglected In the rest of this paper the growth rate of ice crystals on the wall is therefore modeled as

( )2

H Oliq

w bb ice liq b

( )Mk dxG T T x

x M dTρρ

= minus

(212)

0

20

40

60

80

100


Perc

enta

ge o

f tot

al r

esis

tanc

e to

ice

grow

th

Surface integration

Mass transfer

Heat transfer

Figure 25 Contributions to the total resistance to the growth of ice crystals on the wall for

NaCl solutions for a total temperature difference of 10 K

242 Influence of Solute Concentration on Ice Scaling

At the transition temperature difference for ice scaling the removal rate of the fluidized bed just equals the growth rate of ice crystals on the wall

R G= (213)

Chapter 2

26

Combining Equations 212 and 213 leads to an expression for the transition temperature difference

2

liq ice

trans b w bliq H O b

( )MR dTT T x T x

k M dxρρ

∆ = minus = minus

(214)

All parameters at the right-hand side of Equation 214 with the exception of the solute mol fraction are constant or only a weak function of the concentration for a specific solute The transition temperature difference is therefore approximately proportional to the solute fraction

trans 1 bT c x∆ asymp (215)

The mol fraction of dissolved species is approximately proportional to the solute mol fraction for a specific solute in the experimental range Equation 215 can therefore be rewritten as

trans 2 bT c y∆ asymp (216)

The foregoing theoretical analysis explains the proportionality between the concentration of dissolved species and the transition temperature difference observed during the experiments (see Figure 24)

243 Influence of Solute Type

The influence of the solute type on the transition temperature difference mainly manifests itself through the mass transfer coefficient The most widely applied correlation to describe wall-to-bed mass transfer in fluidized beds was proposed by Chilton and Colburn (1934)

13a

h 3 hSh c Re Sc= with ph 1

ReRe

ε=

minus and h p 1

Sh Sh εε

=minus

(217)

According to Schmidt et al (1999) the coefficient c3 and the Reynolds exponent a are equal to 021 and 061 respectively These values result in the following correlation for the mass transfer coefficient k at a constant bed voidage of 81 with 4 mm particles

23

0 61 0 28s liq

0 281 15 D

uk

ρmicro

= (218)

Rewriting of Equation 214 leads to a relation between the removal rate and the mass transfer coefficient on the right-hand side and an experimental parameter on the left-hand side that represents the transition from ice scaling to operation without ice scaling

2

H Oliq trans

ice liq bb

M Tdx RM dT x k

ρρ

∆minus =

(219)

A graphical representation of Equations 218 and 219 in Figure 26 assuming a constant removal rate R confirms that the variation of transition temperature differences among different solute types is caused by the diversity of mass transfer coefficients This diversity is mainly caused by relatively large differences in diffusion coefficients which range from


27

about 2middot10-10 m2s for MgSO4 and D-glucose solutions to 8middot10-10 m2s for KCl solutions as shown in Figure 27 The mass transfer coefficient is strongly influenced by the diffusion coefficient as is shown by the exponent of 23 in Equation 218 Substitution of Equation 218 in Equation 219 gives an expression for the transition temperature difference showing the influence of the various solution properties

23

2

028 liqice

trans b 061 128H O bs liq

087D

M dTT x RM dxu

micro ρρ

∆ = minus

(220)

00

02

04

06

08

10

0 5 10 15 20 25 30Mass transfer coefficient k (10-6 ms)

MgSO4

D-glucoseEthylene glycol

NaClKNO3

KCl

Ice scaling

No ice scaling

y = 59610-6 x-1

Figure 26 Relation between mass transfer coefficient and an experimental parameter that

represents the transition of ice scaling

0001020304050607080910

00 10 20 30 40 50 60 70Mol fraction of dissolved species (mol)

Diff

usio

n co

effic

ient

(10-9

m2 s

)


MgSO4

NaCl

D-glucose

EG

KNO3

KCl

NaCl

MgSO4


Figure 27 Diffusion coefficients at freezing temperature for several aqueous solutions (see

Appendix A for references)

Chapter 2

28

Deviations between the theoretical model and the experimental results in Figure 26 are first of all attributed to the fact that the removal rate has been assumed constant At high MgSO4 and D-glucose concentrations especially the viscosity is relatively high resulting in considerably low superficial velocities and therefore low particle velocities It is expected that the removal rate is relatively low for these solutions compared to the others In the next section a model is developed which takes also these phenomena into account A second cause for deviations between model and experimental results is the fact that values for diffusion coefficients at freezing temperatures are only available in literature for D-glucose solutions (Huige 1972) The diffusion coefficients of the other solutions are deduced from values at room temperatures (Garner and Marchant 1961 Gmelin 1952 Lobo 1989) assuming that DmicroT is constant at constant solute concentration Although this method generally shows accurate results it is expected that small errors in diffusion coefficients are introduced (Garner and Marchant 1961)

244 Prediction Model for Ice Scaling

The preceding analysis has shown that the transition temperature difference for ice scaling depends mainly on the solute concentration and the mass transfer coefficient Since fluidized bed conditions were not completely constant for all experiments it is expected that the removal rate was also not constant In this section the developed model is therefore extended with a removal rate that depends on the operating conditions

It is generally assumed that the removal of deposits from the wall of a fluidized bed is determined by the frequency and the strength of particle-wall impacts However there is discussion whether the removal rate of a single particle hitting the wall is proportional to its perpendicular kinetic energy prior to the impact (Meijer et al 1986) or proportional to the impulse that it exerts on the wall during the impact (Buffiegravere and Moletta 2000) In Chapters 3 and 4 experiments are presented to unravel the actual removal mechanism of ice crystals In this chapter the removal rate is considered proportional to the mean kinetic energy of particles and the impact frequency per square meter

~R Ef (221)

The mean perpendicular kinetic energy of the particles is proportional to the horizontal particle velocity squared According to Meijer et al (1986) this horizontal particle velocity is approximately one tenth of the superficial velocity at a bed voidage of 80

21p x2E m v= in which x s01v u= (222)

The impact frequency of particles on the wall is obtained by the product of the average horizontal particle velocity and the number of particles per unit of volume (Meijer et al 1986)

( )x 3

p

6 1f v

Dε

πminus

= (223)


29

The combination of Equations 221 222 and 223 results in a relation between the removal rate and the superficial velocity for constant particle size and bed voidage

34 sR c u= (224)

The correlation for the removal rate of Equation 224 is substituted in Equation 220 The result is a correlation between the liquid properties and the superficial velocity on the right-hand side and the transition temperature difference for ice scaling on the left-hand side

23

2

028 liq239 ice

trans 5 b s 128H O bliqD

M dTT c x uM dx

micro ρρ

∆ = minus

with 5 4087c c= (225)

Equation 225 contains only one constant namely c5 which has been fitted to the experimental data resulting in a value of 113middot10-4 s2middotm-161 Figure 28 demonstrates that Equation 225 with this constant predicts the experimental results for the transition temperature difference reasonably well showing an average absolute error of 144

00

10

20

30

00 10 20 30∆T transpred (K)

DexEGKClKNO3MgSO4NaClx=y+20-20

∆T

tran

sm

eas (

K) D-glucose

Ethylene glycolKClKNO3

MgSO4

NaCl

+25

-25

Figure 28 Comparison between measured and predicted transition temperature differences

for ice scaling

A similar comparison is shown in Figure 29 in which both transition temperature differences from measurements as well as from the model are displayed The model results show that the transition temperature difference is only a linear function of the mol fraction at low concentrations The more than proportional increase at higher concentrations is caused mainly by the reduction of diffusion coefficients and an increase in viscosity

Although the proposed model predicts transition temperature differences for ice scaling reasonably well small differences between model and experimental results are observed in Figure 28 and Figure 29 It is believed that the main cause for these differences is the error in diffusion coefficients As stated in Section 243 the availability of diffusion coefficients of aqueous solutions at subzero temperatures in literature is limited and therefore some values for diffusion coefficients have been estimated by extrapolation A second plausible cause for differences might be that the removal rate of a single impact is proportional to the impulse that it exerts on the wall instead of to its kinetic energy as assumed in the model A detailed

Chapter 2

30

00

05

10

15

20

25

30


Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scla

ing

∆T

tran

s (K

)


MgSO4

NaCl

D-glucose

EG

KNO3

KCl

NaCl

MgSO4


al

study on the effects of fluidized bed parameters on the removal rate is described in Chapters 3 and 4

Figure 29 Transition temperature differences for ice scaling from measurements (points) and from prediction model (lines) for several aqueous solutions

245 Application of Model for Other Crystallizers

The idea that ice scaling is only prevented when the removal rate exceeds the mass transfer controlled growth rate of ice crystals on the wall may also be applicable for predicting ice scaling in other ice crystallizers with moving parts such as scraped surface crystallizers For this purpose the mass transfer correlation (Equation 218) and the correlation for the removal rate (Equation 224) should be adjusted to the specific ice crystallizer Experiments by Vaessen et al (2002) indicate that the model is also applicable for scraped surface crystallizers In correspondence with the fluidized bed these experiments also showed increasing transition temperature differences for both HNO3 and CaCl2 solutions as the solute concentration was increased indicating mass transfer controlled growth of ice on the walls Furthermore an increase of the rotational speed of the scrapers resulted in an increase of the transition temperature difference which indicates that the removal rate depends on crystallizer parameters such as the rotational speed More extensive experiments to validate these ideas are presented in Chapter 6

246 Application of Surfactants to Prevent Ice Scaling

The analysis in this section has shown that ice crystallizers can only operate without ice scaling when the growth rate of ice crystals on the cooled wall is not too high It has been demonstrated that dissolved solutes cause a mass transfer resistance for ice growth and prevent therefore ice scaling at reasonable temperature differences However the application of the described solutes has also disadvantages such as lowering of the freezing temperature and an increase of viscosity and is therefore not desirable for all applications

In this respect it is interesting to study other measures that also reduce ice growth rates and prevent ice scaling but do not have the advantages described above A promising possibility


31

for this purpose is the application of macromolecules such as poly(vinyl alcohol) (PVA) and antifreeze proteins (AFP) Microscopic studies have shown that these molecules are adsorbed on the ice crystal surface and considerably reduce ice growth rates (Grandum et al 1999 Lu et al 2002) A schematic representation of this adsorption phenomenon is shown in Figure 210

Figure 210 Adsorption of antifreeze protein on ice surface (Inada et al 2000)

In contrast with the other solutes discussed in this chapter the reduction of ice growth rates by PVA and AFP molecules is not based on diffusion of solutes from the ice interface but on inhibition of integrating water molecules into the ice lattice Since PVA and AFP molecules act as surfactants on the ice interface relatively low concentrations of these substances can already been very effective Inada and Modak (2006) showed that recrystallization processes during storage were almost totally prevented when only 09 wt PVA or 001 wt AFP was added to pure water The freezing point depression caused by these solute concentrations was only 001 K and the viscosity hardly changed It is expected that low concentrations of AFP and PVA can also reduce ice growth rates in ice crystallizers and may therefore interesting solutes to reduce ice scaling However experiments that confirm this hypothesis have not been reported up to now

25 Conclusions

Ice scaling during ice crystallization from aqueous solutions in liquid-solid fluidized bed heat exchangers is only prevented when the removal rate induced by fluidized particles exceeds the growth rate of ice crystals attached to the cooled wall This ice growth rate is limited by mass transfer and is therefore inversely proportional to the solute concentration and increases with increasing diffusion coefficient This explains the experimental results showing that the temperature difference above which ice scaling occurs is approximately proportional to the solute concentration and is higher in aqueous solutions with low diffusion coefficients A model based on these physical mechanisms has been proposed to predict ice scaling in fluidized bed heat exchangers A validation with experimental results demonstrates that the model is applicable for a wide variety of solutes and concentrations showing an average absolute error of 144 The basic idea of the model is also applicable to predict ice scaling in other ice crystallizers

Chapter 2

32

Nomenclature

a Hydraulic Reynolds exponent us Superficial velocity (ms) A Heat exchanger area (m2) U Overall heat transfer coefficient c1c5 Constants (Wm2K) D Diffusion coefficient (m2s) xv Horizontal particle velocity (ms) D Diameter (m) Vamp Volume flow rate (m3s) Dp Equivalent particle diameter (m) x Solute mol fraction E Mean perpendicular energy per x Equilibrium solute mol fraction particle (J) y Mol fraction of dissolved species f Impact frequency (1m2s) (ions and molecules) g Gravity (ms2) G Crystal growth velocity (ms) Greek h Height (m) α Heat transfer coefficient (Wm2K) ∆hf Heat of fusion of water (Jkg) δ Thickness (m) k Mass transfer coefficient (ms) ε Bed voidage M Molar mass (kgmol) λ Thermal conductivity (Wm K) m Mass (kg) micro Dynamic viscosity (Pa s) mamp Mass flow rate (kgs) ρ Density (kgm3) p Pressure (Pa) ∆p Pressure drop (Pa) Subscripts Qamp Heat flux (W) b Bulk R Universal gas constant cool Coolant 8314 Jmol K fr Friction R Removal rate (ms) H2O Water Reh Hydraulic Reynolds number i Inside Rep(1-ε) in Inlet Rep Particle Reynolds number inner Inner ρliq us Dpmicroliq int Ice interface Sc Schmidt number microliqρliq D ice Ice Shh Hydraulic Sherwood number l Local Shp ε(1-ε) liq Liquid Shp Particle Sherwood number k DpD liq-w Liquid-wall t Time (s) meas Measured T Temperature (degC) o Outside T Equilibrium temperature (degC) outer Outer ∆Ttrans Transition temperature difference p Particle for ice scaling (K) pred Predicted ∆Tln Logarithmic mean temperature s Suspension difference (K) w Wall

Abbreviations

AFP Antifreeze protein KCl Potassium nitrate CaCl2 Calcium chloride KNO3 Potassium nitrate EG Ethylene glycol MgSO4 Magnesium sulfate FBHE Fluidized bed heat exchanger NaCl Sodium chloride HNO3 Nitric acid PVA Poly(vinyl alcohol)


33

References

Buffiegravere P Moletta R 2000 Collision frequency and collisional particle pressure in three-phase fluidized beds Chemical Engineering Science vol55 pp5555-5563

Chilton TH Colburn AP 1934 Mass transfer (absorption) coefficients ndash prediction from data on heat transfer and fluid friction Industrial and Engineering Chemistry vol26 pp1183-1187

Foumlrster M Augustin W Bohnet M 1999 Influence of the adhesion force crystalheat exchanger surface on fouling mitigation Chemical Engineering and Processing vol28 pp449-461

Garić-Grulović RV Grbavčić ŽB Arsenijević ZL 2004 Heat transfer and flow pattern in vertical liquidndashsolids flow Powder Technology vol145 pp163ndash171

Garner FH Marchant PJM 1961 Diffusivities of associated compounds in water Transactions of the Institution of Chemical Engineers vol39 pp397-408

Gmelin 1952 Gmelins Handbuch der Anorganischen Chemie 8th edition Deutsche Chemische Gesellschaft Weinheim Verlag Chemie

Goede R de Rosmalen GM van 1990 Modelling of crystal growth kinetics A simple but illustrative approach Journal of Crystal Growth vol104 pp392-398

Grandum S Yabe A Nakagomi K Tanaka M Takemura F Kobayashi Y Frivik P-E 1999 Analysis of ice crystal growth for a crystal surface containing adsorbed antifreeze proteins Journal of Crystal Growth vol205 pp382-390

Huige NJJ 1972 Nucleation and Growth of Ice Crystals from Water and Sugar Solutions in Continuous Stirred Tank Crystallizers PhD thesis Eindhoven University of Technology (The Netherlands) p141

Huige NJJ Thijssen HAC 1972 Production of large crystals by continuous ripening in a stirrer tank Journal of Crystal Growth vol1314 pp483-487

Inada T Yabe A Grandum S Saito T 2000 Control of molecular-level ice crystallization using antifreeze protein and silane coupling agent Materials Science and Engineering A vol292 pp149ndash154

Inada T Modak PR 2006 Growth control of ice crystals by poly(vinyl alcohol) and antifreeze protein in ice slurries Chemical Engineering Science vol61 pp3149-3158

Lobo VMM 1989 Handbook of Electrolyte Solutions Amsterdam Elsevier

Lu S-S Inada T Yabe A Zhang X Grandum S 2002 Microscale study of poly(vinyl alcohol) as an effective additive for inhibiting recrystallization in ice slurries International Journal of Refrigeration vol25 pp562-568

Meewisse JW 2004 Fluidized Bed Ice Slurry Generator for Enhanced Secondary Cooling Systems PhD thesis Delft University of Technology (The Netherlands)

Chapter 2

34


Meijer JAM Wesselingh JA Clobus A Goossens MLA 1986 Impacts against the wall of a scaled up fluidized bed Desalination vol58 pp1-18

Mersmann A Eble A Heyer C 2001 Crystal Growth In Mersmann A (Ed) Crystallization Technology Handbook 2nd edition New York Marcel Dekker Inc pp81-143


Schmidt S Buumlchs J Born C Biselli M 1999 A new correlation for the wall-to-fluid mass transfer in liquidndashsolid fluidized beds Chemical Engineering Science vol54 pp829-839

Smith JM Van Ness HC Abbott MM 1996 Introduction to Chemical Engineering Thermodynamics 5th edition New York McGraw-Hill pp526-531


Vaessen RJC Himawan C Witkamp GJ 2002 Scale formation of ice from electrolyte solutions Journal of Crystal Growth vol237-239 pp2172-2177

35

3 Influence of Fluidized Bed Parameters on Ice Scaling Part I Impact Measurements and Analysis

31 Introduction

The previous chapter demonstrated that the solute type and concentration of aqueous solutions strongly influence the prevention of ice scaling in fluidized bed heat exchangers For this purpose the experimental fluidized bed conditions were kept constant However previous work has shown that these fluidized bed conditions such as bed voidage and particle size can also seriously influence the prevention of ice scaling (Meewisse 2004) which is mainly attributed to differences in particle-wall collision characteristics

Due to their importance in fluidized bed systems particle-wall collisions and individual particle movements have been experimentally studied for both stationary and circulating fluidized beds in the past Individual particle velocities were mainly measured by using visual observation techniques with tracer particles (Carlos and Richardson 1968 Kmieć 1978 Grbavčić et al 1990 Garić-Grulović et al 2004) while piezoelectric sensors were used to measure particle-wall collisions (Bordet et al 1968 Meijer et al 1986 Zenit 1997 Zenit et al 1997 Zenit et al 1998 Buffiegravere and Moletta 2000) Although the latter measurements were successful expressions for collision frequencies and particles impact velocities as a function of bed voidage particle size and circulation rate are lacking Furthermore it is not clear how particle-wall collisions are related to the removal of deposits The most plausible options are that the removal is proportional to the total impulse generated by the particles on the wall also referred to as particle pressure or to the total kinetic energy of the particles that hit the wall (Meijer 1983 Meijer 1984 Buffiegravere and Moletta 2000)

The first aim of this chapter is to characterize both frequency and impact velocities of particle-wall collisions in liquid-solid fluidized bed heat exchangers For this purpose a piezoelectric sensor was used to measure collisions in both stationary and circulating fluidized beds at various bed voidages with stainless steel particles of 2 3 or 4 mm The second aim is to use these collision characteristics to formulate expressions for the total kinetic energy of particles that hit the wall and the total impulse exerted by the particles on the wall as a function of bed voidage particle size and circulation rate

32 Experimental Set-up

321 Single-tube Fluidized Bed Heat Exchanger

The experiments were carried out with a single-tube fluidized bed heat exchanger as shown in Figure 31 The heat exchanger consisted of two stainless steel tube-in-tube heat exchangers connected by a stainless steel tube The internal diameter of the inner tubes and the connection tube measured 427 mm and the total length of the heat exchanger was 488 m The fluidized bed consisted of tap water and cylindrical stainless steel particles of approximately 2 3 or 4 mm in both height and diameter with a density of 7900 kgm3 The average equivalent particle diameters were determined from weight measurements and measured 21 32 and 43 mm respectively

Chapter 3

36

Figure 31 Schematic layout of experimental set-up

The fluidized bed was cooled by a 34 wt potassium formate solution flowing countercurrently through the annuli The inlet temperature of the coolant was 17degC while an electrical heater in the water tank controlled the water inlet temperature at 20degC The fluidized bed was operated in both stationary and circulating mode In the latter mode particles were dragged out at the top of the heat exchanger and were recirculated to its inlet via a downcomer tube with an internal diameter of 34 mm A part of the flow from the water tank named control flow was used to transport particles from the bottom of the downcomer to the inlet of the fluidized bed

In order to determine the bed voidage in the fluidized bed pressures were measured at the top and bottom of the heat exchanger The bed voidage was deduced from the measured pressure drop in the fluidized bed which consists of a hydrostatic term a term for the liquid-wall friction and a term for the particle-wall friction (Garić-Grulović et al 2004)

( )( )liq p frliq-w frp-w1p gh p pερ ε ρ∆ = + minus + ∆ + ∆ (31)

The pressure drop by friction between the liquid and the wall was determined from experiments without particles The friction between particles and wall was neglected

322 Measurement of Particle Collisions

A piezoelectric sensor of type KISTLER 601A with a diameter of 55 mm was mounted in the connection tube such that the membrane of the sensor smoothly followed the inner surface of the tube (see Figure 31) The duration of collisions was typically in the order of 30 micros and therefore a sampling frequency of 300 kHz was applied In order to reduce the amount of measurement data only collisions with maximum pressures above a certain threshold value were stored for later analysis The applied threshold values were 005 010 and 025 bar for 2 3 and 4 mm particles respectively

Influence of Fluidized Bed Parameters on Ice Scaling I Impact Measurements and Analysis

37

The piezoelectric sensor was calibrated to determine the elasticity and the effective area of the sensor membrane For this purpose the 2 3 and 4 mm particles were dropped onto the horizontal membrane from heights of 10 50 and 200 cm corresponding to impact velocities of 044 10 and 20 ms (see Figure 32) For the fourth series a 4 mm particle was bound on a 1-meter cord forming a pendulum The sensor was installed such that the particle hit the vertical membrane in the lowest point of the pendulum The particles were released from three different horizontal distances from the sensor namely 10 20 and 50 cm resulting in impact velocities of 0031 0063 and 016 ms respectively (see Figure 32) For each particle size and impact velocity at least 20 impacts were measured The average values of the maximum pressure and duration of a collision were calculated for each condition

Figure 32 Schematic layout of fall set-up to calibrate the piezoelectric sensor

Figure 33 Schematic layout of pendulum set-up to calibrate the piezoelectric sensor

The duration of a collision between a particle and a surface is given by (Goldsmith 1960)

04 042p p

02p

125435E

Dv

ρυτ minus

=

with s p

s p

E EE

E E=

+ (32)

Since the material properties in Equation 32 are constant for all calibration conditions the collision duration should be proportional to Dpvp

02 which is confirmed in Figure 34 The combined elasticity E can now be deduced from this proportionality With a Poissonrsquos ratio of 03 the combined elasticity equals 106middot1010 Nm2

The maximum force of a collision between a particle and a surface is given by (Goldsmith 1960)

0406 2 12

max p p p2

E075741

F D vρυ

= minus (33)

Chapter 3

38

10

100

0001 0010D pv p

02 (m08s02)

τ (1

0-6 s

)

2 mm falling3 mm falling4 mm falling4 mm pendulum

0002 0004 0006

80

60

4030

20

Figure 34 Contact time as a function of Dpvp

02 for 2 3 and 4 mm particles with various impact velocities

This maximum force of a collision is measured by the sensor as a pressure

maxmax

s

FpA

= (34)

Figure 35 confirms Equation 33 and 34 showing a proportionality between the measured maximum pressure and Dp

2vp12 Since the material properties in Equation 33 are known the

effective area of the sensor can now be deduced from the relation shown in Figure 35 The calculated effective area of the sensor is 115 mm2 which corresponds to an effective diameter of 38 mm

10

100

1000

10000

01 10 100 1000D p

2v p12 (10-6 m32s12)


pm

ax (1

03 Pa)

Figure 35 Measured maximum pressures during collisions as a function of Dp

2vp12 for 2 3

and 4 mm particles with various impact velocities


39

323 Experimental Conditions

First of all the influences of particle size and bed voidage on the impact characteristics were investigated for stationary fluidized beds as listed in Table 31 The lowest bed voidage for a certain particle size in the table corresponds to the minimum bed voidage for homogenous fluidization Below this bed voidage the fluidized bed showed heterogeneous behavior with dilute liquid slugs flowing from bottom to top

Table 31 Experimental conditions of stationary fluidized bed experiments Dp (mm) ε () us (ms) Dp (mm) ε () us (ms) Dp (mm) ε () us (ms)

21 694 020 32 760 032 43 798 038 727 022 790 033 826 041 762 024 825 037 866 047 794 027 860 041 897 053 827 031 895 047 934 061 862 035 930 053 963 068 897 040 960 060 932 045 962 051

A second series of experiments was carried out with circulating fluidized beds as listed in Table 32 The average upward particle velocity is used as a measure for the circulation rate and is deduced from the slip velocity between liquid and particles

scfbz slip p

uv v Dε

ε= minus (35)

Table 32 Experimental conditions of circulating fluidized bed experiments Dp ε us vz Dp ε us vz Dp ε us vz

(mm) () (ms) (ms) (mm) () (ms) (ms) (mm) () (ms) (ms) 21 790 058 040 32 790 072 048 43 799 066 036

825 045 017 825 087 061 831 082 048 825 054 029 855 105 075 864 091 051 825 077 056 895 058 013 894 114 069 859 101 077 895 078 034 885 124 097 895 097 056 895 050 012 895 127 090 895 066 029 895 088 054

The relation between the slip velocity on the one hand and the bed voidage and the particle size on the other hand is derived from the stationary fluidized bed experiments

ssfb p

slip p

u Dv D

εε

ε= (36)

The control flow through the bottom of the downcomer enabled to control the circulation of particles up to a certain maximum Most of the experiments were operated at this maximum For three combinations of particle size and bed voidage the control flow was varied in order to change the circulation rate while the bed voidage was kept constant

Chapter 3

40

33 Results

331 Analysis of a Single Experiment

A typical impact measured by the piezoelectric sensor during operation of a stationary fluidized bed of 3 mm particles at a bed voidage of 895 is shown in Figure 36 The contact time of the impact τ is defined as the period that the measured pressure is above the threshold value The frequency distribution of the contact times for the concerned experiment in Figure 37 is bimodal which means that two different types of impacts can be distinguished namely short and long impacts Similar bimodal distributions were obtained by Zenit (1997) and Zenit et al (1997) who also recorded the particle behavior close to the sensor with a high-speed camera Synchronization of these recordings with the pressure measurements revealed that long impacts are caused by particles that hit the sensor and that the short impacts are caused by liquid pressure fronts induced by collisions between particles in the vicinity of the sensor

-10

0

10

20

30

40

50

60

0 20 40 60 80 100Time (10-6 s)

Pres

sure

(10

3 Pa)

p max

τ

Threshold

Figure 36 Measured pressures during a collision of a particle on the sensor

0

10

20

30

40

0 10 20 30 40 50Contact time (10-6 s)

Freq

uenc

y (1

0 9 1

m2 s2 )

Figure 37 Frequency distribution of impacts with various contact times (SFB Dp=32 mm

ε=895)


41

In the analysis of the experiments the two types of impacts are considered separately The particle-wall collisions are characterized by their frequency and their radial impact velocity which is determined from the measured maximum pressure of each collision and Equations 33 and 34 The liquid pressure fronts are characterized by their frequency and maximum pressure

332 Stationary Fluidized Beds

Particle-wall collisions

An analysis of the particle-wall collisions of a single stationary fluidized bed experiment shows that the distribution of radial impact velocities approaches the Maxwell distribution (see Figure 38)

2

A rA r

ravgravg

exp2

f vy vvv π

= minus

(37)

00

10

20

30

40

000 005 010 015 020 025v r (ms)

y A (1

06 1m

3 )

Threshold

Figure 38 Frequency distribution of radial particle impact velocities (SFB Dp=32 mm

ε=895)

This result is in accordance with visual observations by Carlos and Richardson (1968) who draw a parallel between the particle motion in fluidized beds and the motion of molecules in gases The Maxwell distribution was not obtained during the piezoelectric measurements of particle impacts by Meijer et al (1986) since they measured a relatively high number of low-velocity impacts The probable cause for this deviation is the fact that no distinction was made between the two impact types and that the measured distribution therefore contained both particle-wall collisions and liquid pressure fronts

For all 22 stationary fluidized bed conditions listed in Table 31 the measured radial particle impact velocity distribution is approached by a Maxwell distribution by fitting the average radial particle velocity vravg and the frequency of particle-wall collisions fA in Equation 37 (see Figure 38) The results in Figure 39 indicate that the average radial impact particle velocity depends barely on the bed voidage and is approximately one-tenth of the superficial liquid velocity

Chapter 3

42

ravg s010v u= (38)

000002004006008010012014016018020

65 70 75 80 85 90 95 100ε ()

v ra

vgu

ssf

b

2 mm 3 mm 4 mm

Figure 39 Ratio between the average radial particle impact velocity and the superficial

velocity as function of bed voidage for stationary fluidized beds with different particle sizes

The fitted frequencies of particle-wall collisions fA appear to decrease with increasing bed voidage and to be higher for smaller particles Correlations for this frequency in literature can be rewritten into the following form

( ) A ravg 3p

6 1ff v

Dε

επ

minus= (39)

Figure 310 shows that experimentally obtained values for f are indeed only a function of the bed voidage

00

05

10

15

20

25

30

35

40

65 70 75 80 85 90 95 100ε ()

f = ( π

6) f

A D

p3 (v

r (1

- ε))

2 mm3 mm4 mmEq 312

Figure 310 Function fε for stationary fluidized beds with different particle sizes


43

Correlations for fε can be derived from correlations proposed for the particle pressure which is the total impulse exerted by particles per square meter wall per second The particle pressure J of a particle impact velocity distribution as stated in Equation 37 is given by

3

p-w A p r r A p p ravg0

223

J y m v dv f D vπ ρinfin

= =int (310)

If Equations 38 and 310 are applied for the particle pressure correlation proposed by Gidaspow (1994) than function f becomes

( ) 0f 1

3gπε ε= minus with

13

1

0pb

111

g εε

minus minus = minus minus

(311)

An adjusted form of Equation 311 with a packed bed voidage of 40 and a different constant appears to give a good representation of the experimentally obtained values for f as shown in Figure 310

( ) 0adjf 233 1 gε ε= minus with ( )0adj 0max 3g g= (312)

Liquid Pressure Fronts

The measured frequency of liquid pressure fronts induced by particle-particle collisions in stationary fluidized beds is of the same order of magnitude as the number of measured particle-wall collisions However measured maximum pressures and contact times are both about a factor of five lower It is therefore expected that the liquid pressure fronts only give a minor contribution to the total energy and impulse exerted on the wall which is confirmed in Section 342 The influence of liquid pressure fronts on fouling removal in stationary fluidized beds is therefore also expected to be negligible For this reason there is no need to model the characteristics of particle-particle collisions in stationary fluidized beds

333 Circulating Fluidized Beds

Particle-wall Collisions

In analogy with the stationary fluidized bed experiments the average radial particle impact velocities and frequencies were also deduced from the impact measurements of the circulating fluidized bed experiments The results in Figure 311 show an increasing trend of the average radial particle impact velocity as the upward particle velocity increases This trend is similar for the three particle sizes and for various bed voidages In order to calculate the total energy or impulse exerted on the wall as a function of the circulation rate this increasing trend is described by the following empirical expression in which the radial impact velocity for stationary fluidized beds is calculated from Equation 38

( )ravgcfb ravgsfb z1 068v v v= + sdot (313)

Chapter 3

44

000

050

100

150

200

250

000 020 040 060 080 100v z (ms)

v ra

vgc

fbv

rav

gsf

b

2 mm3 mm4 mmEq 313

Figure 311 Relative average radial particle impact velocity in circulating fluidized beds

In contrast with the radial impact velocity the frequency of particle-wall collisions decreases as the upward particle velocity increases as shown in Figure 312 Since the decrease of collisions occurs especially at low upward particle velocities the frequency is described by an empirical exponential expression in which the frequency for stationary fluidized beds is calculated from Equations 39 and 312

( ) 0adjf 233 1 gε ε= minus with ( )Acfb Asfb zexp 109f f v= sdot minus sdot (314)

000

020

040

060

080

100

120

000 020 040 060 080 100v z (ms)

f Ac

fbf

As

fb

2 mm3 mm4 mmEq 314

Figure 312 Relative frequency of particle-wall collisions in circulating fluidized beds

The measured differences between particle-wall collisions in stationary and circulating fluidized beds are attributed to changes in the motion and distribution of particles During homogeneous fluidization in stationary fluidized beds particles are uniformly distributed in both axial and radial direction (Kwauk 1992) For circulating fluidized beds however several researchers have reported non-uniform particle distributions Experiments by Liang et al (1996 1997) for example showed that the concentration of 04 mm glass spheres in a


45

circulating fluidized bed of 140 mm in diameter is higher near the wall than in the core of the bed These experimental results were confirmed by CFD simulations presented by Cheng and Zhu (2005) In addition they showed that the non-uniformity increases as the ratio between the bed and particle diameter increases Opposite experimental results were obtained by Kim and Lee (2001) who observed that 3 mm glass spheres move to the center of a 12 mm tube as the upward particle velocity is increased Moreover it was observed that the frequency of particle-wall collisions decreases with increasing upward particle velocity which is in accordance with the experimental results obtained in this work A lower collision frequency at higher circulation rates was also reported by Garić-Grulović et al (2004) for 5 mm glass spheres in a rectangular fluidized bed of 60x8 mm At low circulation rates the particles move vertically with some radial movement but at higher circulation rates the particles follow vertical streamlines resulting in less particle-wall collisions


The frequency and average maximum pressure of liquid pressure fronts measured during circulation were both considerably higher than during stationary operation It is therefore considered as a possibility that the liquid pressure fronts induced by particle-particle collisions do play a role in the removal of fouling For this reason the distribution of liquid pressure fronts that reach the wall is analyzed for the circulating fluidized bed experiments

As discussed in Section 331 the short impacts measured by the piezoelectric sensor are assumed to be caused by liquid pressure fronts induced by particle-particle collisions in the vicinity of the sensor In order to characterize the liquid pressure fronts the particle-particle collisions are therefore characterized first According to Carlos and Richardson (1968) particle velocities in a fluidized bed are distributed like a Maxwell distribution and it is therefore assumed that particle-particle collision velocities can also be described with this distribution

2

pVV p

pavgpavg

exp2

vfy vvv π

= minus

(315)

According to collision mechanics the maximum force during a collision between two spherical particles is proportional to the collision velocity to the power 12 (Goldsmith 1960) It is therefore assumed that the maximum pressure of a pressure front generated by a particle-particle collision is also proportional to the collision velocity to the power 12 The distribution of maximum pressures at a distance Dp from the point of collision is therefore

53

V maxV max 8

5 max avg maxavg

exp2 2

f py pp pΓ

= minus =

53

V max

maxavg max avg

05596 exp2

f pp p

= minus

(316)

Chapter 3

46

The distribution of pressure fronts reaching a point at the wall is obtained by integration of all pressure fronts coming from particle-particle collisions in an infinite hemispherical volume V Since the maximum pressure of a front decreases approximately quadratically with the distance r (Zenit 1997 Zenit and Hunt 1998) the distribution of maximum pressures at the wall is

( )5

32

max pVj max

maxavg maxavg

05596 exp2V

p r Dfy p dVp p

= minus int (317)

The integration over volume V is performed in polar coordinates where the integral over distance r is taken from Dp2 to infinity since the point of collision cannot be closer to the wall than a half particle diameter

( )5

3

p

2 22max pV p

j maxmaxavg maxavg p0 0 2

05596 exp sin2D

p r Df D ry p drd dp p D

π π

ϕ ϕ θinfin = minus

int int int (318)

Integration for φ and θ and substitution of rDp by l leads to

53

103

3V p 2 max

j maxmaxavg maxavg1 2

3516 exp2

f D py p l l dlp p

infin = minus int with

p

rlD

= (319)

The integral in Equation 319 cannot be solved analytically and is therefore approximated by a numerical solution

3

2

16max

j max max exp py p bpa

minus asymp minus

with max avg9548a p= and

123

V p maxavg3188b f D p= (320)

The maximum pressures of pressure fronts measured during the circulating fluidized bed experiments were used to fit parameters a en b in Equation 320 with a least square method for yj pmax

32 The result of this method for a fluidized bed of 3 mm particles a bed voidage of 895 and an upward particle velocity of 090 ms is compared with the measured distribution in Figure 313 The figure demonstrates that the distribution given by Equation 320 corresponds well with the experimental distribution


47

00

20

40

60

80

100

120

140

0 20 40 60 80 100p max (103 Pa)

y j p

max

32 (1

03 N1

2 m2 s)

Threshold

Figure 313 Distribution yjpmax

32 of liquid pressure fronts (CFB Dp=32 mm ε=895 vz=090 ms)

The average maximum pressure at a distance Dp from a particle-particle collision pmaxavg and the frequency of particle-particle collisions fV are deduced from parameters a and b for each experimental condition by Equation 320 The obtained average maximum pressures increase approximately linearly with the net upward particle velocity which is explained by heavier particle-particle collisions at higher circulation rates From this is expected that the collision velocity is mainly determined by the upward particle velocity However particle-particle collisions also occur during stationary fluidization when the net upward particle velocity is zero The assumption is therefore made that the average collision velocity can be approached by the superposition of the net upward particle velocity and the average particle velocity during stationary fluidization

pavg z pavgsfbv v v= + (321)

According to Carlos and Richardson (1968) the average particle velocity in stationary fluidized beds is approximately three times the average radial particle velocity which can be determined from Equation 38 The average particle-particle collision velocity in circulating fluidized beds is therefore modeled as

pavg z ravgsfb3v v v= + (322)

The assumption that the average maximum pressure of a pressure front induced by a particle-particle collision is proportional to the velocity of this collision is confirmed by Figure 314 From this figure the following correlation is deduced for the average maximum pressure at a distance Dp from a particle-particle collision

653

maxavg pavg3430 10p v= sdot (323)

Chapter 3

48

00

05

10

15

20

25

30

35

40

000 020 040 060 080 100 120v pavg

12 (m12s12)

pm

axa

vg (1

03 Pa)

2 mm3 mm4 mmEq 322

-25

+25

Figure 314 Measured average pressures of pressure fronts as function of particle velocity to

the power 12

Besides the average pressure the particle-particle collision frequency fV also shows an increasing trend as the net upward particle velocity increases According to Gidaspow (1994) the theoretical number of particle-particle collisions in a fluidized bed of spheres per unit of volume per unit time is

( )20 pavg

V 4p

11443

g vf

Dε

π πminus

= (324)

In order to show the isolated effect of the particle velocity as defined in Equation 321 the fitted frequencies fV are multiplied by Dp

4(g0adj(1-ε)2) in Figure 315

00

10

20

30

40

50

60

70

000 020 040 060 080 100 120v pavg (ms)

f Vd

p4 (g0

adj(1

- ε)2 ) (

ms

)

2 mm3 mm4 mmEq 324

-25

+25

Figure 315 Normalized frequency of particle-particle collisions as function of particle

velocity


49

The figure indicates that the correlation in Equation 324 describes the measured trends well but with a different constant The following correlation is deduced from the figure

( )20adj pavg

V 4p

15405

g vf

Dεminus

= (325)

34 Discussion

In the previous section models to characterize the impacts on the wall of a liquid-solid fluidized bed were obtained from experiments In this section these models are used to investigate how the impulse exerted on the wall and the energy of impacts depend on fluidized bed parameters such as particle size bed voidage and circulation rate


Since the contribution of liquid pressure fronts to the total impulse and the total energy are negligible for stationary fluidized beds as stated in Section 332 only contributions of particle-wall collisions are taken into account in the analysis

Impulse Exerted on the Wall

The total impulse exerted by particles hitting the wall is given by

p-w A p-w r

0

J y j dvinfin

= int (326)

The distribution of impact velocities in Equation 37 is substituted in Equation 326 In addition particle-wall collisions are considered as fully elastic with an impulse of 2mpvr per impact

2

3A rp-w p r r A p p ravg

ravg0 ravg

2exp 22 3

f vJ m v dv f D vvv

π ρπ

infin = minus =

int (327)

Substitution of Equations 39 and 312 for the particle-wall frequency fA in Equation 327 gives an expression for the total impulse

( )2 2p-w 0adj ravg p526 1J g vε ρ= minus (328)

The equivalent particle diameter Dp is not explicitly present in Equation 328 The cause for this absence is the fact that the higher impulse per collision for larger particles is exactly compensated by the lower number of collisions

Chapter 3

50

Combining Equations 38 and 328 and the application of a particle material density of 7900 kgm3 gives a final expression for the total impulse exerted by particles on the wall

( )22 2p-w 0adj ssfb415 10 1J g uε= sdot minus (329)

The results of Equation 329 for the studied conditions in Figure 316 show that the impulse on the wall increases monotonously with a decreasing bed voidage The higher impulse for bigger particle sizes is solely caused by the higher particle velocity induced by a higher superficial velocity

00

20

40

60

80

100

120

65 70 75 80 85 90 95 100ε ()

Impu

lse

J (N

m2 ) 2 mm

3 mm

4 mm

Figure 316 Impulse exerted by impacts on the wall of a stationary fluidized bed

Energy of Impacts

The total energy of impacts in stationary fluidized beds is calculated from the kinetic energy of all particles that hit the wall

p-w A p-w r

0

E y e dvinfin

= int (330)

The distribution of particle-wall collision velocities in Equation 37 is substituted in Equation 330 and the kinetic energy per particle is given by frac12mpvr

2

2

2 3 2A r 12p-w p r r A p p ravg

ravg0 ravg

exp2 6

f vE m v dv f D vvv

π ρπ

infin = minus =

int (331)

Substitution of Equations 39 and 312 for the particle-wall frequency fA gives an expression for the total energy

( )2 3p-w 0adj p ravg233 1E g vε ρ= minus (332)


51

Finally the relation between the particle and superficial velocity from Equation 38 and the particle density of 7900 kgm3 are substituted in Equation 332 The result is an expression for the total kinetic energy of all particles hitting the wall

( )2 3p-w 0adj ssfb184 1E g uε= minus (333)

A graphical representation of Equation 333 in Figure 317 shows roughly the same behavior for the total energy as for the total impulse in Figure 316 The total kinetic energy of particles hitting the wall also increases with decreasing bed voidage and is higher for bigger particles However the relative differences between different particle sizes are larger in Figure 317 which is caused by the stronger influence of the superficial velocity

000

002

004

006

008

010

012

014

016

65 70 75 80 85 90 95 100ε ()

Ene

rgy

E (J

m2 s)

2 mm

3 mm

4 mm

Figure 317 Energy of impacts on the wall of a stationary fluidized bed

342 Circulating fluidized beds

In contrast with the analysis for stationary fluidized beds both contributions from particle-wall collisions and liquid pressure fronts need to be taken into account in the analysis of circulating fluidized beds


The total impulse exerted on the wall is given by the sum of the impulse by particle-wall collisions and by liquid pressure fronts

cfb p-w lpfJ J J= + (334)

The impulse by particle-wall collisions in circulating fluidized beds is obtained by substitution of Equations 313 and 314 in Equation 327

( ) ( )3

p-w Asfb p p ravgsfb z z2 1 068 exp 109

3J f D v v vπ ρ= + sdot minus sdot (335)

Chapter 3

52

Analogously with the method described in Section 41 for stationary operation the final expression for the impulse of particle-wall collisions is obtained by substitution of Equations 38 39 and 312 in Equation 335

( ) ( ) ( )22 2p-w 0adj ssfb z z415 10 1 1 068 exp 109J g u v vε= sdot minus + sdot minus sdot (336)

The total impulse exerted by liquid pressure fronts is given by the sum of the impulses of all individual pressure fronts

lpf j lpf max

0

J y j dpinfin

= int (337)

The impulse exerted by a single liquid pressure front per m2 is given by

lpf max lpf

0

2j pdt pτ

τπ

= =int with maxlpf

sin tp t p πτ

=

(338)

Replacement of the impact of a single pressure front and the distribution of pressure fronts in Equation 337 by Equations 338 and 320 respectively leads to

3

2

16max

lpf max max lpf max0

2 exp pJ bp p dpa

τπ

infinminus

= minus int (339)

The duration of a particle-particle collision is given by Goldsmith (1960) The application of the material properties for stainless steel results in an expression for the duration of a collision as a function of the particle size and the collision velocity

1 1

5 5

042

- -04 3p-p p p p p p

p

12922 3016 10E

D v D vυτ ρ minus minus

= = sdot

(340)

The relation between the particle collision velocity and the maximum pressure of the resulting pressure front from Equation 323 is combined with Equation 340

16-2

p-p p max1171 10 D pτ minus= sdot (341)

The calculated results from Equation 341 for the duration of particle-particle collisions correspond fairly to the measured durations of pressure fronts It is therefore assumed that both durations are equal

lpf p-pτ τ= (342)

Substitution of Equations 341 and 342 in Equation 339 gives

2

3

163 max

lpf p max max0

7456 10 exp pJ D b p dpa

infinminusminus

= sdot minus int (343)


53

In Equation 343 the ratio pmaxa is replaced by x

( )1 23 33 16

lpf p0

7456 10 expJ D ba x x dxinfin

minusminus= sdot minusint with maxpxa

= (344)

The integral in Equation 344 is solved numerically and parameters a and b are replaced by the correlation in Equation 320

564

lpf V p maxavg01386J f D p= (345)

Combination of Equations 323 325 and 345 leads to a final expression for the impulse exerted by pressure fronts on the wall

( )22 2lpf 0adj pavg662 10 1J g vε= sdot minus (346)

As stated in Equation 334 the total impulse on the wall is the sum of the impulse exerted by particle-wall collisions (Equation 336) and the impulse exerted by pressure fronts (Equation 346) Figure 318 gives a graphical representation of both contributions as a function of the upward particle velocity for a fluidized bed of 3 mm particles at a bed voidage of 895 The figure shows a slight decrease of impulse exerted by particle-wall collisions as the upward particle velocity increases This decrease is caused by a reduced number of collisions during circulation which is only partly compensated by the higher impact velocity The contribution of pressure fronts strongly increases as the upward particle velocity increases and exceeds the contribution of particle-wall collisions at upward particle velocities higher than 022 ms for this example At stationary circulation (vz=0) however the impulse of pressure fronts is calculated to be only about 10 of the total impulse for all conditions

0

5

10

15

20

25

30

35

00 02 04 06 08 10v z (ms)

Impu

lse

J (N

m2 )


Pressure fronts

Total

Figure 318 Impulse exerted by impacts on the wall of a circulating fluidized bed of 3 mm

particles at a bed voidage of 895

Chapter 3

54

Energy of Impacts

The total energy of impacts on the wall is the sum of the energy of the particles hitting the wall and the energy of liquid pressure fronts

cfb p-w lpfE E E= + (347)

The total kinetic energy of particles hitting the wall in a circulating fluidized bed is obtained by substitution of Equations 313 and 314 in Equation 331

( ) ( )23 2p-w Asfb p p ravgsfb z z1 068 exp 109

6E f D v v vπ ρ= + sdot minus sdot (348)

Analogously with the method described in Section 341 for stationary operation the final expression for the energy of particles is obtained by substitution of Equations 38 39 and 312 in Equation 348

( ) ( ) ( )2 23p-w 0adj ssfb z z184 1 1 068 exp 109E g u v vε= minus + sdot minus sdot (349)

The total energy of pressure fronts is the sum of the energy per m2 of all pressure fronts reaching a point at the wall

lpf j lpf max

0

E y e dpinfin

= int (350)

The energy of a single liquid pressure front per m2 is (Pain 1993)

22max lpf

lpfliq liq liq liq0 2

ppe dtc c

τ τρ ρ

= =int with maxlpf

sin tp t p πτ

=

(351)

Replacement of the energy per pressure front and the distribution of pressure fronts in Equation 350 by Equations 351 and 320 respectively lead to

1

2

16max

lpf max maxliq liq 0

exp2

pbE p dpc a

τρ

infin = minus int (352)

The expression for the duration of a pressure front in Equations 341 and 342 is applied in Equation 352

1

3

16p3 max


586 10 expD b pE p dp

c aρ

infinminus



( )

43

13p3 16

lpfliq liq 0

586 10 expa bD

E x x dxcρ

infinminus= sdot minusint with maxpx

a= (354)


55

The integral for x in Equation 354 is solved numerically The parameters a and b are replaced by the correlations given in Equation 320

1164

V p maxavglpf

liq liq

03061f D p

Ecρ

= (355)

The correlation in Equation 323 is now used to replace the average maximum pressure by the average particle velocity

1154

V p pavg5lpf

liq liq

9273 10f D v

Ecρ

= sdot (356)

Finally the correlation for the frequency of particle-particle collisions in Equation 325 and the values for density (998 kgm3) and speed of sound (1482 ms) are substituted in Equation 356 resulting in a final expression for the energy of pressure fronts reaching the wall

( ) 165

2lpf 0adj pavg3388 1E g vε= minus (357)

Both the kinetic energy of particles hitting the wall (Equation 349) and the energy of liquid pressure fronts (Equation 357) are shown in Figure 319 for a fluidized bed of 3 mm particles at a bed voidage of 895 The kinetic energy of the particles is almost constant in the figure because the lower collision frequency is compensated by the strong increase of the kinetic energy per collision (Equation 349) The energy of liquid pressure fronts is only 06 of the total energy for stationary fluidized beds but increases considerably as the upward particle velocity increases

000

005

010

015

020

025

00 02 04 06 08 10v z (ms)

Ene

rgy

E (J

m2 s)

Total

Particle-wallcollisionsPressure fronts

Figure 319 Energy of impacts on the wall of a circulating fluidized bed of 3 mm particles at

a bed voidage of 895

Chapter 3

56

343 Expectations for Fouling Removal

As already mentioned in the introduction it is not clear up to now how particle-wall collisions are related to fouling removal In literature the removal of deposits is supposed to be proportional to the energy of particles hitting the wall (Meijer 1983 Meijer 1984) or to the total impulse exerted by particles on the wall (Buffiegravere and Moletta 2000) Based on these ideas expectations for the fouling removal ability of various fluidized beds can be made with the help of the expressions for impulse and energy deduced in this paper In the next chapter these expectations are compared to fouling prevention data for a fluidized bed heat exchanger for ice crystal production

Stationary Fluidized Beds

Since both the impulse on the wall in Figure 316 and the kinetic energy of particles in Figure 317 are higher for large particles it is expected that fluidized beds consisting of large particles result in better fouling removal This expectation is in correspondence with experimental results by Meijer (1983 1984) who showed that the prevention of calcium sulfate fouling by 2 mm particles was better than by 1 mm particles Experiments with different bed voidages are lacking but from Figure 316 and Figure 317 is expected that the fouling removal ability enhances as the bed voidage decreases The maximum kinetic energy of particles and the maximum impulse are both obtained at the lowest possible bed voidage with homogeneous fluidization At lower bed voidage heterogeneous fluidization occurs which is believed to have a lower fouling removal ability than the homogeneous regime

Although the particle material density was not varied in the experiments presented in this paper it is expected to be an important factor in fouling removal According to Equations 328 and 332 the impulse and energy are both proportional to the particle density Furthermore it is believed that the radial particle impact velocity is higher for denser particles since a higher superficial velocity is necessary for fluidization This positive influence of the particle density is confirmed by Rautenbach et al (1991) who showed that calcium sulfate fouling was prevented up to higher heat fluxes by stainless steel particles with a density of 7900 kgm3 than by aluminum oxide particles of 3780 kgm3 Another factor that might influence fouling removal is the shape of the particles However this influence cannot be deduced from the analysis in this paper and experimental results on this topic are lacking

Circulating Fluidized Beds

The main difference in impact characteristics between stationary and circulating fluidized beds is the contribution of liquid pressure fronts to the total impulse and the total energy as shown in Figure 318 and Figure 319 Due to this contribution both the impulse exerted on the wall and the kinetic energy of impacts strongly increase as the circulation rate increases It is likely that the liquid pressure fronts contribute to the removal of fouling since acoustic waves are a well-known technique to remove deposits from a wall (Kaye et al 1995) Several researchers even showed that ice crystallization fouling can be removed by acoustics (Duncan and West 1972 Ashley 1974) However it is questionable whether the fouling removal ability of liquid pressure fronts is of the same order of magnitude as the removal ability of particle-wall collisions

If liquid pressure fronts indeed play a role in fouling removal it is expected that circulating fluidized beds have a higher fouling removal ability than stationary fluidized beds Experiments with calcium sulfate fouling by Rautenbach et al (1991) seem to support this


57

statement Although not all operating conditions are clearly stated it is obvious from their results that the maximum heat flux at which fouling is prevented is considerably higher in circulating fluidized beds than in stationary fluidized beds

35 Conclusions

Heat exchanger fouling in liquid-solid fluidized beds is prevented by two types of impacts on the wall The first type of impacts is caused by particles hitting the wall while the second type is caused by liquid pressure fronts induced by particle-particle collisions in the vicinity of the wall The fouling removal ability of a fluidized bed is believed to be determined by the total impulse exerted on the wall or the total kinetic energy of impacts In stationary fluidized beds both parameters are mainly determined by particle-wall collisions and increase as the particle size increases or as the bed voidage decreases In circulating fluidized beds the contribution of liquid pressure fronts to the total impulse and total energy strongly increases as the circulation rate increases Due to this increase the fouling removal ability of circulating fluidized beds is expected to be higher than of stationary fluidized beds

Chapter 3

58

Nomenclature

a Parameter in Eq 320 (Nm2) p Pressure (Pa) A Area (m2) pmax Maximum pressure (Pa) b Parameter in Eq 320 (N12m s) ∆p Pressure drop (Pa) c Speed of sound (ms) r Distance (m) Dp Equivalent particle diameter t Time (s) 613π-13Vp

13 (m) T Temperature (degC) ep-w Energy of single particle-wall us Superficial liquid velocity (ms) collision (J) vslip Slip velocity (ms) elpf Energy of single pressure front per vp Particle velocity (ms) m2 (Jm2) vr Radial particle velocity (ms) E Energy of particles and pressure vz Net upward particle velocity (ms) fronts hitting the wall (Wm2) V Volume (m3) Ep-w Total kinetic energy of particles Vamp Volume flow rate (m3s) hitting the wall (Wm2) x Parameter pmaxa Elpf Total energy of pressure fronts yA Number density of particle-wall reaching the wall (Wm2) collisions (1m3) E Modulus of elasticity (Nm2) yj Number density of liquid pressure fA Particle-wall collision frequency fronts at point at the wall (1s Pa) (1m2s) yV Number density of particle-particle fV Particle-particle collision frequency collisions (1m4) or (1m3s Pa) (1m3s) f Function Greek Fmax Maximum force (N) Γ Gamma function g Gravity (ms2) ε Bed voidage g0 Gidaspow parameter defined in θ Angle in polar coordinates Eq 311 ρ Density kg m-3 g0adj Adjusted Gidaspow parameter τ Contact time s defined in Eq 312 υ Poissonrsquos ratio h Height (m) φ Angle in polar coordinates jp-w Impulse of single particle-wall collision (N s) Subscripts jlpf Impulse of single pressure front per avg Average unit of area (N sm2) cfb Circulating fluidized bed J Impulse exerted by particles and liq Liquid pressure fronts on wall (Nsm2s) liq-w Liquid-wall Jp-w Total impulse exerted by particles lpf Liquid pressure front on the wall (N sm2s) fr Friction Jlpf Total impulse exerted by pressure p Particle fronts on the wall (N sm2s) pb Packed bed l Dimensionless length rdp p-p Particle-particle L Length (m) p-w Particle-wall m Mass (kg) s Sensor mamp Mass flow rate (kgs) sfb Stationary fluidized bed


59

Abbreviations

CFB Circulating fluidized bed SFB Stationary fluidized bed CFD Computational fluid dynamics

References

Ashley MJ 1974 Preventing deposition on heat-exchange surfaces with ultrasound Ultrasonics vol12 pp215-221

Bordet J Borlai O Vergnes F Le Goff P 1968 Direct measurement of the kinetic energy of particles and their frequency of collision against a wall in a liquid-solids fluidized bed Institution of Chemical Engineers Symposium Series vol30 pp165-173


Carlos CR Richardson JF 1968 Solids movement in liquid fluidised beds - I Particle velocity distribution Chemical Engineering Science vol23 pp813-824

Cheng Y Zhu J 2005 CFD modelling and simulation of hydrodynamics in liquid-solid circulating fluidized beds The Canadian Journal of Chemical Engineering vol83 pp177-185

Duncan AG West CD 1972 Prevention of incrustation on crystallizer heat-exchangers by ultrasonic vibration Transactions of the Institution of Chemical Engineers vol50 pp109-114


Gidaspow D 1994 Multiphase Flow and Fluidization Continuum and Kinetic Theory Descriptions Boston Academic Press pp239-296

Goldsmith W 1960 Impact The Theory and Physical Behaviour of Colliding Solids London Arnold pp82-144

Grbavčić ŽB Vuković DV Zdanski FK 1990 Tracer particle movement in a two-dimensional water-fluidized bed Powder Technology vol62 pp199-201

Kaye PL Pickles CSJ Field JE Julian KS 1995 Investigation of erosion processes as cleaning mechanisms in the removal of thin deposited soils Wear vol186-187 pp413-420

Kim NH Lee YP 2001 Hydrodynamic and heat transfer characteristics of glass bead-water flow in a vertical tube Desalination vol133 pp233-243

Kmieć A 1978 Particle distributions and dynamics of particle movement in solid-liquid fluidized beds The Chemical Engineering Journal vol15 pp1-12

Chapter 3

60

Kwauk M 1992 Fluidization Idealized and Bubbleless with Applications Beijing Science Press

Liang W-G Zhu J-X Jin Y Yu Z-Q Wang Z-W Zhou J 1996 Radial nonuniformity of flow structure in a liquid-solid circulating fluidized bed Chemical Engineering Science vol51 pp2001-2010

Liang W-G Zhang S Zhu J-X Jin Y Yu Z-Q Wang Z-W 1997 Flow characteristics of the liquidndashsolid circulating fluidized bed Powder Technology vol90 pp95-102


Meijer JAM 1983 Prevention of calcium sulfate scale deposition by a fluidized bed Desalination vol47 pp3-15

Meijer JAM 1984 Inhibition of Calcium Sulfate Scale by a Fluidized Bed PhD thesis Delft University of Technology (The Netherlands)

Meijer JAM Wesselingh JA Clobus A Goossens MLA 1986 Impacts against the wall of a scaled-up fluidized bed Desalination vol58 pp1-18

Pain HJ 1993 The Physics of Vibrations and Waves 4th edition New York Wiley pp144-163

Rautenbach R Erdmann C Kolbach JS 1991 The fluidized bed technique in the evaporation of wastewaters with severe foulingscaling potential - latest developments applications limitations Desalination vol81 pp285-298

Zenit R 1997 Collisional Mechanics in Solid-liquid Flows PhD thesis California Institute of Technology (USA)

Zenit R Hunt ML Brennen CE 1997 Collisional particle pressure measurements in solid-liquid flows Journal of Fluid Mechanics vol353 pp261-283

Zenit R Hunt ML 1998 The impulsive motion of a liquid resulting from a particle collision Journal of Fluid Mechanics vol375 pp345-361

Zenit R Hunt ML Brennen CE 1998 On the direct and radiated components of the collisional particle pressure in liquid-solid flows Applied Scientific Research vol58 pp305-317

61

4 Influence of Fluidized Bed Parameters on Ice Scaling Part II Coupling of Impacts and Ice Scaling

41 Introduction

Chapter 2 has shown that liquid-solid fluidized bed heat exchangers can be used to produce ice suspensions from aqueous solutions However the ice crystallization process appeared to have a heat flux limit or transition temperature difference above which ice scaling is not prevented anymore This phenomenon is explained by the generally accepted idea that scaling or crystallization fouling is only prevented when the removal rate exceeds the deposition rate In case of ice crystallization the deposition rate is related to the growth rate of ice crystals on the wall which is proportional to the temperature difference between wall and solution (see Section 24) The removal of deposits is attributed to collisions of particles on the wall and to impacts by liquid pressure fronts induced by particle-particle collisions Chapter 3 has shown that the frequency and force of these impacts depend on fluidized bed conditions such as bed voidage particle size and particle density It is therefore most likely that the removal rate also varies with these changing conditions However the influence of fluidization parameters on the removal rate has hardly been studied both practically and fundamentally up to now

The aim of this chapter is to study the influence of fluidized bed parameters on ice scaling prevention and to unravel the mechanisms that determine the removal rate in liquid-solid fluidized beds For this purpose ice scaling is experimentally studied for both stationary and circulating fluidized beds with three different particle sizes at various bed voidages The transition temperature difference which was experimentally determined for each condition is used to evaluate the removal rate The obtained values are compared to two parameters that might determine the removal rate namely the impulse exerted by impacts on the wall and the kinetic energy of impacts (see Chapter 3) In conclusion a model is proposed to predict transition temperature differences in liquid-solid fluidized bed heat exchangers for ice crystallization



A single-tube fluidized bed heat exchanger as shown in Figure 41 was used to produce ice crystals from a 77 wt aqueous sodium chloride solution with an initial freezing temperature of ndash49degC The heat exchanger was made of two stainless steel tube-in-tube heat exchangers connected by a transparent section The fluidized bed in the inner tube consisted of cylindrical stainless steel particles of approximately 2 3 or 4 mm in both height and diameter with a density of 7900 kgm3 The average equivalent particle diameters were determined from weight measurements and measured 21 32 and 43 mm respectively The inner tubes had an inside diameter of 427 mm and the heat exchanger had a total length of 488 m The fluidized bed was operated in stationary or in circulation mode In the latter mode particles were dragged out at the top of the heat exchanger and recirculated to its inlet via a downcomer tube with an internal diameter of 34 mm A part of the flow from the ice suspension tank named control flow was used to transport particles from the bottom of the downcomer to the inlet of the fluidized bed An electrical heater in the tank enabled control of the ice fraction

Chapter 4

62


The fluidized bed was cooled by a 34 wt potassium formate solution which flowed countercurrently through the annuli of the heat exchangers The temperatures at the inlets and the outlets of the heat exchangers were measured by PT-100 elements with an accuracy of 001 K The total heat flux in the heat exchanger was determined from the coolant flow rate and coolant temperatures at the inlet and outlet of the heat exchanger This total heat flux was used to calculate the overall heat transfer coefficient Uo


The overall heat transfer resistance (1Uo) consists of three parts the annular side heat transfer resistance the heat transfer resistance of the tube wall and the fluidized bed heat transfer resistance



1 1 1ln2

D D DU D Dα λ α

= + +

(42)

From Equation 42 the fluidized bed heat transfer coefficient can be determined since a validated heat transfer model is available for the annular heat transfer coefficient (see Appendix C1) Subsequently the ratio of heat transfer coefficients the suspension temperature and the coolant temperature are used to determine the local wall temperature at the inside of the inner tube

( )( )

sll wl oinnero

i iinnersll cooll

T T DUDT T α

minus=

minus (43)

Influence of Fluidized Bed Parameters on Ice Scaling II Coupling of Impacts and Scaling

63


During an experiment the aqueous solution in the fluidized bed was cooled below its freezing temperature by the coolant whose inlet temperature was constant and controlled within 01 K As the aqueous solution reached a certain degree of supercooling ice crystals spontaneously nucleated and an ice suspension was formed

In order to determine the bed voidage in the fluidized bed pressures were measured at the top and bottom of the heat exchanger The bed voidage is deduced from the measured pressure drop in the fluidized bed which consists of a hydrostatic term a term for the liquid-wall friction and a term for the particle-wall friction (Garić-Grulović et al 2004)


The pressure drop by friction between the liquid and the wall is determined from experiments without particles The friction between particles and wall is neglected


The influences of particle size and bed voidage on ice scaling prevention were investigated for stationary fluidized beds as listed in Table 41 In a second series of experiments the ice scaling prevention ability of circulating fluidized beds was studied as listed in Table 42

Table 41 Experimental conditions of stationary fluidized bed experiments Dp ε us Dp ε us Dp ε us

(mm) () (ms) (mm) () (ms) (mm) () (ms) 21 718 017 32 763 026 43 808 037

758 020 792 029 839 042 789 022 813 032 874 047 827 026 847 035 906 052 859 029 939 059

Table 42 Experimental conditions of circulating fluidized bed experiments

Dp ε us vz Dp ε us vz Dp ε us vz (mm) () (ms) (ms) (mm) () (ms) (ms) (mm) () (ms) (ms) 21 788 056 043 32 804 076 056 43 796 068 041

820 075 061 816 081 060 836 084 051 855 100 083 852 105 081 863 103 066 888 122 101 875 128 103 887 126 086

For the circulating fluidized bed experiments the average upward particle velocity is used as a measure for the circulation rate and is deduced from the slip velocity between liquid and particles

scfbz slip

uv v

ε= minus (45)

Chapter 4

64

The slip velocity as function of bed voidage and particle size is derived from the stationary fluidized bed experiments where the upward particle velocity equals zero

ssfbslip p

uv Dε

ε= (46)

The circulation rate was controlled by the control flow through the bottom of the downcomer Ice crystallization experiments were only performed at maximum circulation because at lower circulation rates the downcomer was blocked by ice crystals The probable cause for this blockage is that part of the control flow containing ice crystals flowed upward through the downcomer where the downward moving packed bed of stainless steel particles acted as a filter for the upward flowing ice suspension


431 Determination of Transition Temperature Difference

For the operating conditions listed in Table 41 and 42 the coolant inlet temperature was varied to determine for which temperature differences between wall and solution ice scaling was prevented by the fluidized bed Since the formation of an ice layer could not be observed directly measured fluidized bed heat transfer coefficients were used to detect ice scaling Figure 42 shows fluidized bed heat transfer coefficients during two experiments for which ice crystallization started at t=0 s During the one experiment ice scaling was prevented and heat transfer coefficients were constant for at least 30 minutes after the first nucleation of ice crystals The other experiment showed decreasing heat transfer coefficients after the onset of crystallization indicating that an insulating ice layer built up on the walls

0

1000

2000

3000

4000

5000

6000

-300 0 300 600 900 1200 1500 1800Time (s)

-60

-50

-40

-30

-20

-10

00No ice scaling

Ice scaling

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Nucleation

Susp

ensi

on o

utle

t tem

pera

ture

(degC

)

Figure 42 Fluidized bed heat transfer coefficients and ice suspension outlet temperatures for

a stationary fluidized bed (Dp=43 mm ε=839) during ice crystallization from a 77 wt NaCl solution with (Tcoolin=-102degC) and without ice scaling (Tcoolin=-100degC)

Section 24 has shown that the difference between the wall temperature and the equilibrium temperature of the solution is the parameter that determines whether ice scaling occurs (see


65

also Pronk et al 2006) During all experiments described in this chapter the highest value for this parameter was at the top of the heat exchanger The wall temperature at this location was calculated by using the coolant inlet temperature and the suspension outlet temperature in Equation 43 Since the ice suspension at the outlet of the heat exchanger was slightly supercooled its equilibrium temperature was deduced from the energy balance and the assumption that the suspension entering the heat exchanger was in equilibrium The supercooling at the outlet was 01 K at most

For each set of fluidized bed conditions the transition temperature difference ∆Ttrans was determined as the average value of the highest temperature difference between wall and equilibrium without ice scaling and the lowest temperature difference for which ice scaling did occur (see Section 23)

432 Ice Scaling Prevention in Stationary Fluidized Beds

The results for the transition temperature difference of stationary fluidized beds in Figure 43 demonstrate that the ice scaling prevention ability decreases as the bed voidage increases except for 2 mm particles at low bed voidage At a bed voidage above the maximum values showed it was not possible to obtain ice crystallization without ice scaling because the cooling capacity at these low temperature differences was not sufficient to overcome the heat input by the pump and from the surroundings At lower bed voidages than displayed the fluidized bed showed heterogeneous behavior and ice scaling was not prevented in this regime The decrease of the transition temperature difference for 2 mm particles at low bed voidage may be influenced by this change of regime

00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

2 mm 3 mm 4 mm

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

No ice scaling

Ice scaling

for

ice

scal

ing

∆T

tran

s (K

)

Figure 43 Transition temperature differences with trendlines as function of bed voidage in

stationary fluidized beds

The results for different particle sizes in Figure 43 reveal that the ice scaling prevention ability of fluidized beds consisting of large particles is higher for a constant bed voidage However fluidized beds of smaller particles can be operated homogenously at lower bed voidages and therefore the maximum temperature difference that can be achieved for 3 and 4 mm particles does not differ considerably

Chapter 4

66

433 Ice Scaling Prevention in Circulating Fluidized Beds

In analogy with the stationary fluidized bed experiments the transition temperature difference for ice scaling was also experimentally investigated for circulating fluidized beds As discussed in Section 422 all these experiments were performed with the maximum circulation rate to avoid blockage in the downcomer At maximum circulation however downcomer blockages did also occur when the ice fraction in the control flow exceeded a certain value This phenomenon was especially a problem for circulating fluidized beds of 2 mm particles because blockages already occurred when ice fractions exceeded 2 wt For larger particles blockages occurred at higher ice fractions for example at 14 wt for 4 mm particles In order to assure stable circulation the heater in the tank was used to keep ice fractions below 2 wt for the experiments with 2 mm particles and below 5 wt for the other experiments

The measured ice scaling prevention abilities of circulating fluidized beds were equal or higher than of stationary fluidized beds with the same particles and bed voidage (see Figure 44) The increase of the transition temperature difference with respect to stationary fluidization is especially large for high circulation rates Next it is remarkable that the influence of the particle size on the transition temperature difference of circulating fluidized beds is much smaller than in case of stationary fluidization

00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

2 mm 3 mm 4 mm 043 061

083

101

056060

081 103

041051 066

086

SFB 2 mm

SFB 3 mm

SFB 4 mm

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)

Figure 44 Transition temperature difference for circulating fluidized beds including

trendlines for stationary fluidized bed from Figure 43 The numbers correspond to the upward particle velocity in (ms)

434 Heat Transfer Coefficients

Besides the fouling prevention ability the heat transfer coefficient is an important design parameter for liquid-solid fluidized beds From the experiments fluidized bed heat transfer coefficients were calculated with Equations 41 and 42 resulting in values ranging from 3500 to 5500 Wm2K The measurements with stationary fluidized beds showed increasing heat transfer coefficients with decreasing bed voidage and increasing particle size as shown in Figure 45 The values obtained for circulating fluidized beds were equal or up to 10 higher compared to stationary fluidized beds with equal particle size and bed voidage These results are in accordance with results from Erdmann (1993) who showed that heat transfer


67

coefficients of circulating fluidized beds at low and moderate circulation rates are close to values of comparable stationary beds (see also Rautenbach et al 1991 Rautenbach and Katz 1996) At high circulation rates where the single phase heat transfer coefficient approaches or exceeds the stationary fluidized bed heat transfer coefficient circulating fluidized beds show heat transfer coefficients that are significantly higher than values for stationary fluidized beds Circulation rates of this order were not obtained in the presented experiments

0

1000

2000

3000

4000

5000

6000

70 75 80 85 90 95 100ε ()

SFB 2 mmSFB 3 mmSFB 4 mmCFB 2 mmCFB 3 mmCFB 4 mmH

eat t

rans

fer

coef

ficie

nt (W

m 2 K

)

Figure 45 Fluidized bed heat transfer coefficients during ice crystallization without ice

scaling in stationary (including trendlines) and circulating fluidized beds

44 Model for Removal of Ice Scaling

The experimental results are explained by a fouling model in which the increase of the fouling layer at the wall is assumed to be proportional to the difference between the deposition rate and the removal rate (Kern and Seaton 1959 Chamra and Webb 1994)

layer d r

layer

ddtδ ϕ ϕ

ρminus

= (47)

In case of crystallization fouling the deposition rate φd is proportional to the growth rate of crystals attached to the wall (Helalizadeh et al 2005) Crystallization fouling in fluidized bed heat exchangers is therefore only prevented when the removal rate induced by fluidized particles exceeds this growth rate

R Ggt (48)

Chapter 4

68

441 Determination of Removal Rate

The removal rate of the investigated fluidized beds is calculated from the experimentally determined transition temperature differences ∆Ttrans At these temperature differences ice scaling also referred to as ice crystallization fouling is just prevented and therefore the removal rate equals the growth rate of ice crystals attached to the wall

R G= (49)

According to Section 241 the growth rate of ice crystals attached to the wall of a heat exchanger filled with aqueous solution is determined by mass transfer

( )2H Oliq

w bb ice liq

MkG x xx M

ρρ

= minus (410)

The concentration difference in Equation 410 which is the driving force for mass transfer is rewritten into a temperature difference

( )2

H Oliq

w bb ice liq b

Mk dxG T T xx M dT

ρρ

= minus

(411)

Since the solution was the same 77 wt aqueous sodium chloride solution for all experiments Equation 411 can be simplified

( )

prop w bG c k T T x= minus with 2

H Oliq -1

propb ice liq b

1 0216 KM dxc

x M dTρρ

= =

(412)

The wall-to-fluid mass transfer coefficient k is calculated with an empirical correlation proposed by Schmidt et al (1999) Although this correlation has not been validated for the experimental range it is expected to be most appropriate among other correlations

( )( )( )033 0 33 -033 0 33 0 67p pb p

p

D 0 14 0 13 1 k Re Sc Re Sc ArD

ε ε ε= + minus minus (413)

The removal rates R for each set of fluidized bed conditions can now be determined by calculating the ice crystal growth rate G at the determined transition temperature difference for these conditions from Equations 49 412 and 413

prop transR c k T= ∆ (414)

442 Removal Rate in Stationary Fluidized Beds

The removal of deposits from the walls of liquid-solid fluidized bed heat exchangers is caused by impacts of particles on the wall and by impacts of liquid pressure fronts that are generated by particle-particle collisions close to the wall (see Chapter 3) In case of stationary fluidized beds the contribution of liquid pressure fronts to fouling removal is much smaller than the contribution of particle-wall collisions as will be demonstrated in Section 45 The former contribution is therefore neglected for stationary fluidized beds


69

There are two hypotheses for the relation between particle-wall collisions and the removal rate The first hypothesis is that the removal rate is proportional to the total kinetic energy of particles hitting the wall

e p-wR c E= (415)

According to the analysis in Section 341 the total kinetic energy of stainless steel particles hitting the wall equals (Equation 333)

( )2 3p-w 0adj ssfb184 1E g uε= minus with ( )

( )

13

1

0adjpb

1max 3 1

1g

εε


(416)

The experimentally determined removal rates and the total kinetic energy of particles hitting the wall are only slightly correlated as is shown in Figure 46 Constant ce in Equation 415 is fitted to a value 11010-4 m3J resulting in an empirical expression for the removal rate based on the kinetic energy of particles

4p-w110 10R Eminus= sdot (417)

00

20

40

60

80

100

120

140

000 002 004 006 008 010 012Total energy (Jm2s)

Rem

oval

rat

e (1

0 -6

ms

)

2 mm3 mm4 mmEq 417

Figure 46 Relation between total kinetic energy of fluidized particles hitting the wall and the

removal rate in stationary fluidized beds

The second hypothesis is that the removal rate of stationary fluidized beds is proportional to the total impulse exerted by particles on the wall

j p-wR c J= (418)

Chapter 4

70

According to the analysis in Section 341 the total impulse exerted by a fluidized bed of stainless steel particles is given by (Equation 329)


The removal rate and the total impulse exerted by particles on the wall are much stronger correlated compared to the removal rate and the total kinetic energy (see Figure 47) The proportionality constant cj in Equation 418 is fitted to a value of 14910-6 m3Ns resulting in an empirical expression for the removal rate based on the total impulse exerted on the wall

6p-w149 10R Jminus= sdot (420)

From Figures 46 and 47 is concluded that the best correlation for the fouling removal rate in stationary liquid-solid fluidized beds is based on the total impulse exerted on the wall The transition temperature difference based on this correlation is deduced by substitution of Equations 419 and 420 in Equation 414

( ) ( )2 22 2j 0adj ssfb 0adj ssfb2 3

transsfbprop

1 1415 10 286 10

c g u g uT

c k kε εminusminus minus

∆ = sdot = sdot (421)

00

20

40

60

80

100

120

140

00 20 40 60 80Total impulse (Nm2)

Rem

oval

rat

e (1

0 -6

ms

)

2 mm3 mm4 mmEq 420

Figure 47 Relation between total impulse exerted by fluidized particles on the wall and the


This expression in Equation 421 predicts the experimentally obtained transition temperature differences reasonably well with an average absolute error of 84 (see Figure 48) An exception in this respect is the experiment with a fluidized bed of 2 mm particles at a bed voidage of 718 The probable cause for the measured low transition temperature difference is the change in fluidization regime as discussed in Section 432 If this single experimental condition is neglected constant cj in Equation 418 becomes 15210-6 m3Ns and the model has an average absolute error of 57


71

00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)

2 mm 3 mm 4 mm

Figure 48 Transition temperature differences from experiments (points) and model (lines) as

function of bed voidage in stationary fluidized beds

443 Removal Rate in Circulating Fluidized Beds

Wall-to-fluid mass transfer coefficients are necessary to determine removal rates as is shown in Equation 414 However empirical correlations for mass transfer coefficients in circulating fluidized beds are lacking and therefore the mass transfer correlation for stationary fluidized beds by Schmidt et al (1999) is used here (see Equation 413) The errors introduced by this method are assumed to be small since mass transfer coefficients in both fluidized bed types do probably not differ significantly as is the case for wall-to-fluid heat transfer coefficients (see Figure 45) In most transfer processes an analogy exists between heat and mass transfer rates and it is expected that this analogy is also valid here

The number and maximum pressure of liquid pressure fronts induced by particle-particle collisions heavily increase as the circulation rate of particles is increased (see Section 333) Due to this increase liquid pressure fronts significantly contribute to both the total impulse exerted on the wall and the total energy of all impacts It is therefore expected that the removal rate in circulating fluidized bed is the sum of the removal rate of both particle-wall collisions and liquid pressure fronts

total p-w lpfR R R= + (422)

In correspondence with stationary fluidized beds the removal rate of particle-wall collisions Rp-w is determined by the impulse generated by these collisions A correlation for this impulse is given in Section 342 (Equation 336)

( ) ( ) ( )22 2p-w ssfb 0adj z z415 10 1 1 068 exp 109J u g v vε= sdot minus sdot + sdot sdot minus sdot (423)

Substitution of Equation 423 in the correlation for the removal rate stated in Equation 420 gives

( ) ( ) ( )24 2p-w ssfb 0adj z z618 10 1 1 068 exp 109R u g v vεminus= sdot minus sdot + sdot sdot minus sdot (424)

Chapter 4

72

The removal rate of liquid pressure fronts Rlpf is deduced from the experimentally determined total removal rate (Equation 414) and the removal rate of particle-wall collisions (Equation 424)

lpf total p-wR R R= minus (425)

The removal rate of liquid pressure fronts is shown in Figure 49 as function of the impulse they exert on the wall described by Equation 346 (see Section 342)

( )22 2lpf 0adj pavg662 10 1J g vε= sdot minus with pavg z ssfb03v v u= + (426)

00

20

40

60

80

0 10 20 30 40 50Total impulse of liquid pressure fronts (Nm2)

2 mm3 mm4 mmEq 427

Rem

oval

rat

e ca

used

by

liqui

d pr

essu

re fr

onts

(10-6

ms

)

Figure 49 Relation between total impulse exerted by liquid pressure fronts and the removal

rate induced by these pressure fronts

Analogously with the particle-wall collisions the removal rate of liquid pressure fronts is approximately proportional to the impulse they exerted on the wall From the figure the following empirical correlation is deduced for the removal rate of liquid pressure fronts

7lpf lpf157 10R Jminus= sdot (427)

The proportionality constant of 157middot10-7 m3Ns in Equation 427 for the effect of liquid pressure fronts is a factor 95 lower than the constant in Equation 420 for the effect of particle-wall collisions This means that 1 Ns of impulse exerted by a particle-wall collision removes about 95 times more than the same amount of impulse exerted by a liquid pressure front


73

The total removal rate in a circulating fluidized bed can now be calculated from the two separate contributions An expression for the transition temperature difference in circulating fluidized bed is obtained by combining Equations 414 422 424 426 and 427

( ) ( )( ) ( )2

0adj3 2 4 2trans ssfb z z pavg

1286 10 1 068 exp 109 481 10

gT u v v v

kεminus minus minus

∆ = sdot + sdot sdot minus sdot + sdot (428)

The correspondence between predicted and measured transition temperature differences shown in Figure 410 indicates that the expression in Equation 428 is not only able to give a good prediction of ice scaling in circulating fluidized beds but also for stationary fluidized beds The average absolute error of all experimental conditions is 92

00

05

10

15

20

25

00 05 10 15 20 25

SFB 2 mm SFB 3 mm SFB 4 mm CFB 2 mm CFB 3 mm CFB 4 mm

∆T

tran

sm

eas (

K)

+20

-20

∆T transpred (K) Figure 410 Comparison between predicted and measured transition temperature difference

for ice scaling in stationary and circulating liquid-solid fluidized beds

45 Discussion


The coupling of impact characteristics and experimental results for fouling removal has revealed that the removal rate of stationary fluidized beds is proportional to the total impulse exerted by particles on the wall In this respect it does not seem to matter whether this total impulse is formed by many small impacts or by a relatively small amount of heavy impacts To illustrate this the most important parameters of three stationary fluidized bed experiments with different particle sizes and bed voidages but with comparable removal rates R are listed in Table 43 In the case of small particles superficial velocities are relatively low resulting in low average radial impact velocities (see Section 332) Since both the mass and the impact velocity increase with the particle diameter the average impulse of single particle-wall collisions is much higher for large particles In the table for example the impulse per collision for the fluidized bed of 4 mm particles is about a factor 19 larger compared to the fluidized bed of 2 mm particles However the frequency of particle-wall collisions is much higher in fluidized beds with small particles or at low bed voidage for instance a factor of 18 for the

Chapter 4

74

considered example In spite of these totally different impact characteristics the total impulse of the three systems is comparable as is the removal rate

Table 43 Comparison of parameters for three stationary fluidized bed operation conditions Dp (mm) 21 32 43 ε () 758 847 874 R (10-6 ms) 60 51 61 mp (10-3 kg) 0040 014 033 vravg (10-2 ms) 20 35 52 fp-w (10-6 1m2s) 21 033 012 jp-wavg (10-6 N s) 16 96 31 Jp-w (Nm2) 372 357 437 ep-wavg (10-9 J) 80 84 366 Ep-w (10-3 Jm2s) 28 48 78

For comparison also values for the kinetic energy of a single particle with the average impact velocity and the total kinetic energy of particles hitting the wall are listed in Table 43 The kinetic energy of a single particle depends even more heavily on the particle size than the impulse The average kinetic energy of a 4 mm particle is approximately 46 times higher than of a 2 mm particle The low kinetic energy of a 2 mm particle is only partly compensated by a higher impact frequency The total kinetic energy of particles is therefore about a factor of three higher in the fluidized bed with 4 mm particles than for the case of 2 mm particles Since the removal rates of the three systems are approximately similar it is confirmed that the total kinetic energy and the removal rate are hardly correlated

The conclusion that the removal rate is proportional to the exerted impulse is in contradiction with most experimental studies on material removal by impacting particles (Arjula and Harsha 2006 Hutchings et al 1976 Meijer 1983 Meijer 1984) These studies report that the eroded volume per impact is approximately proportional to the impact velocity squared or in other words to the kinetic energy of the impacting particle A possible cause for this difference is the fact that the erosion experiments reported in literature were performed with single particles in air and not in liquid-solid fluidized beds Another difference is that ice was the eroded material in the present study instead of metal gypsum or a polymer in the experiments described in literature The mechanical properties of ice differ significantly from the other materials and therefore also different abrasion characteristics can be expected (Hobbs 1974 Petrenko and Whitworth 1999)


The presented results reveal that the fouling removal ability of circulating fluidized beds is equal or higher than of stationary fluidized beds This enhancement is attributed to an increase of both frequency and average maximum pressure of liquid pressure fronts reaching the wall The phenomenon that ultrasonic waves in liquids are able to remove ice crystallization fouling was also observed by Duncan and West (1972) and Ashley (1974) The removal rate induced by particle-wall collisions and by liquid pressure fronts are both proportional to the impulse they exert on the wall However the proportionality constant of the particle-wall collisions is about 95 times higher than of the liquid pressure fronts From this result can be concluded that the removal rate is not only influenced by the impulse of the impact but also by the type of the impact In this respect it would be interesting to investigate the fouling removal rate of different impacts for example caused by differently shaped particles such as spheres or caused by particles of different materials such as glass ceramics or aluminum


75

The fouling prevention model of Equation 428 enables to illustrate the influence of the circulation rate on the transition temperature difference which is done for fluidized beds of 3 mm particles and a bed voidage of 895 in Figure 411 For stationary fluidized beds (vz=0) the contribution of liquid pressure fronts to the total transition temperature difference is about 15 which justifies the assumption made in Section 342 At low circulation rates the transition temperature difference slightly decreases as the circulation rate increases because the reduction of the particle-wall contribution exceeds the increase of the contribution of liquid pressure fronts At moderate and high circulation rates the transition temperature difference increases heavily with the upward particle velocity and the impulse exerted by pressure fronts becomes the dominant removal mechanism The highest net upward particle velocity applied in the presented experiments was 103 ms According to the developed model higher circulation rates should result in even better fouling removal abilities Unfortunately these higher circulation rates could not be achieved with the current set-up due to limitations of the pump and the particle recycling system However it would be interesting to study these phenomena in future research

00

05

10

15

20

00 02 04 06 08 10Average upward particle velocity v z (ms)

Pressure fronts

Total

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)

Particle-wallcollisions

Figure 411 Transition temperature difference based on fouling removal by particle-wall collisions and pressure fronts as function of the circulation rate (Dp=32 mm ε=895)

453 Best Fluidized Bed Configuration for Fouling Removal

The foregoing analysis raises the question which operating conditions are most suitable for ice crystallization with a fluidized bed heat exchanger The first important choice in this respect is whether a stationary or a circulating fluidized bed should be applied Circulating fluidized beds show better fouling removal abilities and as a result higher temperature differences can be applied Due to this advantage less heat transfer surface is required and investment costs are reduced A disadvantage of circulating fluidized beds combined with crystallization is the possibility that blockages are formed in the downcomer even at low crystal fractions A possible method to avoid these blockages is the application of internals inside the downcomer for example a vibrating vertical rod (Klaren 2000a Klaren 2000b) Other operating conditions that must be chosen are the particle material particle size and bed voidage Particles with high densities are most attractive since they combine good fouling removal abilities with high heat transfer coefficients In stationary fluidized beds large particles and a low bed voidage are most convenient for the same reasons In this respect it is important to assure that the applied bed voidage is not too low to avoid heterogeneous

Chapter 4

76

fluidization with poor fouling removal abilities In circulating fluidized beds the removal rate depends less on the particle size However large particles are also preferred since downcomer blockages are then avoided Low bed voidages are preferred with respect to fouling removal and heat transfer but hydrodynamic instabilities causing fluidization in the downcomer are more likely to occur (Zheng and Zhu 2000)

46 Conclusions

The fouling removal ability of stationary liquid-solid fluidized bed heat exchangers is proportional to the impulse exerted by fluidized particles on the wall Because of this the transition temperature difference for ice crystallization fouling increases as the bed voidage decreases and the particle size increases In circulating fluidized beds the removal rate is determined by both particle-wall collisions and liquid pressures fronts induced by particle-particle collisions The removal rate of liquid pressure fronts is also proportional to the impulse they exert on the wall but with a lower proportionality constant At higher circulation rates both the number and average maximum pressure of liquid pressure fronts increases resulting in more impulse exerted on the wall and enhanced removal rates Due to this enhancement the transition temperature difference for ice crystallization fouling increases as the circulation rate increases A model based on these phenomena predicts the transition temperature difference for ice crystallization fouling in both stationary and circulating fluidized beds with an average absolute error of 92


77

Nomenclature

A Area m2 x Mol fraction Ar Archimedes number x Equilibrium mol fraction Dp

3(ρp-ρliq)ρliq gmicroliq2

cprop Constant in Eq 412 Greek ce Constant in Eq 415 α Heat transfer coefficient (Wm2K) cj Constant in Eq 418 δ Thickness (m) D Diameter (m) λ Thermal conductivity (Wm K) Dp Equivalent particle diameter (m) ε Bed voidage D Diffusion coefficient (m2s) micro Viscosity (Pa s) E Energy on wall (Wm2) ρ Density (kgm3) g Acceleration due to gravity (ms2) φ Mass flow rate per unit area g0adj Defined in Eq 416 (kgm2s) G Growth rate (ms) h Height (m) Subscripts J Impulse on wall (Nm2) b Bulk k Mass transfer coefficient (ms) cool Coolant mamp Mass flow rate (kgs) cfb Circulating fluidized bed M Molar mass (kgmol) d Deposition p Pressure (Pa) fr Friction ∆p Pressure drop (Pa) H2O Water Qamp Heat (W) i Inside R Removal rate (ms) ice Ice Rep Particle Reynolds number in Inlet ρliq Dp us microliq inner Inner Sc Schmidt number microliqρliq D l Location t Time (s) layer Fouling layer T Temperature (K) liq Liquid T Equilibrium temperature (K) liq-w Liquid-wall ∆Ttrans Transition temperature difference meas Measured (K) o Outside ∆Tln Logarithmic mean temperature p Particle difference (K) p-w Particle-wall us Superficial liquid velocity (ms) pb Packed bed U Overall heat transfer coefficient pred Predicted (Wm2K) lpf Liquid pressure front vslip Slip velocity (ms) r Removal vpavg Average particle velocity see sfb Stationary fluidized bed Eq 426 (ms) sl Slurry vz Upward particle velocity (ms) total Total Vamp Volume flow rate (m3s) w Wall Abbreviations

CFB Circulating fluidized bed SFB Stationary fluidized bed

Chapter 4

78

References

Arjula S Harsha AP 2006 Study of erosion efficiency of polymers and polymer composites Polymer Testing vol25 pp188-196


Chamra LM Webb RL 1994 Modeling liquid-side particulate fouling in enhanced tubes International Journal of Heat and Mass Transfer vol37 pp571-579


Erdmann C 1993 Waumlrmeaustauscher mit zirkulierender Wirbelschicht zur Verhinderung von Belagbildung PhD thesis RWTH Aachen (Germany)


Helalizadeh A Muumlller-Steinhagen H Jamialahmadi M 2005 Mathematical modelling of mixed salt precipitation during convective heat transfer and sub-cooled flow boiling Chemical Engineering Science vol60 pp5078-5088

Hobbs PV 1974 Ice Physics London Oxford University Press

Hutchings IM Winter RE Field JE 1976 Solid-particle erosion of metals the removal of surface material by spherical projectiles Proceedings of the Royal Society of London Series A vol348 pp379-392

Kern DQ Seaton RE 1959 The theoretical analysis of thermal surface fouling British Chemical Engineering vol4 pp258ndash262

Klaren DG 2000a Apparatus for carrying out a physical andor chemical process such as a heat exchanger US Patent No 6073682

Klaren DG 2000b Apparatus for carrying out a physical andor chemical process such as a heat exchanger US Patent No 6109342



Petrenko VF Whitworth RW 1999 Physics of Ice Oxford Oxford University Press

Pronk P Infante Ferreira CA Witkamp GJ 2006 Influence of Solute Type and Concentration on Ice Scaling in Fluidized Bed Ice Crystallizers Chemical Engineering Science vol61 pp4354-4362


79




Zheng Y Zhu J-X 2000 Overall pressure balance and system stability in a liquidndashsolid circulating fluidized bed Chemical Engineering Journal vol79 pp145ndash153

Chapter 4

80

81

5 Fluidized Bed Heat Exchangers for Other Industrial Crystallization Processes

51 Introduction

In the last twenty-five years fluidized bed heat exchangers have mainly been installed to prevent particulate fouling of suspended particles in heat transfer processes or to prevent crystallization fouling of dissolved species during evaporation (see Section 131) The three previous chapters have shown that fluidized bed heat exchangers are also capable to prevent ice crystallization fouling and are therefore suitable as ice crystallizer

The ability to prevent ice crystallization fouling raises the question whether fluidized heat exchangers are also promising for other industrial crystallization processes that suffer from severe fouling on heat exchanging walls Possible applications in this respect are melt crystallization processes cooling crystallization from aqueous electrolyte solutions and eutectic freeze crystallization processes As far as reported in literature none of these processes have been tested in combination with fluidized bed heat exchangers

The aim of this chapter is therefore to investigate the capabilities of liquid-solid fluidized bed heat exchangers to prevent fouling in other industrial crystallization processes From all potential industrial crystallization processes two processes have been selected to be experimentally investigated with a single-tube fluidized bed heat exchanger The first process is cooling crystallization of salts from aqueous solutions of KNO3 and MgSO4 The second process is eutectic freeze crystallization which is the simultaneous crystallization of both salt and ice crystals at eutectic conditions Previous work has shown that this process is very energy efficient but also suffers from severe crystallization fouling This chapter presents experiments on crystallization fouling during eutectic freeze crystallization and compares the results with results of ice crystallization fouling described in Chapter 2 Finally this comparison is used to unravel the mechanisms that cause severe crystallization fouling during eutectic freeze crystallization

52 Perspectives of Fluidized Bed Heat Exchangers for Other Industrial Crystallization Processes

521 Introduction

Crystallization processes can roughly be divided in crystallization from melts and crystallization from solutions (see Figure 51)

In case of melt crystallization the crystallizing species is the main component of a liquid mixture Its concentration is usually close to 100 wt and the component is therefore often called solvent Supersaturation in melt crystallization is mostly created by cooling but can also be achieved by modification of the pressure although rather high pressure difference are required The ice crystallization processes described in previous chapters are an example of melt crystallization since the main component of the solution namely water crystallizes

Chapter 5

82

Figure 51 Overview of crystallization processes

In case of solution crystallization the crystallizing species is one of the minor components of the liquid mixture The concentration of this component is lower than in melt crystallization processes and it is therefore often referred to as solute For highly soluble substances like sugars and highly soluble salts for example NH4NO3 the difference between crystallization from solution and crystallization from the melt becomes obscure A typical example of crystallization from solution is the crystallization of salts such as NaCl from aqueous electrolyte solutions The way in which supersaturation is created can be divided in four methods Cooling crystallization is often applied for substances whose solubility strongly decreases with decreasing temperature For substances whose solubility does hardly depend on the temperature supersaturation is often created by evaporation of the solvent called evaporative crystallization In precipitation or reactive crystallization processes supersaturation is generated by the mixing of two reagents The fourth and last method is anti-solvent or drowning out crystallization In this method the initial solvent in which the solute is dissolved is partly bound by a second solvent in which the solute is not soluble The initial solvent looses its solvent power due to the binding with the second solvent resulting in the crystallization of the solute

Eutectic freeze crystallization can be considered as a combination of both melt and solution crystallization since water and salt crystallize simultaneously Supersaturation in eutectic freeze crystallization processes is generally created by cooling

522 Crystallization from the Melt

Crystallization from the melt can either be realized by prilling layer growth or suspension growth In case of prilling crystals are produced from a very concentrated aqueous solution for example 95 wt ammonium nitrate The solution is sprayed into the top of a tower resulting in falling droplets A countercurrent up-flowing air stream cools the droplets and causes partial evaporation of the water content Consequently the main component of the droplets solidifies resulting in 05 to 2 mm prills A second method applied for melt crystallization is layer growth In this method crystals grow on a cooled wall forming a solid layer which is periodically removed A third method is suspension growth in which the crystal growth takes place in a continuously cooled suspension Since most crystallizing substances have a tendency to adhere and grow on the cooled heat exchanger walls prevention of crystallization fouling is an important aspect in these processes

Fluidized Bed Heat Exchangers for Other Industrial Crystallization Processes

83

From the three methods of melt crystallization discussed above crystallization fouling is especially an issue in suspension growth processes The most important applications of melt crystallization processes using suspension growth in industry are freeze concentration and crystallization of organic species Fluidized bed heat exchangers may be interesting apparatuses to prevent fouling for these applications

Freeze Concentration

Freeze concentration is an ice crystallization process to concentrate aqueous solutions such as beverages and waste waters (see Section 133) In previous chapters the capabilities of fluidized bed heat exchangers for ice crystallization processes have been extensively studied It has been shown that ice crystallization fouling can successfully be prevented by fluidized beds and that fluidized bed heat exchangers are therefore promising ice crystallizers Since freeze concentration processes are very similar to the processes in previous chapters it is expected that fluidized bed heat exchangers can also successfully be applied for this purpose

Organic Melt Crystallization

A second group of melt crystallization processes in which fluidized bed heat exchanger may be attractive is the crystallization of organic species Some examples of organic compounds of commercial importance are para-xylene cyclohexane phenol and caprolactam (Arkenbout 1995 Myerson 1993) Para-xylene is used in the production process of polyester fibers and plastics Cyclohexane phenol and caprolactam are chemical intermediates in the production of nylon fibers and plastics

Organic melt crystallization processes that use suspension growth usually deal with severe crystallization fouling In most application crystallization fouling is prevented by using scraped surface crystallizers (Goede 1988 Goede and Jong 1993 Patience et al 2001) From the similarities between ice crystallization and organic melt crystallization it is expected that fluidized bed heat exchangers are also able to replace scraped surface heat exchangers for this kind of processes In this respect special attention should be paid to the thermophysical properties of organic melts such as density and viscosity These properties can differ significantly from the aqueous solutions used in the previous chapters Different liquid properties may result in serious changes of fluidized bed parameters such as superficial velocities and can therefore also affect the fouling prevention ability

523 Crystallization from Solution

With respect to crystallization from solution crystallization fouling is mainly an important issue in evaporative and cooling crystallization processes

Evaporative Crystallization

In evaporative crystallization processes a part of the solvent is evaporated resulting in an increase of the solute concentration When the maximum solubility of the solute is exceeded crystals are formed in the solution A schematic representation of an evaporative crystallization processes with an aqueous salt solution is shown in Figure 52

Chapter 5

84

Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


Ice + salt

Ice line


0degC

T eut

0 w eut

Evaporativesalt crystallization

Boiling line for p2

Boiling line for p1

aqueous solutionIce +

Figure 52 Schematic phase diagram of water-salt system with evaporative crystallization

process

An apparatus often used for evaporative crystallization processes is the forced circulation evaporation crystallizer as shown in Figure 53 In the lower part of the apparatus the feed liquid with dissolved species is mixed with the recycle stream from the crystallization tank The suspension is heated in an external heat exchanger to a temperature which is slightly below the boiling temperature of the solution at pressure p1 As the suspension subsequently flows upward to the crystallization tank the absolute pressure decreases to a pressure p2 due to a decrease of the hydrostatic liquid column As a result of the reduced pressure in the crystallization tank the temperature of the suspension exceeds the boiling temperature and the solvent starts to evaporate Due to evaporation of the solvent the solution becomes supersaturated resulting in the crystallization of the dissolved species

Figure 53 Forced circulation evaporation crystallizer


85

Supersaturation of the main solute generally occurs only in the crystallization tank and therefore crystallization fouling of this solute on the surfaces of the heat exchanger is not often observed in evaporative crystallizers However some minor solutes that show a reduced solubility at increased temperatures such as CaSO4 and CaCO3 can crystallize on the heat exchanger surface The crystallization of these minor components is generally not the purpose of the process and is even undesirably since it strongly reduces the capacity of the heat exchanger This type of crystallization fouling often occurs in heat exchangers for water heating and is generally referred to as scaling Fluidized bed heat exchangers applied in industrial installations have already proven to be able to prevent this kind of crystallization fouling (Klaren 2000 Meijer 1983 Meijer 1984)

Cooling Crystallization

Cooling crystallization from solution is a separation technique to crystallize dissolved species from solutions on the basis of a reduced solubility at lower temperatures An aqueous solution containing a dissolved solute is cooled until the saturation temperature of the solute is reached (see Figure 54) Further cooling results in salt crystallization and a decreasing solute concentration in the liquid

Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point

S

aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut

Cooling crystallization

Ice +

Salt +aqueous solution

Figure 54 Schematic phase diagram of water-salt mixture with cooling crystallization

process

Cooling crystallization is especially interesting for solutes whose solubility strongly decreases with decreasing temperature Typical electrolyte solutions for which cooling crystallization is applied are copper sulfate magnesium sulfate potassium chloride potassium nitrate sodium carbonate (soda) and sodium sulfate Many heat exchangers applied in cooling crystallization processes are subject to crystallization fouling since the highest supersaturation values occur close to the heat exchanger walls (Mullin 1993) In order to manage these fouling problems cooling crystallizers are often operated in batch In this way the fouling layer built up on the heat exchanger walls can be removed between two batches In most continuous cooling crystallization processes wipers or scrapers are used to keep heat transfer surfaces free of deposits

These heat exchangers with conventional fouling removal techniques may be replaced by fluidized bed heat exchangers resulting in lower investment costs and higher heat transfer

Chapter 5

86

coefficients The thermophysical liquid properties of cooling crystallization processes are comparable with the liquid properties of ice crystallization processes The operating conditions of fluidized beds are therefore comparable and high fouling removal abilities are expected If salt crystallization fouling can indeed be prevented by the fluidized particles than fluidized bed heat exchangers are promising apparatuses for cooling crystallization purposes

524 Eutectic Freeze Crystallization

Eutectic freeze crystallization (EFC) is the simultaneous crystallization of separate salt and ice crystals at eutectic conditions EFC is a promising crystallization technique that has not been applied in industry yet After several studies in the seventies and early eighties of the 20th century (Stepakoff et al 1974 Schroeder et al 1977 Barduhn and Manudhane 1979 Swenne 1983) EFC has again received extensive interest in the last decade mainly at the Delft University of Technology (Ham 1999 Vaessen 2003 Himawan 2005)

There are two paths to achieve eutectic freeze crystallization which are indicated by A and B in the phase diagram shown in Figure 55 (Ham et al 1999) In case of method A the aqueous solution is cooled until the ice line is reached and ice crystals are subsequently formed As cooling is continued the ice fraction increases and the solution becomes more concentrated until the maximum solubility of the solute is reached At this concentration (weut) and temperature (Teut) the solution is called eutectic and further cooling results in simultaneous formation of ice and salt as separate crystals In case of method B the initial solute concentration is higher than the eutectic concentration As the solution is cooled the salt solubility line is reached and salt crystals are formed Continued cooling results in the production of more salt crystals and a decrease of the temperature until the eutectic temperature is reached From this moment on both ice and salt crystals are formed

Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut


A

B

Figure 55 Schematic phase diagram for aqueous electrolyte solution with two possible

eutectic freeze crystallization processes

Although this description is made for a batch process it also possible to operate eutectic freeze crystallization in a continuous process as is shown in Figure 56 The feed stream enters the crystallizer which operates at eutectic conditions resulting in the formation of salt and ice crystals Slurry containing both salt and ice crystals is subsequently separated Since the density of ice is typically lower and the density of the salt is typically higher than the


87

density of the mother liquor it is rather simple to separate the solid phases by gravitational forces The ice slurry is separated into pure ice and aqueous solution in a wash column or a belt filter Subsequently ice is turned into pure water by means of a heat source preferably coming from the feed stream A filter is used to extract salt crystals from the salt slurry

Figure 56 Process scheme of EFC for production of pure water and salt

(adapted from Ham et al 1998)

Several researchers have proposed to combine the crystallizer and the separator within one apparatus One of these proposals is the Cooled Disc Column Crystallizer as shown in Figure 57 which consists of multiple horizontal cooled discs equipped with scrapers (Vaessen et al 2003b Ham et al 2004 Genceli et al 2005) Orifices in the discs enable the transport of crystals between the compartments Ice slurry is withdrawn from the top of the column while salt slurry is extracted from the bottom

Figure 57 Cooled Disc Column Crystallizer a) side view b) cross section view

(Ham et al 1998)

A second apparatus for combined crystallization and separation is the Scraped Cooled Wall Crystallizer as shown in Figure 58 (Vaessen et al 2003a) This crystallizer consists of two

Chapter 5

88

concentric cooled walls that are equipped with scrapers Ice crystals are collected in the conical part at the top while salt crystals settle to the bottom part

Figure 58 Scraped Cooled Wall Crystallizer a) side view b) cross section view

(adapted from Vaessen et al 2003a)

Experiments with both types of crystallizers showed that very high crystal purities can be achieved by means of eutectic freeze crystallization After several washing steps impurities in both ice and salt crystals were hardly measured

Case studies for industrial applications demonstrate that EFC processes are an energy-efficient alternative for conventional crystallization techniques using evaporation (Ham et al 1998 Vaessen 2003 Himawan 2005) The main cause of the lower energy consumption is the fact that the latent heat of crystallization for water is a factor of 68 lower than the latent heat of evaporation An important aspect for the energy-efficiency of an EFC process is the eutectic temperature of the aqueous solution This temperature mainly determines the evaporation temperature of the refrigeration cycle and low evaporation temperatures result in low cycle efficiencies According to Ham et al (1998) an EFC process operating at a eutectic temperature of ndash15degC requires about 70 less primary energy than a triple stage evaporation process For a system with a eutectic temperature of ndash181degC this reduction is smaller but still 30 The application of high pressures to form clathrates instead of ice can even increase the energy efficiency of eutectic freeze crystallization (Ham 1999 Vaessen 2003) Figure 59 shows an overview of eutectic conditions for a number of aqueous electrolyte solutions

The case studies also indicate that EFC processes can be economically attractive (Ham et al 1998 Vaessen 2003 Himawan 2005) The calculated investment costs are usually higher than for evaporative crystallization processes but the lower energy consumption for EFC reduces the exploitation costs The main cause for the relatively high investment costs is the scraped surface crystallizer This type of crystallizer has a high number of parts and requires accurate tolerances for walls and scrapers Furthermore scraped surface crystallizers are difficult to scale-up and therefore multiple units are often used in case of high capacities instead of one large unit However investment costs of large eutectic freeze crystallizers are expected to decrease in the near future since their development is still ongoing The investment costs of the scraped surface crystallizers were also overestimated in the case studies since only limited heat fluxes of 5 kWm2 were applied in order to avoid severe crystallization fouling This maximum heat flux is reasonable for EFC from binary solutions However Vaessen et


89

al (2003a) report that much higher heat fluxes can be applied for EFC processes with ternary solutions Despite these promising prospects the high investment costs of scraped surface crystallizers is one of the main reasons why EFC has not been applied on a large scale in industry yet

-66-58

-43-39-29-21-18-15-15-12

-272

-78-105-106

-156-168

-181-187-190

-362-336

-287-280

-264-212-200-190

38

233390

403190

427214

396

342398

286260

381424

197197

322225

272245

215180

10459

12766

119

-40 -30 -20 -10 0 10 20 30 40 50

Na2SO4 (10)CuSO4 (5)K2SO4 (0)FeSO4 (7)Na2CO3 (10)KNO3 (0)MgSO4 (12)NiSO4 (7)Sr(NO3)2 (4)ZnSO4 (7)BaCl2 (2)MnSO4 (7)KCl (1) NH4Cl (1)NH4NO3 (0)NaNO3 (0)SrCl2 (6)NaNO2 (05)(NH4)2SO4 (0)Ca(NO2)2 (4)NaCl (2) Cu(NO3)2 (6)NaBr (5) NaOH (7)Ca(NO3)2 (4)MgCl2 (12)K2CO3 (6)

Temperature (degC) Solute concentration (wt)

Figure 59 Eutectic temperatures and concentrations of several binary electrolyte solutions

The number between brackets is the hydrate number of the specific salt (Gmelin 1952 Ham 1999 Vaessen 2003)

The application of fluidized bed heat exchangers may lead to a serious reduction of the investment costs of EFC processes and therefore in a breakthrough to the application of EFC technology Fluidized bed heat exchangers show lower costs per unit of heat transfer area compared to scraped surface heat exchangers especially for larger capacities (see Section 65) The disadvantage that separation of salt and ice crystals cannot take place in the crystallizer itself can easily be solved by means of a relatively inexpensive separation tank The liquid properties of eutectic systems with eutectic temperatures above ndash20degC are comparable with the liquid properties in ice crystallization processes described the in previous chapters Fluidized bed heat exchangers can therefore be operated at comparable operating conditions with effective fouling removal rates In order to evaluate whether the fluidized bed

Chapter 5

90

heat exchanger is a serious option for EFC processes experiments should be performed to investigate whether crystallization fouling during eutectic freeze crystallization can be prevented

525 Choice of Processes for Experimental Study

In the previous subsections four industrial crystallization processes have been described for which fluidized bed heat exchangers may be attractive The four processes are freeze concentration organic melt crystallization cooling crystallization from solution and eutectic freeze crystallization

Freeze concentration processes are similar to the ice crystallization processes described in Chapters 2 and 4 The experiments presented in these chapters already proof that ice crystallization with a fluidized bed heat exchanger is possible and freeze concentration is therefore not experimentally studied in the current chapter

Cooling crystallization from aqueous solutions and eutectic freeze crystallization processes are both operated in aqueous solutions with comparable thermophysical properties as in the ice crystallization experiments of Chapters 2 and 4 Experiments to study the prevention of crystallization fouling for these processes can therefore rather conveniently be performed with the experimental fluidized bed heat exchanger described in Section 22

For organic melt crystallization processes the liquid properties such as viscosity and density may differ significantly from the properties of the aqueous solutions used in previous chapters These different liquid properties result in totally different operating conditions of the fluidized bed heat exchanger A literature study is therefore necessary to investigate the possibilities of fluidized bed heat exchangers for organic melt crystallization processes before experiments are performed

In the next sections the fouling prevention ability of fluidized bed heat exchangers for cooling crystallization and eutectic freeze crystallization processes is experimentally studied


For the experiments a single-tube fluidized bed heat exchanger with an internal diameter of 427 mm was applied as shown in Figure 510 In all experiments described in this chapter the fluidized bed was operated in stationary mode and consisted of cylindrical stainless steel particles of 4 mm in diameter and height The fluidized bed was cooled by a 34 wt potassium formate solution which flowed countercurrently through the annulus of the heat exchanger The coolant provided cooling either to the two heat transfer sections or only to the lower heat transfer section A control valve enabled to control the heat exchanger inlet temperature of the coolant within 01 K Temperature and flow rate measurements were used to determine fluidized bed heat transfer coefficients as described in Section 22 The crystals produced in the fluidized bed heat exchanger could be observed with a visualization section consisting of a flow cell as shown in Figure 511 and a microscope equipped with digital camera In the flow cell the suspension formed a thin film of 2 mm which enabled to observe individual crystals with the microscope


91

Figure 510 Schematic layout of the experimental set-up

Figure 511 Flow cell for observation of produced crystals

54 Cooling Crystallization from Solution

This section presents cooling crystallization experiments with the experimental fluidized bed heat exchanger The salts used for these experiments are potassium nitrate (KNO3) and magnesium sulfate (MgSO4) In industry potassium nitrate is mainly produced for fertilizer purposes but it is also used in the glass enamel and ceramics industries as well as for the manufacture of explosives and pyrotechnics Magnesium sulfate and its hydrates are also mainly used as fertilizer Minor applications are found in cement sugar glass and aluminum industry

Chapter 5

92

541 Operating Conditions

Salt crystals were produced from aqueous KNO3 and MgSO4 solutions with initial concentrations of 196 and 252 wt respectively The saturation temperature of the KNO3 solution was 136degC and further cooling of the solution resulted in the formation of anhydrous potassium nitrate crystals (KNO3) The saturation temperature of the MgSO4 solution was 176degC Below this temperature magnesium sulfate heptahydrate crystals (MgSO4middot7H2O) were formed in the solution Phase diagrams of both aqueous systems are shown in Appendices A31 and A34

Experiments were performed with and without fluidized bed in order to examine the role of the fluidized particles with respect to fouling (see Table 51) The bed voidage during the fluidized bed experiments was maintained at 80 resulting in superficial velocities of 037 and 027 ms for the KNO3 and MgSO4 solution respectively The suspension velocity during the experiments without fluidized bed was kept constant at a frequently used heat exchanger velocity of 10 ms In order to achieve high heat fluxes all experiments were performed with the lower heat transfer section only

Table 51 Overview of conditions for cooling crystallization experiments Salt wsol

(wt) Tsat

(degC) Fluidized

bed us

(ms) qamp

(kWm2) Yes 037 15 - 17 KNO3 196 136 No 100 8 - 14 Yes 027 13 - 15 MgSO4 252 176 No 100 6 - 9

Each experiment started with a crystal-free suspension at a temperature of 20degC The coolant temperature at the inlet of the heat exchanger was controlled at 8 K below the outlet temperature of the suspension which resulted in heat fluxes ranging from 6 to 14 kWm2 for the experiments without fluidized bed and 13 to 17 kWm2 for the experiments with fluidized bed When the solution reached a certain supersaturation salt crystals spontaneously nucleated Subsequently cooling was continued resulting in a further decrease of the suspension temperature and an increase of the mass fraction of salt crystals When the suspension in the tank reached a temperature of 30degC for the KNO3 or 80degC for the MgSO4 solution the total crystal content was 83 wt for both systems At these temperatures the heater in the tank was used to achieve steady-state conditions During a steady-state period of at least one hour heat transfer coefficients were analyzed to see whether crystallization fouling occurred or not


The results from the cooling crystallization experiments of KNO3 in Figure 512 show that heat transfer coefficients at the suspension side were higher for the experiment with fluidized bed than for the experiment without fluidized bed This is remarkable since the velocity in the tube with fluidized bed was about a factor of three lower than for the tube without particles The higher heat transfer coefficients for the fluidized bed resulted in higher heat fluxes In order to have the same development of the tank temperature in time during both experiments the electrical heater in the tank was used in the experiment with the fluidized bed


93

0

5

10

15

20

0 1800 3600 5400 7200 9000Time (s)

Susp

ensi

on te

mpe

ratu

re a

t he

at e

xcha

nger

inle

t (degC

)

0

2000

4000

6000

8000

salt nucleation

with fluidized bed

without fluidized bed

steady state Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Figure 512 Suspension temperatures at heat exchanger inlet and heat transfer coefficients of

the suspension side for KNO3 crystallization with and without fluidized bed

Heat transfer coefficients during crystallization without fluidized bed clearly decreased after initial nucleation and continued to decrease during steady state conditions This decrease is attributed to the build-up of a crystalline layer on the heat exchanger wall that increases the heat transfer resistance The figure also shows that fluidized bed heat transfer coefficients remained high during steady state conditions which indicates that the fluidized particles are able to prevent salt crystallization fouling The relatively small decrease of fluidized bed heat transfer coefficients between 1700 and 3900 seconds after the start of the experiment is attributed to an increasing viscosity as the suspension temperature decreases A microscopic picture of the KNO3 crystals produced in the fluidized bed heat exchanger is shown in Figure 513 The size of the crystals varies from 40 to 140 microm

Figure 513 KNO3 crystals produced in the

fluidized bed heat exchanger Figure 514 MgSO4middot7H2O crystals produced

in the fluidized bed heat exchanger

The qualitative results of the experiments with the MgSO4 solution in Figure 515 are similar to the results for KNO3 crystallization Operation without crystallization fouling was observed for the case with fluidized bed and not for the case without fluidized bed Suspension heat transfer coefficients for the fluidized bed during steady state crystallization were about 3400 Wm2K for the MgSO4 solution instead of about 5500 Wm2K for the KNO3 solution This difference is attributed to the higher viscosity of the MgSO4 solution and to the lower

Chapter 5

94

superficial velocity The MgSO4middot7H2O crystals produced in the fluidized bed heat exchanger are needle shaped as shown in Figure 514 The average length of the crystals is approximately 300 microm

5

10

15

20

25

0 1800 3600 5400 7200 9000Time (s)

Susp

ensi

on te

mpe

ratu

re a

t he

at e

xcha

nger

inle

t (degC

)

0

1000

2000

3000

4000

salt nucleation

with fluidized bed


steady state Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)


the suspension side for MgSO4middot7H2O crystallization with and without fluidized bed

543 Discussion

The described experiments have shown that fluidized particles can also be applied to prevent salt crystallization fouling in cooling crystallization processes While experiments without fluidized bed clearly showed excessive fouling resulting in decreasing heat transfer rates the experiments with fluidized bed were performed with stable heat transfer coefficients Furthermore the initial heat transfer coefficients were already considerably higher for the case with fluidized bed despite that the suspension velocity was about a factor of three lower

The applied heat fluxes in both salt crystallization experiments with fluidized bed were higher than the applied heat fluxes during the ice crystallization experiments described in Chapters 2 and 4 Even with these high heat fluxes fluidized particles were able to prevent salt crystallization fouling From this observation is concluded that fouling by KNO3 and MgSO4middot7H2O crystals is less severe compared to ice crystallization fouling For ice crystallization it was shown that there exists a critical heat flux or temperature difference above which fouling is not prevented by the fluidized bed It is expected that a comparable critical heat flux exists for salt crystallization fouling However this critical heat flux could not be determined with the current set-up because the applied heat fluxes were close to the maximum feasible heat flux of the set-up

In the presented experiments salt fouling was prevented by a fluidized bed of 4 mm stainless steel particles at a bed voidage of 80 which has a relatively high fouling removal ability (see Chapter 4) Since the critical heat flux for salt crystallization fouling is high for this fluidized bed it is expected that fluidized beds with lower fouling removal rates are also able to prevent fouling at moderate and high heat fluxes Examples of fluidized beds with lower fouling removal rates are fluidized beds with higher bed voidages smaller particles or particles with a lower density This flexibility in fluidized bed conditions enables to optimize the heat exchanger design concerning investment costs and energy consumption


95

55 Eutectic Freeze Crystallization from Binary Solutions

Application of fluidized bed exchangers for eutectic freeze crystallization (EFC) processes may be beneficial because of the lower investments costs compared to heat exchangers equipped with scrapers (see Section 52) However EFC processes suffer from severe crystallization fouling and it is unknown whether fluidized bed heat exchangers are able to prevent this phenomenon In this section EFC experiments with aqueous binary solutions of potassium nitrate (KNO3) and magnesium sulfate (MgSO4) are described These solutions were chosen because of their relatively high eutectic temperatures of ndash29degC and ndash39degC respectively The aim of the experiments was to study whether fluidized beds are able to prevent crystallization fouling during EFC


The eutectic conditions of KNO3 and MgSO4 solutions as well the operating conditions of the EFC experiments with the experimental fluidized bed heat exchanger are shown in Table 52 Phase diagrams of both aqueous systems are shown in Appendices A31 and A34

Table 52 Overview of conditions for experiments on EFC from binary solutions Salt weut

(wt) Teut

(degC) Salt product wsol

(wt) us

(ms) 102 037 KNO3 104 -29 KNO3 106 037

MgSO4 180 -39 MgSO4middot12H2O 195 027 For the experiments with KNO3 two solutions were used with different concentrations The KNO3 concentration in the first solution was slightly below the eutectic concentration and the EFC process followed route A in Figure 55 The solution was cooled below its freezing temperature after which ice crystals spontaneously nucleated Further cooling resulted in an increase of the ice fraction and an increase of the KNO3 concentration in the liquid As the temperature dropped below the eutectic temperature salt crystals were seeded to start the simultaneous crystallization of ice and salt In the second solution the KNO3 concentration was higher than the eutectic concentration and followed route B in Figure 55 Cooling of this solution resulted in the spontaneous nucleation of salt crystals first After reaching the eutectic temperature ice seeds were added to the suspension tank to start ice crystallization For the EFC experiments with MgSO4 solutions only one concentration was used which was slightly higher than the eutectic concentration Cooling of this solution resulted in the spontaneous nucleation of magnesium sulfate dodecahydrate (MgSO4middot12H2O) As the suspension was cooled further to a temperature below the eutectic temperature ice crystals spontaneously nucleated

During the crystallization process fluidized bed heat transfer coefficients were measured in order to observe whether crystallization fouling occurred Analogously with the experiments in Chapters 2 and 4 it was assumed that crystallization fouling prevention during EFC was successful when heat transfer coefficients remained constant for at least 30 minutes

In the presented EFC experiments both heat transfer sections of the experimental fluidized bed heat exchanger were used (see Section 53) The fluidized bed was operated at a bed voidage of 80 resulting in superficial velocities of 037 and 027 ms for the KNO3 solutions and the MgSO4 solution respectively

Chapter 5

96

552 Expectations based on Previous Experiments

Eutectic freeze crystallization is only feasible in a fluidized bed heat exchanger when besides salt crystallization fouling also ice crystallization fouling is prevented The results in the previous section show that ice crystallization fouling is more severe than fouling by salt It is therefore expected that ice crystallization fouling is the limiting factor for EFC

Chapter 2 shows that ice crystallization from aqueous solutions in fluidized bed heat exchangers is only possible without fouling when the temperature difference between the ice suspension and the cooled wall is kept below a certain transition temperature difference Furthermore it reveals that this transition temperature difference is roughly proportional to the solute concentration as is shown for KNO3 and MgSO4 solutions in Figure 516

00

05

10

15

20

25

30

00 50 100 150 200

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)

Solute concentration (wt)

MgSO4

KNO3

Eutectic

Eutectic

Fouling

No fouling

Figure 516 Transition temperature differences for ice crystallization fouling in KNO3 and

MgSO4 solutions

The linear ice crystallization fouling limits in this figure can be extrapolated to eutectic concentrations This extrapolation leads to expected transition temperature difference for EFC of 08 and 24 K for KNO3 and MgSO4 solutions respectively If EFC can be operated without fouling with these temperature differences heat fluxes of 48 and 82 kWm2 can be realized for KNO3 and MgSO4 solutions respectively


A typical example of an EFC experiment from a KNO3 solution with a concentration lower than the eutectic concentration is shown in Figure 517 The coolant inlet temperature was ndash41degC resulting in a heat flux of 25 kWm2 and a maximum temperature difference of 04 K between wall and suspension Based on separate salt and ice crystallization experiments it was not expected that these conditions would lead to fouling as can be seen in Figure 516

After initial supercooling of the crystal-free solution ice crystals spontaneously nucleated at t=900 s Next ice crystallization was continued while heat transfer coefficients remained high indicating that the fluidized bed was able to avoid ice crystallization fouling However as soon as KNO3 crystals were seeded and secondary nucleation occurred (t=3800 s) heat transfer coefficients dropped drastically as a result of fouling


97

-35

-30

-25

-20

-15

0 900 1800 2700 3600 4500 5400Time (s)

0

2000

4000

6000

8000Ice crystallization EFC

Ice nucleationSalt nucleation

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Susp

ensio

n te

mpe

ratu

re a

t he

at e

xcha

nger

out

let (

degC)

Figure 517 Suspension temperatures and fluidized bed heat transfer coefficients during eutectic freeze crystallization from a KNO3 solution (wKNO3=102 wt Tcoolin=-41degC)

The EFC experiments with a concentration slightly above the eutectic concentration showed similar results The coolant temperature and thus the heat flux of the experiment shown in Figure 518 were equal to the values of the experiment described above After nucleation of salt crystals in the crystal-free suspension the fluidized particles successfully prevented salt crystallization fouling However nucleation of the second crystal type in this case ice resulted in a dramatic decrease of the heat transfer coefficient indicating excessive fouling

EFC without crystallization fouling was not realized for any of the KNO3 solutions even not at low temperature differences Similar results were obtained for the MgSO4 solution A comparison between EFC fouling and ice crystallization fouling in Figure 519 clearly shows that fouling is much more severe during simultaneous crystallization of ice and salt than during crystallization of ice only

-35

-30

-25

-20

-15

0 300 600 900 1200 1500 1800Time (s)

0

2000

4000

6000

8000Salt crystallization EFC

Ice nucleation

Salt nucleation

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Susp

ensio

n te

mpe

ratu

re a

t he

at e

xcha

nger

out

let (

degC)


Chapter 5

98

00

05

10

15

20

25

30

00 50 100 150 200

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)


MgSO4

KNO3

Limit ice crystallization foulingEFC with crystallization fouling

Figure 519 Comparison between transition temperature differences for ice crystallization fouling (lines) and temperature differences for EFC with crystallization fouling (crosses)

554 Discussion

The results in Figure 519 show that crystallization fouling during EFC can not simply be predicted by the model on ice crystallization fouling presented in Section 24 For the tested temperature differences the fluidized bed successfully prevented fouling during separate ice or salt crystallization but failed to prevent fouling during simultaneous crystallization of ice and salt In Section 552 is already discussed that ice crystallization fouling is more severe than fouling by salt It is therefore believed that the observed crystallization fouling during EFC can be attributed to ice crystallization fouling

Although the results for EFC are at first sight in contradiction with the results for ice crystallization the fouling behavior during EFC can be explained by an extension of the original model for ice crystallization fouling In this model it is assumed that ice crystallization fouling is only prevented by the fluidized bed when the removal rate induced by fluidized particles exceeds the growth rate of ice crystals on the wall

R Ggt (51)

The removal rate R is determined by fluidized bed conditions such as operating mode bed voidage and particle properties Since these conditions were equal for both ice crystallization and EFC experiments the difference in crystallization fouling is attributed to differences in the ice growth rate G This ice growth rate is determined by a combination of heat transfer mass transfer and surface integration as is described in Section 241 For aqueous solutions of MgSO4 the relative contributions to the total resistance for ice growth are shown in Figure 520 The figure clearly shows that the growth rate of ice crystals on the wall is mainly determined by mass transfer for concentrations above 2 wt


99

0

20

40

60

80

100

00 50 100 150 200MgSO4 concentration (wt)

Perc

enta

ge o

f tot

al r

esis

tanc

e to

ice

grow

th

Surface integration

Mass transfer

Heat transfer


MgSO4 solutions for a total temperature difference of 10 K

The mass transfer resistance originates from the fact that only water molecules can enter the ice crystal lattice and that therefore solute ions accumulate near the ice interface (see Figure 521a) Since the effect of accumulated ions increases with the number of ions present the ice growth rate is inversely proportional to the solute concentration The growth rate is also proportional to the difference between the equilibrium concentration at the wall and the concentration in the bulk This concentration difference can also be represented by a difference between the wall temperature and the equilibrium temperature in the bulk (see also Equation 212)

( ) ( )2 2

H O H Oliq liq

w b w bb ice liq b ice liq b

M Mk k dxG x T x T T xx M x M dT

ρ ρρ ρ

= minus asymp minus

(52)

Figure 521 Process near ice interface a) during ice crystallization and b) during eutectic

freeze crystallization from binary solution

Chapter 5

100

Since crystallization fouling by ice during EFC is more severe than during ice crystallization only it is expected that the growth rate of ice crystals on the wall increases by the presence of salt crystals A possible explanation for this increased ice growth rate is the breakdown of the mass transfer resistance Due to the ice growth and the accumulation of ions the boundary layer of the ice interface is supersaturated in terms of the crystallizing salt Small salt crystals that are present in the boundary layer take up these ions for growth which strongly reduces the concentration of accumulated ions (see Figure 521b) Since ions are no longer accumulated near the ice interface the mass transfer resistance for ice growth disappears

Due to the breakdown of the mass transfer resistance the ice growth rate during EFC is only limited by heat transfer and surface integration These two resistances are relatively small compared to the mass transfer resistance as is shown for MgSO4 solutions in Figure 520 At eutectic conditions (wMgSO4=18 wt) the heat transfer and surface integration resistances are together only 1 of the total resistance for ice growth The breakdown of the mass transfer resistance by salt crystals results therefore into ice growth rates that are a factor of hundred higher than for ice crystallization only The expected transition temperature difference for EFC is consequently a factor of hundred lower than for ice crystallization which explains the results of Figure 519 This means that the transition temperature difference for EFC from MgSO4 solutions in fluidized bed heat exchangers is approximately 002 K Due to this value application of fluidized bed heat exchangers for EFC from binary solutions is very unlikely

The simultaneous production of salt and ice crystals may be possible at higher temperature differences when the ice growth rate can be slowed down by an additional non-crystallizing component The dissolved molecules or ions of this component may accumulate near the ice interface and reduce the ice growth rate while the main component crystallizes The reduction of the ice growth rate enables to apply considerably higher temperature differences while ice crystallization fouling is prevented In the next section this hypothesis is examined by EFC experiments from ternary and quaternary aqueous solutions

56 Eutectic Freeze Crystallization from Ternary and Quaternary Solutions

This section presents eutectic freeze concentration experiments from ternary and quaternary solutions in the fluidized bed heat exchanger It is expected that crystallization fouling from these solutions is less severe than for EFC from binary solutions discussed in the previous section


Two series of experiments were performed with ternary aqueous solutions based on KNO3 and KCl and one with quaternary aqueous solutions based on KNO3 and NaCl (see Table 53) The terms ternary and quaternary refer to the number of different ions that are dissolved

In the two series with ternary solutions the KCl concentration was kept constant at 43 and 84 wt respectively while the KNO3 concentration was varied In the quaternary solution experiments the NaCl concentration was kept constant at 33 wt In the first three or four experiments of a series only ice crystals were produced and ice crystallization fouling was studied In the last experiment of each series eutectic conditions were achieved and both ice and KNO3 crystals were produced The eutectic temperatures of these solutions were 15 to 29 K lower than the eutectic temperature of the binary aqueous solution of KNO3


101

Table 53 Overview of conditions for crystallization experiments Solution Added

component wadd

(wt) wKNO3 (wt)

Tfr or Teut (degC)

Type of crystals

Ternary KCl 43 00 -19 Ice 30 -28 Ice 61 -38 Ice 74 -43 Ice 75 -44 Ice + KNO3

Ternary KCl 84 00 -39 Ice 24 -50 Ice 56 -57 Ice 58 -58 Ice + KNO3

Quaternary NaCl 33 00 -20 Ice 41 -35 Ice 92 -48 Ice 102 -51 Ice + KNO3

Measured fluidized bed heat transfer coefficients were used to observe whether crystallization occurred It was assumed that crystallization fouling was successfully prevented when heat transfer coefficients remained constant for at least 30 minutes after the onset of crystallization

Both heat transfer sections of the experimental fluidized bed heat exchanger were used (see Section 53) The fluidized bed was operated at a bed voidage of 80 and the superficial velocity was 037 ms for all solutions

562 Experimental Results for Ternary Solutions

The results for ice scaling in ternary solutions in Figures 522 and 523 are in accordance with the experimental results from Chapter 2 Both figures show an increasing transition temperature difference as the KNO3 concentration increases Operating conditions with higher temperature differences resulted in ice scaling with decreasing heat transfer coefficients while ice scaling was prevented for temperature differences below this value The slopes of the ice scaling limit lines for ternary solutions are comparable with the slope of the line for the binary KNO3 solution in Figure 516

In contrast with EFC from binary solutions crystallization fouling during EFC from ternary solutions was successfully prevented by the fluidized bed heat exchanger at reasonable temperature differences However crystallization fouling during EFC appeared again to be more severe than during ice crystallization only as transition temperature differences for EFC were lower than for ice crystallization For the ternary solution with a KCl concentration of 43 wt the transition temperature difference for EFC was 049 K which corresponded to a maximum heat flux of 22 kWm2 The other ternary solution with a KCl concentration of 84 wt showed a transition temperature difference of 073 K and a corresponding heat flux of 33 kWm2

Chapter 5

102

00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

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re d

iffer

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for

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zatio

n fo

ulin

g ∆

Ttr

ans (K

)

Concentration KNO3 (wt)

Limit ice scalingEFC with foulingEFC without fouling

Ice scaling

No ice scaling

Figure 522 Comparison between transition temperature differences for ice crystallization

(lines) and EFC (crosses and circles) from KNO3-KCl solutions with wKCl=43 wt

00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

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iffer

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n fo

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g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling



A remarkable detail in Figures 522 and 523 is that the transition temperature differences for EFC are almost equal to the temperature difference for ice scaling for the case without KNO3 in the solution This observation means that crystallization fouling during EFC from a ternary solution is as severe as fouling during ice crystallization from a binary solution of the non-crystallization component with the same concentration as in the ternary solution

During the EFC experiment with the ternary solution containing 84 wt KCl and 58 wt KNO3 fouling was successfully prevented at a temperature difference of 071 K The crystals produced during this experiment were observed with the visualization section described in Section 53 Due to density differences ice crystals floated to the top of the film in the flow cell while KNO3 crystals settled at the bottom This phenomenon enabled to make separate microscopic pictures of both crystal types by changing the focal point of the microscope The


103

results are shown in Figures 524 and 525 The size of the ice crystals ranged from 50 to 250 microm while the size of the KNO3 crystals ranged from 25 to 100 microm

Figure 524 Ice crystals produced during

EFC from ternary solution with 84 wt KCl and 58 wt KNO3

Figure 525 KNO3 crystals produced during EFC from ternary solution with 84 wt KCl

and 58 wt KNO3

563 Experimental Results for Quaternary Solutions

The experiments with the quaternary solutions showed similar results as the experiments with ternary solutions described above (see Figure 526) The limit for ice scaling increases with increasing KNO3 concentration and crystallization fouling during EFC is more severe than ice crystallization only The transition temperature difference for crystallization fouling during EFC was 062 K with a corresponding heat flux of 30 kWm2 This value is almost equal to the transition temperature difference of ice crystallization from a binary NaCl solution with the same NaCl concentration as in the ternary solution

00

05

10

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00 20 40 60 80 100 120

Tra

nsiti

on te

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re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling


(lines) and EFC (crosses and circles) from KNO3-NaCl solutions with wNaCl=33 wt

Chapter 5

104

564 Discussion

The phenomena observed during the experiments with ternary and quaternary solutions are in accordance with the expectations described in Section 55 The transition temperature difference for ice scaling increases as a second solute is introduced in the solution The explanation for this phenomenon is that all different kind of solutes present in the liquid accumulate near the growing ice interface and therefore jointly slow down the ice growth rate A schematic representation of this accumulation process is shown for a quaternary solution of KNO3 and NaCl in Figure 527a The transition temperature difference in ternary and quaternary solutions can therefore be approximated by superposition of the contributions of the individual solutes A small error is introduced when this method is applied since the diffusion coefficient of a specific solute in solution alters when a second solute is introduced


freeze crystallization of KNO3 and ice from quaternary KNO3-NaCl solution

The EFC experiments with ternary and quaternary solutions clearly showed that the transition temperature difference for crystallization fouling decreases when besides ice also salt crystallizes This phenomenon is explained by means of Figure 527b in which the processes near the ice interface are shown for a quaternary solution of KNO3 and NaCl When only ice is produced K+ NO3

- Na+ and Cl- ions accumulate near the ice interface and slow down the ice growth rate (Figure 527a) As the solubility of one of the salts is exceeded in this case KNO3 salt crystals nucleate and grow in the solution (see Figure 527b) Salt crystals that are present in the boundary layer of the ice interface grow even faster since the solution is highly supersaturated with K+ and NO3

- ions there This salt crystallization process neutralizes the accumulation of K+ and NO3

- ions and as a result these ions do not hinder the ice growth process anymore The ice growth rate increases therefore but only to a limited extent since Na+ and Cl- ions are still accumulated near the ice interface The non-crystallizing components in the solution control the growth rate of ice crystals attached to the wall and enable to operate EFC at reasonable heat fluxes without crystallization fouling On the contrary the crystallizing component in this case KNO3 appears to have a negligible role in the prevention of ice crystallization fouling during EFC This negligible role explains the similarity between fouling during EFC from ternary and quaternary solutions on the one hand and fouling during ice crystallization from a binary solution of the non-crystallizing component with the same concentration on the other hand


105

It is expected that the presented model is not only valid for fluidized bed heat exchangers but also for other EFC crystallizers with mechanical removal of crystallization fouling This proposition is supported by experimental results on EFC with scraped surface heat exchangers by Vaessen et al (2003a) They report that fouling during simultaneous crystallization of KNO3 and ice is less severe in ternary solutions of KNO3 and HNO3 than in a binary solution of KNO3 only This phenomenon was initially attributed to the lower pH of the system by Vaessen (2003) However it is more likely that the H3O+ and NO3

- ions which are not involved in the crystallization process of KNO3 slow down the ice growth rate as is described for other ternary and quaternary solutions above The function of the H3O+ ions near the ice interface can also be fulfilled by ions that do not influence the pH for example Na+ ions It is believed that the acidity of the solution itself does therefore not determine the transition temperature difference for ice crystallization fouling

565 Perspectives of Fluidized Bed Heat Exchangers for EFC

The described experiments have shown that fluidized bed heat exchangers are able to prevent crystallization fouling during eutectic freeze crystallization from ternary and quaternary solutions Fluidized bed heat exchangers are relatively inexpensive compared to scraped surface crystallizers which have been considered for EFC processes up to now (see Section 524) As a result fluidized bed heat exchangers are interesting crystallizers for eutectic freeze crystallization processes A disadvantage with respect to the scraped surface crystallizers is that separation of the produced crystals can not be performed within the crystallizer itself and a separate solid-solid separator is therefore necessary

The EFC experiments with the fluidized bed heat exchanger showed transition temperature differences for crystallization fouling up to 073 K which corresponded to heat fluxes up to 33 kWm2 These values can be increased by adding non-crystallizing component to the solution For the quaternary solution for example the NaCl can be increased to 90 wt resulting in a eutectic temperature for KNO3 of about ndash9degC Based on the NaCl concentration a transition temperature difference of 20 K is expected for the simultaneous crystallization of KNO3 and ice which corresponds to a heat flux of 10 kWm2 This increased heat flux reduces the required heat transfer surface and with that the investment costs It is believed that this method to increase the maximum heat flux is not only applicable for fluidized bed heat exchangers but also for other crystallizers with mechanical removal of fouling

When EFC is applied to binary aqueous solutions an additional component can simply be added to the crystallizer to increase the transition temperature difference for crystallization fouling Since this component is neither part of the feed stream nor the product streams its concentration in the crystallizer remains constant An example of an EFC process with KNO3 as crystallizing salt and NaCl as non-crystallizing component is shown in Figure 528 The non-crystallizing component is not necessarily a salt like NaCl but can be any solute with a lower eutectic temperature than the crystallizing component Important in this respect is that the maximum solubility of the additional component is not exceeded to avoid crystallization Moreover the additional component should not interfere with the crystal lattice of the originally crystallizing component in order to achieve high crystal purities

A disadvantage of adding non-crystallizing component is the decrease of the eutectic temperature To achieve this lower temperature lower evaporation temperatures are necessary in the refrigeration system which reduces its efficiency and therefore the energy efficiency of the total system

Chapter 5

106

Figure 528 Example of a process scheme for EFC of pure water and KNO3 with NaCl as

non-crystallizing component in the crystallizer

57 Conclusions

Fluidized bed heat exchangers are promising apparatuses for both cooling crystallization of salts and eutectic freeze crystallization processes In case of cooling crystallization of salts fouling crystallization did not occur in the fluidized bed heat exchanger for heat fluxes up to 17 kWm2 It is therefore concluded that salt crystallization fouling is less severe than ice crystallization fouling Crystallization fouling during simultaneous crystallization of salt and ice from binary solutions can however not be prevented by fluidized particles The addition of a non-crystallizing component creating a ternary or quaternary solution reduces the fouling potential considerably and achieves that eutectic freeze crystallization in fluidized bed heat exchangers can be operated at heat fluxes of 10 kWm2 or higher The observed phenomena are explained by an extension of the model described in Chapter 2 that states that ice crystallization fouling is only prevented when the removal rate of fluidized particles exceeds the growth rate of ice crystals on the wall The ice growth rate is determined by all non-crystallizing components in the solution which jointly accumulate near the ice interface Due to the salt crystallization process during EFC ions of the crystallizing component that accumulate near the ice interface as a result of the ice growth process are immediately taken up by the growing salt crystals and therefore do not hinder the growth of ice crystals on the wall


107

Nomenclature

G Growth rate (ms) Subscripts k Mass transfer coefficient (ms) add Additional component mamp Mass flow (kgs) b Bulk M Molar mass (kgmol) cool Coolant p Pressure (Pa) eut Eutectic Qamp Heat (W) fr Freeze qamp Heat flux (kWm2) H2O Water R Removal rate (ms) ice Ice T Temperature (degC) in Inlet T Equilibrium temperature (degC) KCl Potassium chloride ∆Ttrans Transition temperature difference KNO3 Potassium nitrate (K) liq Liquid us Superficial velocity (ms) MgSO4 Magnesium sulfate Vamp Volume flow rate (m3s) NaCl Sodium chloride w Mass fraction in solution salt Salt x Solute mol fraction sat Saturation x Equilibrium solute mol fraction sol Solute w Wall Greek ρ Density (kgm3) φ Mass fraction of crystals

Abbreviations

CaCO3 Calcium carbonate KNO3 Potassium nitrate EFC Eutectic freeze crystallization NaCl Sodium chloride H2O Water Na2SO4 Sodium sulfate KCl Potassium chloride

References

Arkenbout GF 1995 Melt Crystallization Technology Lancaster Technomic

Barduhn AJ Manudhane A 1979 Temperatures required for eutectic freezing of natural wasters Desalination vol28 pp233-241

Genceli FE Gaumlrtner R Witkamp GJ 2005 Eutectic freeze crystallization in a 2nd generation cooled disk column crystallizer for MgSO4-H2O system Journal of Crystal Growth vol275 pp e1369-e1372


Goede R de 1988 Crystallization of paraxylene with scraped surface heat exchangers PhD thesis Delft University of Technology (The Netherlands)

Chapter 5

108

Goede R de Jong EJ de 1993 Heat transfer properties of a scraped-surface heat exchanger in the turbulent flow regime Chemical Engineering Science vol48 pp1393-1404

Ham F van der 1999 Eutectic Freeze Crystallization PhD thesis Delft University of Technology (The Netherlands)

Ham F van der Witkamp GJ Graauw J de Rosmalen GM van 1998 Eutectic freeze crystallization Application to process streams and waste water purification Chemical Engineering and Processing vol37 pp207-213

Ham F van der GJ Witkamp Graauw J de Rosmalen GM van 1999 Eutectic freeze crystallization simultaneous formation and separation of two solid phases Journal of Crystal Growth vol198-199 pp744-748

Ham F van der Seckler MM Witkamp GJ 2004 Eutectic freeze crystallization in a new apparatus the cooled disk column crystallizer Chemical Engineering and Processing vol43 p161-167

Himawan C 2005 Characterization and Population Balance Modelling of Eutectic Freeze Crystallization PhD thesis Delft University of Technology (The Netherlands)




Mullin JW 1993 Crystallization 3rd edition Oxford Butterworth-Heinemann

Myerson AS 1993 Handbook of Industrial Crystallization Boston Butterworth-Heinemann

Patience DB Rawlings JB Mohameed HA 2001 Crystallization of para-xylene in scraped-surface crystallizers AIChE Journal vol47 pp2441-2451

Schroeder PJ Andrew SC Khan AR 1977 Freezing processes - the standard of the future Desalination vol21 pp125-136

Stepakoff GL Siegelman D Johnson R Gibson W 1974 Development of a eutectic freezing process for brine disposal Desalination vol15 pp25-38

Swenne DA 1983 The Eutectic Crystallization of NaCl2H2O and Ice PhD thesis Eindhoven University of Technology (The Netherlands)

Vaessen RJC 2003 Development of Scraped Eutectic Freeze Crystallizers PhD thesis Delft University of Technology (The Netherlands)


109

Vaessen RJC Janse BJH Seckler MM Witkamp GJ 2003a Evaluation of the performance of a newly developed eutectic freeze crystallizer - Scraped cooled wall crystallizer Chemical Engineering Research amp Design vol81 pp1363-1372

Vaessen RJC Seckler MM Witkamp GJ 2003b Eutectic freeze crystallization with an aqueous KNO3-HNO3 solution in a 100-l cooled-disk column crystallizer Industrial amp Engineering Chemistry Research vol42 pp4874-4880

Chapter 5

110

111

6 Comparison between Fluidized Bed and Scraped Surface Ice Slurry Generators

61 Introduction

Previous chapters have demonstrated that fluidized bed heat exchangers are promising apparatuses for ice crystallization processes Experiments at various operating conditions have shown that fluidized bed particles are able to remove ice crystals from the cooled walls and additionally enhance heat transfer coefficients Fluidized bed heat exchangers can therefore continuously produce ice slurry without ice scaling at relatively high heat fluxes Due to their relatively simple shell-and-tube design it is expected that fluidized bed heat exchangers are rather inexpensive compared to other ice slurry generators and may therefore lead to a serious reduction of investment costs of ice slurry systems

In the last two decades a large number of ice slurry generator types have been invented which all have their own method to treat the problem of ice scaling An extensive overview of existing ice slurry generation methods is given by Kauffeld et al (2005) Scraped surface heat exchangers are the most frequently applied ice slurry generators at this moment These apparatuses use mechanical devices to remove the ice crystals from the wall Main drawbacks of these systems are the high investment and maintenance costs Consequently alternative ice slurry generator types have been developed and introduced in recent years In Japan for example several air-conditioning systems are equipped with a supercooled water ice slurry generator (Bellas and Tassou 2005 Wakamoto et al 1996) In this generator water is cooled below its freezing temperature of 0degC without the formation of ice crystals A supercooling releaser is subsequently used to convert the supercooled liquid into an ice slurry by means of a spraying nozzle ultrasonic waves or the presence of other ice crystals (Kurihara and Kawashima 2001 Mito et al 2002 Nagato 2001 Tanino et al 2000) Another commercially available system is the vacuum ice slurry generator with water as refrigerant (Ophir and Koren 1999 Paul 1996) This ice slurry generator consists of a water tank at triple point conditions at which liquid water water vapor and ice exist simultaneously Water vapor is removed from the tank by a compressor and as a result liquid water partially evaporates The required heat of evaporation is extracted from the liquid resulting in the formation of more ice Due to the high specific volume of water vapor at triple point conditions relatively large compressors are required to operate this ice slurry generator Vacuum ice slurry generators with water as refrigerant are therefore only applied for high cooling capacities of 1 MW and higher for example for cooling of deep mines (Paul et al 1999 Sheer et al 2001) Other ice slurry generators are currently under development but have not been applied in practice yet Examples are the ice slurry generator with direct evaporation of refrigerant (Kiatsiriroat et al 2003 Sari et al 2005 Vuarnoz et al 2004) or with an immiscible heat transfer fluid (Wijeysundera et al 2004) indirect vacuum ice slurry generators (Jellema and Nijdam 2005 Roos et al 2003 Zakeri 1997) and heat exchangers with special coatings (Zwieg et al 2002)

The objective of this chapter is to compare the fluidized bed ice slurry generator with the most frequently applied ice crystallizer type namely the scraped surface ice slurry generator First the main configurations of this ice slurry generator type are introduced and its main features are discussed Subsequently both ice slurry generator types are quantitatively compared on the basis of the most important aspects of ice crystallizers These aspects are the ability to prevent of ice scaling the heat transfer performance investment and maintenance costs and

Chapter 6

112

energy consumption In order to compare the ice scaling prevention ability of both apparatuses ice crystallization experiments were performed with an experimental scraped surface heat exchanger

62 Scraped Surface Ice Slurry Generators

Scraped surface ice slurry generators are characterized by the application of mechanical devices to remove ice crystals from the walls In general two different types of mechanical removal devices can be distinguished namely scraper blades and orbital rods Ice slurry generators using these devices are described below

621 Ice Slurry Generators with Scraper Blades

There exist various ice slurry generators in which scraper blades remove ice crystals from the heat exchanger walls Most of these configurations consist of a tubular heat exchanger with a rotating scraping mechanism in the inner tube as is shown in Figure 61 (Stamatiou et al 2005) The primary refrigerant evaporates in the annulus between the two tubes and removes therefore heat from the inner tube in which ice slurry is produced

Figure 61 Scraped surface heat exchanger with rotating blades (Stamatiou et al 2005)

The scraper blades are connected to a rotating shaft which is driven by an electric motor at a typical speed of 450 RPM Usually springs are used to push the blades to the wall in order to

Comparison between Fluidized Bed and Scraped Surface Ice Slurry Generators

113

avoid the formation of an insulating ice layer However it is also possible that a small gap exists between the blades and the wall for example of 1 mm in size (Ben Lakhdar et al 2005) During ice slurry production an ice layer is then formed on the inner wall which is periodically removed as soon as the thickness of the ice layer exceeds the size of the gap

The configuration of the scraper blades can deviate from the configuration shown in Figure 61 Bel and Lallemand (1999) for example showed that screw-type scrapers as shown in Figure 62 are also able to keep heat exchanger walls free of ice Stamatiou and Kawaji (2003) and Stamatiou (2003) successfully produced ice slurry from plate heat exchangers in which translating scrapers kept the walls free of ice (see Figure 63)

Figure 62 Heat exchanger with screw-type scraper (Bel and Lallemand 1999))

Figure 63 Heat exchanger with translating scraper blades (Stamatiou 2003)

Commercially available ice slurry generators with scraper blades only prevent ice scaling when a certain amount of solute is added to water According to the manufacturers of this equipment ice slurry can therefore only be produced from aqueous solutions with freezing temperatures of ndash2degC and lower (Kauffeld et al 2005) Besides the removal of ice crystals the scraper blades also disturb the thermal boundary layer close to the heat exchanger wall resulting in an enhancement of slurry-side heat transfer coefficients Since the evaporating process in the annulus can also be operated with high heat transfer coefficients overall heat transfer coefficients in this type of ice slurry generators are generally high Main disadvantages of ice slurry generators with scraper blades are the relatively high investment and maintenance costs The high investment costs are mainly induced by the relatively high number of moving parts and the required tolerances for the blades Furthermore mechanical restrictions limit the maximum size of the ice slurry generator resulting in maximum capacities of about 35 kW per unit For applications with higher required cooling capacities multiple units must be installed with only limited benefits of scale-up The high maintenance costs are caused by the fact that the scraper blades are subject to wear and need to be replaced after a given time interval

Ice slurry generators with scraper blades have been applied for various applications such as for air-conditioning systems in large office buildings (Wang and Kusumoto 2001) cooling of products in food industry (Soe et al 2004 Wang et al 2002) and cooling of display cabinets in supermarkets (Field et al 2003) Besides ice slurry production purposes these heat exchangers are widely used in food and chemical industry to prevent fouling in heat transfer and crystallization processes In food industry for example heat exchangers with scraper blades are used for freeze concentration of beverages production of ice cream and slushndashice beverages and processing of margarine butter and cheese (Drewett and Hartel 2006 Mil and

Chapter 6

114

Bouman 1990) In chemical industry this type of heat exchangers is for example applied to prevent fouling during the crystallization of paraxylene from its isomers (Goede and Jong 1993 Patience et al 2001) The heat exchangers used in both types of industries are very similar to the ones used for ice slurry production

622 Ice Slurry Generators with Orbital Rods

Another configuration of scraped surface ice slurry generators is the orbital rod heat exchanger (Gladis et al 1996) In this heat exchanger ice slurry flows as a falling film on the inner surface of a cooled tube as shown in Figure 64 A metal orbital rod roles over the inner wall of this tube and prevents ice scaling According to Gladis et al (1996) the movement of the orbital rod prevents that ice crystals adhere to the heat exchanger surface but fundamental research on the physical mechanisms of ice scaling prevention in this ice slurry generator is lacking in literature

The orbital rod is connected with a crank mechanism that is driven by a motor The rotational speeds are usually higher than in heat exchangers with scraper blades Typically the rod makes around 850 orbits per minute while the rotational speed of the rod is even higher

Figure 64 Working principle of orbital rod

ice slurry generator (Gladis et al 1996) Figure 65 Orbital rod ice slurry generator

(Gladis et al 1996)

One of the main advantages of the orbital rod ice slurry generator is that it can be operated in a shell-and-tube configuration as shown in Figure 65 In this configuration the primary refrigerant evaporates in the shell while ice slurry is produced inside the tubes The rotating shaft from the motor drives an eccentric crank that provides a rotating movement to a drive plate This drive plate passes the rotating movement on to all individual orbital rods such that ice scaling is prevented in all tubes The number of tubes in one shell varies from 40 up to 159 depending on the required cooling capacity


115

In correspondence with heat exchangers with scraper blades ice slurry generators with orbital rods can only prevent ice scaling for freezing temperatures of ndash22degC and lower Another similarity is that relatively high heat transfer coefficients can be achieved as a result of the continuous disturbance of the thermal boundary layer The maximum cooling capacity of a single shell-and-tube heat exchanger is 450 kW which implies that for higher cooling duties multiple heat exchangers are necessary These specific characteristics makes this ice slurry generator mainly economically attractive for cooling capacities between 100 and 1000 kW In similarity to scraper blades the orbital rods the cranks and the drive plate of this ice slurry generator are subject to wear and need to be replaced after a certain period of operation

In the last decade orbital rod ice slurry generators have successfully been installed for various cooling applications such as air-conditioning systems (Nelson 1998 Nelson et al 1999) and refrigeration in food industry (Gladis 1997) and beer breweries (Kauffeld et al 2005 Nelson 1998)

63 Prevention of Ice Scaling

631 Introduction

In Chapters 2 and 4 the ice scaling prevention abilities of fluidized bed ice slurry generators at various operating conditions have been determined This analysis has shown that for each set of operating conditions a maximum difference exists between the wall temperature and the equilibrium temperature at which ice scaling is just prevented This so-called transition temperature difference appeared to be approximately proportional to the solute concentration

Experiments on ice crystallization by Vaessen et al (2002) showed that ice scaling is not always prevented in scraped surface heat exchangers and depends on operating conditions such as the rotational speed of the scraper blades and the solute type and concentration Kauffeld et al (2005) report that scraper blades can only prevent ice scaling when the aqueous solution contains a minimum concentration of solute corresponding to a freezing temperature of ndash2degC According to Gladis et al (1996) the same is valid for ice slurry generators with orbital rods All these observations suggest that a transition temperature difference for ice scaling can be determined for scraped surface ice slurry generators analogously to fluidized bed ice slurry generators Furthermore it seems that the solute type and concentration also play an important role for ice scaling in these apparatuses

From the foregoing analysis is concluded that the ice scaling prevention abilities of scraped surface and fluidized bed ice slurry generators can be compared by analyzing their transition temperature differences For fluidized bed ice slurry generators these values are available from Chapter 2 and 4 for different aqueous solutions and for different operating conditions However transition temperature differences for scraped surface ice slurry generators with similar aqueous solutions are not available

In order to compare the ice scaling prevention ability of both ice slurry generators ice crystallization experiments have been performed with an experimental ice slurry generator with rotating scraper blades The experimental ice scaling results are subsequently compared to results from the fluidized bed ice slurry generator

Chapter 6

116

632 Experimental Scraped Surface Heat Exchanger and Conditions

The experimental scraped surface ice slurry generator consists of a 10-liter cylindrical crystallizer with a cooled bottom plate which is continuously scraped by rotating blades as shown in Figure 66 The stainless steel bottom plate has a thickness of 1 mm and a diameter of 020 m which corresponds to a heat transfer area of 0031 m2 The upper surface of the bottom plate is scraped by four rotating PTFE blades that are driven by a vertical shaft The rotational speed of this shaft is 100 RPM which means that every 015 seconds a scraper blade passes a certain point on the bottom plate The scraper blades are loaded by springs in order to put pressure on the scraped surface Halfway the shaft a turbine mixer is installed to keep the slurry in the crystallizer homogeneous The bottom plate is cooled by a 50 wt potassium formate solution which follows a spiral channel below the bottom plate of the crystallizer The height and width of the coolant channel measure 5 and 17 mm respectively The coolant flow rate is 10 m3h and its inlet temperature is controlled within 01 K by a cooling machine The crystallizer overflows to an ice melting tank were the produced ice crystals are melted and from which aqueous solution is pumped back to the crystallizer

Figure 66 Experimental set-up with scraped surface ice slurry generator

During the experiments the shaft torque the coolant flow rate and the temperatures in the crystallizer and at the inlet and outlet of the coolant were measured The total amount of transferred heat through the bottom plate is calculated from the measured coolant flow rate and temperatures Subsequently the overall heat transfer coefficient U is determined from the transferred heat and the temperature difference between the coolant and the slurry in the tank

lnQ UA T= ∆amp with

( ) ( )( ) ( )( )iscrys coolin iscrys coolout

lniscrys coolin iscrys cooloutln

T T T TT

T T T T

minus minus minus∆ =

minus minus (61)

The overall heat transfer coefficient U is now used to calculate the heat transfer coefficient at the slurry side αcrys For this calculation the coolant heat transfer coefficient αcool is determined from a validated heat transfer model (see Appendix C4)


117

plate

crys plate cool

1 1 1U

δα λ α

= + + (62)

The most probable place on the bottom plate for ice scaling is the location with the lowest temperature This lowest plate temperature is located at the place where the coolant enters the crystallizer The ratio of heat transfer coefficients the crystallizer temperature and the coolant inlet temperature are used to determine this minimum plate temperature

( )( )

iscrys platemin

crysiscrys coolin

T T UT T α

minus=

minus ( 63)

Measurement accuracies of the physical parameters obtained with the experimental scraped surface heat exchanger are given in Appendix D3

The ice crystallization experiments were performed with aqueous KNO3 solutions with various concentrations as listed in Table 61 At the beginning of each experiment the inlet temperature of the coolant was set below the freezing temperature of the solution in the crystallizer After some time of operation the temperature in the crystallizer decreased below the freezing temperature and ice seeds were introduced to start the crystallization process After the onset of ice crystallization the coolant inlet temperature was stepwise lowered every 20 minutes until the heat transfer coefficient dropped indicating ice scaling

Table 61 Experimental conditions Exp wKNO3 Tfr Slurry nr (wt) (degC) pump on 1 229 -073 Yes 2 245 -078 Yes 3 318 -100 Yes 4 331 -104 No 5 523 -159 Yes 6 690 -205 Yes 7 942 -270 Yes

In all experiments except experiment 4 the slurry pump was in operation in order to melt ice crystals in the ice melting tank and to keep ice fractions in the crystallizer below 8 wt During experiment 4 however ice crystals were not melted and therefore the ice fraction in the crystallizer increased up to approximately 24 wt

633 Experimental Results on Ice Scaling Prevention

The experimental results on ice scaling are described on the basis of a single experiment first namely experiment 3 After that the ice scaling results of all experiments are discussed

Analysis of a Single Experiment

Figure 67 shows the characteristic temperatures of a single ice crystallization experiment namely experiment 3 with a KNO3 concentration of 318 wt The experiment started with a crystal-free solution in which ice crystals were seeded (t=850 s) The seed crystals resulted in the onset of the ice crystallization process and a rapid increase of the temperature in the

Chapter 6

118

crystallizer towards the equilibrium temperature Subsequently the coolant inlet temperature was gradually decreased with 10 K per step

-80

-70

-60

-50

-40

-30

-20

-10

00

0 1200 2400 3600 4800 6000Time (s)

Tem

pera

ture

(degC

)

T iscrys

T platemin

T coolin

Ice nucleation

Figure 67 Temperatures in the crystallizer at the inlet of the coolant and at the bottom plate

during experiment 3

Heat transfer coefficients and the shaft torque were used to identify ice scaling (see Figure 68) At the onset of ice crystallization the heat transfer coefficient at the crystallizer side increased from approximately 1900 to 3000 Wm2K while the shaft torque was more or less constant The first two stepwise decreases of the coolant inlet temperature resulted in even higher heat transfer coefficients resulting in values up to 4000 Wm2K Such a heat transfer enhancement due to ice crystallization was also observed by other researchers working on scraped surface ice slurry generators (Vaessen et al 2002 Stamatiou and Kawaji 2003 Qin et al 2003 Qin et al 2006) Section 64 discusses this phenomenon in more detail

0

1000

2000

3000

4000

5000

6000

0 1200 2400 3600 4800 6000Time (s)

00

01

02

03

04

05

06Uα crys

Torque

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Tor

que

(Nm

)

Ice nucleation

Figure 68 Heat transfer coefficients and shaft torque during experiment 3


119

After the coolant inlet temperature was lowered for the third time (t=4600 s) the heat transfer coefficient decreased considerably indicating that an insulating ice layer built up on the bottom plate The continuous decrease of heat transfer coefficients demonstrates that the scraper blades were not able to remove this insulating ice layer which is referred to as ice scaling This observation is confirmed by the measured shaft torque which initially shows a rapid increase during the same period The temporarily decrease of the shaft torque at t=5500 s may be explained by the idea that the scrapers start lsquoskatingrsquo at the ice layer which reduces friction forces Finally the shaft torque rises again which is probably caused by an increasing ice layer leading to higher normal forces on the scrapers

Analysis of All Experiments

Figure 69 shows the temperature differences between crystallizer and bottom plate for all operating conditions of the seven experiments Operating conditions at which ice scaling was prevented are marked with a circle while conditions with ice scaling are represented by a cross

00

05

10

15

20

25

30

35

40

00 20 40 60 80 100Concentration KNO3 (wt)

Tis

cry

s-Tpl

ate

min

(K)

No ice scalingIce scalingLimit

No ice scaling

Ice scaling

-50

-40

-30

-20

-10

00



No ice scaling

Ice scaling

Tpl

ate

min

(degC

)

Figure 69 Temperature differences between plate and ice slurry for conditions with and

without ice scaling

Figure 610 Minimum plate temperatures for conditions with and without ice scaling

The results in Figure 69 can be divided into two parts At concentrations up to approximately 4 wt the temperature difference at which ice scaling was just prevented is proportional with the KNO3 concentration This observation is in accordance with the results from the fluidized bed ice slurry generator reported in Chapter 2 The proportionality has been explained in Chapter 2 by a model that assumes that ice scaling is only prevented when the growth rate of ice crystals attached to the wall does not exceed the removal rate

R Ggt (64)

The ice growth rate G is assumed to be mass transfer limited which results in lower ice growth rates at higher solute concentrations

Chapter 6

120

( )liq eq

eq crys plateminice

dwkG T w Tw dT

ρρ

= minus minus

(65)

The ice slurry in the crystallizer is assumed to be in equilibrium and therefore the temperature measured in the crystallizer is supposed to be the equilibrium temperature

( )liq eq

iscrys plateminice

dwkG T Tw dT

ρρ

= minus minus

(66)

This means that for a constant removal rate R higher temperature differences without ice scaling can be applied in solutions with higher solute concentrations The temperature difference at which ice scaling is just prevented is called transition temperature difference ∆Ttrans

eqice

trans iscrys plateminliq

dTwT T T Rk dw

ρρ

∆ = minus = minus

(67)

On the basis of the results in Figure 69 can be concluded that this model is also valid for scraped surface ice slurry generators at least at low KNO3 concentrations However this model seems not applicable for KNO3 concentrations higher than 4 wt because the maximum temperature difference without ice scaling decreases from that concentration on This behavior can be explained by considering the bottom plate temperatures as shown in Figure 610 This figure indicates that for higher KNO3 concentrations ice scaling started when the plate temperature was lower than ndash40degC At this plate temperature it is supposed that KNO3 crystals spontaneously nucleate near the ice crystals on the bottom plate and that therefore the eutectic freeze crystallization process locally takes place The eutectic temperature of the KNO3-H2O system is ndash29degC and it is therefore plausible that nucleation of KNO3 crystals only occurs when a certain degree of supersaturation is reached This salt crystallization process takes up the accumulated ions near the growing ice interfaces on the bottom plate as described in Section 554 As a result of this the ice growth rate is no longer mass transfer limited and increases strongly resulting in ice scaling

634 Comparison of Ice Scaling Prevention

The experimental results presented above demonstrate that ice scaling in scraped surface ice slurry generators shows the same trends as in fluidized bed ice slurry generators In both crystallizers the transition temperature difference is proportional with the solute concentration This statement is valid when crystallization of the solute does not occur which is at least guaranteed when the wall temperature is higher than the eutectic temperature In this subsection the ice scaling prevention abilities of both ice slurry generators are quantitatively compared by analyzing the proportionality constants Furthermore the experimental ice scaling results are compared to results from commercially available scraped surface ice slurry generators

A comparison of transition temperature differences for ice crystallization from KNO3 solutions in Figure 611 demonstrates that the transition temperature difference in scraped surface ice slurry generators is 75 times higher than in fluidized bed ice slurry generators The stationary fluidized bed used in this comparison consists of a stainless steel cylinders of 4 mm in size and has a bed voidage of 81 Its ice scaling prevention ability is based on the


121

model presented in Section 244 and is relatively high in relation with other stationary fluidized bed conditions as is shown in Section 43 Despite of this relatively high ice scaling prevention ability the transition temperature difference is much smaller than of the experimental scraped surface ice slurry generator

00

05

10

15

20

25

30

35

40


∆T

tran

s (K

)

00 05 10 15 20 25Freezing point depression (K)

Fluidized bedexperiments

Scraped surfaceexperiments

0

5

10

15

20

25


Hea

t flu

x (k

Wm

2 )

Ice scaling




Scraperblades

Orbitalrods

No ice scaling

Figure 611 Comparison of transition temperature differences of scraped surface

and fluidized bed ice slurry generators

Figure 612 Comparison of maximum heat flux for ice scaling in scraped surface and

fluidized bed ice slurry generators

Another method to compare the performance of both ice crystallizers is to evaluate the maximum heat flux at which ice scaling is just prevented Figure 612 shows that this value for the scraped surface heat exchanger ranged from 5 to 10 kWm2 Analogously to the transition temperature difference this maximum heat flux is proportional to the solute concentration for low concentrations of KNO3 The same is valid for the maximum heat flux in the fluidized bed heat exchanger which is deduced from the transition temperature difference and a measured fluidized bed heat transfer coefficient of 6300 Wm2K The maximum heat flux in the set-up with scraper blades is a factor of four higher than in the set-up with the fluidized bed

Figure 612 also shows some maximum heat fluxes of commercially available ice slurry generators discussed in Section 62 Ice slurry generators with scraper blades or orbital rods can operate at freezing temperatures of ndash20 or ndash22degC and lower respectively (Stamatiou et al 2005 Gladis et al 1996) The maximum heat fluxes at these temperatures are deduced from typical operating conditions of these crystallizers described in literature (Kauffeld et al 2005 Stamatiou et al 2005) and appear to be comparable with the maximum heat fluxes of the experimental set-up with scraper blades However it must be noted that the maximum heat fluxes of these commercial crystallizers are valid for aqueous solutions of ethylene glycol ethanol and NaCl which are expected to exhibit higher transition temperature differences and maximum heat fluxes than KNO3 solutions (see also Section 24)

In the experimental study described above the operating parameters of the scraper blades such as rotational speed normal force plate material and scraper geometry were kept constant Vaessen (2003) showed that all these parameters influence the ice scaling

Chapter 6

122

prevention ability of the crystallizer Sharp blades or higher normal forces for example enhance the removal of ice crystals from the cooled surface considerably Furthermore the ice scaling prevention increases as the rotational speed of the scrapers is higher (see also Vaessen et al 2002) The parameters of the experimental scraper blades were randomly chosen and were therefore not optimized This means that with an optimized scraper configuration even higher maximum heat fluxes can be realized than the heat fluxes shown in Figure 612

The obtained results for both scraped surface and fluidized bed ice slurry generators indicate that at low solute concentrations and high freezing temperatures only low heat fluxes can be applied These low heat fluxes result in relatively large required heat transfer surfaces and therefore to high investment costs For this reason commercial scraped surface ice slurry generators are only operated at freezing temperatures of ndash20degC or lower in order to apply heat fluxes of about 15 to 20 kWm2 The ice scaling prevention ability of fluidized bed ice slurry generators is lower but the investment costs per square meter of heat transfer surface are also expected to be lower especially for large cooling capacities It is therefore questionable at which cooling capacities and freezing temperatures the investment costs of fluidized bed ice slurry generators are lower than of scraped surface ice slurry generators A detailed study on this topic is presented in Section 65

64 Heat Transfer Performance

The heat transfer performance is an important characteristic of an ice slurry generator since it strongly influences its investment costs This section compares heat transfer coefficients in scraped surface and fluidized bed ice slurry generators In the analysis both the influences of crystallizer conditions and thermophysical properties of ice slurry are studied

641 Influence of Operating Conditions

Several empirical correlations have been proposed to predict heat transfer coefficients in liquid-solid fluidized bed heat exchanger (Haid et al 1994) A number of these correlations have been tested for the operating range of ice slurry production by Meewisse and Infante Ferreira (2003) and Pronk et al (2005) This experimental study has shown that the correlation proposed by Haid (1997) generally gives good results and slightly overestimates fluidized bed heat transfer coefficient with 94 on average

0 75 063

h h liq0 0734 Nu Re Pr= with ph

liq 1D

Nuα ελ ε

=minus

and ( )

liq s ph

liq 1u D

Reρ

micro ε=

minus (68)

The superficial velocity us can be determined from the well-known Richardson-Zaki correlation for homogeneously expanding stationary fluidized beds (Meewisse 2004 Richardson and Zaki 1954) This correlation relates the superficial velocity to the bed voidage and the terminal velocity of a single particle The latter parameter can be calculated by correlations proposed by Chhabra (1995) and Chhabra et al (1999)

In Section 434 of this thesis experimental fluidized bed heat transfer coefficients have been reported for a 77 wt NaCl solution at its freezing temperature of ndash49degC Measured heat transfer coefficients ranged from 3500 to 5200 Wm2K depending on the size of the fluidized particles and the bed voidage (see also Figure 613) The highest values were achieved with large particles of 4 mm in size at low bed voidages of about 80


123

0

2000

4000

6000

8000

70 80 90 100Bed voidage ()

2 mm3 mm4 mmH

eat t

rans

fer

coef

ficie

nt (W

m 2 K

)

0

2000

4000

6000

8000

00 50 100 150 200Scraper passes (1s)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Re-Pr Eq611

Re-Pr Eq610

Penetration theory Eq69

Figure 613 Measured heat transfer coefficients in fluidized bed heat exchanger

for 77 wt NaCl solution at freezing temperature of ndash49degC (see also Section 43)

Figure 614 Calculated heat transfer coefficients in scraped surface heat

exchangers for 77 wt NaCl solution at freezing temperature of ndash49degC

Heat transfer coefficients in scraped surface heat exchangers can be calculated with two different methods The first method has a theoretical approach and is based on the penetration theory (Goede and Jong 1993 Qin et al 2003 Vaessen et al 2004) This theory is based on conductive heat transfer and assumes that the thermal boundary layer is stagnant between two scraper passes As a scraper blade passes the stagnant boundary layer is completely removed and mixes instantaneously with the bulk The temperature of the new boundary layer initially equals the bulk temperature and subsequently decreases until the next scraper passes The average heat transfer coefficient of this unsteady-state heat conduction process is given by

liq liq pliq

4 c Nα λ ρπ

= (69)

The assumption that the boundary layer is completely replaced after a scraper pass may not be fulfilled in real scraped surface heat exchangers To compensate for this incomplete mixing the correlation of Equation 69 can be adjusted with a compensation factor (Goede and Jong 1993 Vaessen 2003)

The second calculation method has an empirical character and uses correlations based on dimensional numbers to calculate heat transfer coefficients The most frequently applied correlations use Nusselt Reynolds and Prandtl numbers such as the correlation proposed by Trommelen et al (1971) The Reynolds number in these correlations is based on the rotational speed of the scrapers

0 5 025

scr scr liq2 26 Nu Re Pr= with 2

liq scrscr

liq

NDRe

ρmicro

= ( 610)

Chapter 6

124

A comparable correlation has been formulated in Appendix C4 for the experimental set-up used in the previous section

0 5 033


liq scrscr

liq

NDRe

ρmicro

= and scrscr

liq

DNu αλ

= (611)

For tubular scraped surface heat exchanger as shown in Figure 61 the heat transfer correlation can be extended with a convection term for the axial flow Goede and Jong (1993) for example combined the penetration theory with a convective heat transfer correlation based on the axial velocity Bel and Lallemand (1999) successfully combined empirical heat transfer correlations for both convection induced by the scrapers and convection induced by the axial flow

Heat transfer coefficients calculated on the basis of Equations 69 610 and 611 are shown in Figure 614 as a function of the scraping rate for a 77 wt NaCl solution at its freezing temperature of ndash49degC Commercial ice slurry generators with scraper blades are normally operated at 450 RPM with two scraper passes per rotation resulting in 15 scraper passes per second According to the presented correlations the heat transfer coefficient for these conditions is approximately 4000 Wm2K which is slightly lower than heat transfer coefficients in fluidized bed heat exchangers (see Figure 613)

Values or correlations for slurry-side heat transfer coefficients in orbital rod heat exchangers are not reported in literature However overall heat transfer coefficients are reported ranging from 2000 to 3800 Wm2K depending on the primary refrigerant used (EPS Ltd 2006) These relatively high overall heat transfer coefficients imply that slurry-side heat transfer coefficients are also high and comparable with ice slurry generators with scraped blades or fluidized beds

642 Influence of Thermophysical Properties

Besides the operating conditions heat transfer coefficients in scraped surface and fluidized bed ice slurry generators are also influenced by the thermophysical properties of the liquid phase such as density dynamic viscosity specific heat and thermal conductivity The values of these properties are determined by the solute type and its concentration in the aqueous solution These parameters also determine the freezing temperature of the solution Since ice slurry generators are operated at the freezing temperature of a solution it is possible to analyze the influence of thermophysical properties on heat transfer coefficients on the basis of freezing temperatures

Figures 615 and 616 show such an analysis for aqueous solutions of sodium chloride ethylene glycol and D-glucose in fluidized bed and scraped surface ice slurry generators respectively Both figures indicate that heat transfer coefficients decrease as the freezing temperatures decreases which is mainly caused by an increase of the dynamic viscosity However the decrease is much stronger in scraped surface than in fluidized bed ice slurry generators Heat transfer coefficients in fluidized bed ice slurry generators are therefore expected to be much higher at low freezing temperatures The cause for these relatively high values is that the influence of viscosity on fluidized heat transfer coefficients is small compared to other convective heat transfer processes


125

0

2000

4000

6000

8000

-20 -15 -10 -5 0Freezing temperature (degC)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

NaCl

EGD-glucose

0

2000

4000

6000

8000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

NaCl

EG D-glucose

Figure 615 Fluidized bed heat transfer (Dp=4 mm ε=81) for various solutions at

their freezing temperature according to Eq 68

Figure 616 Scraped surface heat transfer coefficients (N=15 1s) for various solutions at their freezing temperature according to

Eq 610

643 Influence of Ice Crystallization

Meewisse and Infante Ferreira (2003) and Pronk et al (2005) have demonstrated that the ice crystallization process does not influence heat transfer coefficients in fluidized bed ice slurry generators as long as ice scaling is successfully prevented During ice crystallization heat transfer coefficients can be calculated by Equation 68 using the thermophysical properties of the liquid phase Although ice crystallization has no direct effect on the heat transfer process an increase of the ice fraction reduces the heat transfer coefficient This effect is caused by the fact that the solute concentration in the liquid and thus the dynamic viscosity increases as the ice fraction increases This reduction in heat transfer coefficient is however small for ice slurries with high initial freezing temperatures as is shown in Figure 617

0

2000

4000

6000

8000

0 5 10 15 20 25 30Ice fraction (wt)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K

)

T fr= ndash20degC

T fr= ndash10degC

T fr= ndash5degC

Figure 617 Heat transfer coefficients in a fluidized bed heat exchanger (Dp=4 mm ε=81)

for ice slurry based on ethylene glycol at various initial freezing temperatures

Chapter 6

126

In contrast with fluidized bed ice slurry generators the ice crystallization process does influence heat transfer coefficients in scraped surface ice slurry generators Measured heat transfer coefficients are reported to be higher than for the case without ice crystals During the experimental study on ice scaling prevention in Section 63 heat transfer coefficients increased from 2000 to 3000 Wm2K as a result of the onset of ice crystallization (see Figure 68) A similar relative enhancement was observed by Vaessen (2003) who measured heat transfer coefficients of 4000 Wm2K prior to ice nucleation and 7000 Wm2K after the onset of ice crystallization Comparable results were obtained by Stamatiou and Kawaji (2003) and by Qin et al (2003 2006) The latter researchers attribute the enhanced heat transfer coefficients to growing ice crystals that partly cover the cooled wall between two scraper passes According to Qin et al the unsteady-state heat conduction process at the covered parts is determined by the phase transition from water to ice which results in higher local heat transfer coefficients compared to the parts without ice crystals where only conduction to the liquid occurs The effective heat transfer coefficient for the entire wall is determined as the weighed average of both heat transfer coefficients

Section 641 has indicated that fluidized bed heat exchangers show slightly higher heat transfer coefficients compared to scraped surface heat exchangers when both are operated with liquids at standard conditions However it is expected that the heat transfer performance of both ice slurry generators is comparable for the case of ice crystallization because of the enhancement in scraped surface ice slurry generators as a result of ice crystallization

65 Investment and Maintenance Costs

651 Investment Costs

Scraped surface heat exchangers are currently the most frequently applied ice slurry generators in commercial systems It is believed that the relatively high investment costs of these crystallizers have limited a widespread use of ice slurry as secondary refrigerant up to now Lower investment costs of alternative ice slurry generators such as the fluidized bed ice slurry generator may therefore realize that ice slurry becomes economically more attractive

Investment costs of commercial ice slurry generators with rotating scraper blades and orbital rods are deduced from Kauffeld et al (2005) and Stamatiou et al (2005) and are shown as function of the heat transfer area in Figure 618 The costs are based on heat exchangers made of 304 grade stainless steel The figure also shows the investment costs of an industrial scraped surface crystallizer made as produced by GMF (1992) The investment costs of the various machines show a trend which can be approximated by the following expression

0 77SSHE he7 0 I A= with A in m2 and I in keuro ( 612)

According to Rautenbach and Katz (1996) the investment costs of fluidized bed heat exchangers are about 16 to 21 times higher than of standard shell-and-tube heat exchangers A survey by Katz (1997) pointed out that this factor is even higher and ranges from 215 to 245 According to Katz the costs of 304 grade stainless steel shell-and-tube heat exchangers is approximated by the following expression which is corrected for inflation

0 65STHE he1 5 I A= with A in m2 and I in keuro ( 613)


127

1

10

100

1000

01 1 10 100 1000Heat transfer area (m2)

Inve

stm

ent c

osts

(keuro)

Scraper bladesOrbital rodsGMFTrendline

1

10

100

1000


Inve

stm

ent c

osts

(keuro)

STHESSHE

FBHE

Figure 618 Investment costs of various scraped surface heat exchangers with

trendline

Figure 619 Investment costs of shell-and-tube fluidized bed and scraped surface heat

exchangers

If the conservative assumption is made that fluidized bed heat exchangers are 24 times more expensive than standard shell-and-tube heat exchangers then the investment of fluidized bed ice slurry generators can be approximated by

0 65FBHE he3 6 I A= with A in m2 and I in keuro (614)

A comparison between the investment costs of both heat exchanger types in Figure 619 shows that fluidized bed heat exchangers are less expensive especially for larger heat transfer areas

Despite the lower investment costs per square meter of heat transfer area fluidized bed ice slurry generators are not necessarily less expensive per kilowatt cooling capacity The more effective ice scaling prevention of scraped surface heat exchangers enables to apply higher heat fluxes especially at high ice slurry temperatures and therefore less heat transfer surface is required (see Figure 612) In order to compare investment costs both crystallizers are considered for the production of ice slurry from an aqueous solution with a eutectic temperature lower than ndash25degC for instance based on ethylene glycol The transition temperature difference for ice scaling in ethylene glycol solutions is about 50 higher than in aqueous solutions of KNO3 (see Section 24) This fact and the ice scaling prevention results of Section 634 are used to formulate maximum heat fluxes for ice slurry production from ethylene glycol solutions in both crystallizer types These maximum heat fluxes are subsequently used to formulate design heat fluxes as shown in Figure 620 These design heat fluxes are chosen at 70 of the maximum heat flux to exclude ice scaling with a maximum of 20 kWm2 High heat fluxes are preferred to reduce investment costs but a maximum heat flux of 20 kWm2 is chosen to avoid high energy consumption The overall heat transfer coefficient in both ice slurry generators is estimated at 2000 Wm2K which results in a logarithmic mean temperature difference of 10 K at 20 kWm2 Higher heat fluxes lead to higher logarithmic mean temperature differences resulting in rather low evaporation temperatures in the primary cycle and a high energy consumption A more detailed analysis on energy consumption is presented in Section 66

Chapter 6

128

0

5

10

15

20

25

-12 -10 -8 -6 -4 -2 0Ice slurry temperature (degC)

Hea

t flu

x (k

Wm

2 )SSHE

FBHE

0

100

200

300

400

500

10 100 1000 10000Cooling capacity (kW)

Inve

stm

ent c

osts

(eurok

W)

SSHE

FBHE -5degC

FBHE -10degC

FBHE -2degC

Figure 620 Design heat fluxes for ice slurry production in fluidized bed and scraped

surface heat exchangers as function of the ice slurry temperature

Figure 621 Investment costs of fluidized bed and scraped surface ice slurry generators for different ice slurry

temperatures and capacities

The investment costs per kilowatt of cooling capacity for both ice slurry generators are calculated on the basis of Equations 612 and 614 and the design heat fluxes shown in Figure 620 Due to the temperature dependence of the design heat flux the costs per kilowatt also depend on the ice slurry temperature In Figure 621 the investment costs of scraped surface ice slurry generators with an ice slurry temperature of ndash2degC or lower are compared with the costs of fluidized bed ice slurry generators with ice slurry temperatures of ndash2 ndash5 and ndash10degC The fluidized bed ice slurry generator operating with an ice slurry temperature of ndash2degC and a heat flux of 4 kWm2 is only less expensive for cooling capacities of 480 kW and larger because of the relatively large required heat transfer area However more substantial savings also at lower capacities are realized when an ice slurry temperature of ndash5degC is applied In this case investment costs decrease with 30 to 60 with respect to scraped surface ice slurry generators for systems of 100 kW and larger It is expected that the considerable lower investment costs of fluidized bed ice slurry generators can seriously reduce the costs of ice slurry system resulting in a more widespread use of ice slurry as secondary refrigerant

652 Maintenance Costs

In general little is know about the maintenance costs of both scraped surface and fluidized bed heat exchangers According to Stamatiou et al (2005) and Kauffeld et al (2005) the rotating blades or orbital rods in scraped surface heat exchangers wear over time and have to be replaced at a given time interval Quantitative information on the costs and the time intervals of these replacements is however not mentioned in literature Fluidized bed heat exchangers generally need less maintenance Rautenbach and Katz (1996) report that numerous fluidized bed installations in food paper and petrochemical industries operate for years without extensive maintenance measures In case of circulating fluidized bed operation tube inlets and outlets are subject to erosion and need replacement after several years of operation However the mass loss of particles due to erosion is less than 25 per year and the erosion of tubes is negligible (Kollbach 1987)


129

66 Energy Consumption

The energy consumption of ice slurry generators consists of the compressor power of the primary refrigeration cycle and the additional power required to prevent ice scaling The latter contribution in fluidized bed ice slurry generators is formed by the additional pump power to fluidize the steel particles In scraped surface ice slurry generators the additional power is consumed by the motors that drive the scraper blades or the orbital rods

661 Additional Power Consumption of Ice Slurry Generators

Fluidized Bed Ice Slurry Generators

The additional power required to fluidize steel particles is calculated from the extra pressure drop due to fluidization

( )( )p is tube1p g Lρ ρ ε∆ = minus minus ( 615)

The pressure drop per square meter of heat exchanging area is then given by

( )( )p is

he tube

1gpA D

ρ ρ επminus minus∆

= ( 616)

The required work per square meter of heat exchanging area to overcome this pressure drop with a flow rate Vamp is

( )( )p is s tubepd

he he

14

g u DW pVA A

ρ ρ εminus minus∆= =

amp amp (617)

This work is provided by a pump with an efficiency ηpump The power consumed by the pump is added to the ice slurry system and thus has to be removed by the primary cycle

( )( )p is s tubepump pdadd

he he he pump pump

14

g u DW WQA A A

ρ ρ ε

η η

minus minus= = =

amp ampamp ( 618)

The power consumption for the removal of ice crystals is obtained by using the efficiency of the motor that drives the pump

( )( )p is s tubepumpadd

he he motor pump motor

14

g u DWWA A

ρ ρ ε

η η η

minus minus= =

ampamp ( 619)

In this section a fluidized bed ice slurry generator is considered with a tube diameter of 45 mm and a fluidized bed consisting of stainless steel particles with a bed voidage of 81 resulting in a superficial velocity of 037 ms The pump and motor efficiencies are estimated at 60 and 80 respectively With these assumptions the extra energy input by the fluidized bed is 009 kWm2 and the additional power consumption is 011 kWm2

Chapter 6

130

Scraped Surface Ice Slurry Generators

Ice slurry generators with scraper blades usually show additional power consumptions of 12 to 18 kWm2 for rotating the scraper blades (Stamatiou et al 2005 Kauffeld et al 2005) The average of these values namely 15 kWm2 is used here for comparison with the other systems The energy input by the scraper blades is estimated at 12 kWm2 by using an electric motor efficiency of 80 Analogously the power consumption of orbital rods is reported to be about 022 kWm2 (Stamatiou et al 2005 Kauffeld et al 2005) With an electric motor efficiency of 80 their extra energy input into the ice slurry system is estimated at 018 kWm2

Comparison

A comparison of the additional energy inputs and power consumptions in Table 62 demonstrates that scraper blades have relatively high power consumptions compared to the other two removal mechanisms

Table 62 Comparison of additional energy input and power consumption Removal Qamp addAhe Wamp addAhe

mechanism (kWm2) (kWm2) Fluidized bed 009 011 Scraper blades 12 15

Orbital rods 018 022

The additional power consumption for the prevention of ice scaling can be related to the net cooling capacity of the ice slurry generator This relative additional power is obtained by dividing the additional power consumptions per square meter listed in Table 62 by the design heat fluxes shown in Figure 620 A comparison of the results in Figure 622 shows that for ice slurry temperatures of ndash2degC and lower the additional power consumption of scraper blades is about 8 of the net cooling capacity The relative additional power consumption of fluidized beds and orbital rods is significantly smaller namely less than 3

000

005

010

015

020


Scraper blades

Orbital rods

Fluidized bed

Rel

ativ

e ad

ditio

nal p

ower

Figure 622 Relative additional power consumption of various ice slurry generators


131

662 Compressor Power Consumption of Ice Slurry Generators

The heat that the primary refrigeration cycle removes from the ice slurry system is the sum of the net cooling capacity and the additional energy input by the ice scaling prevention mechanism

evap net addQ Q Q= +amp amp amp ( 620)

It is assumed that the primary cycle is a single stage compression cycle with ammonia as refrigerant and has a condensation temperature of 40degC and an isentropic compressor efficiency of 70 The evaporation temperatures of the primary refrigerant are deduced from the design heat fluxes shown in Figure 620 and an estimated overall heat transfer coefficient of 2 kWm2K for all three ice slurry generators (see Figure 623) The coefficient of performance of the primary cycle is calculated on the basis of these data and subsequently used to calculate the compressor power

net add

cyclecomp

Q QCOPW

+=amp amp

amp ( 621)

-25

-20

-15

-10

-5

0


scraper bladesOrbital rods or

Fluidized bed

Eva

pora

tion

tem

pera

ture

(degC

)

00

01

02

03

04

05

06


Scraper bladesOrbital rods

Fluidized bed

Rel

ativ

e co

mpr

esso

r po

wer

Figure 623 Design evaporation temperatures of various generators


The relative compressor power is defined as the ratio between the compressor power and the net cooling capacity Figure 624 shows that this parameter increases as the ice slurry temperature decreases for ice slurry temperatures below ndash2degC The explanation for this phenomenon is that the evaporation temperature decreases with decreasing ice slurry temperature This results in a lower coefficient of performance and thus in a higher required compressor power At temperatures close to 0degC the compressor power increases with increasing ice slurry temperature This trend is explained by the relatively high additional energy input as the ice slurry temperature approaches 0degC (see also Figure 622)

Chapter 6

132

663 Total Power Consumption of Ice Slurry Generators

The total coefficient of performance is defined as the ratio of the net cooling capacity and the power consumption of both the compressor and the ice scaling prevention mechanism

net

totalcomp add

QCOPW W

=+

amp

amp amp (622)

Figure 625 shows that the considered crystallizers should not be operated at ice slurry temperatures close to 0degC In this region the coefficient of performance seriously drops because the additional power consumptions of the removal mechanisms are relatively high

00

05

10

15

20

25

30

35


Scraper blades

Orbital rods

Fluidized bed

CO

P

Figure 625 Coefficients of performance as function of the ice slurry temperature for various

removal mechanisms

Section 65 has shown that investment costs of fluidized bed ice slurry generators of 100 kW and larger operated with an ice slurry temperature of ndash5degC are 30 to 60 lower than the investment costs of scraped surface ice slurry generators operated with an ice slurry temperature of ndash2degC Figure 625 shows that the coefficient of performance of this fluidized bed ice slurry generator is 5 higher than of ice slurry generators with orbital rods and 26 higher than of the ice slurry generators with scraper blades The cause for this higher coefficient of performance is the higher evaporation temperature of ndash10degC in case of the fluidized bed compared to ndash12degC for the case of the scraper blades or the orbital rods

664 Total Annual Costs of Ice Slurry Generators

In order to analyze both energy consumption and investment costs the total annual costs of the various ice slurry generators are considered here The annual investment costs are calculated by assuming a 5-year depreciation period with a 5 interest rate The energy costs are estimated by assuming an electricity price of 005 eurokWh and an average cooling load that is 50 of the installed capacity The total annual costs per kilowatt cooling capacity of the three crystallizers are shown in Figures 626 and 627 for installations of 100 kW and 1 MW respectively


133

0

50

100

150

200

250


Rel

ativ

e an

nual

cos

ts (euro

kW

) 100 kW


Fluidized bed

0

50

100

150

200

250


Rel

ativ

e an

nual

cos

ts (euro

kW

) 1 MW


Fluidized bed

Figure 626 Total annual costs per kW of various ice slurry generators for a 100 kW

system

Figure 627 Total annual costs per kW of various ice slurry generators for a 1 MW

system

The total costs of fluidized bed ice slurry generators shows minimums at ice slurry temperatures of ndash6 and ndash4degC respectively The applied heat flux at these ice slurry temperature is about 10 kWm2 while the logarithmic mean temperature difference in the heat exchanger is approximately 5 K The lowest total costs of ice slurry generators with orbital rods or scraper blades are achieved when ice slurry temperatures of ndash2degC are applied The heat flux at these conditions is 10 kWm2 with a logarithmic mean temperature difference of 10 K A comparison of the three different crystallizers for capacities between 100 kW and 1 MW shows that the minimum total costs of fluidized bed ice slurry generators is 17 to 29 lower than the minimum total costs of ice slurry generators with scraper blades or orbital rods

67 Conclusions

The temperature difference between wall and slurry at which ice scaling is just prevented in a scraped surface ice slurry generator also referred to as transition temperature difference increases with decreasing ice slurry temperature or increasing solute concentration This trend is in correspondence with the fluidized bed ice slurry generator However the transition temperature difference in scraped surface ice slurry generators is about 75 times higher for the same solution while the heat flux at which ice scaling occurs is more than four times higher The heat transfer coefficients of both type of crystallizers are comparable

Due to the low ice scaling prevention ability at temperatures close to 0degC fluidized bed ice slurry generators should be operated at ice slurry temperatures of about ndash5degC with a heat flux of approximately 10 kWm2 Scraped surface ice slurry generators are often operated with an ice slurry temperature of ndash2degC and a heat flux of 20 kWm2 A comparison between these two systems for capacities of 100 kW and larger shows that the investment costs of crystallizers with fluidized beds are about 30 tot 60 lower than of scraped surface ice slurry generators Furthermore the energy consumption of fluidized bed ice slurry generators is about 5 to 21 lower It can therefore be concluded that the fluidized bed ice slurry generator is an attractive ice crystallizer concerning both investment costs and energy consumption

Chapter 6

134

Nomenclature

A Area (m2) Vamp Volume flow (m3s) cp Specific heat (Jkg K) Wamp Power (W) COP Coefficient of performance w Solute mass fraction Dtube Tube diameter (m) Dp Equivalent particle diameter (m) Greek Dscr Scraper diameter (m) α Heat transfer coefficient (Wm2K) G Growth rate (ms) δ Thickness (m) g Gravity (ms2) ε Bed voidage I Investment costs (keuro) η Efficiency k Mass transfer coefficient (ms) λ Thermal conductivity (Wm K) L Length (m) micro Viscosity (Pa s) N Scraper passes per second (1s) ρ Density (kgm3) Nuscr Liquid Nusselt number α Dscrλliq Nuh Hydraulic Nusselt number Subscripts αi Diinnerλliq add Additional p Pressure (Pa) comp Compressor ∆p Pressure drop (Pa) crys Crystallizer Prliq Liquid Prandtl number cpliq microliqλliq cool Coolant ampQ Heat (W) eq Equilibrium

R Removal rate (ms) FBHE Fluidized bed heat exchanger Reliq Liquid Reynolds number he Heat exchanger ρliq u Diinnermicroliq ice Ice Reh Hydraulic Reynolds number in Inlet ρliq u Diinnermicroliq is Ice slurry Ret Liquid Reynolds number KNO3 Potassium nitrate ρliq N Diinnermicroliq liq Liquid T Temperature (degC) min Minimum Tfr Initial freezing temperature (degC) motor Motor ∆Tln Logarithmic mean temperature net Net difference (K) out Outlet ∆Ttrans Transition temperature difference p Particle (K) pd Pressure drop t Time (s) plate Plate U Overall heat transfer coefficient pump Pump (Wm2K) scr Scrapers us Superficial velocity (ms) SSHE Scraped surface heat exchanger STHE Shell-and-tube heat exchanger

References

Bel O Lallemand A 1999 Etude drsquoun fluide frigoporteur diphasique ndash 2 Analyse expeacuterimentale du comportement thermique et rheacuteologique International Journal of Refrigeration vol22 pp175-187



135

Ben Lakhdar M Cerecero R Alvarez G Guilpart J Flick D Lallemand A 2005 Heat transfer with freezing in a scraped surface heat exchanger Applied Thermal Engineering vol25 pp45-60

Chhabra RP 1995 Wall effects on free-settling velocity of non-spherical particles in viscous media in cylindrical tubes Powder Technology vol85 pp83-90

Chhabra RP Agarwal L Sinha NK 1999 Drag on non-spherical particles An evaluation of available methods Powder Technology vol101 pp288-295

Drewett EM Hartel RW 2006 Ice crystallization in a scraped surface freezer Journal of Food Engineering in press

EPS Ltd 2006 Orbital Rod Evaporator Capacity Curves httpwwwepsltdcouk

Field BS Kauffeld M Madsen K 2003 Use of ice slurry in a supermarket display cabinet In Proceedings of 21st IIR International Congress of Refrigeration 17-23 August 2003 Washington DC (USA) Paris International Institute of Refrigeration

Gladis SP Marciniak MJ OHanlon JB Yundt B 1996 Ice crystal slurry TES system using orbital rod evaporator In Conference Proceedings of the EPRI International Conference on Sustainable Thermal Energy Storage 7-9 August 1996 Bloomington (USA)

Gladis S 1997 Ice slurry thermal energy storage for cheese process cooling ASHRAE Transactions vol103 part 2 pp725-729

GMF 1992 Personal communication Goudsche Machine Fabriek BV Gouda (The Netherlands)


Haid M Martin H Muumlller-Steinhagen H 1994 Heat transfer to liquid-solid fluidized beds Chemical Engineering and Processing vol33 pp211-225


Jellema P Nijdam JL 2005 Ice slurry production under vacuum In Proceedings of the 6th IIR Workshop on Ice Slurries 15-17 June 2005 Yverdon-les-Bains (Switzerland) Paris International Institute of Refrigeration pp74-78

Katz T 1997 Auslegung und Betrieb von Wirbelschichtwaumlrmeaustauscher PhD Thesis RWTH Aachen (Germany)


Kiatsiriroat T Vithayasai S Vorayos N Nuntaphan A Vorayos N 2003 Heat transfer prediction for a direct contact ice thermal energy storage Energy Conversion and Management vol44 pp497-508

Chapter 6

136

Kollbach JS 1987 Entwicklung eines Verdampfungsverfahrens met Wirbelschicht-Waumlrmeaustauscher zum Eindampfen krustenbildender Abwaumlsser PhD Thesis RWTH Aachen (Germany)

Kurihara T Kawashima M 2001 Dynamic ice storage system using super cooled water In Proceedings of the 4th IIR Workshop on Ice Slurries 12-13 November 2001 Osaka (Japan) Paris International Institute of Refrigeration pp61-69



Mil PJJM van Bouman S 1990 Freeze concentration of dairy products Netherlands Milk Dairy Journal vol44 pp21-31

Mito D Mikami Y Tanino M Kozawa Y 2002 A new ice-slurry generator by using actively thermal-hydraulic controlling both supercooling and releasing of water In Proceedings of the 5th IIR Workshop on Ice Slurries 30-31 May 2002 Stockholm (Sweden) Paris International Institute of Refrigeration pp185-196

Nagato H 2001 A dynamic ice storage system with a closed ice-making device using supercooled water In Proceedings of the 4th IIR Workshop on Ice Slurries 12-13 November 2001 Osaka (Japan) Paris International Institute of Refrigeration pp97-103

Nelson KP Pippin J Dunlap J 1999 University ice slurry system In 12th Annual IDEA College-University Conference 10-12 February 1999 New Orleans (USA) Westborough International District Energy Association

Nelson KP 1998 Ice slurry generator In 89th Annual IDEA Conference 13-16 June 1998 San Antonio (USA) Westborough International District Energy Association



Paul J 1996 Compressors for refrigerating plants and ice makers with water as refrigerant In Applications for Natural Refrigerants 3-6 September 1996 Aarhus (Denmark) Paris International Institute of Refrigeration pp577-584

Paul J Jahn E Lausen D Schmidt K-P 1999 Chillers and ice machines with ldquowater as refrigerantrdquo In Proceedings of 20th IIR International Congress of Refrigeration 19-24 September 1999 Sydney (Australia) Paris International Institute of Refrigeration


137


Qin FGF Chen XD Ramachandra S Free K 2006 Heat transfer and power consumption in a scraped-surface heat exchanger while freezing aqueous solutions Separation and Purification Technology vol48 pp150ndash158

Qin FGF Chen XD Russell AB 2003 Heat transfer at the subcooled-scraped surface withwithout phase change AIChE Journal vol49 pp1947-1955


Richardson JF Zaki WN 1954 Sedimentation and fluidization Transactions of the Institute of Chemical Engineers vol32 pp35-53

Roos AC Verschuur RJ Schreurs B Scholz R Jansens PJ 2003 Development of a vacuum crystallizer for the freeze concentration of industrial waste water Chemical Engineering Research and Design vol81 part A pp881ndash892

Sari O Egolf PW Ata-Caesar D Brulhart J Vuarnoz D Lugo R Fournaison L 2005 Direct contact evaporation applied to the generation of ice slurries modelling and experimental results In Proceedings of the 6th IIR Workshop on Ice Slurries 15-17 June 2005 Yverdon-les-Bains (Switzerland) Paris International Institute of Refrigeration pp57-72

Sheer TJ Butterworth MD Ramsden R 2001 Ice as a coolant for deep mines In Proceedings of the 7th International Mine Ventilation Congress 17-22 June 2001 Krakow (Poland) pp355-361

Soe L Hansen T Lundsteen BE 2004 Instant milk cooling system utilising propane and either ice slurry or traditional ice bank In Proceedings of the 6th IIR Gustav Lorentzen Conference on Natural Working Fluids 29 August-1 September 2004 Glasgow (UK) Paris International Institute of Refrigeration

Stamatiou E 2003 Experimental Study of the Ice Slurry Thermal-Hydraulic Characteristics in Compact Plate Heat Exchangers PhD thesis University of Toronto (Canada)

Stamatiou E Kawaji M 2003 Heat transfer characteristics in compact scraped surface ice slurry generators In Proceedings of 21st IIR International Congress of Refrigeration 17-23 August 2003 Washington DC (USA) Paris International Institute of Refrigeration


Tanino M Kozawa Y Mito D Inada T 2000 Development of active control method for supercooling releasing of water In Proceedings of the 2nd IIR Workshop on Ice Slurries 25-26 May 2000 Paris (France) Paris International Institute of Refrigeration pp127-139

Chapter 6

138

Trommelen AM Beek WJ Westelaken HC van de 1971 A mechanism for heat transfer in a Votator-type scraped-surface heat exchanger Chemical Engineering Science vol26 pp1987-2001



Vaessen RJC Seckler MM Witkamp GJ 2004 Heat transfer in scraped eutectic crystallizers International Journal of Heat and Mass Transfer vol47 pp717-728

Vuarnoz D Sletta J Sari O Egolf PW 2004 Direct injection ice slurry generator In Proceedings of the 6th IIR Gustav Lorentzen Conference on Natural Working Fluids 29 August-1 September 2004 Glasgow (UK) Paris International Institute of Refrigeration

Wakamoto S Nakao K Tanaka N Kimura H 1996 Study of the stability of supercooled water in an ice generator ASHRAE Transactions vol102 part 2 pp142-150


Wang MJ Lopez G Goldstein V 2002 Ice slurry for shrimp farming and processing In Proceedings of the 5th IIR Workshop on Ice Slurries 30-31 May 2002 Stockholm (Sweden) Paris International Institute of Refrigeration pp161-168

Wijeysundera NE Hawlader MNA Andy CWB Hossain MK 2004 Ice-slurry production using direct contact heat transfer International Journal of Refrigeration vol27 pp511-519

Zakeri GR 1997 Vacuum freeze refrigerated circuit (VFRC) a new system design for energy effective heat pumping applications In Proceedings of the IIRIIF Linz lsquo97 Conference Heat Pump Systems Energy Efficiency and Global Warming 28 September-1 October 1997 Linz (Austria) Paris International Institute of Refrigeration pp182-190

Zwieg T Cucarella V Worch H 2002 Novel bio-mimetically based ice-nucleating coatings for ice generation In Proceedings of the 5th IIR Workshop on Ice Slurries 30-31 May 2002 Stockholm (Sweden) Paris International Institute of Refrigeration pp142-150

139

7 Long-term Ice Slurry Storage

71 Introduction

Ice slurries are interesting secondary refrigerants compared to single-phase fluids since they use the latent heat of ice resulting in high heat capacities An important advantage of this high heat capacity is the possibility of cold storage where ice slurry is produced during off-peak hours and is stored in insulated tanks for later use Cold storage with ice slurry can lead to economic and environmental benefits such as reduced installed refrigeration power lower average electricity tariffs and lower energy consumption due to lower condensing temperatures in the primary refrigeration cycle during nighttime operation (see Chapter 1)

Ice slurry can be stored as a homogeneous or heterogeneous suspension In case of homogeneous storage (see Figure 71) a stirring device keeps the ice crystals in suspension which is achievable for ice fraction up to 35 wt (Christensen and Kauffeld 1998) In case of heterogeneous storage (see Figure 72) the tank does not contain a stirring device and as a result the ice crystals float to the top of the tank and the lower part of the tank contains only liquid (Kozawa et al 2005)

Figure 71 Homogeneous ice slurry storage

(Egolf et al 2001) Figure 72 Heterogeneous ice slurry storage

(adapted from Kozawa et al 2005)

An advantage of homogeneous storage compared to heterogeneous storage is the possibility to pump ice crystals to the application heat exchangers which is beneficial since the high heat capacity of ice is then also applied in these heat exchangers and in the piping network A disadvantage of homogeneous storage is however the required mixing power to maintain a homogeneous suspension According to Christensen and Kauffeld (1998) approximately 70 Wm3 mixing power is required to keep an ice slurry homogeneously mixed In their experiments Christensen and Kauffeld used ice slurries made of a 10 wt ethanol solution with an density of approximately 980 kgm3 The density difference between the solution and the ice crystals (917 kgm3) was therefore relatively resulting in a relatively low required mixing power It is expected that the required mixing power is higher in aqueous solutions with higher densities which is the case for most other solutions discussed in this thesis Parts of this chapter have been published in the International Journal of Refrigeration vol28 pp27-36 2005 and in the Journal of Crystal Growth vol275 ppe1361-e1367 2005

Chapter 7

140

Egolf et al (2001) proposed to combine the advantages of both storage methods Their proposal consisted of a storage tank without mixing device from which ice slurry with a high ice fraction is pumped from the top and is mixed with liquid from the bottom (see Figure 73) In this way every desired ice fraction can be achieved It is also possible to operate with an intermittent mixing device that is switched off when no cooling load is applied Meili et al (2001) showed that stratified slurries with all ice crystals floating on the top can easily be turned into an homogeneously suspension by mixing even after 15 hours without mixing

Figure 73 Heterogeneous ice slurry storage with mixing device (Egolf et al 2001)

If heat uptake from the surroundings and mixing power are neglected storage of ice slurry can be considered as an adiabatic process with a virtually constant temperature and ice fraction Although the amount of ice hardly changes during storage the size and shape of crystals may alter due to recrystallization mechanisms Changes in size and shape are supposed to have significant influences on other components of an ice slurry system For example Kitanovski and Poredoš (2002) showed that an increased average crystal size has an effect on the rheological behavior of ice slurry in pipes Analogously Frei and Egolf (2000) measured different pressure drop values for freshly produced ice slurry and for the same ice slurry after storage probably caused by difference in crystal size Furthermore it is shown in Chapter 8 that the average ice crystal size influences the performance of heat exchangers Large crystals with a relatively small surface-to-volume ratio will cause higher superheating values at heat exchanger outlets resulting in reduced cooling capacities Finally crystal characteristics might also have an effect on pump performance and on the minimum required power to keep the ice slurry homogeneously mixed in a storage tank

Next to ice slurry systems for refrigeration recrystallization of ice crystals during storage is also interesting for other industrial processes such as freeze concentration and long-term storage of ice cream In freeze concentration processes ice crystals are stored for a certain period in order to increase the average crystal size which enables a more efficient washing of the crystals in wash columns (Huige and Thijssen 1972 Verschuur et al 2002) In case of ice cream storage the ice crystal size strongly determines the product quality and therefore several investigations have been carried out on the role of storage conditions on crystal sizes (Adapa et al 2000 Donhowe and Hartel 1996 Hagiwari and Hartel 1996)

The objective of this chapter is to give more insight in the physical phenomena that alter ice crystals during adiabatic storage The development of the ice crystals size distribution during adiabatic storage is experimentally studied for ice crystals stored in different solutions Subsequently the obtained experimental results and results from other researchers are used to develop a computer-based dynamic model of ice crystals in aqueous solutions placed in

Long-term Ice Slurry Storage

141

adiabatic storage tanks Finally this model is used to simulate the development of the ice crystal size distribution in time and is validated with the experimental results

72 Recrystallization Mechanisms

When ice crystals are stored in a saturated aqueous solution three mechanisms are distinguished that may alter its size and shape namely attrition agglomeration and Ostwald ripening These three mechanisms are separately discussed in this section

721 Attrition

In mechanically agitated vessels crystals can be damaged by collisions with solids such as the stirrer the walls or other crystals All these kinds of damaging mechanisms are called attrition In general two types of attrition can be distinguished namely breakage and abrasion (Mazzarotta 1992) In case of breakage the collision energy is relatively high and the collision subdivides the initial crystal into a number of fragments with a wide spectrum of sizes When the collision energy is not high enough to break the crystal into numerous pieces it may occur that only a small part of the crystal will be pulled off This phenomenon is called abrasion The fragments produced by abrasion are in most cases much smaller than the parent crystals In order to study abrasion Biscans et al (1996) carried out experiments with a suspension of sodium chloride crystals and acetone which is an anti-solvent for these crystals In these experiments the size of the initial crystals ranged from 100 to 500 microm while the fragments produced by abrasion ranged from 5 to 50 microm (see Figure 74) Besides the production of small fragments abrasion will round off the parent crystals

00

01

02

03

04

05

1 10 100 1000Crystal size (microm)

Mas

s fr

actio

n (-

)

(a)

00

01

02

03

04

05


Mas

s fr

actio

n (-

)

(b)

Figure 74 Crystal size distributions before (a) and after (b) an attrition experiment of 12 hours (Biscans et al 1996)

In literature no information is available for attrition effects on ice crystals but the attrition behavior of ice crystals can be deduced from a comparison with other crystals Gahn and Mersmann (1995) carried out experiments to study the attrition behavior of several kinds of crystals From these experiments it was concluded that the crystals with high hardness values are more sensitive for attrition than softer crystals The hardness of ice strongly depends on the temperature and varies between 0 to ndash15degC from 10 to 100 MPa which are rather low values compared to other crystals (Barnes et al 1971) As far as the hardness is concerned ice

Chapter 7

142

crystals can be compared with sodium chloride crystals and potassium chloride crystals with hardness values of 166 MPa and 91 MPa respectively (Gahn and Mersmann 1995) In spite of the low hardness sodium chloride crystals are affected by abrasion as was shown by Biscans et al (1996) Since hardness values are comparable it is therefore expected that ice crystals are also affected by abrasion It is however not expected that breakage of crystals will occur in ice slurry systems

722 Agglomeration

Agglomeration or accretion is the adherence of two small crystals resulting in one large polycrystalline particle In case of strong agglomeration the average diameter of crystals increases seriously while the number of crystals decreases According to Kasza and Hayashi (1999) ice crystals have a strong tendency to agglomerate in storage tanks and it is therefore important to study this phenomenon

In order to study agglomeration of ice crystals in solution Shirai et al (1987) carried out experiments in which ice crystals were produced and stored in lactose and glucose solutions with different concentrations Microscopic pictures of ice crystals after storage clearly indicated whether agglomeration had occurred since agglomerated crystals could clearly be distinguished from mono-crystalline crystals During the experiments with lactose solutions agglomeration was only observed at concentrations of 10 wt lactose (Tfr=ndash06degC) and not in solutions of 15 wt (Tfr=ndash10degC) A similar phenomenon was observed for glucose solutions in which agglomeration took place in solutions of 5 75 and 10 wt with freezing temperatures of ndash06 ndash09 and ndash12degC respectively but not in a 15 wt solution with a freezing temperature of ndash19degC Kobayshi and Shirai (1996) experimentally confirmed the strong influence of solutes on agglomeration During storage experiments with glucose solutions extensive agglomeration did only occur at glucose concentrations of 10 wt (Tfr=ndash12degC) and lower but not with concentrations of 20 wt (Tfr=ndash27degC) and 30 wt (Tfr=ndash47degC) In experiments with agglomeration the average ice crystal size increased from 100 to 500 microm at the start to 1 to 3 mm after two hours of storage Finally Hayashi and Kasza (2000) observed similar trends during storage experiments with ethylene glycol solutions during which agglomeration only occurred at concentrations below 04 wt (Tfr=ndash01degC)

723 Ostwald Ripening

Ice slurries normally consist of a spectrum of crystal sizes both large and small Due to surface energy contributions small ice crystals have a lower equilibrium temperature than larger ones During isothermal storage of ice slurries these differences in equilibrium temperature result in the growth of large ice crystals and the melting of small ones This phenomenon is called Ostwald ripening or migratory recrystallization and provides an increase in average crystal size over relatively long periods

Theory

The difference in equilibrium temperature between differently sized crystals is deduced from the free Gibbsrsquo energy of a single crystal with respect to the liquid phase (Nielsen 1964)

32V

Am

n micro microB LG A B LV

γ γ∆ = ∆ + = ∆ + (723)


143

In this equation n represents the number of moles in the crystal γ is the surface tension between the crystal and the liquid A is the total surface of the crystal Vm is the molar volume of the solid state BV is the volume shape factor and BA is the surface shape factor Parameter ∆micro is the difference in chemical potential of water between the solid and the liquid state

liq sol smicro micro ( ) -micro ( )T w T∆ = (724)

Equation 72 can be rewritten into the following equation since the chemical potential of the solid state equals the chemical potential of the liquid at equilibrium conditions of a crystal with infinite dimensions

( ) ( ) liq sol liq sol s s liq sol smicro micro ( ) -micro ( ) - micro ( ) -micro ( ) since micro ( ) micro ( )T w T w T T T w Tinfin infin infin infin∆ = = (725)

The chemical potential of the liquid state can be split up into a concentration dependant and independent contribution

( ) ( ) sol

0liq 0liq s ssol

( )micro ln micro ( ) -micro ( ) - micro ( ) -micro ( )( )T wRT T T T TT w

ψψ infin infin

infin

∆ = +

(726)

Since the activity coefficient Ψ is only a weak function of temperature the ratio of the activity coefficients in the first term is close to unity as a result of which the contribution of the first term can be neglected Subsequently the differences in chemical potential of the liquid and the solid state at different temperatures can be calculated with the integral over the entropy

( ) ( )

fliq s f f fmicro - - - - since

T T

T T

hs dT s dT s T T T T h T sT

infin infin

infin infin infininfin

∆∆ = + = ∆ = ∆ = ∆int int (727)

Equations 723 and 727 can be combined into Equation 728

( )3

2V fA

m

-B L hG T T B LV T

γinfininfin

∆∆ = + (728)

A crystal with size L is in equilibrium with the surrounding liquid when its free Gibbsrsquo energy reaches its minimum

( ) 0d G

dL∆

= (729)

Applying Equation 77 to Equation 728 results in the equilibrium temperature of a crystal with size L

A

V ice f

2( ) 1-3

BT L TB h L

γρinfin

= ∆

(730)

Chapter 7

144

Previous Studies on Ostwald Ripening in Ice Slurries

A number of experimental studies have been carried out on Ostwald ripening in ice slurries during isothermal storage In several of these studies ripening experiments were performed with ice crystals in thin liquid films placed under a microscope (Savory et al 2002 Sutton et al 1994 Sutton et al 1996 Williamson et al 2001) Since convection did not occur in the films the location of ice crystals did not change during storage and the evaluation of individual crystals could be observed Microscopic pictures were taken at regular intervals to analyze the growth or dissolution of ice crystals All these studies suggest that Ostwald ripening is the main recrystallization mechanism for the tested conditions since small crystals became smaller and larger ones grew However during some experiments agglomeration of small crystals was also observed Analyses of the shapes of crystal size distributions after storage and the developments of the average crystal size in time indicated that the crystallization kinetics of Ostwald ripening can be considered diffusion controlled for the tested conditions

In other experimental studies Ostwald ripening of ice slurries was investigated during isothermal storage in mixed or unmixed tanks The operating conditions of these experiments were much closer to the storage conditions of ice slurries for refrigeration applications as discussed in Chapter 1 Because of this agreement these experimental studies are discussed in more detail below

Huige and Thijssen (1972) proposed using Ostwald ripening to increase the average ice crystal size of ice slurries produced from sucrose solutions (see also Huige 1972) Ice slurry was produced in a scraped-surface crystallizer with a mean residence time of only five seconds resulting in ice crystal sizes of about 10 to 20 microm These small nuclei were added to a recrystallization tank which contained larger crystals whose residence time was varied at values of 115 20 and 32 hours Since neither cooling nor heating was applied to the slurry in the recrystallization tank the temperature in the tank was between the equilibrium temperature of large crystals and the equilibrium temperature of the small crystals (see Equation 730) As a result the smaller crystals dissolved and the larger grew even larger resulting in an increase of the average crystals size in time Through their experimental study Huige and Thijssen showed that applied method can be used to produce large ice crystals which is very useful in freeze concentration processes where the efficiency of wash columns increases with the average ice crystal size

Smith and Schwartzberg (1985) studied Ostwald ripening of ice crystals in aqueous solutions in more detail (see also Smith 1984) In their experiments they produced ice slurry from aqueous sucrose solutions with different concentrations varying from 9 to 36 wt After production up to ice fractions of 9 to 16 wt ice crystals with an average diameter of about 100 microm were stored in an insulated homogeneously mixed tank of 10 liter The experimental results displayed in Figure 75 clearly show that Ostwald ripening changes the crystal size distribution in a sucrose solution with an initial concentration of 9 wt and an ice fraction of 16 wt The average crystal size increased from 90 to 250 microm within five hours of storage Storage experiments with different sucrose solutions showed that the ripening rate decreases strongly with increasing sucrose concentrations (see Figure 76) Smith and Schwartzberg explained the slower ripening process at higher concentrations of sucrose by the lower mass transfer rate of crystal growth and dissolution at higher concentrations


145

00020406081012141618

0 50 100 150 200 250 300 350Crystal diameter (microm)

Num

ber

dens

ity (1

06 1

m) Initial

After 1 hr

After 2 hrs

After 3 hrs

0

50

100

150

200

250

0 1 2 3 4 5 6Storage time (hours)

Ave

rage

dia

met

er (micro

m)

10

15

223342

Figure 75 Development of ice crystal size distribution during Ostwald ripening in a 9 wt sucrose solution (adapted from Smith

and Schwartzberg 1985)

Figure 76 Ostwald ripening of ice crystals in different sucrose solutions (adapted from

Smith and Schwartzberg 1985)

In some of their storage experiments Smith and Schwartzberg (1985) added relatively small amounts of gelatin to a sucrose solution of 10 wt The experiments showed that gelatin concentrations of 001 to 005 seriously slowed down Ostwald ripening to rates comparable with the ripening rate in sucrose solutions of 22 to 44 wt Smith and Schwartzberg ascribed this phenomenon to a strong reduction of mass transfer coefficients by gelatin

Ice slurry storage experiments in a continuously mixed 6-liter tank with solutions of sucrose and betaine by Louhi-Kultanen (1996) confirmed the strong influence of the solute concentration on Ostwald ripening described above For both sucrose and betaine solutions the ripening rate was significantly lower at solute concentrations of 15 wt compared to 8 wt

Hansen et al (2003) performed ice storage experiments with ethanol and propylene glycol solutions with initial concentrations of 10 (Tfr=ndash43degC) and 15 wt (Tfr=ndash51degC) respectively (see also Hansen et al 2002) Ice slurries with ice fractions of 10 and 30 wt were homogeneously stored in a 1000 liter tank and ice slurries with ice fractions of 30 and 46 wt were heterogeneously stored in a 285 liter tank For both storage methods ice crystals were isothermally stored for about 90 hours The crystal size distribution of the stored ice crystals was determined by analyzing microscopic pictures of ice crystals after 0 20 40 and 90 hours of storage The results displayed in Figure 77 show that the average crystal size increased during all experiments as a result of Ostwald ripening For one experiment the average crystal size even increased from 100 microm to more than 500 microm after 90 hours of storage In general it was concluded from all experiments that the ripening rate was higher during experiments with lower ice fractions Furthermore it appeared that the ripening rate was higher during homogeneous storage than during heterogeneous storage Finally Ostwald ripening in the 10 wt ethanol solution was faster compared to the 15 wt propylene glycol solution

Chapter 7

146

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100Storage time (hours)

Ave

rage

cry

stal

siz

e (micro

m)

pg-m-30 eth-m-10 eth-m-30 pg-t-30 pg-t-46 eth-t-30 eth-t-46

15 wt PG homo φ =01015 wt PG homo φ =03010 wt EtOH homo φ =01010 wt EtOH homo φ =03015 wt PG hetero φ =03015 wt PG hetero φ =04610 wt EtOH hetero φ =03010 wt EtOH homo φ =046

Figure 77 Development of average crystal size during homogeneous and heterogeneously storage at different ice fraction in two different solutions (adapted from Hansen et al 2003)

Besides the described experiments Hansen et al (2002) experimentally studied the influence of air access and a surfactant (015 wt polyoxyethylensorbitan-trioleate) on the ripening process However during the experiments no significant influence on crystal size distributions was observed of neither air access nor the surfactant

724 Conclusions

From the analysis of the three recrystallization mechanisms described in this section can be concluded that Ostwald ripening is likely the most important mechanism altering the crystal size distribution during ice slurry storage for thermal storage applications The average crystal size can increase seriously as a result of Ostwald ripening in isothermally stored ice slurries Attrition might occur in storage tanks by contacts with the mixer the walls or other ice crystals In this respect it is most likely that only abrasion takes place and no breakage which means that only small fragments are pulled off larger crystals These small fragments will however dissolve as a result of Ostwald ripening and the crystal mass will subsequently be attached to the larger crystals in the storage tank Agglomeration might occur in ice slurry tanks for thermal storage especially when low amounts of freezing point depressants are applied However in most applications with ice slurry temperatures below ndash1degC agglomeration plays a minor role

73 Experiments on Ice Slurry Storage

The literature review in the previous section revealed that Ostwald ripening is likely the main recrystallization mechanism during ice slurry storage for thermal storage applications In order to obtain more knowledge on parameters that determine the rate of Ostwald ripening in different ice slurries experiments were performed with different solutions of both sodium chloride and ethylene glycol Only homogeneous storage was studied experimentally and in this respect the influence of the mixing rate was investigated


147


For the ice slurry storage experiments an experimental setup as shown in Figure 78 was applied

Figure 78 Experimental setup for ice slurry storage experiments

The main part of the experimental setup is a stirred crystallizer which consists of a double-wall cylindrical glass tank The inner diameter of the tank is 125 mm and its inner height is 130 mm The outside of the tank is insulated to minimize heat uptake The fluid in the vessel can be mixed with a circulator impeller with 3 blades and has a diameter of 47 mm A variable speed motor drives the impeller with a controllable frequency between 40 and 2000 RPM The temperature of the fluid inside the tank is measured with a PT-100 element which is connected to an ASL F250 temperature measurement set This combination enables temperature measurements within an accuracy of 001 K

During the experiments the tank was filled with 10 kg of aqueous solution of sodium chloride (NaCl) or ethylene glycol (EG) of the desired concentration Pure ethylene glycol was pumped through the annular space between the two glass walls to control the temperature inside the tank A low-temperature thermostat controlled the temperature of ethylene glycol

732 Experimental Procedure

The experimental procedure is described here by means of Figure 79 At the start of an experiment the temperature of ethylene glycol in the thermostat was set at a value of 30 K below the initial freezing temperature of the solution inside the vessel In case of the lowest NaCl concentration (26 wt) this value was only 15 K to avoid ice scaling on the wall The initial number of revolutions of the impeller was set at 400 RPM At a certain degree of supercooling (∆Tmaxsuper) initial nucleation of crystals was forced by putting a small steel rod in contact with the impeller After formation of the first crystals crystallization was continued until an ice fraction of approximately 14 wt was reached At this moment the temperature of ethylene glycol was increased in order to provide global thermal equilibrium in the tank and to keep the ice fraction constant The temperature difference for equilibrium was deduced from another experiment in which the temperature of ethylene glycol was constant and the temperature of the solution inside the vessel was measured after a long time After the increase of the ethylene glycol temperature ice slurry was stored for at least 22 hours with a constant mixing rate temperature and ice fraction

Chapter 7

148

-70

-60

-50

-40

-30

-20

-10

00

-2 -1 0 1 2Time (hours)

Tem

pera

ture

(degC

)

Slurry in tankInlet ethylene glycol

CrystallizationCooling Storage

Seeding

∆T maxsuper

24

Figure 79 Temperature profiles during experiment 2 (see Table 71)

Just after the onset of storage a sample of produced ice slurry was taken from the tank The ice crystals in this sample were photographed with a microscope and a CCD camera The microscope was equipped with a thermostatic glass which ensured that the crystals of the sample would neither melt nor grow during the observation After 2 6 and 22 hours this procedure was repeated in order to investigate the development of crystal size and shape in time The ice crystals on the 2-D photographs were analyzed by measuring both the projected area (Ap) and the perimeter (P) At least 80 crystals were measured from each ice slurry sample

For each single crystal the projected area and the perimeter were used to calculate two characteristics parameters The first parameter is the Feret diameter and is defined as the diameter of a circle with the same area as the projection of the crystal

p

Feret

4 AD

π= (731)

The second parameter is the roundness and is defined as the ratio between the perimeter of a circle with the same area as the crystal and the crystal perimeter

FeretDΓP

π= (732)

The roundness varies between 0 and 1 If the roundness is close to 1 the crystal is almost circular As the ratio decreases from 1 the object departs from a circular form

733 Results

During this study five experiments with different conditions were carried out An overview of the experimental conditions is given in Table 71


149

Table 71 Experimental series of ice slurry storage experiments No Solute type Solute

concentration Initial freezing

temperature Temperature

during storageIce fraction

during storage Mixing rate

during storage (wt) (degC) (degC) (wt) (RPM)

1 NaCl 26 ndash15 ndash18 15 400 2 NaCl 49 ndash30 ndash35 15 400 3 NaCl 92 ndash60 ndash71 14 400 4 NaCl 49 ndash30 ndash35 15 750 5 EG 166 ndash62 ndash77 15 400

Four typical microscopic photographs of experiment 2 are shown in Figure 710 The photos have the same scale and were taken after 0 2 6 and 22 hours of storage as described above The four photos clearly show that the crystal size increases in time It is supposed that the main cause for this increase is Ostwald ripening and that agglomeration plays a minor role Two typical examples of agglomeration can be seen in Figure 710c and Figure 710d in which it is obvious that two crystals are cemented together and became one crystal However this cementing behavior is only observed for the minority of the crystals It seems that some ice crystals in Figure 710a and Figure 710b are also agglomerated but in reality they are only overlapping each other forming flocks

a b

c d

Figure 710 Microscopic photographs of experiment 2 (a) 0 hours (b) 2 hours (c) 6 hours and (d) 22 hours of storage

From crystal measurements crystal size distributions were constructed and characteristic parameters such as Feret diameter and roundness were calculated Figure 711 shows the

Chapter 7

150

crystals size distributions at the four sampling moments during experiment 2 In these crystal size distributions the crystals are divided into classes of 100 microm Because the change in crystal size is not quite clear in this figure the development of crystal sizes is also shown in Figure 712 by means of cumulative crystal size distributions From this figure it is more obvious that the average crystal size increases in time

00

01

02

03

04

0 250 500 750 1000 1250Feret diameter (microm)

Num

ber

frac

tion

(10 4 1

m) 0 h

2 h6 h22 h

00

02

04

06

08

10


Cum

ulat

ive

num

ber

frac

tion

(-)

0 h2 h6 h22 h

Figure 711 Development of crystal size distributions in time for experiment 2

Figure 712 Development of cumulative crystal size distributions in time for

experiment 2

Effect of Solute Type and Concentration

Figure 713 shows that the increase of the Feret diameter in time is smaller in solutions with higher sodium chloride concentrations This observation is in accordance with the studies mentioned in Section 723 The figure also shows that Ostwald ripening was slower in a ethylene glycol solution than in a sodium chloride solution with approximately the same freezing temperature (92 wt NaCl and 166 wt EG)

0

100

200

300

400

500

0 4 8 12 16 20 24Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)

26 wt NaCl49 wt NaCl92 wt NaCl166 wt EG

Figure 713 Development of average Feret diameter for different types of ice slurry

Figure 714 shows that the roundness of crystals slightly increases during storage for all types of ice slurries Besides it can be concluded that ice slurries with lower solute concentrations resulted in rounder crystals


151

080

085

090

095

100

0 4 8 12 16 20 24Time (hours)

Ave

rage

cry

stal

rou

ndne

ss (-

)26 wt NaCl49 wt NaCl92 wt NaCl166 wt EG

Figure 714 Development of crystal roundness for different types of ice slurry

Effect of Stirring Rate

The effect of the stirring rate was studied by storing the same type of ice crystals at stirring rates of 400 and 750 RPM The results shown in Figure 715 and Figure 716 indicate that the difference in mixing rate has only a marginal effect on the average crystal size However the average crystal roundness increases faster for the storage experiment with the higher stirring rate

0

100

200

300

400

500

0 4 8 12 16 20 24Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)

400 rpm750 rpm

080

085

090

095

100

0 4 8 12 16 20 24Time (hours)

Ave

rgae

cry

stal

rou

ndne

ss (-

)

400 rpm750 rpm

Figure 715 Development of average Feret diameter at different stirring rates

Figure 716 Development of average crystal roundness at different stirring rates

A possible explanation for this behavior is that abrasion rounds off the parent crystals and produces new relatively small crystals (see Section 721) These small crystals will melt because of their relatively low equilibrium temperature and their crystal mass subsequently attaches to larger crystals Due to this phenomenon crystals become rounder but the average Feret diameter follows the same trend as with intermediate mixing

734 Comparison of Results with Results from Literature

Both the results reported in literature and the experimental results obtained in this study clearly show that the average crystal size increases during isothermal storage which can be

Chapter 7

152

ascribed to Ostwald ripening The results from different researchers show some interesting similarities

Influence of Solute Type and Concentration

Figure 717 shows that the type of solute strongly influences the ripening rate for example ripening of ice crystals in a 10 wt sucrose solution was much faster than in a 10 wt ethanol solution Besides the type of solute also its concentration appears to be very important since the ripening rate increases with decreasing sodium chloride concentration

0

100

200

300

400

500

0 10 20 30 40 50Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)

10 wt sucrose (Smith et al 1985)10 wt EtOH (Hansen et al 2002)15 wt PG (Hansen et al 2002)166 wt EG (present study)26 wt NaCl (present study)49 wt NaCl (present study)92 wt NaCl (present study)

Figure 717 Average Feret diameter during homogeneous storage in different aqueous

solutions

Separate experiments with constant initial concentrations of ethanol or propylene glycol and different ice fractions showed that the increase of the average Feret diameter was smaller at higher ice fractions At higher ice fractions the actual solute concentration is higher and it is likely that this higher solute concentration decreases the ripening rate in case of higher ice fractions

Influence of Mixing Regime

Experimental results by Hansen et al (2002) shown in Figure 718 demonstrate that ripening is faster during homogeneous than during heterogeneous storage in a 10 wt ethanol solution since the slope of the curve for homogeneous storage is steeper than the curve for heterogeneous storage for the same average crystal size However experiments with different mixing rates namely 400 and 750 RPM in a 49 wt NaCl solution show that the increase in crystal size is hardly influenced by the mixing rate


153

0

100

200

300

400

500

0 20 40 60 80 100Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)10 wt EtOH homogeneous(Hansen et al 2002)10 wt EtOH heterogeneous(Hansen et al 2002)

49 wt NaCl homogeneous400 RPM (Present study)49 wt NaCl homogeneous750 RPM (Present study)

Figure 718 Average Feret diameters during experiments with heterogeneous and

homogeneous storage

735 Discussion

Since the crystal size distribution is an important parameter of ice slurries for several applications it would be useful to be able to predict the development of this crystal size distribution in time Existing models for Ostwald ripening are based on a theoretical description of the asymptotic increase of the crystal size and have the following form (Lifshitz and Slyozov 1961 Wagner 1961)

2avg avginit 1= + CL L C t (733)

Since storage conditions in practice do rarely correspond with the assumptions of this theoretical model this equation is mostly used as empirical correlation Because of its empirical character the correlation is not applicable to explain differences in ripening rates at different conditions In this section the crystallization kinetics of ice crystals are studied in order to explain different ripening rates in different ice slurries

Ice crystal growth can be divided into three stages namely heat transport from the crystal surface due to the release of the heat of fusion diffusion of solute from the surface towards the bulk and integration of molecules into the crystal lattice During dissolution of crystals the opposite of these three processes occur where the detachment of molecules from the lattice is assumed to be infinitely fast

A schematic representation of temperature and concentration profiles near a growing ice crystal is shown in Figure 719

Chapter 7

154

Figure 719 Temperature and concentration profiles near a growing ice crystal

The temperature difference in the boundary layer TindashTb can be calculated from the heat balance (Mersmann 2001)

( )Ai b

V ice f

-3

=∆

BG T TB h

αρ

(734)

The heat transfer coefficient α for spherical particles is mostly calculated from a correlation proposed by Brian et al (1969)

0 173 4 3 4liq equiv liq equiv0 25 6

3 3liq liq

2 1 3 for lt10

D DNu Pr

ξ ρ ξ ρmicro micro

= +

(735)

Analogously the mass balance gives the concentration difference in the boundary layer

( )2 2

liqAdsi H Ob H Oi

V ice

-3BG k w wB

ρρ

= (736)

In this equation parameter kdsi represents the mass transfer coefficient to a semi-permeable interface which can be deduced from the normal mass transfer coefficient (Mersmann 2001)

2

ddsi

H Ob1-kk

w= (737)

A correlation by Levins and Glastonbury (1972) can be used to determine this mass transfer coefficient for small spherical particles in agitated tanks

0207 0173 4liq equiv 036 mix

3liq tank

2 047D DSh Sc

Dξ ρ

micro

= + (738)

The concentration difference in Equation 736 can be transformed into a temperature difference which enables a comparison with the heat transfer growth rate


155

( )2 2

2

b i H Ob H OiH O

- - dTT T w wdw

= (739)

Finally the difference between the temperature at the crystal interface and the equilibrium temperature can be calculated from the integration speed of crystals into the crystal lattice

( )int i i-=

rG k T T (740)

Huige and Thijssen (1969) proposed the following fitted correlation for the growth rate of ice crystals when the integration stage is limiting

( )155-3 i i27 10 -=G T T (741)

This correlation was deduced from experimental results with pure water It is possible that the growth rate decreases with an increasing concentration of solute because of adsorption of solute molecules on the crystal surface

Combining Equations 734 to 741 results in the following equation from which the total growth rate can be determined by iteration at a given supercooling Tb

-Tb by

2

2

155

H Ob-3 V ice ice fb b

A d liq H O

1-327 10wB hdTG T T G

B k dwρ ρρ α

∆ = minus minus +

(742)

In order to analyze which crystallization stage controls Ostwald ripening of ice crystals and what the effect of solute is on ripening a spherical ice crystal of 300 microm in diameter is considered here which is surrounded by liquid with a concentration wsoluteb and a bulk temperature Tb which is equal to the equilibrium temperature of a crystal of 200 microm The overall temperature driving force because of Ostwald ripening is about 12 10-4 K

Figure 720 shows the three isolated growth rates and the total growth rate without mixing as a function of the sodium chloride concentration for the considered crystal The isolated growth rates have been calculated by neglecting the growth resistance of the other two processes The figure shows that the isolated mass transfer growth rate highly depends on the solute concentration while the heat transfer and the integration growth rate only slightly decrease with increasing solute concentration Furthermore it can be seen that at low solute concentrations integration and heat transfer mainly determine the total growth rate while at higher concentrations mass transfer is the limiting stage The fact that the calculated total growth rate decreases with increasing solute concentration explains the observations shown in Figure 717 that higher solute concentrations decrease the ripening rate

Chapter 7

156

10E-11

10E-10

10E-09

10E-08

0 5 10 15 20w soluteb (wt)

G (m

s)

Heat transferMass transferSurface integrationTotal

Figure 720 Isolated growth rates and total growth rate of a 300 microm crystal at the considered

conditions without mixing in sodium chloride solutions

A surfactant can slow down the integration stage and it is therefore plausible that a surfactant only influences the ripening speed if the integration stage is limiting In cases where the diffusive or convective resistance is limiting a surfactant has a minor effect explaining the observations discussed in Section 723

Figure 721 shows the total growth rate for the considered crystal for different mixing regimes The figure shows that mixing increases the total growth rate but that increasing the mixing input has a minor effect This explains the results displayed in Figure 718 showing higher ripening rates during homogeneous storage compared to heterogeneous storage but that the mixing rate hardly influences the ripening process However higher mixing rates probably lead to more abrasion reducing the effect of increased mass and heat transfer coefficients

10E-11

10E-10

10E-09

10E-08

0 5 10 15 20w soluteb (wt)

G (m

s)

00 Wkg01 Wkg10 Wkg

Figure 721 Total growth rate of a 300 microm crystal at the considered conditions with different

values for mixing input in sodium chloride solutions

Figure 722 shows the total growth rates of the considered ice crystal during ripening without mixing for different aqueous solutions In most liquids the mass transfer stage determines the


157

ripening rate at solute concentration above 5 wt which implies that the ripening rate highly depends on the solute concentration This is in correspondence with the experiments presented in Figure 717 The growth rate of ice crystals in sucrose solutions is higher than in the other solutions at the same concentration which is not expected on the first sight since diffusion coefficients of sucrose solutions are quite low However the derivative of the freezing line dTdwH2O has a relatively small value and therefore the growth rate is high with respect to the growth rate in other solutions

10E-12

10E-11

10E-10

10E-09

10E-08

0 5 10 15 20 25 30w soluteb (wt)

G (m

s)

NaClEthylene glycolEthanolPropylene glycolSucrose

Figure 722 Total growth rate of considered crystal as a function of concentration without

stirring

Figure 723 shows the total growth rates of different aqueous solutions as a function of the freezing temperature and can be used to compare different solutes for ice slurry applications Ostwald ripening in solutions of sodium chloride appears to be faster than in other solutions at the same freezing temperature At a freezing temperature of ndash5degC for example the growth rate of the considered crystal in a sodium chloride solution is approximately twice the growth rate in an ethanol solution Furthermore the figures show that fast ripening mainly occurs in slurries with high freezing temperatures

The preceding analysis on crystallization kinetics shows that the differences in observed ripening rates can be explained by theory on mass transfer heat transfer and surface integration kinetics A qualitative comparison of the ripening rate of two different ice slurries can be made with Figure 722 or Figure 723 However a quantitative prediction of the increase of the average crystal size in time is not possible with this analysis and therefore a dynamic model is developed for this purpose in the next section

Chapter 7

158

10E-12

10E-11

10E-10

10E-09

10E-08

-120 -100 -80 -60 -40 -20 00T freeze (degC)

G (m

s)


Figure 723 Total growth rate of considered crystal as a function of freezing temperature

without stirring

736 Conclusions

The rate of Ostwald ripening decreases with increasing solute concentration which is caused by the fact that crystal growth at solute concentrations above 5 wt is mainly determined by mass transfer resistance At low solute concentrations integration of molecules into the crystal lattice and heat transfer resistance play a major role The mass transfer growth resistance increases as the solute concentration increases while the heat transfer and surface integration resistance are hardly influenced by the solute concentration Mixing increases the ripening rate which can be explained by the fact that mass transfer coefficients are enhanced Increasing the mixing rate however hardly influences the ripening rate

74 Dynamic Modeling of Ostwald Ripening

The previous analysis showed that Ostwald ripening is the dominant recrystallization mechanism during storage of ice slurry for thermal storage applications This section presents a dynamic model to predict the development of the crystal size distribution based on these conclusions

741 Model Development

A dynamic model of an ice slurry storage tank has been developed in which ice slurry is assumed to be a perfectly mixed suspension During isothermal storage small crystals melt and large crystals grow as a result of Ostwald ripening The storage tank is considered as a closed and insulated system without transport of mass or energy across its boundaries However it is possible to adapt the model to include these fluxes in future versions

The most important equations of the dynamic model are the population the total mass the solute mass and the energy balance as shown in Table 72


159

Table 72 The balance equations Population balance ( )( ) ( )( ) -

G L t n L tn L tt L

partpart=

part part (743)

with boundary conditions (0 ) 0n t = and (744) init( 0) ( )n L n L= (745) Total mass balance ( )( )( )liq ice1- 0V

tρ φ φ ρpart

+ =part

(746)

Solute mass balance ( )( )sol liq 1- 0V wt

ρ φpart=

part (747)

Energy balance ( ) ( )( )( )liq pliq ice pice f icetot1- 0V c T c T h At

ρ φ ρ φ γpart+ + ∆ + =

part (748)

with Mass fraction of ice

3ice V

tot 0

( )L

L

B n L L dLm

ρφ=infin

=

= int (749)

Total surface of crystals

2icetot A

0

( )L

L

A B n L L dL=infin

=

= int (750)

Because the storage tank is considered as a closed system neither inlet nor outlet mass flows can be found in the presented set of equations Next the storage tank is considered adiabatic which means that both heat transport from the surroundings and heat input by a mixing are neglected It is supposed that the size of ice crystals can only change as a result of Ostwald ripening and that other recrystallization mechanisms such as attrition and agglomeration can be neglected During Ostwald ripening the equilibrium temperature of the smallest crystals is below the actual slurry temperature and it can therefore be assumed that nucleation does not occur Since the formation of ice crystals from aqueous solutions is a very selective process (Vaessen 2002) it is assumed in the model that ice crystals do not contain any solute

In order to solve the equations shown in Table 72 the right-hand side of the population balance is discretized for the crystal size into a finite number of intervals resulting in a set of differential equations (Heijden and Rosmalen 1994) The width of each interval is chosen to be 5 microm and the maximum crystal size is set at 2000 microm The time integration of the total set of equations is performed in MATLAB using a differential equation solver based on an implicit Runge-Kutta formula (MATLAB 2002)

The crystallization kinetics of the considered ice crystals are given by the growth rate which is determined by transport phenomena and the temperature driving force given by the Gibbs-Thomson equation (see Table 73)

Chapter 7

160

Table 73 Crystallization kinetics used in simulations Growth rate ( )A

ice f ice solV

liq d sol

1 13

BG T Th w dTB

k dwρ ρ

α ρ

= minus ∆ +

(751)

with Equilibrium temperature

A

V ice lat

21-3

BT TB h L

γρinfin

= ∆

(730)

Heat transfer (Brian et al 1969)

0173 4liq equiv 025

3liq

2 13D

Nu Prξ ρ

micro

= +

(735)

Mass transfer (Levins and Glastonbury 1972)

0207 0253 4liq equiv 036 mix

3liq tank

2 047D DSh Sc

Dξ ρ

micro

= + (738)

The ice crystal shape and the surface tension between aqueous solution and ice are important parameters for Ostwald ripening but unequivocal values are lacking in literature Hillig (1998) has reviewed literature on determination of the surface tension with different kind of measurement techniques reporting values between 20 and 44 mJm2 Experiments by Hillig discussed in the same work give a value of 317plusmn27 mJm2 In the model presented here a constant value of 30 mJm2 is used for the surface tension and it is assumed that this value is not influenced by the solute type or concentration Literature references on the geometry of bulk ice crystals report disc-shaped ice crystals with height-to-diameter ratios varying from 01 to 05 (Margolis et al 1971 Huige 1972 Swenne 1983 Shirai et al 1985) During the experiments used for the validation of the model only two-dimensional pictures of ice crystals were analyzed and therefore it was not possible to determine their three dimensional shape Therefore ice crystals were modeled as circular discs with the disc diameter as characteristic crystal size L and a constant height-to-diameter ratio of 025 which was taken as an average value from the mentioned references

Heat transfer mass transfer and integration kinetics determine the growth rate of ice crystals while the former two transfer resistances determine the melting rate In the model heat and mass transfer correlations by Brian et al (1969) and Levins and Glastonbury (1972) have been applied in which an equivalent diameter Dequiv of the disc-shaped crystals is used as characteristic length An unequivocal model for surface integration kinetics is lacking in literature and therefore a model by Huige (1972) is considered here

( )155-3 27 10 -G T T= (741)

Figure 724 shows the isolated growth rates of mass transfer heat transfer and integration kinetics as a function of the crystal size in a 49 wt sodium chloride solution that is in equilibrium with a crystal of 200 microm in size which is called the neutral diameter Crystals smaller than this neutral diameter show negative growth rates which means that these crystals are melting The dominant transport resistance for a specific crystal size can be determined from the smallest isolated growth or melting rate for this crystal size The figure reveals that mass transfer resistance is the dominant stage for most crystal sizes and that the integration kinetics are only of importance for crystal sizes slightly larger than the neutral diameter Because of the latter conclusion the model assumes that crystal growth kinetics are controlled


161

by heat and mass transfer resistances while the resistance of integrating water molecules into the lattice of a growing ice crystal is neglected

-15

-10

-05

00

05

0 200 400 600 800 1000Crystal size (microm)

Cry

stal

gro

wth

rat

e (1

0 -7 m

s)

G heat

G surf G mass

Figure 724 Isolated growth rates for mass transfer heat transfer and surface integration

kinetics for a crystal in a 49 wt NaCl solution in equilibrium with 200 microm crystals

742 Validation Conditions

The developed model has been validated with experimental results for Ostwald ripening in homogeneously mixed tanks described in Sections 72 and 73 of this thesis (see Table 74)

Table 74 Parameters of experimental studies used for model validation Solute Reference Solute conc

(wt) Ice fraction (wt)

Tank volume (l)

Time (h)

Betaine Louhi-Kultanen (1996) 8 and 15 - 6 2 Ethylene glycol This thesis 166 15 1 25 Sodium chloride This thesis 26 49 and 92 15 1 25 Sucrose Louhi-Kultanen (1996) 8 and 15 - 6 2 Smith and Schwartzberg (1985) 9 to 38 9 to 16 10 5 Different types of experimental facilities were used to carry out the ripening experiments listed in Table 74 During the experiments by Louhi-Kultanen (1996) and the experiments carried out during the present study stirred tank crystallizers of 6 and 1 liter were used The crystallizers were equipped with a 3-blade propeller and cooling jacket enabling to operate at adiabatic conditions Hansen et al (2002) applied an insulated storage tank of 1000 liter equipped with two 3-blade propellers In order to compensate for heat penetration from the surroundings and to keep a constant ice fraction in the tank a continuous flow of ice slurry was pumped through an ice slurry generator Smith and Schwartzberg (1985) used a 10-liter insulated flask equipped with an auger-type impeller which was placed in a cold room to achieve adiabatic conditions The ratio between the diameter of the mixer and the tank was 06 for the experiments performed by Louhi-Kultanen (1996) and about 04 for the other experiments The mixing power per unit of mass was mentioned by none of the researchers but it was assumed that ice slurry was gently mixed and therefore an estimated value of 02 Wkg was used Measured initial crystal size distributions of experiments were transformed into Rosin-Rammler distributions and used as initial size distributions for simulations

Chapter 7

162

743 Validation Results

After simulation the development of the average crystal size in time was deduced from the changing crystal size distribution during simulation and compared to experimental results First the validation with experimental results obtained in closed adiabatic storage tanks is discussed followed by the validation with results obtained from a storage tank combined with an ice slurry generator

Figure 725 shows the comparison for ripening in sodium chloride and ethylene glycol solutions Both simulation and experimental results show that Ostwald ripening is slower at higher solute concentrations which can be attributed to the increased mass transfer resistance of transporting solute from or to the ice crystal surface in case of growing or melting respectively The model seems to be able to predict average crystal sizes after one day of storage fairly although the real process seems to be faster in the early stage of ripening than the model predicts The figure also shows that the developed model confirms the experimental conclusion that the mixing rate does hardly have any influence on the ripening rate for mixing rates of 400 and 750 rpm corresponding with 02 and 13 Wkg respectively

0

100

200

300

400

500

600

0 5 10 15 20 25Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)

26 wt NaCl 400 rpm 49 wt NaCl 400 rpm 49 wt NaCl 750 rpm 92 wt NaCl 400 rpm 166 wt EG 400 rpm

Figure 725 Development of average ice crystal size obtained from model (lines) and

experiments (points) for solutions of sodium chloride (NaCl) and ethylene glycol (EG) for different mixing rates

The validation for ripening in sucrose solutions shown in Figure 726 reveals that the development of the crystal size during simulation is qualitatively in accordance with the experiments since higher solute concentrations show lower ripening rates However quantitative errors of predicted average crystal size after five hours of storage show values up to 40 microm The initial average crystal sizes of simulations shown in this figure slightly differ from the experimental values since experimental distributions could not exactly be represented by Rosin-Rammler distributions


163

0

50

100

150

200

250

300

00 10 20 30 40 50 60Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)

8 wt φ =1

86 wt φ =0142

130 wt φ =0142

15 wt φ =1

190 wt φ =0132

369 wt φ =0122

Figure 726 Development of average crystal size obtained from model (lines) and

experiments (points) by 1Louhi-Kultanen (1996) and 2Smith and Schwartzberg (1985) for aqueous sucrose solutions

Besides the average crystals size the crystal size distribution is also an important parameter of ice slurry Figure 727 and Figure 728 show the validation of crystal size distributions before and after ripening in aqueous solutions of 8 wt betaine and 26 wt sodium chloride respectively The crystal size distributions obtained from simulations generally resemble the experimental ones but latter distributions seem to have a longer tail from which is concluded that the dynamic model underestimates the fraction of relatively large crystals

00102030405060708090

100


Num

ber

frac

tion

(10 3 1

m) 5

After 0 hours of storage After 2 hours of storage

00

10

20

30

40

50

0 200 400 600 800 1000 1200Crystal size (microm)

Num

ber

frac

tion

(10 3 1

m) After 0 hours of storage

After 22 hours of storage

Figure 727 Comparison of crystal size distributions obtained from model (lines) and experiments (points) before and after

storage for solutions of 8 wt betaine

Figure 728 Comparison of crystal size distributions obtained from model (lines) and experiments (points) before and after storage for solutions of 26 wt sodium

chloride

Figure 729 displays the validation of the model with the experimental results of ethanol and propylene glycol solutions obtained by Hansen et al (2002) who used an ice slurry generator to keep a constant ice fraction in the storage tank The figure clearly shows that the increase of the average crystal size is faster during these experiments than in simulations The fact that

Chapter 7

164

the storage tank was not closed and adiabatic during the experiments might be an explanation for these deviations

0

100

200

300

400

500

600

700

0 20 40 60 80 100Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)

10 wt EtOH φ =010 10 wt EtOH φ =030 15 wt PG φ =010 15 wt PG φ =030


experiments (points) for solutions of ethanol (EtOH) and propylene glycol (PG) in a storage tank combined with ice slurry generator

744 Discussion

The figures discussed in the previous section showed that the developed dynamic model is able to predict the development of the average crystals size in aqueous sodium chloride ethylene glycol and sucrose solutions at different concentrations fairly but that there are also relatively small deviations between simulations and experiments

A first cause for these deviations can be revealed by means of the development of crystals size distributions shown in Figure 727 and Figure 728 in which the right-hand side of the experimental distributions after several hours of storage is longer and flatter compared to the ones obtained from simulations Limited agglomeration of ice crystals during experiments could be a cause for this observation which is supported by the fact that some agglomerated ice crystals were identified during experiments Although Ostwald ripening is believed to be the main cause for the increase of ice crystals during adiabatic storage limited agglomeration can influence the development of the average crystals size

Another justification for deviations is the fact that the dynamic model assumed crystals to be circular discs with a constant height-to-diameter ratio while the experiments did not show perfect circular discs and experimental height-to-diameter ratios might differ from the constant value taken from literature Simulations with other height-to-diameter ratios have shown that a smaller ratio results in faster Ostwald ripening (see Figure 730) Furthermore experiments showed that the crystal discs become rounder during the first hours of storage which might explain the faster development of the crystal size in the early stages of ripening observed during experiments shown in Figure 725


165

0

100

200

300

400

500

600

700

0 5 10 15 20 25Time (hours)

Ave

rage

cry

stal

siz

e (m

m)

ExperimenthD=015hD=020hD=025hD=030

HD =015 HD =020 HD =025HD =030

Figure 730 Development of average crystal size obtained from model with different height-

to-diameter ratios (HD) and experiment for an aqueous solution of 26 wt sodium chloride

A third explanation for differences between simulations and experiments is the error introduced by the method of modeling crystallization kinetics namely the neglect of the integration kinetics and the implicit errors introduced by the applied heat and mass transfer models The error of these models might be increased by the fact that they have been used for circular discs while they were originally proposed for spherical particles

The final explanation for deviations is the uncertainty in the surface tension between liquid and ice for which a constant value has been taken from literature For this surface tension exact values or models are not available while it might also depend on the solute type and concentration

Figure 730 demonstrates that the developed model for Ostwald ripening in closed adiabatic storage tanks is not applicable for ripening of ice crystals in storage tanks that are connected to an ice slurry generator that compensates for heat penetration In order to simulate the development of the crystal size in this type of storage tanks the model can be extended with the ice slurry generator This extended system is both closed and adiabatic since there is no transport of mass over the system boundaries and the heat that is added to the storage tank equals the heat that is removed by the ice slurry generator For these reasons heat and mass balances are not modified and only the population balance (see Equation 743) is extended with a crystal size distribution flowing to (nin) and from (n) the storage tank respectively

( ) ( )isgin

tot

( ) ( )( ) ( ) ( )mG Lt n Ltn Lt - n Lt - n Lt

t L mpartpart

= +part part

amp (752)

It is assumed that the crystal size distribution n(Lt) coming from the storage tank is subject to growth in the ice slurry generator resulting in crystal population with a larger average crystal size and a higher ice fraction flowing back to the storage tank The growth rate in the ice slurry generator can be approached to be independent of the crystal size and is just enough to compensate for heat penetration Nucleation is neglected in the ice slurry generator and the mass flow through the ice slurry generator has no influence on simulation results and is therefore arbitrarily chosen The results of the extended model shown in Figure 731 demonstrate that the extended model is able to simulate ripening and that the cold loss

Chapter 7

166

compensation by the ice slurry generator accelerates the ripening process For these simulations the value for heat penetration has been tuned at 925 W which represents thermal convection to the storage tank and piping and heat input by the circulation pump

0

100

200

300

400

500

600

700

0 20 40 60 80 100Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)


Figure 731 Development of average crystal size obtained from extended model (lines) and experiments (points) by Hansen et al (2002) for solutions of ethanol (EtOH) and propylene

glycol (PG)

745 Conclusions

A dynamic model for Ostwald ripening of bulk ice crystals during adiabatic storage has been developed Validation of the developed model with experimental data has shown that the model is able to predict the development of the ice crystal size in time fairly In analogy with the considered experiments the simulations showed that mass transfer is the limiting transport mechanism for the considered ice suspensions Deviations between model and experiments are believed to be mainly the result of limited agglomeration and differences in crystal shape

75 Conclusions

Ostwald ripening is the most important recrystallization mechanism during isothermal storage of ice slurry for thermal storage applications During storage small crystals dissolve while larger crystals grow resulting in an increase of the average crystal size The rate of Ostwald ripening decreases with increasing solute concentration which is caused by the fact that crystal growth is mainly determined by mass transfer resistance Mixing increases the ripening rate which can be explained by the fact that mass transfer coefficients are enhanced Increasing the mixing rate however hardly influences the ripening rate A developed dynamic model enables to predict the development of the bulk ice crystals size distribution by Ostwald ripening in time fairly


167

Nomenclature

A Surface area of crystal (m2) V Volume of crystal (m3) Ap Projected area of crystal (m2) Vm Molar volume (m3mol) BA Surface shape factor equal to A L-2 w Mass fraction BV Volume shape factor equal to V L-3 c1 Ripening constant in Eq 733 Greek c2 Ripening exponent in Eq 733 α Heat transfer coefficient (Wm2K) cp Specific heat (Jkg K) γ Surface tension between ice and D Diameter of disc (m) liquid (Jm2) DFeret Feret diameter defined in Eq 731 Γ Roundness defined by Eq 710 (m) δ Boundary layer thickness (m) Dmix Mixer diameter (m) λ Heat conductivity (Wm K) Dtank Tank diameter (m) micro Viscosity (Pa s) D Mutual diffusion coefficient (m2s) micro Chemical potential (Jmol) G Crystal growth rate (ms) ∆micro Chemical potential difference ∆G Free Gibbsrsquo energy (J) (Jmol) ∆hf Heat of fusion (Jkg) ξ Power input by mixer (Wkg)

fh∆ Heat of fusion (Jmol) ρ Density (kgm3) H Height of disc (m) φ Ice mass fraction kd Mass transfer coefficient (ms) Ψ Activity coefficient kdsi Mass transfer coefficient to a semi- permeable interface (ms) Subscripts kint Integration kinetics constant avg Average (ms Kr) b Bulk L Characteristic crystal size (m) equiv Equivalent m Mass H2O Water mamp Mass flow (kgs) heat Heat transfer n Number of moles i Interface n Number of crystals ice Ice Nu Particle Nusselt number α Lλ init Initial P Perimeter in Inlet Pr Prandtl number cp microλ int Surface integration r Order of crystal growth isg Ice slurry generator s Entropy (Jmol) liq Liquid

fs∆ Entropy of fusion (Jmol) m Mass transfer Sc Schmidt number microρliq D mass Mass transfer Sh Sherwood number kd LD max Maximum T Temperature (K or degC) s Solid Tfr Freezing temperature (degC) solute Solute

T Equilibrium temperature (K) super Supercooling Tinfin

Equilibrium temperature of infinite surf Surface integration crystal (K) th Thermal ∆T Temperature difference (K) tot Total t Time (hours)

Chapter 7

168

Abbreviations

EG Ethylene glycol NaCl Sodium chloride EtOH Ethanol PG Propylene glycol

References

Adapa S Schmidt KA Jeon IJ Herald TJ Flores RA 2000 Mechanisms of ice crystallization and recrystallization in ice cream A review Food Reviews International vol16 pp259-271

Barnes P Tabor D Walker FRS Walker JCF 1971 The friction and creep of polycrystalline ice Proceedings of the Royal Society of London Series A vol324 pp127-155

Biscans B Guiraud P Lagueacuterie C Massarelli A Mazzarotta B 1996 Abrasion and breakage phenomena in mechanically stirred crystallizers The Chemical Engineering Journal vol63 pp85-91

Brian PLT Hales HB Sherwood TK 1969 Transport of heat and mass between liquids and spherical particles in an agitated tank AIChE Journal vol15 pp727-733

Christensen KG Kauffeld M 1998 Ice slurry accumulation In Proceedings of the Oslo Conference IIR commission B1B2E1E2 Paris International Institute of Refrigeration pp701-711

Donhowe DP Hartel RW 1996 Recrystallization of ice during bulk storage of ice cream International Dairy Journal vol6 pp1209-1221

Egolf PW Vuarnoz D Sari O 2001 A model to calculate dynamical and steady-state behaviour of ice particles in ice slurry storage tanks In Proceedings of the 4th IIR Workshop on Ice Slurries 12-13 November 2001 Osaka (Japan) Paris International Institute of Refrigeration pp25-39

Frei B Egolf PW 2000 Viscometry applied to the Bingham substance ice slurry In Proceedings of the 2nd IIR Workshop on Ice Slurries 25-26 May 2000 Paris (France) Paris International Institute of Refrigeration pp48-60

Gahn C Mersmann A 1995 The brittleness of substances crystallized in industrial processes Powder Technology vol85 pp71-81

Hagiwari T Hartel RW 1996 Effect of sweetener stabilizer and storage temperature on ice recrystallization in ice cream Journal of Dairy Science vol79 pp735-744

Hansen TM Radošević M Kauffeld M 2002 Behavior of Ice Slurry in Thermal Storage systems ASHRAE Research project ndash RP 1166

Hansen TM Radošević M Kauffeld M Zwieg T 2003 Investigation of ice crystal growth and geometrical characteristics in ice slurry ASHRAE HVACampR Research Journal vol9 pp9-32


169

Hayashi K Kasza KE 2000 A method for measuring ice slurry particle agglomeration in storage tanks ASHRAE Transactions vol106 pp117-123

Heijden AEDM van der Rosmalen GM van 1994 Industrial mass crystallization In Hurle (Ed) Handbook of Crystal Growth Part 2A ndash Bulk Crystal Growth Basic Principles pp372-377

Hillig WB 1998 Measurement of interfacial free energy for icewater system Journal of Crystal Growth vol183 pp463-468

Huige NJJ Thijssen HAC 1969 Rate controlling factors of ice crystal growth from supercooled water glucose solutions In Industrial Crystallization Proceedings of a Symposium on Industrial Crystallization April 15-16 London (Great Britain) London The Institution of Chemical Engineers pp69-86

Huige NJJ 1972 Nucleation and Growth of Ice Crystals from Water and Sugar Solutions in Continuous Stirred Tank Crystallizers PhD thesis Eindhoven University of Technology (The Netherlands)


Kasza KE Hayashi K 1999 Ice slurry cooling research storage tank ice agglomeration and extraction ASHRAE Transactions vol105 pp260-266

Kitanovski A Poredoš A 2002 Concentration distribution and viscosity of ice-slurry in heterogeneous flow International Journal of Refrigeration vol 25 pp827-835

Kobayashi A Shirai Y 1996 A method for making large agglomerated ice crystals for freeze concentration Journal of Food Engineering vol27 pp1-15

Kozawa Y Aizawa N Tanino M 2005 Study on ice storing characteristics in dynamic-type ice storage system by using supercooled water Effects of the supplying conditions of ice-slurry at deployment to district heating and cooling system International Journal of Refrigeration vol28 pp73-82

Levins BE Glastonbury JR 1972 Particle-liquid hydrodynamics and mass transfer in a stirred vessel Part II ndash Mass transfer Transactions of the Institution of Chemical Engineers vol50 pp132-146

Lifshitz IM Slyozov VV 1961 The kinetics of precipitation from supersaturated solid solutions Journal of Physics and Chemistry of Solids vol19 pp35-50

Louhi-Kultanen M 1996 Concentration and Purification by Crystallization PhD thesis Lappeenranta University of Technology (Finland)

MATLAB 2002 Version 6 Mathwork Inc Natwick

Margolis G Sherwood TK Brian PLT Sarofim AF 1971 The performance of a continuous well stirred ice crystallizer Industrial and Engineering Chemistry Fundamentals vol10 pp439-452

Chapter 7

170

Mazzarotta B 1992 Abrasion and breakage phenomena in agitated crystal suspensions Chemical Engineering Science vol47 pp3105-3111

Meili F Sari O Vuarnoz D Egolf PW 2001 Storage and mixing of ice slurries in tanks In Proceedings of the 3rd IIR Workshop on Ice Slurries 16-18 May 2001 Lucerne (Switzerland) Paris International Institute of Refrigeration pp97-104

Mersmann A 2001 Crystallization Technology Handbook Second edition New York Marcel Dekker Inc

Nielsen AE 1964 Kinetics of Precipitation Oxford Pergamon Press

Savory RM Hounslow MJ Williamson AM 2002 Isothermal coarsening anisotropic ice crystals In Proceedings of the 15th International Symposium on Industrial Crystallization September 15-18 Sorrento (Italy)

Shirai Y Nakanishi K Matsuno R Kamikubo T 1985 Effects of polymers on secondary nucleation of ice crystals Journal of Food Science vol50 pp401-406

Shirai Y Sugimoto T Hashimoto M Nakanishi K Matsuno R 1987 Mechanism of ice growth in a batch crystallizer with an external cooler for freeze concentration Agricultural and Biological Chemistry vol51 pp2359-2366

Sutton RL Evans ID Crilly JF 1994 Modeling ice crystal coarsening in concentrated disperse food systems Journal of Food Science vol59 pp1227-1233

Sutton RL Lips A Piccirillo G Sztehlo A 1996 Kinetics of ice recrystallization in aqueous fructose solutions Journal of Food Science vol61 pp741-745

Smith CE 1984 Ice Crystal Growth Rates during the Ripening Stage of Freeze Concentration (Mass-transfer Sequential Analysis Neutral Diameter) PhD thesis University of Massachusetts (USA)

Smith CE Schwartzberg HG 1985 Ice crystal size changes during ripening in freeze concentration Biotechnology Progress vol1 pp111-120

Swenne DA 1983 The Eutectic Crystallization of NaClmiddot2H2O and Ice PhD thesis Eindhoven University of Technology (The Netherlands)

Verschuur RJ Scholz R Nistelrooij N van Schreurs B 2002 Innovations in freeze concentration technology In Proceedings of the 15th International Symposium on Industrial Crystallization September 15-18 Sorrento (Italy)

Wagner C 1961 Theorie der Alterung von Niederschlaumlgen durch Umloumlsen (Ostwald-Reifung) Zeitschrift fuumlr Elektrochemie vol65 pp581-591

Williamson A Lips A Clark A Hall D 2001 Ripening of faceted ice crystals Powder Technology vol121 pp74-80

171

8 Melting of Ice Slurry in Heat Exchangers

81 Introduction

After production and storage ice slurry is transported to applications where it provides cooling to rooms products or processes (see Chapter 1) Due to the absorption of heat the ice slurry temperature increases and ice crystals melt The melting process is expected to be strongly influenced by the properties of ice slurry such as the ice fraction and the average ice crystal size Since these properties are mainly determined during the production and storage stage it is important to know their influences on the melting process Furthermore knowledge on heat and mass transfer processes during melting may improve the knowledge of ice slurry production processes or vice versa

In general two different methods of ice slurry melting can be distinguished The first method is called direct contact melting and is mainly applied in food industry for cooling of fish fruit and vegetables (Fikiin et al 2005 Torres-de Mariacutea et al 2005) In this method ice slurry is poured directly onto fresh harvested products resulting in high cooling rates which ensure a high product quality In the second method ice slurry is pumped through a regular heat exchanger absorbing heat from air or another fluid This method is frequently applied in refrigerated display cabinets for supermarkets and in air conditioning systems for buildings

This chapter focuses on the melting process of ice slurries in heat exchangers First a literature review on hydrodynamics and heat transfer aspects of melting ice slurries is presented to investigate which aspects of melting ice slurries are not fully understood yet The second part consists of an experimental study of ice slurry melting in a tube-in-tube heat transfer coil which aims to give a contribution to the understanding of these aspects

82 Literature Review on Ice Slurry Melting in Heat Exchangers

The performance of ice slurry as secondary refrigerant is partly determined by its performance during melting in application heat exchangers Important design aspects in this respect are the heat transfer coefficient between the melting ice slurry and the heat exchanger wall and the pressure drop of the ice slurry flow between inlet and outlet Both heat transfer and pressure drop are influenced by the flow pattern and rheology of the flowing ice slurry Another aspect that plays a role during melting is superheating of ice slurry which can seriously reduce the heat transfer capacity of a heat exchanger

This section gives a brief literature review on these various aspects of ice slurry melting in heat exchangers More extensive reviews on this subject have been presented by Ayel et al (2003) Egolf et al (2005) and Kitanovski et al (2005)

821 Flow Patterns

According to Kitanovski et al (2002) three different patterns can be distinguished for ice slurry flows in horizontal tubes namely moving bed flow heterogeneous flow and homogeneous flow (see Figure 81) In moving bed flow ice crystals accumulate in the upper part of the tube forming a crystal bed while the liquid flows underneath it The velocity of the

Chapter 8

172

crystal bed is lower than the liquid velocity In heterogeneous flows the crystals are suspended over the entire cross section of the tube but their concentration is higher in the upper part of the tube than in the lower part In case of a homogeneous flow ice crystals are randomly distributed and the crystal concentration is therefore constant over the entire cross section

Figure 81 Flow patterns for ice slurry flow in horizontal tubes

The boundaries between the different flow patterns are mainly determined by the ice slurry velocity the average crystal size the density ratio between ice and solution and the ice fraction In case of low velocities large crystals or high density ratios between liquid and ice the ice crystals have the tendency to float to the top of the tube forming a moving bed flow As the velocity increases the ice crystals are smaller or the liquid density is closer to the density of ice the flow pattern turns initially to heterogeneous flow and finally to homogeneous flow According to Lee et al (2002) the flow pattern tends also more towards the homogeneous flow regime when the ice fraction increases Validated correlations to predict flow patterns for ice slurry are lacking in literature General correlations to predict flow patterns of suspension flows are given by Wasp et al (1977) Shook and Roco (1991) and Darby (1986)

Kitanovski et al (2002) presented experiments to determine flow patterns of ice slurry with ice crystals of 01 to 03 mm in 10 wt ethanol solutions The transition from moving bed flow to heterogeneous flow occurred at velocities between 01 to 03 ms At velocities above 02 to 05 ms the ice slurry flow became homogeneous

822 Rheology

Several researchers have studied the rheological behavior of homogeneous ice slurry flows They generally agree that ice slurry with ice fractions up to 15 wt can be considered as Newtonian which means that the shear rate is proportional to the yield stress (Ayel et al 2003 Meewisse 2004 Kitanovski et al 2005) For ice fractions above 15 wt two different types of rheology have been proposed namely pseudo-plastic (Guilpart et al 1999) and Bingham type of flow behavior (Doetsch 2001 Frei and Egolf 2000 Niezgoda-Żelasko and Zalewski 2006) Doetsch (2002) proposed to use the Casson model which combines Newtonian behavior at low ice fractions with Bingham behavior at higher ice fractions

823 Pressure Drop

Most experimental studies on pressure drop of ice slurries were performed with horizontal tubes In general these studies report an increase in pressure drop with increasing ice fraction especially at low ice slurry velocities (Christensen and Kauffeld 1997 Jensen et al 2000

Melting of Ice Slurry in Heat Exchangers

173

Bedecarrats et al 2003 Lee et al 2006 Niezgoda-Żelasko and Zalewski 2006) Bedecarrats et al (2003) for example measured pressure drop values for a velocity of 05 ms and an ice fraction of 20 wt that were a factor of six higher than for the case without ice crystals At higher ice slurry velocities pressure drop values also increased with increasing ice fraction but to a lower extent

At high velocities of about 1 to 2 ms and ice fractions of about 20 wt Bedecarrats et al (2003) and Niezgoda-Żelasko and Zalewski (2006) observed a sudden decrease in pressure drop with increasing ice fraction When the ice fraction was further increased the pressure drop restarted to rise resulting in a local minimum in pressure drop Niezgoda-Żelasko and Zalewski (2006) attribute this sudden decrease in pressure drop to a laminarization of the ice slurry flow at high ice fractions This explanation can also be used for the experimental results of Knodel et al (2000) which showed a decrease in pressure drop of 8 as the ice fraction increased from 0 to 10 wt

Experiments with ice slurry in plate heat exchangers were performed by Bellas et al (2002) Frei and Boyman (2003) and Noslashrgaard et al (2005) All three studies showed an increase in pressure drop with increasing ice fraction especially at low ice slurry velocities Frei and Boyman (2003) reported that the pressure drop for low velocities increased with 44 as the ice fraction increased from 0 to 29 wt At higher velocities this increase was 32


Experimental results for wall-to-slurry heat transfer coefficients in horizontal tubes showed approximately the same results as the pressure drop measurements discussed above Christensen and Kauffeld (1997) Jensen et al (2000) and Lee et al (2006) found that heat transfer coefficients increased up to a factor of three with increasing ice fraction The highest relative increase was measured for low ice slurry velocities up to 1 ms while the enhancement at high ice slurry velocities of about 3 to 4 ms was only small Bedecarrats et al (2003) and Niezgoda-Żelasko (2006) measured approximately the same trends but at high velocities and ice fractions around 20 wt they also observed a decrease in heat transfer coefficient as the ice fraction increased This decrease was attributed by Niezgoda-Żelasko to a laminarization of the ice slurry flow Knodel et al (2000) used the same explanation for their experimental results which showed a continuous decrease of the heat transfer coefficient as the ice fraction increased from 0 to 10 wt at high ice slurry velocities of about 5 ms

The influence of the heat flux on wall-to-slurry heat transfer coefficients was investigated by several researchers (Christensen and Kauffeld 1997 Jensen et al 2000 Lee et al 2006 Niezgoda-Żelasko 2006) All these experimental studies demonstrated that the heat flux has no effect on heat transfer coefficients of melting ice slurry

Ice slurry melting experiments with plate heat exchangers by Noslashrgaard et al (2005) Frei and Boyman (2003) and Stamatiou and Kawaji (2005) showed increasing heat transfer coefficients with increasing ice fractions In accordance with the experiments with horizontal tubes the relative increase of the heat transfer coefficient was especially high at low mass flow rates Experiments with a plate heat exchanger by Bellas et al (2002) showed different trends since the results indicated that ice fractions up to 22 did not have any influence on heat transfer

In none of the experimental studies on heat transfer coefficients of melting ice slurry the influence of the ice crystal size has been studied

Chapter 8

174

825 Superheating

Ice slurry is called superheated when its liquid temperature is higher than its equilibrium temperature Superheating can be explained by considering the melting process of ice slurry in heat exchangers as a two-stage process First the heat exchanger wall heats the liquid and consequently the superheated liquid melts the ice crystals The relation between the rates of both processes determines the degree of superheating For example when crystal-to-liquid heat and mass transfer processes are relatively slow compared to the wall-to-liquid heat transfer process then the degree of superheating is high Superheating always occurs in melting heat exchangers but its degree depends on the operating conditions

Due to superheating the average ice slurry temperature in the heat exchanger is higher than is expected from equilibrium calculations and as a result the heat exchanger capacity is lower Figure 82 shows an example to explain the effect of superheating on the heat exchanger capacity The figure represents the temperature of an ice slurry on its path from the storage tank via the pump to the heat exchanger and back to the storage tank The ice slurry that enters the heat exchanger is in equilibrium and has an ice fraction of 10 wt and a temperature of ndash50degC The ice slurry is heated by a heat source of 20degC and as a result the ice crystals melt According to equilibrium calculations the ice fraction at the outlet is zero and the temperature of the solution equals its freezing temperature of ndash45degC However the real temperature of the ice slurry in the heat exchanger is higher and the slurry leaves the heat exchanger with a temperature of ndash15degC A fraction of the ice crystals is still present at the outlet of the heat exchanger and the melting process continues in the tubing between the heat exchanger and the tank resulting in a decrease of the slurry temperature The figure clearly shows that the real temperature difference between the slurry and the heat source is smaller than is expected from equilibrium calculations As a result of this smaller temperature difference the heat exchanger capacity is also significantly lower

Figure 82 Example of real and equilibrium temperature profiles of ice slurry in a melting

loop

Up to now superheated ice slurry at the outlet of melting heat exchangers has been observed by Hansen et al (2003) Kitanovski et al (2003) and Frei and Boyman (2003) Only the latter


175

researchers reported superheating values indicating that superheating especially occurs at low ice fractions This trend is explained by the reduced crystal surface at low ice fractions which slows down the crystal-to-liquid heat and mass transfer processes

826 Outlook for Experiments

The preceding literature review has shown that the influences of ice slurry velocity and ice fraction on pressure drop and heat transfer coefficients have extensively been studied by various researchers Although the reported pressure drop and heat transfer data show approximately the same trends in the various studies more experiments are required to fully understand the role of all parameters In particular the role of the average ice crystal size and the crystal size distribution on the heat transfer process needs attention in this respect because these aspects have not been considered in any experimental study up to now

Another issue that has only attained little attention is superheating of ice slurry in heat exchangers Superheating can seriously reduce the capacity of melting heat exchangers and it is therefore important to investigate the physical phenomena behind it In this respect it is interesting to study the influences of ice slurry velocity and heat flux on superheating Furthermore the average crystal size and the ice fraction are expected to have a strong effect on the degree of superheating since they determine the available crystal surface for the crystal-to-liquid process The melting of ice crystals may be limited by mass transfer and in that case the solute concentration also has a strong influence on the degree of superheating

In the next sections an experimental study on melting of ice slurry in a heat exchanger is presented This study gives a contribution to the knowledge on ice slurry melting especially on the subjects that have been mentioned above



The experiments on melting of ice slurry in a heat exchanger were performed with the experimental set-up shown in Figure 83 A fluidized bed heat exchanger as described in Section 22 was used to produce ice slurry from aqueous sodium chloride solutions The produced ice slurry was stored in an insulated tank that was equipped with a mixing device to keep the ice slurry homogeneous The tank could easily be disconnected from the set-up and be placed in a cold room After production and eventually isothermal storage in the cold room a visualization section consisting of a flow cell and a microscope was applied to analyze the produced ice crystals (see Figure 511)

The ice slurry was subsequently pumped through the inner tube of a tube-in-tube heat transfer coil which had an internal diameter of 70 mm an outside diameter of 95 mm and a total external heat-exchanging surface of 0181 m2

A 20 wt ethylene glycol solution which was extracted from a thermostatic bath flowed counter currently through the annulus and heated the ice slurry in the inner tube The hydraulic diameter of this annulus measured 62 mm The melting process was continued until all ice crystals had melted and the tank contained only liquid

Chapter 8

176

Figure 83 Schematic overview of the experimental set-up

PT-100 elements with an accuracy of 001 K measured the temperatures of the ice slurry and the ethylene glycol solution at the inlets and outlets of the heat exchanger A pressure difference sensor was used to measure the pressure drop of ice slurry The mass flow of ice slurry was measured using a coriolis mass flow meter and a magnetic flow meter measured the flow rate of ethylene glycol solution The coriolis mass flow meter was also able to measure the temperature of ice slurry downstream of the heat exchanger All flow rates and temperatures were automatically measured every ten seconds with the exception of the temperature measured in the coriolis mass flow meter which was manually read


This chapter presents a series of ten melting experiments In this experimental series the operating conditions were systematically varied as shown in Table 81 in order to study their effect on superheating heat transfer coefficients and pressure drop

Table 81 Experimental conditions of melting experiments Exp w0 Tfr uis TEGin τstor DFeret ininitφ no (wt) (degC) (ms) (degC) (h) (microm) (wt) 1 66 -41 10 30 0 2491 17 2 66 -41 15 30 0 249 18 3 66 -41 20 30 0 2491 18 4 66 -41 25 30 0 2491 16 5 66 -41 15 30 16 283 16 6 35 -21 15 52 0 338 14 7 110 -74 15 -07 0 133 17 8 71 -44 18 26 0 148 10 9 70 -44 17 26 15 277 9

10 71 -44 18 00 0 1482 10 1Assumed equal as in experiment 2 2Assumed equal as in experiment 8


177

The varied operating conditions were the ice slurry velocity the heat flux the ice crystal size and the sodium chloride concentration The ice slurry velocity was varied by controlling the gear pump to the desired mass flow rate The heat flux was adjusted by varying the inlet temperature of the aqueous ethylene glycol solution In most experiments the difference between the initial freezing temperature of the aqueous solution and the inlet temperature of the ethylene glycol solution was 71plusmn01 K except for experiment 10 in which this temperature difference was only 44 K For the latter experiment the heat flux varied from 4 to 7 kWm2 while the heat flux in the other experiments was 7 to 13 kWm2 The average crystal size was determined by analyzing the crystals with the visualization section In this respect the Feret diameter was used as characteristic crystal size which is defined as the diameter of a circle with the same area as the projection of the crystal (see Section 732) Ice crystals produced from aqueous solutions with equal solute concentration and equal production procedure appeared to have approximately the same average crystal size The average crystal sizes at the start of experiments 1 3 and 4 were therefore assumed equal to the average crystal size determined at the start of experiment 2 The same assumption was made for the crystal sizes of experiment 8 and 10 Ice crystals produced from aqueous solutions with higher solute concentrations appeared to have smaller crystals In order to vary the average crystal size for a certain solute concentration ice slurry was isothermally stored in the cold room During isothermal storage the average crystal size increased as a result of Ostwald ripening (see Chapter 7)

833 Data Reduction

The total heat flux in the heat exchanger was determined from the flow rate and the inlet and outlet temperatures of the ethylene glycol solution This total heat flux was used to calculate the overall heat transfer coefficient Uo

he o o lnQ U A T= ∆amp (81)

The logarithmic temperature difference in Equation 81 was calculated from the measured temperatures at the inlets and outlets of the heat exchanger The use of the logarithmic temperature difference to determine the overall heat transfer coefficient is only valid when the specific heat of both fluids in the heat exchanger is constant In case the ice slurry is superheated in the heat exchanger this condition is not completely fulfilled However the errors introduced by this method are expected to be small and a more sophisticated method is not available Therefore the overall heat transfer coefficient is based here on the logarithmic temperature difference as is shown in Equation 81

The overall heat transfer resistance (1Uo) consists of three parts the annular side heat transfer resistance the heat transfer resistance of the tube wall and the wall-to-liquid heat transfer resistance



1 1 1ln2

D D DU D Dα λ α

= + +

(82)

The Wilson plot calibration technique was used to formulate single-phase heat transfer correlations for both sides of the heat exchanger (see Appendix C3) The correlation for the annular side was used to calculate the heat transfer coefficient of the ethylene glycol flow αo Subsequently this heat transfer coefficient was used to determine the heat transfer coefficient for the ice slurry flow αi from Equation 82 Finally this experimentally determined heat

Chapter 8

178

transfer coefficient for ice slurry flow was compared with the heat transfer coefficient predicted from the correlation for single-phase flow The measurement accuracies of the physical parameters obtained with the melting heat exchanger are given in Appendix D2

84 Results and Discussion on Superheating

In general the ten melting experiments listed in Table 81 showed mutually the same trends on superheating The observed phenomena are therefore initially discussed for one experiment only namely experiment 1 Subsequently results of the different experiments are compared


The ice slurry temperatures measured at the inlet and outlet of the heat exchanger during melting experiment 1 are shown in Figure 84 At the start of the experiment the ice fraction at the inlet was 17 wt at a temperature of ndash50degC According to the heat balance the reduction in ice fraction was initially approximately 9 wt per pass which resulted in an expected outlet ice fraction of about 8 wt Since ice crystals were present at the outlet the equilibrium temperature at this location was at least lower than the initial freezing temperature of -41degC However the measured outlet temperature exceeded this initial freezing temperature with about 1 K which means that the ice slurry at the outlet was superheated The temperature measured in the coriolis mass flow meter was below the temperature measured at the outlet of the heat exchanger This decrease in temperature is attributed to the release of superheating downstream of the heat exchanger

-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

00

50

100

150

200

250

300

350

400

Ice

frac

tion

(wt

)

Tfr

T inmeas

T outmeas

T coriomeas

ineqinφ

Figure 84 Measured ice slurry temperatures and ice fraction at the inlet based on

equilibrium during melting experiment 1

If it assumed that ice slurry entering the heat exchanger is in equilibrium than the ice fraction at the inlet is calculated by

ineqin 0ineqin

ineqin

w ww

φminus

= (83)


179

In Equation 83 the mass fraction of solute in the solution wineqin is determined from the measured inlet temperature assuming equilibrium (see Equation A2 in Appendix A11)

ineqin eq inmeasw w T= (84)

The development of this inlet ice fraction φineqin in Figure 84 suggests that all ice crystals had melted at t=2400 s However by that time ice crystals were still observed in the ice suspension tank Another indication that ice crystals were still present in the system is that the slope of the measured inlet temperature does not change significantly at t=2400 s A considerable change of this slope is however observed at t=3200 s indicating that all ice crystals had melted by that time

The described observations indicate that ice slurry is also not in equilibrium at the inlet of the heat exchanger at least during the final stage of the experiment In order to quantify superheating of ice slurry at the inlet and outlet of the heat exchanger the enthalpy of ice slurry at both locations is considered

Enthalpy at Inlet

First the enthalpy of ice slurry at the inlet is considered for the assumption of equilibrium at this location

( ) isineqin ineqin liq ineqin inmeas ineqin ice inmeas1 h h w T h Tφ φ= minus + for inmeas frT Tle (85)

isineqin liq 0 inmeash h w T= for inmeas frT Tgt (86)

For temperatures above the freezing temperature the enthalpy simply equals the enthalpy of the aqueous solution (see Equation A18 in Appendix A14) At temperatures below the freezing temperature the enthalpy of ice slurry is the weighed average of the enthalpy of the solution and the enthalpy of ice (see Equation B8 in Appendix B23)

The enthalpy based on equilibrium calculations can be compared with the enthalpy based on the cumulative heat input which consists of the heat transferred in the heat exchanger and the heat input by other components such as the pump and the mixing device in the tank

( )he rest

isinreal isineqinis0

0t Q Q

h t h t dtm

+= = + int

amp amp (87)

The enthalpy at t=0 is determined by assuming that the ice slurry is in equilibrium at the beginning of the experiment The integral in Equation 87 is rewritten into a summation in order to apply it to the measured data

( )he rest

isinreal isineqin0 is

0tn t

n

Q Q th t h t

m

= ∆

=

+ ∆= = + sum

amp amp (88)

Initially the heat input by other components is set equal to zero Now both the enthalpy based on equilibrium at the inlet and the enthalpy based on the cumulative heat input are compared in Figure 85

Chapter 8

180

-800

-700

-600

-500

-400

-300

-200

-100

00

0 600 1200 1800 2400 3000 3600Time (s)

Ent

halp

y (k

Jkg

)

h isineqin

h isinreal

h isinreal rest( 170 W)Q =amp

rest

( 0 W)Q =amp

Figure 85 Ice slurry enthalpies at the inlet during melting experiment 1

At the end of the experiment (t=3400 s) the tank contained only liquid and the enthalpy based on equilibrium is supposed to represent the correct enthalpy for this time The difference between this enthalpy and the enthalpy based on the cumulative input is attributed to the heat input by the other components In order to estimate this heat input both enthalpies are equated for the final measurement of the experiment

isineqin isinreal endforh h t t= = (89)

If the heat input from the other components is assumed constant then substitution of Equation 88 in 89 gives a correlation for this heat input

end

is herest isineqin end isineqin

0end is

0tn t

n

m Q tQ h t t h tt m

= ∆

=

∆ = = minus = +

sum

ampamp (810)

Application of Equation 810 for melting experiment 1 results in a heat input by the other components of 170 W (see also Figure 85) Heat input values calculated for the other melting experiments showed similar numbers

Enthalpy at Outlet

Now the real enthalpy at the inlet of the heat exchanger is known from Equation 88 the enthalpy at the outlet can be calculated by

is

isoutreal isinrealis

Qh hm

= +amp

amp (811)


181

Ice Fractions and Equilibrium Temperatures at Inlet and Outlet

The foregoing analysis clearly indicates that ice slurry is neither in equilibrium at the inlet nor at the outlet of the heat exchanger The ice fraction can therefore not be calculated by using the initial solute concentration and the measured temperature only as is shown in Equations 83 and 84 The non-equilibrium state requires a third thermodynamic property to calculate the ice fraction for example the enthalpy

The enthalpy of ice slurry which is not in equilibrium is given by

( ) isreal real liq real meas real ice eq real1 h h w T h T wφ φ= minus + (812)

At the inlet and outlet of the heat exchanger the enthalpies are known from Equations 88 and 811 and the temperature is known from measurements Equation 812 contains therefore only two unknown variables namely the solute concentration in the solution wreal and the ice fraction φreal Since ice slurry is homogenously mixed in the tank it is assumed that the solute concentration in the slurry always equals the initial solute concentration w0 The ice fraction φreal is therefore directly related to the solute concentration in the solution wreal by means of the solute mass balance

( )0 real real1w wφ= minus (813)

The ice fraction φreal and the solute concentration wreal can now be solved iteratively from Equations 812 and 813 The ice fractions at the inlet and outlet calculated with this method are shown for experiment 1 in Figure 86

-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

0

5

10

15

20

25

30

35

40Ic

e fr

actio

n (w

t)

T inmeas

T outmeas

inreal

outreal

φφ

Figure 86 Measured ice slurry temperatures and calculated ice fractions during melting

experiment 1

The solute concentration in the liquid wreal is now used to calculate the equilibrium temperature at the inlet and outlet of the heat exchanger

eq eq realT T w= (814)

Chapter 8

182

Figure 87 shows that the measured outlet temperatures exceed the calculated equilibrium temperatures at the outlet indicating that the ice slurry is significantly superheated

-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

0

5

10

15

20

25

30

35

40

Ice

frac

tion

(wt

)

T outmeas

T outeq

outrealφ

∆Tsh

Figure 87 Measured ice slurry temperature and calculated ice fractions and equilibrium

temperatures at the outlet of the heat exchanger during melting experiment 1

Superheating Definition

In order to quantify superheating at the outlet of the heat exchanger the degree of superheating ∆Tsh is defined as the difference between the measured temperature and the equilibrium temperature

sh liqmeas eq realT T T w∆ = minus (815)

Melting of ice slurry in a heat exchanger can be considered as a process consisting of two stages as shown in Figure 88 (see also Section 825) The first stage consists of the heat transfer process from the wall to the liquid The driving force of this process is the temperature difference between the wall and the liquid phase The second stage is the actual melting of the ice crystals where the difference between the liquid temperature and the equilibrium temperature hence the degree of superheating is the driving force

Figure 88 Schematic representation of temperatures during melting of ice slurry in a heat

exchanger


183

The degree of superheating can be seen as a fraction of the total driving force of the melting process

meas eqsh

w-liq sh w eq

T TTT T T T

ζminus∆

= =∆ + ∆ minus

(816)

This relative superheating ζ enables to compare superheating results from experiments with different mass flow rates and different heat fluxes

For the analysis of superheating it is necessary to calculate the wall temperature at the outlet of the ice slurry flow Here the ratio of heat transfer coefficients the ice slurry temperature and the temperature of the ethylene glycol solution are used to determine this temperature

( )( )

oinnerw is o

EG is i iinner

DT T UT T Dα

minus=

minus (817)

842 Influence of Ice Fraction and Ice Slurry Velocity

The superheating results for different ice slurry velocities in Figure 89 clearly show that the degree of superheating increases as the ice fraction decreases The figure also shows that for ice fractions higher than 5 wt the degree of superheating is higher in the experiments with low ice slurry velocities This higher degree of superheating is mainly the result of the higher wall temperature caused by the lower wall-to-liquid heat transfer coefficient at low slurry velocities The results for the relative superheating ζ in Figure 810 take these different wall temperatures into account This figure shows that the relative superheating of the experiments with slurry velocities of 10 15 and 20 ms are very similar but that the relative superheating at a velocity of 25 ms is slightly lower

00

10

20

30

40

50

00 50 100 150Outlet ice fraction (wt)

Deg

ree

of s

uper

heat

ing

(K)

10 ms15 ms20 ms25 ms

00

02

04

06

08

10


Rel

ativ

e su

perh

eatin

g ζ


Figure 89 Degree of superheating at the outlet for various ice slurry velocities

(Experiments 1 2 3 and 4)

Figure 810 Relative superheating ζ at the outlet for various ice slurry velocities


Chapter 8

184

843 Influence of Heat Flux

The results from the experiments with different ethylene glycol solution inlet temperatures in Figure 811 show that the degree of superheating increases as the heat flux increases However the relative superheating ζ is similar for different heat fluxes as is shown in Figure 812

00

10

20

30

40

50

00 20 40 60 80 100Outlet ice fraction (wt)

Deg

ree

of s

uper

heat

ing

(K)

26degC 148 microm00degC 148 microm26degC 277 microm

00

02

04

06

08


Rel

ativ

e su

perh

eatin

g ζ


Figure 811 Degree of superheating at the outlet for various heat fluxes (TEG) and crystal sizes (Experiments 8 9 and 10)

Figure 812 Relative superheating ζ at the outlet for various heat fluxes (TEG) and crystal sizes (Experiments 8 9 and 10)

844 Influence of Crystal Size

The results of experiments 8 and 10 in Figure 811 indicate that ice slurries consisting of larger crystals exhibit higher degrees of superheating Accordingly the relative superheating also increases as the average ice crystal size increases (see Figure 812) A comparison of the superheating results of experiments 2 and 5 in which the crystal size was also the only varied variable gives the same conclusion

845 Influence of Solute Concentration

The superheating results of the experiments with different solute concentrations are shown in Figures 813 and 814 The two figures indicate that both the degree of superheating and the relative superheating are higher in liquids with low solute concentration However it is difficult to compare the presented results because not only the solute concentration was different in these experiments but also the average crystal size As is shown above the average crystal size influences superheating significantly A more comprehensive analysis is therefore presented in the next subsection to unravel the influence of the solute concentration on superheating


185

00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)

35 wt 338 microm66 wt 249 microm110 wt 133 microm

00

02

04

06

08

10


Rel

ativ

e su

perh

eatin

g ζ


Figure 813 Degree of superheating at the outlet for various solute concentrations

(Experiments 2 6 and 7)

Figure 814 Relative superheating ζ at the outlet for various solute concentrations


846 Discussion

The presented results for superheating at the outlet of the heat exchanger can be explained by a model of the melting process This model is based on the heat and mass transfer processes in a control volume of the heat exchanger as shown in Figure 815 It is assumed that the control volume is ideally mixed which means that ice slurry is homogeneously distributed and that the liquid temperature is constant in the entire control volume

Figure 815 Schematic representation of melting process in a control volume

The control volume is considered as a steady state system and the heat balance is therefore

( )is isout isinQ m h h= minusamp amp (818)

The heat transferred from the wall to liquid in the control volume is given by

( )i i w liqQ A T Tα= minusamp with i iinnerA D xπ= ∆ (819)

Chapter 8

186

The increase of the enthalpy of ice slurry in Equation 818 is represented by

( )( ) ( )( )isout isin out liqout out iceout in liqin in icein1 1h h h h h hφ φ φ φminus = minus + minus minus + (820)

The ice fraction at the outlet in Equation 820 can be replaced by

out inφ φ φ= minus ∆ (821)

Combining Equations 820 and 821 gives the following expression for the change in enthalpy

( ) ( )( ) ( )isout isin liqout iceout in liqout liqin in iceout icein1h h h h h h h hφ φ φminus = ∆ minus + minus minus + minus (822)

The change in liquid enthalpy is approximated by the product of the temperature increase and the specific heat of the liquid It is assumed here that the heat of mixing can be neglected and that specific heats are constant for small temperature changes With these assumptions Equation 822 becomes

( )( )isout isin f in pliq in pice1h h h T c cφ φ φminus asymp ∆ ∆ + ∆ minus + (823)

Equation 823 shows that the increase of the enthalpy consists of a latent heat contribution represented by a decrease of the ice fraction and a sensible heat contribution represented by an increase of the temperature During the initial stage of the melting experiments the sensible heat contribution was 20 of the total enthalpy increase on average For simplicity the sensible heat contribution is neglected in this analysis and the enthalpy difference is assumed equal to the product of the change in ice fraction and the latent heat of fusion

isout isin fh h hφminus asymp ∆ ∆ (824)

Combining Equations 818 819 and 824 leads to the following heat balance for the control volume

( )i iinner w liq is fD x T T m hα π φ∆ minus = ∆ ∆amp (825)

The decrease of the ice fraction is caused by the melting of individual ice crystals The mass reduction of ice in the control volume is proportional to the total surface of ice crystals Aice and the negative growth rate G

ice ice icem A Gρ∆ = minusamp (826)

The decrease of the ice fraction is now calculated as the ratio between the reduction of the ice mass and the mass flow rate of ice slurry

ice ice ice

is is

m A Gm m

ρφ ∆∆ = = minus

amp

amp amp (827)


187

The total available crystal surface Aice for the melting process is proportional to the number of crystals in the control volume and the characteristic crystal size squared

2ice 1 FeretA c N D= (828)

It is assumed here that both the shape of the individual crystals as well as the shape of the crystal size distribution were the same in the various experiments The number of crystals N in Equation 828 is deduced from the total mass of ice in the control volume with the same assumptions

ice3

2 ice Feret

mNc Dρ

= with 2ice is is iinner4

m m D xπφ φρ= = ∆ (829)

The negative crystal growth rate G in Equation 827 is determined by mass and heat transfer between the crystal surface and the liquid phase of the slurry

eq liqA

eqice V f

liq cr

3T TBG

dTB hwk dw

ρρ α

minus=

∆minus +

(830)

Rearranging of Equation 830 shows explicitly the ratio between the heat and mass transfer coefficient

eq liqA

ice V eqcrf

cr f liq

31

T TBGB dTh w

k h dwρ α

α ρ

minus=

∆minus + ∆

(831)

This ratio of the coefficients is determined from the analogy between heat and mass transfer close to the crystal surface

1 1 1 23 3 3 3

1 23 3

cr liq liq pliq liq liqcr

cr D D DNu Pr c

k Sh Scλ λ ρ λα

= = = (832)

The expression of Equation 832 is substituted in Equation 831 resulting in a new expression for the crystal growth rate

1 2

3 3

2 23 3

eq liqcrA

ice V f pliq liq eq

f liq

31

D

T TBGB h c w dT

dwh

αρ λ

ρ

minus=

∆ minus + ∆

(833)

Equation 833 shows that both heat and mass transfer resistances determine the total resistance for melting However the ratio of these contributions strongly depends on the solute concentration as is shown in Figure 816 At low solute concentration of 35 wt for example the crystal growth rate is determined by equal contributions of heat and mass transfer resistance while at high concentrations the growth rate is almost completely determined by mass transfer

Chapter 8

188

00

10

20

30

40

50

60

70

00 20 40 60 80 100 120 140NaCl concentration in the liquid (wt)

Con

trib

utio

n to

cry

stal

gro

wth

re

sist

ance

rel

ativ

e to

hea

t tra

nsfe

r

Total

Mass transfer

Heat transfer

Figure 816 Contributions to crystal growth resistance relative to heat transfer resistance

Equations 828 829 and 833 are now substituted in Equation 827

1 2

3 3

2 23 3

2liq eqiinneris cr1 A

2 V ice Feret is f pliq liq eq

f liq

121

D

T TD xc Bc B D m h c w dT

dwh

φρ απφρ λ

ρ

minus∆∆ =

∆ minus + ∆

amp

(834)

Substitution of Equation 834 in the heat balance of Equation 825 finally gives an expression for the degree of superheating

( )

1 23 3

2 23 3

pliq liq eqV ice Feret2 ish liq eq w liq

1 A is iinner cr f liq

12 1 1Dc w dTB DcT T T T T

c B D dwhλρ α

ρ φ α ρ

∆ = minus = minus + minus ∆

(835)

Equation 835 shows that the degree of superheating is higher for slurries with large crystals which is in accordance with the experiments Ice slurries with large crystals have a relatively small crystal surface resulting in a slow melting process and exhibit therefore high degrees of superheating Ice slurries with low ice fractions have also relatively little crystal surface and exhibit therefore also high degrees of superheating This phenomenon is represented in Equation 835 by the ice fraction in the denominator

In correspondence with the experiments Equation 835 shows that the degree of superheating increases with increasing heat flux which is represented here by the temperature difference between wall and liquid However the ratio between the driving forces of the two stages of melting is not influenced by the heat flux Therefore the relative superheating does not depend on the heat flux which is in accordance with the experiments (see Figure 812)

The experiments showed that the relative superheating is hardly influenced by the ice slurry velocity This observation can also be explained by Equation 835 A higher ice slurry velocity results first of all in a higher heat transfer coefficient between wall and liquid However the heat and mass transfer coefficients between crystals and liquid also increase It is expected that the relative increases of all these coefficients are approximately similar as the


189

velocity increases and that therefore the relative superheating is almost independent of the ice slurry velocity

According to Equation 835 the degree of superheating is higher in aqueous solutions with higher solute concentrations This trend can not directly be confirmed by the experiments because the experiments with different solute concentrations also had different average crystals sizes In order to confirm the influence of the solute concentration all variables that have been varied in the experiments have been considered simultaneously For this purpose all experimental constants of Equation 835 are combined in one constant c3

( )

1 23 3

2 23 3

pliq liq eqice Feretsh 3 w liq

is f liq

1Dc w dTDT c T T

dwhλρ

ρ φ ρ

∆ = minus + minus ∆

with V2 i3

1 A iinner cr

12Bccc B D

αα

= (836)

The ratio of the heat transfer coefficients in the expression for c3 is assumed constant here The experiments with different ice slurry velocities showed similar relative superheating values indicating that this assumption is reasonable

The experimental variables at the right-hand side of Equation 836 are considered at the start of each experiment This analysis is limited to the initial phase of the experiments since the average ice crystal size was only determined prior to each experiment It is expected that the average crystal size decreases in the course of an experiment but this was not quantified

The results of this analysis for all ten melting experiments shown in Figure 817 confirm proportionality between the variables and the degree of superheating stated in Equation 836

00

05

10

15

20

000 001 002 003 004 005

∆T

shm

eas (

K) 1

2 34

56

7

8

9

10

-25

+25

(m K)( )1 2

3 3

2 23 3

pliq liq eqice Feretw liq

is f liq

1Dc w dTD T T

dwhλρ

ρ φ ρ

minus + minus ∆

Figure 817 Relation between variables at right-hand side of Equation 836 and measured

degrees of superheating the numbers in the figure represent the experiment number as listed in Table 81

Chapter 8

190

The expression in Equation 835 shows that the degree of superheating also depends on the tube diameter According to the expression the degree of superheating decreases with increasing tube diameter Since the diameter of the heat exchanger tube was not varied in the experiments this influence can not be confirmed

847 Conclusions

The degree of superheating at the outlet of melting heat exchangers is proportional to the average ice crystal size and the heat flux It is furthermore inversely proportional to the ice fraction and therefore superheating increases as the ice fraction decreases The negative growth rate of melting ice crystals is determined by both mass and heat transfer The degree of superheating increases therefore with increasing solute concentration especially at higher concentrations at which the heat transfer resistance plays a minor role Finally the degree of superheating is expected to be higher in heat exchangers with small hydraulic diameters but does hardly depend on the ice slurry velocity

85 Results and Discussion on Heat Transfer Coefficients


The experimental results of all ten melting experiments show that the wall-to-liquid heat transfer coefficient increases with increasing ice fraction as is shown for four experiments in Figure 818 The figure also shows that the relative increase of the heat transfer coefficient is especially high at low ice slurry velocities For an ice slurry velocity of 10 ms for example the heat transfer coefficient at an ice fraction of 13 wt is approximately 50 higher than for the case that all crystals have melted The relative increase of the heat transfer coefficient at a velocity of 25 ms for the same ice fractions is rather small The relatively high increase at low velocities and the limited increase at higher velocities is in accordance with the results in literature discussed in Section 824

0

1000

2000

3000

4000

5000

6000

00 50 100 150 200Average ice fraction (wt)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)


Figure 818 Wall-to-slurry heat transfer coefficients versus average ice fraction for different

ice slurry velocities (Experiments 1 2 3 and 4)


191

It is interesting to compare the measured heat transfer coefficients of Figure 818 with the values predicted by a heat transfer correlation for single-phase flow Such a heat transfer correlation has been formulated on the basis of calibration experiments with aqueous solutions and the Wilson plot calibration technique The entire procedure is described in Appendix C3 The heat transfer correlation for the inner tube is based on the Reynolds Nusselt and Prandtl number

3 0 903 0 33liq liq liq7 36 10 Nu Re Prminus= sdot for liq 6700Re le (837)

2 0 687 0 33liq liq liq5 06 10 Nu Re Prminus= sdot for liq 6700Re gt (838)

When this correlation is applied for ice slurry flow the dimensionless numbers can either be based on the thermophysical properties of the two-phase mixture or on the thermophysical properties of the liquid phase only The dynamic viscosity of a slurry is for example always higher than the viscosity of the liquid phase and the thermal conductivities of slurry and liquid can also strongly deviate (see also Appendix B2)

In order to compare measured heat transfer coefficients with heat transfer coefficients predicted on the basis of thermophysical liquid properties the heat transfer factor based on liquid properties is defined as

measliq

predliq

αα

Ψ = with predliqα based on liq liqNu Re and liqPr (839)

In analogy the heat transfer factor based on slurry properties is defined as

measis

predis

αα

Ψ = with predisα based on is isNu Re and isPr (840)

Figure 819 shows heat transfer factors based on liquid properties for the four experiments with different velocities while Figure 820 shows heat transfer factors based on slurry properties For high velocities the heat transfer factor based on liquid properties is close to unity for all ice fractions This means that the heat transfer coefficient of ice slurry for these velocities can be predicted within 10 by the heat transfer correlation in Equations 837 and 838 in combination with the thermophysical liquid properties For low velocities however real heat transfer coefficients are up to 50 higher than calculated by the heat transfer correlation using liquid properties The same is valid for heat transfer coefficients calculated on the basis of ice slurry properties For high ice fractions the heat transfer factors show values much higher than unity (see Figure 820) Real heat transfer coefficients are in fact up to 75 higher than expected from the heat transfer correlation based on slurry properties

A possible explanation for the relative steep increase in heat transfer as a function of the ice fraction at low velocities is that the ice crystals are not homogeneously distributed over the cross section of the tube Due to low turbulence levels at low velocities ice crystals float to the top of the tube It is plausible that these ice crystals touch the tube wall and disturb the thermal boundary layer which enhances the heat transfer coefficient At higher velocities the ice slurry flow shows a more homogeneous flow pattern For these conditions ice crystals are hardly present in the relatively hot vicinity of the tube wall It is therefore expected that the thermal boundary layer mainly consists of liquid and that the heat transfer coefficient can be predicted by the heat transfer correlation based on liquid properties

Chapter 8

192

08

10

12

14

16

18

20

00 50 100 150Average ice fraction (wt)


Hea

t tra

nsfe

r fa

ctor

Ψliq

08

10

12

14

16

18

20



Hea

t tra

nsfe

r fa

ctor

Ψis

Figure 819 Heat transfer factors based on liquid properties for various ice slurry velocities (Experiments 1 2 3 and 4)

Figure 820 Heat transfer factors based on slurry properties for various ice slurry velocities (Experiments 1 2 3 and 4)

In the rest of this section measured heat transfer coefficients are only compared to values calculated on the basis of slurry properties

852 Influence of Heat Flux and Ice Crystal Size

The experimental results in Figure 821 indicate that neither the heat flux nor the average ice crystal size influence the heat transfer coefficient This negligible influence of the heat flux is in accordance with several experimental studies reported in literature (see Section 824) The effect of the ice crystal size on heat transfer coefficients has not been studied before but this effect seems to be small according to the presented results It is however possible that even larger crystals do influence the heat transfer coefficient Larger crystals have namely a stronger tendency to float to the top of the tube and may therefore enhance heat transfer coefficients


Figure 822 shows that the enhancement of the heat transfer coefficient with increasing ice fraction is stronger at higher solute concentrations This phenomenon may be explained by the higher density difference between the liquid phase and the ice crystals At an ice fraction of 10 wt the density difference between liquid and solid phase is 113 kgm3 for the slurry with an initial solute concentration of 35 wt while this value is 179 kgm3 for the slurry with an initial solute concentration of 110 wt This higher density difference increases the buoyancy force on the ice crystals and therefore more ice crystals are located in the upper part of the tube It is expected that these crystals are in touch with the tube wall increasing heat transfer coefficients analogously to the heat transfer enhancement at low velocities


193

08

10

12

14

16

18

20

00 20 40 60 80 100Average ice fraction (wt)

Hea

t tra

nsfe

r fa

ctor

Ψis


08

10

12

14

16

18

20


Hea

t tra

nsfe

r fa

ctor

Ψis


Figure 821 Heat transfer factor based on slurry properties for various heat fluxes (TEG)

and crystal sizes (Experiments 8 9 and 10)

Figure 822 Heat transfer factors based on slurry properties for various solute

concentrations (Experiments 2 6 and 7)

854 Conclusions

Wall-to-liquid heat transfer coefficients of ice slurry during melting increase with increasing ice fraction This enhancement is especially high at low slurry velocities and for high density differences between liquid and ice For the studied operation conditions the heat flux and the average ice crystal size have no influence on the heat transfer coefficient

86 Results and Discussion on Pressure Drop


Figure 823 shows the pressure drop results as a function of the average ice fraction for the four experiments with different ice slurry velocities The figure shows that the pressure drop increases as the ice fraction increases which was observed for all ten melting experiments The measured pressure drop values can be compared with values predicted by the pressure drop model formulated in Appendix C34 According to this model the pressure drop of a single-phase flow in the inner tube of the heat exchanger can be predicted by

0 404liq liq2

pred 0 118liq liqiinner

1 42 for 67001 with 0 112 for 67002

f Re ReLp f uf Re ReD

ρminus

minus

= lt∆ = = ge (841)

Analogously to the prediction of heat transfer coefficients the pressure drop of solid-liquid flows can be predicted either on the basis of the thermophysical properties of the liquid phase or on the basis of the properties of the slurry The main difference in thermophysical properties with respect to pressure drop is the dynamic viscosity The viscosity of an ice slurry with an ice fraction of 10 wt is namely 45 higher than the viscosity of the liquid phase only This higher viscosity leads to a lower Reynolds number and therefore to a higher friction factor f

Chapter 8

194

000

020

040

060

080

100

120

140


Pres

sure

dro

p (b

ar)


Figure 823 Pressure drop versus average ice fraction for different ice slurry velocities


The pressure drop factor based on liquid properties compares measured pressure drop values with values predicted on the basis of liquid properties and is defined as

measliq

predliq

pp

∆Π =

∆ with predliqp∆ based on liqRe (842)

In the same way the pressure drop factor based on slurry properties is defined as

measis

predis

pp

∆Π =

∆ with predisp∆ based on isRe (843)

Figures 824 and 825 show the pressure drop factors for the experiments with different ice slurry velocities The pressure drop factor based on liquid properties in Figure 824 increases up to values of 13 as the ice fraction increases from 0 to 15 wt This means that the application of liquid properties in the pressure drop model of Equation 841 leads to underestimation of real pressure drop values for ice slurry flow However the pressure drop factor based on slurry properties in Figure 825 shows values close to unity for all tested ice fractions and velocities The pressure drop of ice slurry with ice fractions up to 15 wt can thus be predicted by the model of Equation 841 using slurry properties

862 Influence of Heat Flux Ice Crystal Size and Solute Concentration

The results of the experiments with different heat fluxes and different average ice crystal sizes show the same relation between ice fraction and pressure drop which means that the pressure drop is not influenced by any of these parameters Figure 826 confirms this observation by showing pressure drop factors close to unity for all different conditions


195

08

10

12

14

16



Pres

sure

dro

p fa

ctor

Πliq

08

10

12

14

16



Pres

sure

dro

p fa

ctor

Πis

Figure 824 Pressure drop factor based on liquid properties for various ice slurry velocities (Experiments 1 2 3 and 4)

Figure 825 Pressure drop factor based on slurry properties for various ice slurry velocities (Experiments 1 2 3 and 4)

The pressure drop results for the experiments with different solute concentrations show approximately the same results In accordance with the other experiments the pressure drop factor for the experiments with initial solute concentrations of 35 and 66 wt is also close to unity However the experiment with the highest solute concentration of 110 wt shows a slightly increasing pressure drop factor as the ice fraction increases (see Figure 827) This behavior may be caused by the relative high density difference between the liquid and the solid phase at high solute concentration As a result the buoyancy force on the crystals is stronger and the flow pattern may change from homogeneous to heterogeneous flow or even moving bed flow This changing flow pattern may be the cause for the 10 difference between the measured and the predicted pressure drop value

08

10

12

14

16


Pres

sure

dro

p fa

ctor

Πis


08

10

12

14

16


Pres

sure

dro

p fa

ctor

Πis


Figure 826 Pressure drop factor based on slurry properties for various heat fluxes (TEG)


Figure 827 Pressure drop factor based on slurry properties for various solute


Chapter 8

196

863 Conclusions

Pressure drop values of ice slurry flows with ice fractions up to 15 wt can be predicted by using pressure drop correlations for single-phase flow The application of the thermophysical properties of the slurry in these correlations leads to absolute errors of 10 and smaller

87 Conclusions

The liquid temperature of ice slurry in melting heat exchangers can be significantly higher than the equilibrium temperature This phenomenon is referred to as superheating and can lead to a serious reduction of heat exchanger capacities The degree of superheating at the outlet of heat exchangers is proportional to the average ice crystal size and the heat flux It is furthermore inversely proportional to the ice fraction and therefore superheating increases as the ice fraction decreases The negative growth rate of melting ice crystals is determined by both heat and mass transfer The degree of superheating increases therefore with increasing solute concentration especially at higher concentrations at which the heat transfer resistance plays a minor role Finally the degree of superheating is expected to be higher in heat exchangers with small hydraulic diameters

Wall-to-liquid heat transfer coefficients and pressure drop values increase with increasing ice fraction The heat transfer enhancement is especially high at low slurry velocities or high density differences between liquid and ice Pressure drop values for ice fractions up to 15 wt can be predicted within 10 by applying a single-phase flow pressure drop correlation in which the slurry properties are used Both heat flux and average ice crystal size do neither influence the heat transfer coefficient nor the pressure drop


197

Nomenclature

A Area (m2) Greek BA Area shape factor α Heat transfer coefficient (Wm2K) BV Volume shape factor δ Boundary layer thickness (m) c13 Constants ζ Relative superheating defined in cp Specific heat (Jkg K) Eq 816 DFeret Average crystal Feret diameter (m) λ Thermal conductivity (Wm K) D Tube diameter (m) micro Viscosity (Pa s) D Diffusion coefficient (m2s) Πliq Pressure drop factor based on liquid f Friction factor properties defined in Eq 842 G Growth rate (ms) Πis Pressure drop factor based on slurry h Enthalpy (Jkg) properties defined in Eq 843 ∆hf Latent heat of fusion of ice (Jkg) ρ Density (kgm3) k Mass transfer coefficient (ms) τ Period (h) L Tube length (m) φ Ice mass fraction m Mass (kg) Ψliq Heat transfer factor based on liquid ampm Mass flow (kgs) properties defined in Eq 839

N Number of crystals Ψis Heat transfer factor based on slurry n Number of measurements properties defined in Eq 840 Nucr Liquid Nusselt number αcr DFeretλliq Nuliq Liquid Nusselt number αi Diinnerλliq Subscripts Nuis Slurry Nusselt number αi Diinnerλis corio Coriolis mass flow meter Prliq Liquid Prandtl number cpliq microliqλliq cr Crystal Pris Slurry Prandtl number cpsensis microisλis EG Ethylene glycol solution ∆p Pressure drop (Pa) end End of experiment ampQ Heat (W) eq Equilibrium

Reliq Liquid Reynolds number eqin Equilibrium assumed at inlet ρliq u Diinnermicroliq fr Freezing point Reis Slurry Reynolds number ρis u Dmicrois he Heat exchanger Sc Schmidt number microliq(ρliq D) i Inside Shcr Crystal Sherwood number k DFeretD ice Ice T Temperature (degC) in Inlet heat exchanger Tfr Initial freezing temperature (degC) init Initial ∆Tln Logarithmic mean temperature inner Inner difference (K) is Ice slurry ∆Tsh Degree of superheating (K) defined liq Liquid in Eq 815 meas Measured t Time (s) o Outside ∆t Measurement interval (s) out Outlet heat exchanger U Overall heat transfer coefficient pred Predicted (Wm2K) real Real u Velocity (ms) rest Other components Vamp Volume flow (m3s) sens Sensible w Solute mass fraction src Source w0 Initial solute mass fraction in liquid stor Storage ∆x Length of control volume (m) w Wall

Chapter 8

198

References


Bedecarrats J Strub F Peuvrel C Dumas J 2003 Heat transfer and pressure drop of ice slurry in a heat exchanger In Proceedings of 21st IIR International Congress of Refrigeration 17-23 August 2003 Washington DC (USA) Paris International Institute of Refrigeration

Bellas J Chaer I Tassou SA 2002 Heat transfer and pressure drop of ice slurries in plate heat exchangers Applied Thermal Engineering vol22 pp721-732

Christensen K Kauffeld M 1997 Heat transfer measurements with ice slurry In International ConferencendashHeat Transfer Issues in Natural Refrigerants Paris International Institute of Refrigeration pp127ndash141

Darby R 1986 Hydrodynamics of slurries and suspensions In Cheremisinoff NP (Ed) Encyclopedia of fluid mechanics ndash Volume 5 Slurry Flow Technology Houston Gulf pp49-92

Doetsch C 2001 Pressure drop and flow pattern In Proceedings of the 3rd IIR Workshop on Ice Slurries 16-18 May 2001 Lucerne (Switzerland) Paris International Institute of Refrigeration pp53-68

Doetsch C 2002 Pressure drop calculation of ice slurries using the Casson model In Proceedings of the 5th IIR Workshop on Ice Slurries 30-31 May 2002 Stockholm (Sweden) Paris International Institute of Refrigeration pp15-21

Egolf PW Kitanovski A Ata-Caesar D Stamatiou E Kawaji M Bedecarrats JP Strub F 2005 Thermodynamics and heat transfer of ice slurries International Journal of Refrigeration vol28 pp51-59

Fikiin K Wang M-J Kauffeld M Hansen TM 2005 Direct contact chilling and freezing of foods in ice slurries In Kauffeld M Kawaji M Egolf PW (Eds) Handbook on Ice Slurries Fundamentals and Engineering Paris International Institute of Refrigeration pp251-271



Guilpart J Fournaison L Ben-Lakhdar MA Flick D Lallemand A 1999 Experimental study and calculation method of transport characteristics of ice slurries In Proceedings of the 1st IIR Workshop on Ice Slurries 27-28 May 1999 Yverdon-les-Bains (Switzerland) Paris International Institute of Refrigeration pp74-82


199

Hansen TM Radošević M Kauffeld M Zwieg T 2003 Investigation of ice crystal growth and geometrical characteristics in ice slurry International Journal of HVACampR Research vol9 pp9-32

Jensen E Christensen K Hansen T Schneider P Kauffeld M 2000 Pressure drop and heat transfer with ice slurry In Proceedings of the 4th IIR Gustav Lorentzen Conference on Natural Working Fluids 25-28 July 2000 Purdue (USA) Paris International Institute of Refrigeration pp521ndash529

Kitanovski A Poredoš A Reghem P Stutz B Dumas JP Vuarnoz D Sari O Egolf PW Hansen TM 2002 Flow patterns of ice slurry flows In Proceedings of the 5th IIR Workshop on Ice Slurries 30-31 May 2002 Stockholm (Sweden) Paris International Institute of Refrigeration pp36-46

Kitanovski A Sarlah A Poredoš A Egolf PW Sari O Vuarnoz D Sletta JP 2003 Thermodynamics and fluid dynamics of phase change slurries in rectangular channels In Proceedings of the 21st IIR International Congress of Refrigeration 17-223 August 2003 Washington DC (USA) Paris International Institute of Refrigeration

Kitanovski A Vuarnoz D Ata-Caesar D Egolf PW Hansen TM Doetsch C 2005 The fluid dynamics of ice slurry International Journal of Refrigeration vol28 pp37-50

Knodel BD France DM Choi U Wambsganss M 2000 Heat transfer and pressure drop in ice-water slurries Applied Thermal Engineering vol20 pp671ndash685

Lee DW Yoon CI Yoon ES Joo MC 2002 Experimental study on flow and pressure drop of ice slurry for various pipes In Proceedings of the 5th IIR Workshop on Ice Slurries 30-31 May 2002 Stockholm (Sweden) Paris International Institute of Refrigeration pp22-29

Lee DW Yoon ES Joo MC Sharma A 2006 Heat transfer characteristics of the ice slurry at melting process in a tube flow International Journal of Refrigeration vol29 pp451-455


Niezgoda-Żelasko B 2006 Heat transfer of ice slurry flows in tubes International Journal of Refrigeration vol29 pp437-450

Niezgoda-Żelasko B Zalewski W 2006 Momentum transfer of ice slurry flows in tubes experimental investigations International Journal of Refrigeration vol29 pp418-428

Noslashrgaard E Soslashrensen TA Hansen TM Kauffeld M 2005 Performance of components of ice slurry systems pumps plate heat exchangers and fittings International Journal of Refrigeration vol28 pp83-91

Shook CA Roco MC 1991 Slurry Flow Principles and Practice Boston Butterworth-Heinemann

Chapter 8

200

Stamatiou E Kawaji M 2005 Thermal and flow behavior of ice slurries in a vertical rectangular channel - Part II Forced convective melting heat transfer International Journal of Heat and Mass Transfer vol48 pp3544-3559

Torres-de Mariacutea G Abril J Casp A 2005 Coefficients deacutechanges superficiels pour la reacutefrigeacuteration et la congeacutelation daliments immergeacutes dans un coulis de glace International Journal of Refrigeration vol28 pp1040-1047

Wasp EJ Kenny JP Gandhi RL 1977 Solid-liquid Flow Slurry Pipeline Transportation Clausthal Trans Tech

201

9 Conclusions

Ice Scaling Prevention in Fluidized Bed Heat Exchangers

Ice scaling during ice crystallization from aqueous solutions in liquid-solid fluidized bed heat exchangers can only be prevented when a certain difference between the wall temperature and the equilibrium temperature of the solution is not exceeded This so-called transition temperature difference depends on operating parameters such as fluidized bed parameters and liquid properties The explanation for this phenomenon is that ice scaling is only successfully prevented when the removal rate induced by fluidized particles exceeds the growth rate of ice crystals attached to the cooled wall

The scale removal rate in stationary fluidized beds is proportional to the impulse exerted by particles-wall collisions The transition temperature difference increases therefore as the bed voidage decreases or the particle size increases Of all tested fluidized bed conditions the highest transition temperature difference was achieved for a fluidized bed with a bed voidage 81 consisting of 4 mm stainless steel particles In circulating fluidized beds the scale removal rate is determined by both particle-wall collisions and liquid pressures fronts induced by particle-particle collisions The scale removal rate by liquid pressure fronts is also proportional to the impulse they exert on the wall but with a lower proportionality constant At higher circulation rates both the frequency and the average maximum pressure of liquid pressure fronts increases resulting in a higher total exerted impulse on the wall and enhanced removal rates Due to this enhancement the transition temperature difference for ice scaling increases as the circulation rate increases A disadvantage of circulating fluidized beds for ice slurry production is the high risk of blockages in the downcomer tube

The growth rate of ice crystals attached to a cooled wall in an aqueous solution is determined by mass transfer The ice crystals that grow on the wall absorb only water molecules and therefore dissolved solute molecules or ions accumulate near the ice interface and slow down the crystal growth rate The growth rate of ice crystals on the wall is therefore inversely proportional to the solute concentration and increases with increasing diffusion coefficient Besides the growth rate is proportional to the difference between the wall temperature and the equilibrium temperature of the solution Due to these two effects the transition temperature difference for ice scaling is proportional to the solute concentration and is higher in aqueous solutions with low diffusion coefficients A model based on these physical mechanisms has been proposed to predict ice scaling in fluidized bed heat exchangers A validation with experimental results demonstrates that the model is applicable for a wide variety of solutes and concentrations showing an average absolute error of 144

Fluidized Bed Heat Exchangers for other Crystallization Processes

Besides ice crystallization processes fluidized bed heat exchangers are also attractive for other industrial processes that suffer from severe crystallization fouling such as cooling crystallization of salts and eutectic freeze crystallization In case of cooling crystallization of salts fluidized bed heat exchangers are able to prevent crystallization fouling of KNO3 and MgSO47H2O for heat fluxes up to 17 kWm2 Crystallization fouling during eutectic freeze crystallization from binary solutions is however not prevented by fluidized particles which can be explained by an extension of the ice scaling model It is supposed that salt crystallization during eutectic freeze crystallization takes up the salt ions that accumulate near

Chapter 9

202

the ice interface during ice growth The crystallizing ions therefore do not hinder the growth of ice crystals on the wall resulting in higher growth rates and more severe ice scaling The addition of a non-crystallizing solute considerably reduces fouling and achieves that eutectic freeze crystallization can be operated at heat fluxes of 10 kWm2 or higher From these results can be concluded that the ice growth rate and thus ice scaling is only determined by the non-crystallizing solutes

Comparison between Fluidized Bed and Scraped Surface Heat Exchangers

The transition temperature difference for ice scaling in a scraped surface heat exchanger is about 75 times higher than in a stationary fluidized bed heat exchanger with stainless steel particles of 4 mm in size operated at a bed voidage of 81 The heat flux at which ice scaling occurs is more than four times higher than in the fluidized bed heat exchanger The transition temperature difference in scraped surface heat exchangers increases with decreasing ice slurry temperature or with increasing solute concentration which is in correspondence with fluidized bed ice slurry generators The heat transfer performance of both ice slurry generators is comparable

The investment costs of fluidized bed heat exchangers per square meter of heat transfer surface are relatively low compared to the costs of scraped surface heat exchangers Fluidized bed ice slurry generators should be operated at ice slurry temperatures of about ndash5degC with a heat flux of approximately 10 kWm2 while scraped surface ice slurry generators are normally operated at ndash2degC with a heat flux of 20 kWm2 A comparison between these two crystallizers for installations of 100 kW and higher shows that the investment costs of fluidized bed ice slurry generators are about 30 tot 60 lower than of commercially available scraped surface ice slurry generators In addition the energy consumption of systems using fluidized bed ice slurry generators is about 5 to 21 lower It can therefore be concluded that the fluidized bed ice slurry generator is an attractive ice crystallizer concerning both investment costs and energy consumption

Ice Crystallization Phenomena during Storage and Melting of Ice Slurry

Besides the ice slurry production stage ice crystals are also subject to crystallization phenomena in other components of ice slurry systems such as storage tanks and melting heat exchangers During isothermal storage in tanks the crystal size distribution alters by means of recrystallization mechanisms of which Ostwald ripening is most important Due to surface energy contributions small crystals dissolve while larger crystals grow resulting in an increase of the average crystal size The rate of Ostwald ripening decreases with increasing solute concentration and depends furthermore on the solute type and initial average ice crystal size In melting heat exchangers ice slurry can seriously be superheated which means that the liquid temperature is significantly higher than the equilibrium temperature This phenomenon may result in reduced heat exchanger capacities The degree of superheating at the outlet of heat exchangers is proportional to the average ice crystal size and the heat flux It is furthermore inversely proportional to the ice fraction and depends also on the solute concentration

The described phenomena in storage tanks and melting heat exchangers can be explained by crystallization kinetics The growth and melting rates of suspended ice crystals are mainly determined by heat and mass transfer resistances while surface integration plays a minor role during growth The mass transfer resistance is proportional to the solute concentration while the heat transfer resistance hardly depends on the solute At low solute concentrations

Conclusions

203

corresponding to equilibrium temperatures of about ndash2degC and higher the crystallization kinetics are therefore dominated by heat transfer while mass transfer dominates at higher concentrations These crystallization kinetics result in slow crystal growth and melting processes at high solute concentrations or for solutes with relatively small diffusion coefficients Slow growth and melting processes lead to low Ostwald ripening rates in storage tanks and high degrees of superheating at the outlet of melting heat exchangers The latter effect is also achieved when the available ice crystal surface is small which occurs at low ice fractions or for relatively large ice crystals

Overall Conclusions

Fluidized bed heat exchangers are attractive crystallizers for ice slurry production in indirect refrigeration systems Installations using fluidized bed ice slurry generators have lower investment costs and lower energy consumptions compared to systems that use scraped surface heat exchangers Besides ice slurry production fluidized bed heat exchangers are also attractive for other industrial crystallization processes that suffer from severe crystallization fouling such as cooling crystallization and eutectic freeze crystallization

Several phenomena in ice slurry systems can be explained by the crystallization kinetics of ice crystals in aqueous solutions which are determined by heat transfer mass transfer and surface integration Ice scaling during ice slurry production in fluidized bed heat exchangers is for example only prevented when the growth rate of ice crystals attached to the heat exchanger wall does not exceed the removal rate induced by fluidized particles This ice growth rate is mainly determined by mass transfer and is therefore lower in solutions with higher solute concentrations and with lower diffusion coefficients resulting in less severe ice scaling The crystallization kinetics of suspended ice crystals in storage tanks and melting heat exchangers are also strongly influenced by mass transfer although heat transfer also plays a role at low solute concentrations In these components the crystallization kinetics determine the rate of Ostwald ripening during storage and the degree of superheating during melting in heat exchangers

Chapter 9

204

205

Appendix A Properties of Aqueous Solutions

This appendix describes models to predict properties of the aqueous solutions used in this thesis The solution properties that are discussed are phase equilibrium data density specific heat thermal conductivity dynamic viscosity enthalpy and diffusion coefficient The first part of this appendix gives the general models to calculate these properties the second part contains coefficients for these models for each specific aqueous solution Some of the coefficients were directly taken from literature sources while other coefficients were fit with help of measurement data points from literature or were determined with models that had been expressed in a different form

A1 Model Description

A11 Phase Equilibrium Data

Figure A1 shows a characteristic phase diagram of a binary water-solute system The ice line represents the relation between the solute concentration and the temperature at which solution and ice crystals are in equilibrium The solubility line analogously represents the equilibrium between the solution and the solid phase of the solute Some of the electrolyte solutes used have more than one solid state since they can form different hydrates In these cases also more than one solubility line exists

Solute concentration

Tem

pera

ture

Aqueous solution

Eutectic point

Solid solute +aqueous solution

Ice +aqueous solution

Ice + solid solute

Ice line

Solubility line

0degC

T eut

0 wt w eut

Figure A1 Typical binary phase diagram of water-solute system

The point where the ice line intersects the solubility line is called the eutectic point At this temperature (Teut) and solute concentration (weut) solid solute ice and aqueous solution are in equilibrium and can exist simultaneously

In this appendix phase equilibrium lines are represented by polynomials as shown in Equations A1 and A2

5i

eq ii 0

T C w=

= sum with T in (degC) and w in (wt) (A1)

Appendix A

206

5i

eq ii 0

w C T=

= sum with w in (wt) and T in (degC) (A2)

The coefficients Ci for the different solutes used are given in the second part of this appendix Coefficients that are not given are equal to zero

A12 Density Specific Heat and Thermal Conductivity

Density specific heat and thermal conductivity are a function of both the solution temperature and the solute concentration Equation A3 presents the general expression that is used to calculate these three properties for different solutions (Melinder 1997)

( ) ( )( )

5 3i j

ij m mi 0 j 0

f C w w T T= =

= sdot minus sdot minussumsum with w in (wt) and T in (degC) (A3)

The function f in this expression represents the density ρ in (kgm3) the specific heat cp in (Jkg K) or the thermal conductivity λ in (Wm K) Coefficients Cij and constants wm and Tm for different solutions are listed in the second part of this appendix

A13 Dynamic Viscosity

In analogously with the previous properties the dynamic viscosity micro in (Pa s) can be calculated with Equation A4 (Melinder 1997)

( ) ( ) ( )( )5 3

i j3ij m m

i 0 j 0

ln 10 C w w T Tmicro= =

sdot = sdot minus sdot minussumsum with T in (degC) and w in (wt) (A4)

Coefficients Cij and constants wm and Tm for different solutions are listed in the second part of this appendix

A14 Enthalpy

In this thesis the enthalpy of water in a liquid state at 0degC and the enthalpy of solute in its normal state at 0degC are defined as zero

2H O 0degC 0h equiv (A5)

solute 0degC 0h equiv (A6)

With this definition it is possible to formulate the enthalpy of an aqueous solution

2

diss

sol solute diss H O diss diss diss psol 1 100 100

T

T

w wh w T h T h T h w T c w T dT = + minus + ∆ + int (A7)

The enthalpy of an aqueous solution firstly consist of the partial sensible heat contributions to heat both solute and water from 0degC to the temperature Tdiss at which the heat of dissolution ∆hdiss is defined For the case where the solute is mixed with water instead of dissolved the enthalpy of dissolution should be replaced by the enthalpy of mixing ∆hmix and the dissolution temperature by the mixing temperature Tmix The second contribution is the heat of dissolution

Properties of Aqueous Solutions

207

or mixing itself and the last contribution is sensible heat contribution of the solution Below all three contributions will be discussed in more detail

The sensible heat contribution of the solute is estimated by

solute psolute psolute

0degC

T

h T c T dT c T= asympint with T in (degC) (A8)

The sensible heat contribution of water is estimated by an expression which is deduced from specific heat measurements cited by Dorsey (1940) and which is valid between 0 and 30degC

2 2

2 2 3H O pH O

0degC

42163 1495 1925 10T

h T c T dT T T Tminus= asymp minus + sdotint with T in (degC) (A9)

The heat of dissolution or mixing is a function of both the solute concentration and the temperature However most literature sources provide only data on heats of dissolution or mixing at a specific temperature Tdiss or Tmix The data for different solutions found in literature have all been transformed into the following form

3i

diss diss ii 1

h w T C w=

∆ = sum with w in (wt) (A10)

The sensible heat contribution of the solution can be split up into two parts

m

diss diss m

psol psol psol TT T

T T T

c w T dT c w T dT c w T dT= +int int int with w in (wt) (A11)

The first part of the right-hand side of Equation A11 can be simplified by using the expression for specific heat given in Equation A3

m

diss

psol T

T

c w T dTint ( )diss

0

psol m mmT T

c w T T d T Tminus

= minus minusint (A12)

( ) ( )( ) ( )

diss 5 3i j

ij m m mi 0 j 00

mT T

C w w T T d T Tminus

= =

= minus sdot minus sdot minus minussumsumint (A13)

( ) ( )

5 3i j+1

ij m diss mi 0 j 0

1j+1

C w w T T= =

= sdot minus sdot minus

sumsum (A14)

( )( )5

ii ij diss m m

i 0 c j C T T w w

=

= sdot minussum (A15)

Appendix A

208

Analogously the second part of the right-hand side of Equation A11 can be simplified by the same method as shown above

m

psol T

T

c w T dTint ( ) ( )( ) ( )m 5 3

i jij m m m

i 0 j 00

T T


= =

= sdot minus sdot minus minussumsumint (A16)

( ) ( )

5 3i j+1

ij m mi 0 j 0

1j+1

C w w T T= =


sumsum (A17)

Equations A8 A9 A10 A15 and A17 can be combined into Equation A7 as a result of which one general enthalpy model can be derived for a specific aqueous solution The model can be transformed into the same form as the expressions for density specific heat and thermal conductivity as proposed by Melinder (1997)

( ) ( )( )

5 4i k

ik m mi 0 k 0

h C w w T T= =

= sdot minus sdot minussumsum with h in (Jkg) w in (wt) and T in (degC) (A18)

The coefficients Cij and constants wm and Tm for calculating the enthalpy of aqueous solutions can be found in the second part of this appendix

A15 Diffusion Coefficient

The binary diffusion coefficient of an aqueous solution depends on the solute concentration and the temperature (Cussler 1997) Calculation models for binary diffusion coefficients of aqueous solutions that are suitable over a large temperature range are not available in literature Therefore an expression for the diffusion coefficient at the lowest reported temperature T0 is deduced from measured data available in literature

5i

0 ii 1

D wT C w=

= sum with D in (m2s) w in (wt) and T in (degC) (A19)

According to Reid et al (1987) and Cussler (1997) the product of the diffusion coefficient and the dynamic viscosity divided by the temperature in Kelvin does hardly depend on the temperature

D constant273 15T

micro=

+ (A20)

This statement was experimentally confirmed for aqueous solutions by Garner and Marchant (1961) for a temperature range from 15 to 40degC and by Byers and King (1966) for a temperature range from 20 to 70degC In this thesis binary diffusion coefficients of aqueous solutions are therefore estimated by using Equation A20 in which the diffusion coefficient at T0 is estimated from Equation A19

0

00

273 15D D273 15

wT T wT wTwT T

micromicro

+= +

(A21)


209

A2 Organic Aqueous Solutions

A21 D-glucose (C6H12O6)

Other names Dextrose grape sugar

CAS number 50-99-7

Molecular mass 18016 gmol

State at 0degC Solid

-100

-50

00

50

100

150

200

250

00 50 100 150 200 250 300 350 400 450 500Dextrose concentration (wt)

Tem

pera

ture

(degC

)

Aqueous solution

Ice + aqueous solution

Ice linedextrose

α-monohydrate + aqueous solution

Solubility line

Figure A2 Phase diagram of the water-dextrose system

Table A1 Ice line of water-dextrose system (see Equations A1 and A2) Function Domain C1 C2 C3 C4 C5 weqT1 -5hellip0degC -9291 -08127 -4617E-02 -1389E-03 -1666E-05Teqw1 0hellip31 wt -01217 1179E-03 -1185E-04 1832E-06 -1811E-08

1Deduced from Young (1957)

Table A2 Solubility line of C6H12O6middotH2O in water (see Equations A1 and A2) Function Domain C0 C1 C2 C3 C4 weqT1 -5hellip52degC 3378 06215 3080E-03 -2310E-05 - Teqw2 31hellip71 wt -6929 2632 -2097E-02 1116E-04 -

1Young (1957) 2Deduced from Young (1957)

Appendix A

210

Density specific heat thermal conductivity dynamic viscosity and diffusion coefficient data of aqueous dextrose solutions are only available at the ice line Because of this the properties of dextrose solutions are not presented here in the standard form as described in Section A1 Below expressions for the mentioned thermophysical properties at the ice line are given as a function of the freezing temperature Teq in (degC) for the range from ndash7 to 0degC (Huige 1972)

Density in (kgm3) 2eq eq1000 0 3606 2 266 T Tρ = minus minus (A22)

Specific heat in (Jkg K) 2p eq eq4216 244 3 15 77c T T= minus + (A23)

Thermal conductivity (Wm K) 2 4 2eq eq0 5576 2 307 10 9 595 10 T Tλ minus minus= + sdot + sdot (A24)

Dynamic viscosity (Pa s) ( )3 4 2eq eqln 10 0 5179 0 3208 9 793 10 T Tmicro minussdot = minus minus sdot (A25)

Diffusion coefficient (m2s) 10 11 12 2eq eqD 3 541 10 6 683 10 4 322 10 T Tminus minus minus= sdot + sdot + sdot (A26)


211

A22 Ethanol (C2H6O)

Other names Ethyl alcohol alcohol

CAS number 64-17-5


State at 0degC Liquid

Specific heat 2438 Jkg K at 25degC (Lide 1995)

-250

-200

-150

-100

-50

00

50

00 50 100 150 200 250 300 350 400Ethanol concentration (wt)

Tem

pera

ture

(degC

) Aqueous solution


Ice line

Figure A3 Phase diagram of water-ethanol system

Table A3 Ice line of water-ethanol system (see Equations A1 and A2) Function Domain C1 C2 C3 C4 C5 weqT1 -30hellip0degC -2635 -8340E-02 -1583E-03 -7171E-06 - Teqw1 0hellip40 wt -04268 3709E-03 -4336E-04 -1806E-06 1347E-07

1Deduced from Flick (1998)

Table A4 Heat of mixing of water-ethanol system (see Equation A10) Function Domain Tmix C1 C2 C3 ∆hmixw1 0hellip40 wt 00degC -3394E+03 5666 1055E-02

1Deduced from Beggerow (1976)

Appendix A

212

Table A5 Coefficients of water-ethanol system for calculating thermophysical properties (see Equations A3 A4 and A18)

Property Density1 Specific heat1 Thermal conductivity1

Dynamic viscosity1 Enthalpy

Symbol ρ cp λ micro h Unit kgm3 Jkg K Wm K Pa s Jkg

w 11hellip60 wt 11hellip60 wt 11hellip60 wt 11hellip60 wt 11hellip40 wt T Teqhellip20degC Teqhellip20degC Teqhellip20degC Teqhellip20degC Teqhellip20degC

wm 389250 389250 389250 389250 389250 Tm -49038 -49038 -49038 -49038 -49038 C00 9544E+02 3925E+03 03545 2214 -6381E+04 C01 -06416 3876 4421E-04 -5710E-02 3925E+03 C02 -2495E-03 2300E-04 -2942E-07 4679E-04 1938 C03 1729E-05 1322E-05 -1115E-08 -1374E-06 7667E-05 C04 - - - - 3305E-06 C10 -1729 -2795 -4334E-03 8025E-04 1316E+03 C11 -1824E-02 01773 -2021E-05 2618E-04 -2795 C12 3116E-04 4769E-05 -4865E-09 -8472E-06 8865E-02 C13 -6425E-07 3008E-06 2972E-10 1478E-07 1590E-05 C14 - - - - 7520E-07 C20 -2193E-02 -9620E-02 3021E-05 -7330E-04 5844 C21 5847E-04 -3908E-03 4239E-07 7056E-06 -9620E-02 C22 -2517E-06 1951E-05 1007E-09 2473E-07 -1954E-03 C23 -2875E-08 3366E-08 -7325E-12 -1329E-08 6503E-06 C24 - - - - 8415E-09 C30 6217E-04 7580E-03 6904E-07 4285E-07 -2686E-02 C31 4208E-06 2283E-05 -3203E-09 3239E-07 7580E-03 C32 -3460E-07 -9149E-07 -1439E-11 -1234E-08 1142E-05 C33 - - - - -3050E-07 C40 2288E-06 -1213E-04 -1512E-08 4313E-08 5642E-04 C41 -4141E-07 2545E-06 -3486E-10 8582E-09 -1213E-04 C42 - - - - 1273E-06 C50 -6412E-07 2235E-07 -1012E-09 7654E-09 -1096E-06 C51 - - - - 2235E-07

1Melinder (1997)

Table A6 Diffusion coefficient of water-ethanol system (see Equation A19) Function Domain T0 C0 C1 C2 C3 C4 Dw 1 0hellip35 wt 250degC 1240E+09 3237E+11 2835E-13 - -

1Deduced from Hammond and Stokes (1953)


213

A23 Ethylene Glycol (C2H6O2)

Other names 12-ethanediol ethylene alcohol

CAS number 107-21-1



Specific heat 2350 Jkg K on average between 0 and 25degC (Holman 1997)

-250

-200

-150

-100

-50

00

50

00 50 100 150 200 250 300 350 400Ethylene glycol concentration (wt)

Tem

pera

ture

(degC

) Aqueous solution


Ice line

Figure A4 Phase diagram of water-ethylene glycol system

Table A7 Ice line of water-ethylene glycol system (see Equations A1 and A2) Function Domain C1 C2 C3 C4 C5 weqT1 -40hellip0degC - 3409 -01429 -4401E-03 -7259E-05 -4809E-07Teqw1 0hellip54 wt -02869 -5450E-03 1230E-04 -8090E-06 8911E-08

1Deduced from Melinder (1997)

Table A8 Heat of mixing of water-ethylene glycol system (see Equation A10) Function Domain Tmix C1 C2 C3 ∆hmixw1 0hellip100 wt 250degC -10865 12534 -1675E-02


Appendix A

214

Table A9 Coefficients of water-ethylene glycol system for calculating thermophysical properties (see Equations A3 A4 and A18)





wm 381615 381615 381615 381615 381615 Tm 63333 63333 63333 63333 63333 C00 1056E+03 3501E+03 04211 1453 -2971E+03 C01 -03987 3954 7995E-04 -3747E-02 3501E+03 C02 -3068E-03 6065E-05 -5509E-08 2842E-04 1977 C03 1233E-05 -5979E-06 -1460E-08 -8025E-07 2022E-05 C04 - - - - -1495E-06 C10 1505 -2419 -3694E-03 2920E-02 -2300E+02 C11 -8953E-03 01031 -1751E-05 -1131E-04 -2419 C12 6378E-05 4312E-05 6656E-08 1729E-06 5155E-02 C13 -1152E-07 5168E-06 2017E-09 -5073E-08 1437E-05 C14 - - - - 1292E-06 C20 -1634E-03 4613E-03 2095E-05 1264E-04 1052 C21 1541E-04 -6595E-05 2078E-07 6785E-09 4613E-03 C22 -1874E-06 1620E-05 -2394E-09 -1685E-08 -3298E-05 C23 -9809E-09 -3250E-07 -6772E-11 -1082E-09 5400E-06 C24 - - - - -8125E-08 C30 -2317E-04 6028E-03 3663E-07 4386E-06 -01374 C31 2549E-06 5642E-05 -5272E-09 -2191E-07 6028E-03 C32 -5523E-08 -7777E-07 -1126E-10 -9117E-11 2821E-05 C33 - - - - -2592E-07 C40 -8510E-06 -7977E-05 -6389E-09 -9223E-08 1399E-03 C41 -3848E-08 5190E-07 -1112E-10 -4294E-09 -7977E-05 C42 - - - - 2595E-07 C50 -1128E-07 -3380E-06 -1820E-10 -3655E-09 6309E-05 C51 - - - - -3380E-06

1Melinder (1997)

Table A10 Diffusion coefficient of water-ethylene glycol system (see Equation A19) Function Domain T0 C0 C1 C2 C3 C4 Dw1 0hellip100 wt 250degC 1189E-09 1152E-11 2837E-14 -5773E-17 -

1Fernaacutendez-Sempere et al (1996)


215

A24 Propylene Glycol (C3H8O2)

Other names 12-propanediol

CAS number 57-55-6



Specific heat 2481 Jkg K at 20degC (Bosen et al 2000)

-250

-200

-150

-100

-50

00

50

00 50 100 150 200 250 300 350 400 450Propylene glycol concentration (wt)

Tem

pera

ture

(degC

) Aqueous solution


Ice line

Figure A5 Phase diagram of water-propylene glycol system

Table A11 Ice line of water-propylene glycol system (see Equations A1 and A2) Function Domain C1 C2 C3 C4 C5 weqT1 -35hellip0degC -3465 -01190 -2696E-03 -2669E-05 - Teqw1 0hellip51 wt -01617 -1592E-02 3924E-04 -5471E-06 -


Table A12 Heat of mixing of water-ethylene glycol system (see Equation A10) Function Domain Tmix C1 C2 C3 ∆hmixw1 0hellip60 wt 250degC -1300 1100 5974E-02

1Deduced from Christensen et al (1984)

Appendix A

216

Table A13 Coefficients of water-propylene glycol system for calculating thermophysical properties (see Equations A3 A4 and A18)





wm 427686 427686 427686 427686 427686 Tm 53571 53571 53571 53571 53571 C00 1042E+03 3679E+03 3806E-01 2274E+00 -1692E+04 C01 -4907E-01 1571E+00 5765E-04 -5342E-02 3679E+03 C02 -2819E-03 1331E-02 -3477E-07 5372E-04 07855 C03 -5895E-07 1975E-07 -6041E-09 -4955E-06 4437E-03 C04 - - - - 4938E-08 C10 8081E-01 -1933E+01 -3815E-03 4500E-02 -9801 C11 -9652E-03 1118E-01 -1423E-05 -5488E-04 -1933 C12 7168E-05 -1108E-03 -1203E-08 1845E-06 5590E-02 C13 2404E-07 4924E-06 -5854E-10 1192E-07 -3693E-04 C14 - - - - 1231E-06 C20 -7156E-03 -4879E-02 8420E-06 -7808E-05 1961 C21 1088E-04 -2338E-04 1081E-07 1453E-06 -4879E-02 C22 -3328E-06 2753E-05 1959E-09 -2816E-07 -1169E-04 C23 1153E-07 -3148E-07 1271E-10 8562E-09 9177E-06 C24 - - - - -7870E-08 C30 1190E-04 4749E-03 -1110E-06 6565E-06 -3174E-02 C31 -6226E-06 -2621E-05 -1612E-09 -4032E-07 4749E-03 C32 -3026E-08 1286E-06 3005E-10 -1212E-09 -1311E-05 C33 - - - - 4287E-07 C40 -1170E-05 -2871E-04 5503E-09 6441E-07 5657E-03 C41 -2915E-07 -9050E-08 1437E-10 -1430E-08 -2871E-04 C42 - - - - -4525E-08 C50 -6033E-07 -1068E-05 1290E-09 1092E-08 2098E-04 C51 - - - - -1068E-05

1Melinder (1997)

Table A14 Diffusion coefficient of water-propylene glycol system (see Equation A19) Function Domain T0 C0 C1 C2 C3 C4 Dw 1 0hellip45 wt 20degC 9004E-10 -1477E-11 -1420E-13 3892E-15 -

1Deduced from Garner and Marchant (1961)


217

A3 Inorganic Aqueous Solutions

A31 Magnesium Sulfate (MgSO4)

Other name Epsom salt

CAS number 7487-88-9



Specific heat 800 JkgK (Seeger et al 2000)

-100

-50

00

50

100

150

200

250

00 50 100 150 200 250 300MgSO4 concentration (wt)

Tem

pera

ture

(degC

)

Aqueous solution

Ice + aqueous solutionIce line

Ice + MgSO412H2O

aqueous solution + MgSO412H2O

aqueoussolution +

MgSO47H2O

Solubility lineMgSO 4 7H 2 O

Eutectic point


Figure A6 Phase diagram of water-MgSO4 system

Table A15 Ice line of water-MgSO4 system (see Equations A1 and A2) Function Domain C1 C2 C3 C4 C5 weqT1 -39hellip0degC -6733 -06153 -2952E-02 - - Teqw1 0hellip18 wt - 01293 -3892E-03 -2725E-05 - -

1Deduced from Gmelin (1952)

Table A16 Solubility line of MgSO4middot12H2O in water (see Equations A1 and A2) Function Domain C0 C1 C2 C3 C4 weqT1 -39hellip27degC 203 0594 - - - Teqw1 18hellip22 wt -342 1684 - - -


Table A17 Solubility line of MgSO4middot7H2O in water (see Equations A1 and A2) Function Domain C0 C1 C2 C3 C4 weqT1 27hellip25degC 213 0206 833E-04 - - Teqw1 22hellip27 wt -1339 7759 -694E-02 - -


Appendix A

218

Table A18 Heat of dissolution of MgSO4 in water (see Equation A10) Function Domain Tmix C1 C2 C3 ∆hdissw1 0hellip25 wt 18degC -7161E+03 - -


Table A19 Coefficients of water-MgSO4 system for calculating thermophysical properties (see Equations A3 A4 and A18)




w 0hellip30 wt 0hellip40 wt 0hellip30 wt 0hellip24 wt 0hellip40 wt T Teqhellip30degC 0hellip23degC3 Teqhellip40degC 15hellip55degC4 0hellip30degC3

wm 0 0 0 0 0 Tm 0 0 0 0 0 C00 10004E+03 4216E+03 05607 05743 3230 C01 2045E-02 -2990 2027E-03 -3278E-02 4216E+03 C02 -5390E-03 5775E-02 -6852E-06 2355E-04 -1495 C03 - - - -1009E-06 1925E-02 C04 - - - - - C10 1021 -5046 -6369E-04 5200E-02 -6940E+03 C11 -2381E-02 3611E-02 -2302E-06 5234E-05 -5046 C12 2644E-04 -6974E-04 7784E-09 -6310E-07 1806E-02 C13 - - - - 1204E-02 C14 - - - - - C20 5561E-02 03493 - 8370E-04 -6257 C21 4243E-04 -2477E-04 - -1974E-05 03493 C22 -5402E-06 4785E-06 - 1256E-07 -1239E-04 C23 - - - - 1595E-06 C30 - - - 2496E-05 -

1Deduced from Gmelin (1952) 2Deduced from Lobo (1989) 3Extrapolated values are used below 0degC 4Extrapolated values are used below 15degC Viscosity measurements have shown that errors of this extrapolation are below 20

Table A20 Diffusion coefficient of water-MgSO4 system (see Equation A19) Function Domain T0 C0 C1 C2 C3 C4 Dw1 0hellip35 wt 181degC 5725E-10 -8984E-12 1112E-13 - -



219

A32 Potassium Chloride (KCl)

Other name -




Specific heat 694 Jkg K (Schultz et al 2000)

-150

-100-50

0050

100150

200250

300

00 50 100 150 200 250 300KCl concentration (wt)

Tem

pera

ture

(degC

) Aqueous solution


Ice line

Ice + KClH2O

aqueous solution + KCl

Eutectic point

Solubility line

aq sol + KClH2O

Figure A7 Phase diagram of water-KCl system

Table A21 Ice line of water-KCl system (see Equations A1 and A2) Function Domain C1 C2 C3 C4 C5 weqT1 -106hellip0degC -2245 -3454E-02 3300E-04 - - Teqw1 0hellip197 wt - 04502 -1680E-03 -1553E-04 - -


Table A22 Solubility line of KCl in water (see Equations A1 and A2) Function Domain C0 C1 C2 C3 C4 weqT1 -66hellip80degC 2193 01929 -4398E-04 -6186E-06 5677E-08 Teqw1 207hellip34 wt -4685E+02 6124 -3234 7982E-02 6957E-04


Table A23 Solubility line of KClmiddotH2O in water (see Equations A1 and A2) Function Domain C0 C1 C2 C3 C4 weqT1 -106hellip-66degC 2428 07524 3063E-02 - - Teqw1 197207 wt -9896E+02 9301 -2199 - -


Appendix A

220

Table A24 Heat of dissolution of KCl in water (see Equation A10) Function Domain Tmix C1 C2 C3 ∆hdissw1 0hellip23 wt 00degC 2973E+03 -25575 -


Table A25 Coefficients of water-KCl system for calculating thermophysical properties (see Equations A3 A4 and A18)




w 0hellip30 wt 0hellip40 wt 0hellip25 wt 0hellip25 wt 0hellip23 wt T Teqhellip40degC Teqhellip40degC Teqhellip25degC 0hellip85degC2 Teqhellip40degC

wm 0 0 0 0 0 Tm 0 0 0 0 0 C00 10000 41772 05607 05767 0000 C01 2674E-02 -028626 2027E-03 -3267E-02 4177E+03 C02 -5394E-03 - -6852E-06 2214E-04 -01431 C03 - - - -8117E-07 - C10 6647 -3172 -2243E-03 -1175E-02 2973E+03 C11 -2446E-02 -7126E-02 -8106E-06 4996E-04 -3172 C12 2401E-04 - 2741E-08 -3400E-06 -3563E-02 C13 - - - 6261E-09 - C20 1711E-02 -01368 - 2675E-04 -2558 C21 4005E-04 6843E-03 - -6164E-06 -01368 C22 -4094E-06 - - 3697E-08 3421E-03 C30 - - - -2262E-06 - C31 - - - -1389E-08 - C40 - - - 1607E-07 -

1Deduced from Gmelin (1952) 2Extrapolated values are used below 0degC Viscosity measurements have shown that errors of this extrapolation are below 20

Table A26 Diffusion coefficient of water-KCl system (see Equation A19) Function Domain T0 C0 C1 C2 C3 C4 Dw 1 05hellip23 wt 18degC 1566E-09 -1269E-11 3542E-12 -1897E-13 3712E-15

1Deduced from Lobo (1989)


221

A33 Potassium Formate (KCOOH or KFo)

Other name -

CAS number 590-29-4


State at 0degC Solid (Aittomaumlki 1997)

-450-400-350-300-250-200-150-100-500050

100

00 50 100 150 200 250 300 350 400 450 500KCOOH concentration (wt)

Tem

pera

ture

(degC

) Aqueous solution


Ice line

Figure A8 Phase diagram of water-KCOOH system

Table A27 Ice line of water-KCOOH system (see Equations A1 and A2) Function Domain C1 C2 C3 C4 C5 weqT1 -45hellip0degC -2150 -4183E-02 -3696E-04 - - Teqw1 0hellip45 wt -04658 -1151E-03 -2261E-04 - -


Data on the heat of dissolution of potassium formate in water has not been found in literature

Appendix A

222

Table A28 Coefficients of water-KCOOH system for calculating thermophysical properties (see Equations A3 A4 and A18)


Dynamic viscosity1 Enthalpy2



wm 25 25 25 25 25 Tm 0 0 0 0 0 C00 1156E+03 3314E+03 05111 08142 0000 C01 -04035 1520 1292E-03 -2982E-02 3314E+03 C02 1054E-04 1757E-03 2949E-06 1849E-04 7600E-01 C03 - - - - 5857E-04 C10 6691 -2982 -1584E-03 1486E-02 0000 C11 5108E-04 7153E-02 -6271E-06 -1751E-04 -2982E+01 C12 -1724E-05 -1737E-04 -2135E-07 5847E-06 3577E-02 C13 - - - - -5790E-05 C20 3977E-02 01262 8820E-06 5258E-04 0000 C21 -1549E-05 -2274E-04 -1852E-07 3712E-06 1262E-01 C22 - - - - -1137E-04 C30 5434E-07 3619E-06 4430E-09 -9631E-08 0000 C31 - - - - 3619E-06

1Deduced from Melinder (1997) 2The enthalpy function does not contain the heat of dissolution The function can therefore only be applied to calculate enthalpy differences at a constant solute concentration

Data on the diffusion coefficient of aqueous potassium formate solution has not been found in literature


223

A34 Potassium Nitrate (KNO3)

Other name -




Specific heat 953 Jkg K at 25degC (Laue et al 2000)

-100

-50

00

50

100

150

200

250

300

00 50 100 150 200 250 300KNO3 concentration (wt)

Tem

pera

ture

(degC

)

Aqueous solution


Ice line

Ice + KNO3

aqueous solution + KNO3

Eutectic point

Solubility line

Figure A9 Phase diagram of water-KNO3 system

Table A29 Ice line of the water-KNO3 system (see Equations A1 and A2) Function Domain C1 C2 C3 C4 C5 weqT1 -29hellip0degC -3026 01498 -8989E-03 - - Teqw1 0hellip10 wt -03304 5361E-03 -7069E-05 - -


Table A30 Solubility line of KNO3 in water (see Equations A1 and A2) Function Domain C0 C1 C2 C3 C4 weqT1 -29hellip115degC 1182 04489 1077E-02 -1494E-04 5578E-07 Teqw1 10hellip75 wt -2837 2918 -5053E-02 5777E-04 -1208E-06


Table A31 Heat of dissolution of KNO3 in water (see Equation A10) Function Domain Tdiss C1 C2 C3 ∆hdissw1 0hellip15 wt 147degC 36034 -36091 -


Appendix A

224

Table A32 Coefficients of water-KNO3 system for calculating thermophysical properties (see Equations A3 A4 and A18)





wm 0 0 0 0 0 Tm 0 0 0 0 0 C00 9999E+02 4216E+03 056848 05379 4559E-02 C01 4285E-02 -2990 1616E-03 -3603E-02 4216E+03 C02 -6099E-03 5775E-02 -4309E-06 4062E-04 -1495 C03 - - - -3693E-06 1925E-02 C04 - - -1653E-03 - - C10 6630 -4745 -4698E-06 7153E-03 3746E+03 C11 -2521E-02 3365E-02 1253E-08 -1901E-06 -4745 C12 2187E-04 3365E-02 - 1445E-06 1683E-02 C13 - - -465E-12 5716E-08 -2166E-04 C14 - - 744E-14 - - C20 1728E-02 04911 - -1166E-03 -4328 C21 1775E-04 -3482E-04 - 1768E-05 04911 C22 - 6726E-06 109E-13 -3043E-07 -1741E-04 C23 - - - - 2242E-06 C30 2098E-04 - - 5434E-05 - C31 - - - -1422E-07 - C40 - - - -9349E-07 -

1Deduced from Gmelin (1952) 2Deduced from Vaessen (2003)

Table A33 Diffusion coefficient of water-KNO3 system (see Equation A19) Function Domain T0 C0 C1 C2 C3 C4 Dw 1 0hellip15 wt 185degC 1460E-09 -3275E-11 9739E-13 - -



225

A35 Sodium Chloride (NaCl)

Other name Table salt




Specific heat 850 Jkg K at 25degC (Westphal et al 2000)

-250

-200

-150

-100

-50

00

50

00 50 100 150 200 250NaCl concentration (wt)

Tem

pera

ture

(degC

)

Aqueous solution


Ice line

Ice + NaCl2H2O

aqueous solution + NaCl2H2O

Eutectic point

Solubility lineNaCl 2H 2 O

Figure A10 Phase diagram of water-NaCl system

Table A34 Ice line of water-NaCl system (see Equations A1 and A2) Function Domain C1 C2 C3 C4 C5 weqT1 -211hellip0degC -1758 -3830E-02 -3147E-04 6977E-07 - Teqw1 0hellip232 wt - 05615 -1057E-02 3132E-04 -2202E-05 -

1Deduced from Lide (2004)

Table A35 Solubility line of NaClmiddot2H2O in water (see Equations A1 and A2) Function Domain C0 C1 C2 C3 C4 weqT1 -211hellip01degC 26086 01409 - - - Teqw1 232hellip261 wt - 1851 7097 - - -


Table A36 Heat of dissolution of NaCl in water (see Equation A10) Function Domain Tmix C1 C2 C3 ∆hdissw1 0hellip25 wt 200degC 90224 -3522 04973


Appendix A

226

Table A37 Coefficients of water-NaCl system for calculating thermophysical properties (see Equations A3 A4 and A18)





wm 0 123539 123539 123539 123539 Tm 0 92581 92581 92581 92581 C00 10002 3619E+03 5692E-01 4951E-01 4334E+04 C01 4487E-02 1893 1677E-03 -2743E-02 3619E+03 C02 -6919E-03 -2804E-04 -2661E-06 2397E-04 09465 C03 1657E-05 - - - -9347E-05 C10 7767 -3384 -8528E-04 2277E-02 -4872 C11 -3773E-02 6473E-02 -1519E-05 -9952E-06 -3384 C12 5316E-04 -1467E-03 3244E-07 4419E-06 3237E-02 C13 - - - - -4890E-04 C20 -1174E-02 07992 -9082E-06 4907E-04 -2453 C21 6761E-04 -1458E-02 -4241E-08 -9974E-06 07992 C22 -1318E-05 - - - -7290E-03 C30 7610E-04 -1959E-02 -3147E-07 -2524E-06 07077 C31 - - - - -1959E-02

1Deduced from Lobo (1989) 2Melinder (1997)

Table A38 Diffusion coefficient of water-NaCl system (see Equation A19) Function Domain T0 C0 C1 C2 C3 C4 Dw 1 0hellip15 wt 185degC 1259E-09 -4266E-11 1094E-11 -8930E-13 2567E-14



227

Nomenclature

cp Specific heat (Jkg K) micro Dynamic viscosity (Pa s) C Constant ρ Density (kgm3) D Diffusion coefficient (m2s) f Function Subscripts h Enthalpy (Jkg) diss Dissolution T Temperature (K or degC) eut Eutectic Tm Constant in Eqs A3 and A4 (degC) eq Equilibrium w Solute concentration (wt) mix Mixing wm Constant in Eqs A3 and A4 (wt) sol Solution solute Solute Greek λ Thermal conductivity (Wm K)

References


Beggerow G 1976 Heats of mixing and solution In Landolt-Boumlrnstein Numerical Data and Functional Relationships in Science and Technology - New Series Group 4 Physical Chemistry Band 2 Berlin Springer

Bosen SF Bowles WA Ford EA Perlson BD 2000 Antifreezes In Ullmanns encyclopedia of industrial chemistry 6th edition Electronic Release 2000 Weinheim Wiley-VCH

Christensen C Gmehling J Rasmussen P Weidlich U 1984 Heats of mixing data collection Part 1 Binary systems Frankfurt am Main DECHEMA (Deutsche Gesellschaft fuumlr Chemisches Apparatewesen)

Cussler EL 1997 Diffusion Mass Transfer in Fluid Systems 2nd edition Cambridge Cambridge University Press

Dorsey NE 1940 Properties of ordinary water-substance in all its phases Water-vapor water and all the ices New York Reinhold Publishing Corporation

Fernaacutendez-Sempere J Ruiz-Beviaacute Colom-Valiente J Maacutes-Peacuterez F 1996 Determination of diffusion coefficients of glycols Journal of Chemical and Engineering Data vol41 pp47-48

Flick EW 1998 Industrial Solvents Handbook 5th edition Westwood Noyes

Garner FH Marchant PJM 1961 Diffusivities of associated compounds in water Transactions of the Institution of Chemical Engineers vol 39 pp397-408


Appendix A

228

Hammond BR Stokes RH 1953 Diffusion in binary liquid mixtures Transactions of the Faraday Society vol49 pp890-895

Holman JP 1997 Heat Transfer 8th edition New York McGraw-Hill Inc


Kemira Chemicals 2003 Product Brochure Freezium Kemira Chemicals BV Europoort-Rotterdam (The Netherlands)

Laue W Thiemann Scheibler E Wiegand KW 2000 Nitrates and nitrites In Ullmanns Encyclopedia of Industrial Chemistry 6th edition Electronic Release 2000 Weinheim Wiley-VCH

Lide DR 1995 Handbook of Organic Solvents Boca Raton CRC Press

Lide DR 2004 CRC Handbook of Chemistry and Physics A Ready-reference Book of Chemical and Physical Data 84th edition Boca Raton CRC Press



Plessen H von 2000 Sodium sulfate In Ullmanns Encyclopedia of Industrial Chemistry 6th edition Electronic Release 2000 Weinheim Wiley-VCH

Reid RC Prausnitz JM Poling BE 1987 The Properties of Gases and Liquids 4th edition New York McGraw-Hill Inc

Schultz H Bauer G Schachl E Hagedorn F Schmittinger P 2000 Potassium compounds In Ullmanns Encyclopedia of Industrial Chemistry 6th edition Electronic Release 2000 Weinheim Wiley-VCH

Seeger M Otto W Flick W Bickelhaupt F Akkerman OS 2000 Magnesium compounds In Ullmanns Encyclopedia of Industrial Chemistry 6th edition Electronic Release 2000 Weinheim Wiley-VCH


Westphal G et al 2000 Sodium chloride In Ullmanns Encyclopedia of Industrial Chemistry 6th edition Electronic Release 2000 Weinheim Wiley-VCH

Young FE 1957 D-Glucose-water phase diagram Journal of Physical Chemistry vol61 pp616-619

229

Appendix B Properties of Ice and Ice Slurries

B1 Properties of Ice

B11 Density

The density of ice between ndash100 and 001degC is given by the following expression deduced from an expression for the specific volume of ice by Hyland and Wexler (1983)

4 2ice 916 67 0 15 3 0 10 T Tρ minus= minus sdot + sdot sdot with ρ in (kgm3) and T in (degC) (B1)

B12 Thermal Conductivity

An expression for the thermal conductivity of ice between ndash100 and 001degC is given by the following expression deduced from data points given by Dorsey (1940)

3 5 2ice 2 23 9 7 10 4 7 10 T Tλ minus minus= minus sdot sdot + sdot sdot with λ in (Wm K) and T in (degC) (B2)

B13 Enthalpy

The enthalpy of ice between ndash100 and 001degC is given by an expression deduced from Hyland and Wexler (1983) in which the enthalpy of water in liquid state at 00degC equals zero

2 3 3ice 333430 2106 9 3 7991 1 0876 10h T T Tminus= + sdot + sdot + sdot sdot with h in (Jkg)

and T in (degC)(B3)

B14 Specific Heat

The specific heat of ice between ndash100 and 001degC has been deduced by taking the derivative of the expression for the enthalpy of ice stated in Equation B4

3 2pice 2106 9 7 5982 3 2628 10c T Tminus= + sdot + sdot sdot with cp in (Jkg K) and T in (degC) (B4)

B2 Properties of Ice Slurries

The properties of ice slurries are both influenced by the properties of ice and the liquid properties In this section models are presented to determine density thermal conductivity enthalpy specific heat and dynamic viscosity of ice slurry

B21 Density

The specific volume of ice slurry is given by the weighted average of the specific volumes of both phases

( )is ice liq1-v v vφ φ= + (B5)

Appendix B

230

The specific volumes in Equation B5 can be replaced by the reciprocal value of the density which gives a relation for the density of ice slurry

( )is

ice liq

11-

ρφ ρ φ ρ

=+

(B6)

Values for the density of ice are given in Section B1 and values for the density of several aqueous solutions can be found in Appendix A


The thermal conductivity of ice slurry can be calculated with a model proposed by Tareef (1940) for liquid-solid mixtures

( )( )

liq ice liq iceis liq

liq ice liq ice

2 2

2

λ λ ξ λ λλ λ

λ λ ξ λ λ

+ minus minus = + + minus

(B7)

Bel and Lallemand (1999) proposed to use the model presented by Jeffrey (1973) to calculate the thermal conductivity of ice slurries However the differences between the results of Jeffreyrsquos and Tareefrsquos model applied to ice slurries appear to be smaller than 05 for ice fractions up to 40 vol

Values for the thermal conductivity of ice and aqueous solutions can be found in Section B12 and Appendix A respectively

B23 Enthalpy

The enthalpy of an ice slurry can simply be deduced from the weighted average of the enthalpy of the liquid phase and the enthalpy of ice

( )is ice liq1h h hφ φ= + minus (B8)

Values for the enthalpies of ice and aqueous solutions can be found in Section B13 and Appendix A respectively

B24 Specific Heat

The specific heat cp is defined as the temperature derivative of the enthalpy

p

hcT

part=

part (B9)

The formula for the enthalpy of ice slurry in Equation B9 can be written more explicitly

( ) is ice pice liq pliq

0degC 0degC

0degC 1 0degCT T

h h c dT h c dTφ φ

= + + minus +

int int (B10)

The first term in Equation B10 represents the enthalpy contribution of the ice phase with the latent heat at 0degC and the sensible heat respectively The second part of Equation B10

Properties of Ice and Ice Slurries

231

represents the enthalpy contribution of the liquid phase constructed of the enthalpy of the liquid at 0degC and a sensible heat contribution

The derivative of Equation B10 is shown in Equation B11

( ) is

ice pice pice liq pliq0degC 0degC

10degC 0degC

T Th h c dT c h c dTT T T

φφ φ part minuspart part

= + + + + + part part part int int

( ) pliq1 cφ+ minus

(B11)

The infinitesimal temperature change partT causes a infinitesimal change of ice fraction and with that also a change of the solute concentration in the liquid phase The effect of this change on the liquid enthalpy at 0degC is neglected in this analysis

Rearranging Equation B11 leads to Equation B12 in which the right-hand side shows a clear separation between latent and sensible heat contributions to the specific heat

( ) ( )is

ice pice pliq liq pice pliq0degC

0degC 0degC 1Th h c c dT h c c

T Tφ φ φ

part part= + minus minus + + minus part part

int (B12)

If both latent and sensible contributions are taken into account than the derivative of the enthalpy is called apparent specific heat cpappis

( ) ( )ice

pappis ice pice pliq liq pice pliq0degC

0degC 0degC 1Twc h c c dT h c c

Tφ φ

part= + minus minus + + minus part

int (B13)

If the latent heat is neglected and only sensible contributions are used than the derivative of the enthalpy is called sensible specific heat cpsensis

( )psensis pice pliq1c c cφ φ= + minus (B14)

B25 Dynamic Viscosity

The dynamic viscosity of ice slurry increases with the ice fraction In most publications on ice slurries a viscosity model by Thomas (1965) is used to estimated the viscosity of the ice slurry from the dynamic viscosity of the liquid and the volumetric ice fraction

( )2 3 16 6is liq 1 2 5 10 05 2 73 10 e ξmicro micro ξ ξ minus= + + + sdot (B15)

Values for the viscosity of aqueous solution used in this thesis can be found in Appendix A

Experimental validation of Thomasrsquo model for ice slurry by Kauffeld et al (1999) has shown that the model is able to predict viscosities of ice slurries reasonably well below volumetric ice fractions of 020 At higher ice fractions considerable errors have been found which is ascribed to the fact that the ice slurry behaves no longer as a Newtonian but as a non-Newtonian fluid at higher fractions A study by Kitanovski and Poredoš (2002) has shown that the average ice crystal size and the velocity also influence the viscosity of ice slurries

Appendix B

232

Nomenclature

cp Specific heat (Jkg K) ρ Density (kgm3) h Enthalpy (Jkg) φ Ice mass fraction T Temperature (K or degC) v Specific volume (m3kg) Subscripts app Apparent Greek ice Ice λ Thermal conductivity (Wm K) is Ice slurry micro Dynamic viscosity (Pa s) liq Liquid ξ Ice volume fraction sens Sensible

References

Bel O Lallemand A 1999 Etude drsquoun frigoporteur diphasique 1 Caracteacuteristiques thermophysiques intrinsegraveques drsquoun coulis de glace International Journal of Refrigeration vol22 pp164-174

Dorsey NE 1940 Properties of Ordinary Water-substance in all its Phases Water-vapor Water and all the Ices New York Reinhold Publishing Corporation

Jeffrey DJ 1973 Conduction through a random suspension of spheres Proceedings of the Royal Society London volA335 pp355-367

Kauffeld M Christensen KG Lund S Hansen TM 1999 Experience with ice slurry In Proceedings of the 1st IIR Workshop on Ice Slurries 27-28 May 1999 Yverdon-les-Bains (Switzerland) Paris International Institute of Refrigeration pp42-73


Hyland W Wexler A 1983 Formulations for the thermodynamic properties of the saturated phases of H2O from 17315 K to 47315 K ASHRAE Transactions vol89 (2A) pp500-519

Tareef BM 1940 Colloidal Journal USSR vol6 p545

Thomas DG 1965 Transport characteristics of suspension VIII A note on the viscosity of Newtonian suspensions of uniform spherical particles Journal of Colloid Science vol20 pp267-277

233

Appendix C Calibration of Heat Exchangers

In this thesis four different heat exchangers have been used to study ice crystallization phenomena The first two are vertical tube-in-tube heat exchangers that have been used for fluidized bed experiments The third one is a tube-in-tube heat transfer coil that has been applied for the ice slurry melting experiments described in Chapter 8 The final heat exchanger is a scraped surface heat exchanger that consisted of a crystallization tank with a scraped cooled bottom plate

In all four heat exchangers temperature and flow rate measurements have been used to determine characteristic parameters such as heat flux heat transfer coefficients and wall temperatures To be able to calculate these parameters heat uptake from the surroundings friction losses and heat transfer models were verified or determined during sets of calibration experiments For the inner tube of the tube-in-tube heat transfer coil also a pressure drop model was determined

This appendix describes the four heat exchangers used in this thesis in detail and presents the calibration methods and results

C1 Small Fluidized Bed Heat Exchanger

C11 Dimensions

The small fluidized bed heat exchanger consists of two identical tube-in-tube heat exchangers made of stainless steel with a transparent section in between (see Figure C1) A 34 wt potassium formate solution flows through the annuli of the heat exchanger and is able to cool the inner tube in which the fluidized bed is located The outer tube is well insulated to reduce heat uptake from the surroundings

The most important dimensions of the small fluidized bed heat exchanger are listed in Table C1

Table C1 Dimensions of the small fluidized bed heat exchanger Dimension Value Inside diameter of inner tube Diinner (m) 427 10-3 Outside diameter of inner tube Doinner (m) 483 10-3 Thickness inner tube δinner (m) 277 10-3 Inside diameter of outer tube Doouter (m) 548 10-3 Outside diameter of outer tube Diouter (m) 603 10-3 Thickness outer tube δouter (m) 277 10-3 Hydraulic diameter annulus Dhyd (m) 653 10-3

Heat transfer length per part L1 (m) 214 Length of one part L2 (m) 234 Length of transparent section L3 (m) 020 Total outside heat transfer surface inner tubes (m2) 0649

Figure C1 Schematic overview of small fluidized

bed heat exchanger

Appendix C

234

C12 Determination of Heat Uptake from Surroundings

The heat flux through the inner wall can be determined from the energy balance of the coolant

( ) ( )

2 2out in out in

cool p out in out in inner uptakecool2

p p u um c T T g z z Q Qρ

minus minusminus + + + minus = +

amp ampamp (C1)

Since the coolant velocities at inlet and outlet are equal and the energy contributions due to gravity and pressure can be combined the energy balance can be rewritten into Equation C2

( ) fr

cool p out in inner uptakecool

pm c T T Q Qρ

∆minus minus = +

amp ampamp (C2)

The mass flow and temperatures at inlet and outlet are measured during experiments In order to calculate the heat flux through the inner tube from these measurements the contributions by fluid friction and heat uptake through the insulation must be known The former contribution is estimated by the Blasius correlation for turbulent flow in smooth tubes (Fox and McDonald 1994)

2frcool

cool hyd

12

p Lf uDρ

∆= with

hyd

0 250 3164 Df Re minus= for

hyd

52300 10DRele le (C3)

The heat uptake from the surroundings is proportional to the difference between the ambient temperature and the average temperature of the coolant

( ) ( )uptake amb iouter amb avgcool uptake amb avgcoolQ U A T T c T T= minus asymp minusamp (C4)

Since the overall heat transfer coefficient Uamb does hardly depend on the coolant properties the factor cuptake can be assumed to be constant and experiments have been performed to quantify this constant During these experiments the inner tube was filled with air and its inlet and outlet were closed so the heat flux through the inner tube could be neglected The experiments consisted of circulating coolant through the annulus with four different flow rates at three temperature levels namely 20 5 and ndash10degC For each condition the heat uptake was determined from Equation C2 Figure C2 shows the results of these experiments indicating that Equation C4 with a heat uptake constant of 35 WK can represent the heat uptake through the insulation

Calibration of Heat Exchangers

235

-50

0

50

100

150

0 5 10 15 20 25 30 35 40T amb -T avgcoolant (K)

Hea

t upt

ake

from

sur

roun

ding

s (W

)c uptake=35 WK

Figure C2 Heat uptake of the small fluidized bed heat exchanger as a function of the

difference between the ambient temperature and the average coolant temperature

Figure C2 also shows that the maximum error of the energy balance is about 25 W Since the total heat flux in the heat exchanger was between 1000 and 5000 W during most experiments described in this thesis the maximum error of the heat flux varies from 05 tot 25 which is acceptable

During some experiments described in this thesis only the lower part of the heat exchanger was used For these experiments the length L in Equation C3 was only taken for one heat exchanger part and the heat uptake constant was halved to 175 WK

C13 Validation of Heat Transfer Model for Annulus

The overall heat transfer coefficient of the inner tube can be deduced from the heat flux which is calculated from Equation C2

inner

ooinner ln

QUA T

=∆

amp (C5)

The heat transfer coefficient at the coolant side the heat resistance of the inner tube wall and the heat transfer coefficient of the fluidized bed inside the inner tube determine the overall heat transfer coefficient

( )oinner oinner iinner oinner

o o ss i iinner

ln1 1 12

D D D DU Dα λ α

= + + (C6)

Appendix C

236

Equation C6 enables to determine the heat transfer coefficient of the fluidized bed αi from the overall heat transfer coefficient and the heat transfer coefficient of the coolant in the annulus The latter can be predicted by using a heat transfer model for turbulent flow in annuli (Gnielinski 1976 VDI 1988)

hyd hyd

23

iouter

oinner

086D D

DNu Nu

D

=

in which (C7)

( )( )

hyd

hyd

23

hyd

2 13

10008 1

1 12 7 18

D

D

f Re Pr DNu

Lf Pr

minus = + + minus with ( )hyd

21 82log 1 64Df (Re )

minus= minus (C8)

The accuracy of the fluidized bed heat transfer coefficient calculation strongly depends on the accuracy of the heat transfer model stated in Equations C7 and C8 To verify its validity heat transfer experiments without fluidized bed present in the inner tube were performed

During these experiments water or an aqueous sodium chloride solution flowed upward through the inner tube and was cooled by the coolant flowing downward through the annulus For three different temperature levels the flow rate in the inner tube and the coolant flow rate were systematically varied as shown in Table C2 For each of the 60 measurements conditions the overall heat transfer coefficient was measured while the heat exchanger was in steady state

Table C2 Parameters of the heat transfer validation experiments Parameter Tested conditions Inlet temperature coolant (degC) 200 60 ndash60 Inlet temperature liquid inner tube (degC) 240 105 ndash05 NaCl concentration liquid inner tube (wt) 00 00 50 Flow rate coolant (m3h) 400 359 318 277 Flow rate liquid inner tube (m3h) 250 350 450 550 650

The heat transfer coefficient of the liquid flowing through the inner tube can accurately by calculated with the heat transfer correlation for single-phase flow in circular tubes proposed by Gnielinski (1976)

( )

( )iinner

23

iinner

23

10008 11 12 7 1

8

i innerD

D

f Re Pr DNu

Lf Pr

minus = + + minuswith ( )iinner

21 82log 1 64Df (Re )

minus= minus (C9)

The overall heat transfer coefficient for the data points of Table C2 can either be predicted with Equations C6 C7 C8 and C9 or experimentally determined with Equation C5 A comparison between the two different determination methods is shown in Figure C3


237

0

500

1000

1500

2000

0 500 1000 1500 2000Experimental U o (Wm2K)

Pred

icte

d U

o (W

m2 K

)

+5

-5

Figure C3 Experimental versus predicted overall heat transfer coefficients

The figure shows good agreement between experimental and predicted values which indicates that the heat transfer models of Equations C7 and C8 for the annulus and Equation C9 for the inner tube are valid for the heat exchanger concerned Figure C4 shows that heat transfer coefficients for the inner tube experimentally determined with Equations C5 C6 C7 and C8 are in correspondence with predicted values from Equation C9

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000 Experimental α i (Wm2K)

Pred

icte

d α

i (W

m2 K

)

+5

-5

Figure C4 Experimental versus predicted heat transfer coefficients of the liquid flowing

through the inner tube

In this thesis fluidized bed heat transfer coefficients have been experimentally determined according to the latter method From the correspondence shown in Figure C4 can be concluded that this method is suitable for this purpose and that expected errors are smaller than 5

Appendix C

238

C2 Large Fluidized Bed Heat Exchanger

C21 Dimensions

The large fluidized bed heat exchanger is also a tube-in-tube like the small one discussed in the previous section but consists only of one part (see Figure C5) The fluidized bed is also located in the inner tube which diameter is slightly bigger compared to the small fluidized bed heat exchanger The annulus contains the same coolant and the outer tube is also well insulated to reduce heat uptake from the surroundings

The most important dimensions of the large fluidized bed heat exchanger are given in Table C3

Table C3 Dimensions of the large fluidized bed heat exchanger Dimension Value Inside diameter of inner tube Diinner (m) 548 10-3 Outside diameter of inner tube Doinner (m) 603 10-3 Thickness inner tube δinner (m) 277 10-3 Inside diameter of outer tube Doouter (m) 720 10-3 Outside diameter of outer tube Diouter (m) 762 10-3 Thickness outer tube δouter (m) 211 10-3 Hydraulic diameter annulus Dhyd (m) 117 10-3 Heat transfer length L1 (m) 448 Total length L2 (m) 475 Total outside heat transfer surface inner tube (m2) 0850

Figure C5 Schematic overview of large fluidized

bed heat exchanger

C22 Determination of Heat Uptake from the Surroundings

The energy balance of the coolant in the large fluidized bed heat exchanger is similar to Equation C2

( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C10)

The fluid friction contribution was calculated with Equation C3 In analogy with Section C12 the heat uptake constant as defined in Equation C4 was determined at 55 WK as is shown in Figure C6 The figure also shows that the maximum error of the energy balance is about 30 W Since the total heat flux in the heat exchanger was between 1000 and 5000 W during most experiments described in this thesis the maximum error of the heat flux varies from 06 tot 30 which is acceptable


239

-50

0

50

100

150

200

250

0 5 10 15 20 25 30 35T amb -T avgcoolant (K)

Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=55 WK

Figure C6 Heat uptake of the large fluidized bed heat exchanger as a function of the


C23 Validation of Heat Transfer Model for the Annulus

The heat transfer model for the annulus stated in Equations C7 and C8 was validated for the large fluidized bed heat exchanger in analogy with Section C13 The validation conditions are listed in Table C4


The Figure C7 shows the results of this validation demonstrating a good agreement between experimental and predicted overall heat transfer coefficients

Appendix C

240

0

500

1000

1500

2000


Pred

icte

d U

o (W

m2 K

)

+5

-5


Figure C8 shows that heat transfer coefficients for the inside of the inner tube that are experimentally determined with Equations C5 C6 C7 and C8 are in correspondence with predicted heat transfer coefficients from Equation C9 for the range from 1000 to 3000 Wm2K Higher single-phase heat transfer coefficients could not be obtained since the flow rate of the aqueous sodium chloride solution was limited by the installed pump capacity Since most measured fluidized bed heat transfer coefficients are above the upper limit of this validation range the accuracy of this heat transfer calculation method is not exactly known However the trend of Figure C7 indicates that the applied method is also suitable to determine heat transfer coefficients above 3000 Wm2K

0

1000

2000

3000

4000

5000

6000


Pred

icte

d α

i (W

m2 K

)

+5

-5




241

C3 Melting Heat Exchanger

A tube-in-tube heat transfer coil is used in this thesis to perform melting experiments with ice slurry (see Figure C9) Ice slurry flows upward through the inner tube and is heated by a 20 wt ethylene glycol solution that flows countercurrently through the annulus The heat exchanger is insulated to reduce heat uptake from the surroundings

The aim of this section is to describe the dimensions of the heat exchanger to quantify the heat uptake and friction losses in the heat transfer coil and to formulate expressions to calculate heat transfer coefficients for both the flow in the inner tube and the flow through the annulus

Figure C9 Layout of heat transfer

coil

C31 Dimensions

The dimensions of the heat transfer coil are listed in Table C5

Table C5 Dimensions of the melting heat exchanger


The heat flux from the ethylene glycol solution to the tube wall innerQamp can be determined from the energy balance of the ethylene glycol solution

( ) fr

EG p out in inner uptakeEG

pm c T T Q Qρ

∆minus minus = +

amp ampamp (C11)

The pressure drop due to fluid friction is not measured during experiments and is therefore estimated by a correlation for pressure drop of turbulent flow in spiral tubes (VDI 1988)

2fr

EGEG hyd

12

p Lf uD

∆=

ρ with

hyd

hyd

0 5hyd 0 25

0 25c

0 3164 1 0 095

D

D

Df ReRe D

= +

(C12)

Dimensions Value Inside diameter of inner tube Diinner (m) 704 10-3 Outside diameter of inner tube Doinner (m) 953 10-3 Thickness inner tube δinner (m) 125 10-3 Inside diameter of outer tube Doouter (m) 157 10-3 Outside diameter of outer tube Diouter (m) 191 10-3 Thickness outer tube δouter (m) 165 10-3 Hydraulic diameter annulus Dhyd (m) 622 10-3 Curve diameter heat transfer coil Dc (m) 0197 Heat transfer length L1 (m) 606 Outside heat transfer surface inner tube (m2) 0181

Appendix C

242

In analogy with Section C12 the heat uptake constant as defined in Equation C4 has been determined from heat uptake experiments with different ethylene glycol flow rates at three temperature levels namely 20 10 and ndash1degC During these experiments the inner tube was filled with air as a result of which the heat flux from the inner tube to the coolant could be neglected For each condition the heat uptake from the surroundings was determined from Equation C11 The results shown in Figure C10 indicate that a heat uptake constant of 095 WK can represent the heat uptake through the insulation of the melting heat exchanger

-10

0

10

20

30

0 5 10 15 20 25T amb -T avgcoolant (K)

Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=095 WK

Figure C10 Heat uptake of the melting heat exchanger as a function of the difference

between the ambient temperature and the average coolant temperature

C33 Formulation of Heat Transfer Expressions

When a fluid flows through a heat transfer coil the curve flow results in centrifugal forces on the fluid (VDI 1988) These centrifugal forces create a secondary flow pattern that consists of a double eddy It is assumed that this secondary flow pattern plays a role in the inner tube of the heat transfer coil but not in the annulus because it is assumed that the secondary flow pattern does not occur here As a result of the secondary flow pattern in the inner tube the transition from laminar to turbulent flow occurs at higher Reynolds numbers Apparently small disturbances in the fluid flow are dimmed by the secondary flow pattern resulting in higher velocities at which turbulence occurs According to Schmidt (1967) the transition from laminar to turbulent flow is determined by

iinner

0 45iinner

critc

2300 1 8 6

D

DRe

D

= +

(C13)

For the dimensions of the inner tube the transition from laminar to turbulent is expected to occur at

iinner crit 6715DRe = (C14)


243

The transition from laminar to turbulent flow in the annulus is expected to take place at

hyd crit 2300DRe = (C15)

Available heat transfer models for helical tubes generally show deviations up to 15 (VDI 1988) Since a more accurate model is necessary to compare heat transfer coefficients of melting ice slurry with heat transfer coefficients of single-phase flow heat transfer expressions are fitted with the help of calibration experiments

For the flow in the inner tube the following expression for the Nusselt number congruent with the Dittus-Boelter expression (Holman 1997) is fitted by experiments

1

iinner iinner

0 331

r D DNu c Re Pr= for

iinner6700DRe lt (C16)

2

iinner iinner

0 332


iinner6700DRe gt (C17)

For the flow in the annulus the same expression for the Nusselt number is used

3

hyd hyd

0 333


hyd2300DRe gt (C18)

In order to fit the constants in the correlations above heat transfer measurements have been performed with the 20 wt ethylene glycol solution in the annulus and a 75 wt sodium chloride solution flowing through the inner tube Overall heat transfer coefficients were measured for four different velocities in the annulus and seven different velocities in the inner tube at two temperature levels according to Table C6

Table C6 Parameters of the heat transfer calibration experiments Parameter Tested conditions Inlet temperature EG solution annulus (degC) 01 81 Inlet temperature NaCl solution inner tube (degC) ndash34 40 Velocity EG solution annulus (ms) 107 160 215 267 Velocity NaCl solution inner tube (ms) 179 214 253 287 323 356 394

In total heat transfer measurements were performed for 56 conditions For each condition the flow pattern was turbulent for both liquids and the overall heat transfer coefficients were determined from the heat flux calculated from Equation C11 and the measured logarithmic temperature difference in analogy with Equation C5

The measured overall heat transfer coefficients were used in a modified Wilson Plot method to fit the constants and exponents of Equations C17 and C18 For each of the measurements the overall heat transfer coefficient is given by

oinnerss

o o i iinner

1 1 1 DR

U Dα α= + + (C19)

Appendix C

244

In Equation C19 αi and αo represent the heat transfer coefficients at the inside and the outside of the inner tube respectively The term Rss represents the thermal resistance of the stainless steel inner tube which is constant for all experiments

( )oinner oinner iinnerss

ss

ln2

D D DR

λ= (C20)

Combining Equations C17 C18 and C19 leads to the following equation which contains the variables c2 c3 r2 and r3

3 6 2

hyd iinner

hyd oinnerss 0 33

o EG 3 EG NaCl 2 NaCl

1r c r D D

D DR

U c Re Pr r Re Prλ λminus = + (C21)

Multiplying both sides of Equation C21 with Uo leads to an equation of which both sides are close to unity

3 6 2

hyd iinner

o hyd o oinnero ss 0 33

EG 3 EG NaCl 2 NaCl

1 r c r D D

U D U DU R

c Re Pr c Re Prλ λminus = + (C22)

Equation C22 can be rewritten as

Z AX BY= + in which

3

hyd

o hydo ss 0 33

3 EG EG

11 r D

U DZ U R A X

c Re Prλ= minus = =

2

iinner

o oinner0 33

2 NaCl NaCl

1 and r D

U DB Y

c Re Prλ= =

(C23)

Equation C23 is valid for all 56 experiments and can therefore be represented as matrix equation in which A and B are scalars and andX Y Z are 56x1 vectors

( ) ( )AX Y Z

B

=

(C24)

For given values of exponents r2 and r3 a least squares fit (LSQ) of Equation C24 can be made for variables A and B (Lay 1994) Subsequently constants c2 and c3 can be calculated out of A and B

Since both the constants c2 and c3 and the exponents r2 and r3 need to be fitted a calculation scheme as shown in Figure C11 is developed First of all initial values for r2 and r3 are guessed for example 08 for both exponents as in the Dittus-Boelter expression (Holman 1997) Next a least squares fit is made for constants c2 and c3 Exponent r2 is subsequently adjusted to achieve a least square fit for constants c2 and c3 with the smallest error With these new values for exponent r2 also exponent r2 is adjusted to minimize the error of the least squares fit The procedure is repeated until the global minimum for the least squares error has been found


245

Figure C11 Calculation scheme for parameter fit

The calculation scheme as described above results in the following expression for heat transfer coefficients at the inside and outside of the tube respectively

iinner iinner

2 0 687 0 335 06 10 D DNu Re Prminus= sdot for


hyd hyd


hyd2300DRe gt (C26)

Figure C12 shows a comparison between the measured and predicted overall heat transfer coefficients calculated with Equations C25 and C26 for the 56 experiments of Table C6 The average absolute error is 058 and the maximum absolute error is 25

Appendix C

246

0

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500Experimental U o (Wm2K)

Pred

icte

d U

o (W

m2 K

)

+5

-5


A second set of heat transfer measurements has been performed to fit constant c1 and exponent r1 of the heat transfer correlation for the laminar flow in the inner tube stated in Equation C16 In total 24 experiments were performed at two temperature levels and velocities at both sides of the heat exchanger were varied according to Table C7

Table C7 Parameters of the heat transfer calibration experiments Parameter Tested conditions Inlet temperature EG solution annulus (degC) 01 81 Inlet temperature NaCl solution inner tube (degC) ndash34 40 Velocity EG solution annulus (ms) 107 160 215 267 Velocity NaCl solution inner tube (ms) 072 108 142

Since a heat transfer correlation is available for the annulus (Equation C26) the heat transfer coefficient at the inside of the inner tube can be determined for each of the experiments from

iinner

ssi oinner o o

1 1 1DR

D Uα α

= minus minus

(C27)

Subsequently constant c1 and exponent r1 can been fit as shown in Figure C13 resulting in the following expression for laminar flow

iinner iinner



A comparison between measured and predicted overall heat transfer coefficients for the experiments of Table C7 shows an average absolute error is 143 and a maximum absolute error is 38


247

00

50

100

150

200

250

0 2000 4000 6000 8000Re D iinner

Nu

Pr -0

33

iinner iinner

3 0 903 0 337 36 10 D DNu Re Prminus= sdot

Figure C13 Fit of constant c1 and exponent r1 for Equation C16

C34 Formulation of Pressure Drop Expressions for the Inner Tube

During the heat transfer calibration experiments described above the pressure drop in the inner tube was measured using a pressure difference sensor The measured data are used in this subsection to formulate pressure drop expressions for the inner tube

It is assumed that the pressure drop in the inner tube can be described by the general expression for pressure drop in tubes

2frpred

iinner

12

Lp f uD

ρ∆ = (C29)

The friction factor f generally depends on the tube geometry and the Reynolds number For many tube geometries friction factor expressions have been reported in literature but not for the geometry of the concerned tube Therefore new friction factor expressions are formulated using the measurement data For each of flow condition the friction factor was determined by

iinner frmeas22

D pf

u Lρ∆

= (C30)

In accordance with the literature models the experimentally determined friction factors strongly depend on the Reynolds number as is shown in Figure C14 According to Appendix C33 the transition from laminar to turbulent flow occurs at a Reynolds number of 6700 Since the experimental friction factor in Figure C14 also shows a change in slope at this Reynolds number two sets of constants are fitted in the following friction factor model

4

iinner4rDf c Re= (C31)

Appendix C

248

000

001

002

003

004

005

006

007

0 5000 10000 15000 20000Re Diinner

Fric

tion

fact

or f

Figure C14 Determined friction factors as function of the Reynolds number

This procedure leads to the following friction factor expressions which are also shown in Figure C14

iinner

0 4041 42 Df Reminus= for


iinner


iinner6700DRe ge (C33)

A comparison between measured and predicted pressure drop values for the calibration experiments in Figure C15 shows an average absolute error is 156

0

50

100

150

200

250

0 50 100 150 200 250Experimental ∆p (kPa)

Pred

icte

d ∆

p (k

Pa)

+5

-5

Figure C15 Experimental versus predicted pressure drop values


249

C4 Scraped Surface Heat Exchanger

A scraped surface heat exchanger is used in this thesis to perform reference experiments for ice scaling (see Figure C16) The heat exchanger consists of a cylindrical tank of which the bottom plate with a diameter of 020 m is cooled and scraped by three rotating blades The center of the heat exchanging plate is not scraped and is therefore insulated by a PTFE cylinder of 43 mm in diameter A 50 wt potassium formate solution flows below the cooling plate following a rectangular shaped spiral path

Figure C16 Experimental set-up with scraped surface heat exchanger

The aim of this section is to describe the dimensions of the heat exchanger to quantify the heat uptake from the surroundings and to formulate expressions to calculate heat transfer coefficients for both the coolant flow in the spiral path and the fluid near the scraped surface

C41 Dimensions

The dimensions of the scraped surface heat exchanger are listed in Table C8


The energy balance of the coolant is used to determine the heat flux through the plate plateQamp

Table C8 Dimensions of the scraped surface heat exchanger Dimensions Value Diameter cooling plate Dplate (m) 020 Diameter insulated PTFE cylinder DPTFE (m) 43middot10-3 Thickness of cooled plate δplate (m) 10middot10-3 Heat transfer surface ASSHE(m2) 0031 Height of cooling path Hpath (m) 50middot10-3 Width of cooling path Wpath (m) 170middot10-3 Hydraulic diameter cooling path Dhydpath (m) 773middot10-3

Appendix C

250

( ) fr

cool p out in plate uptakecool

pm c T T Q Qρ

∆minus minus = +

amp ampamp (C34)

In analogy with Section C12 the heat uptake constant as defined in Equation C4 has been determined from experiments with different coolant flow rates at four temperature levels namely 16 4 ndash8 and ndash20degC During these experiments the upper surface of the plate was insulated and as a result the heat flux from the tank to the coolant could be neglected For each condition the heat uptake from the surroundings was determined from Equation C34 The results in Figure C17 show that a heat uptake constant of 151 WK fits the experiments

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50T amb -T avgcoolant (K)

Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=151 WK

Figure C17 Heat uptake of the scraped surface heat exchanger as a function of the



The overall heat transfer coefficient of the scraped surface heat exchanger is deduced from the heat flux through the plate

plate

SSHE ln

QU

A T=

∆

amp with

( ) ( )tank coolin tank cooloutln

tank coolin

tank coolout

ln

T T T TT

T TT T


minus minus

(C35)

The overall heat transfer coefficient is determined by the heat resistance of the plate and the heat transfer coefficients at both sides of the plate

ss

scr cool

1 1 1RU α α

= + + with platess

ss

Rδλ

= (C36)

The heat transfer coefficient for the coolant is modeled by the following heat transfer model

5

hydpath hydpath

0 335


hydpath2300DRe gt (C37)


251

According to Vaessen (2003) heat transfer coefficients in scraped surface heat exchangers can be modeled by

plate plate

0 5 0 336

D DNu c Re Pr= with

plate

2plate

D

NDRe

ρmicro

= (C38)

To fit the constants c4 and c5 and exponent r4 in the correlations above steady state heat transfer measurements have been performed with the coolant and a 215 wt potassium formate solution in the tank Overall heat transfer coefficients were measured for five coolant velocities and four scraping rates at three temperature levels according to Table C9

Table C9 Parameters of the heat transfer calibration experiments Parameter Tested conditions Inlet temperature coolant (degC) ndash150 ndash50 50 Tank temperature (degC) ndash50 50 150 Flow rate coolant (dm3h) 500 640 780 920 1060 Scraping rate (1s) 418 313 209 105

A similar algorithm as described in Section C33 is used to fit the constants and the exponent from the experimental results The resulting heat transfer models are

hydpath hydpath

0 699 0 330 0507 D DNu Re Pr= for


plate plate

0 5 0 330 997 D DNu Re Pr= with

plate

2plate

D

NDRe

ρmicro

= (C40)


0

250

500

750

1000

1250

1500

0 250 500 750 1000 1250 1500Experimental U (Wm2K)

Pred

icte

d U

(Wm

2 K)

+5

-5


Appendix C

252

Nomenclature

A Area (m2) Subscripts c Constant amb Ambient cp Specific heat (Jkg K) avg Average D Diameter (m) cool Coolant f Friction factor crit Critical g Gravity (ms2) c Curve H Height (m) EG Ethylene glycol solution L Length (m) fr Friction mamp Mass flow (kgs) hyd Hydraulic N Scraper passes (1s) i Inside Nu Nusselt number α Dλ in Inlet Nu Nusselt number straight tube inner Inner tube p Pressure (Pa) NaCl Sodium chloride solution ∆p Pressure difference (Pa) o Outside Pr Prandtl number cp λmicro out Outlet Qamp Heat (W) outer Outer tube r Exponent path Cooling path R Heat resistance (KW m2) plate Cooling plate Re Reynolds number ρ u Dmicro PTFE Polytetrafluoroethylene T Temperature (K or degC) scr Scraper ∆Tln Logarithmic mean temperature ss Stainless steel difference (K) tank Tank u Velocity (ms) uptake Uptake from surroundings U Overall heat transfer coefficient (Wm2K) W Width (m) z Height (m) Greek α Heat transfer coefficient (Wm2K) δ Thickness (m) λ Thermal conductivity (Wm K) micro Dynamic viscosity (Pa s) ρ Density (kgm3)

References

Fox RW McDonald AT 1994 Introduction to Fluid Mechanics 4th edition New York John Wiley amp Sons

Gnielinski V 1976 New equation for heat and mass transfer in turbulent pipe and channel flow International Chemical Engineering vol16 pp359ndash368

Holman JP 1997 Heat Transfer 8th edition New York McGraw-Hill

Lay DC 1994 Linear Algebra and its Applications Reading Addison-Wesley Publishing Company


253

Schmidt EF 1967 Heat transfer and pressure loss in spiral tubes Chemie Ingenieur Technik vol13 pp781-789


VDI 1988 VDI-Waumlrmeatlas Berechnungsblaumltter fuumlr den Waumlrmeuumlbergang 5th edition Duumlsseldorf Verein Deutscher Ingenieure

Appendix C

254

255

Appendix D Accuracy of Heat Exchanger Measurements

A large number of physical parameters in this thesis are deduced from heat exchanger measurements This appendix presents an error analysis of these experimentally obtained parameters Each section of this appendix deals with one heat exchanger type and starts with an overview of the accuracy of the applied sensors Subsequently these sensor accuracies are used to determine the maximum errors of the physical parameters that are calculated on the basis of measurements

D1 Fluidized Bed Heat Exchangers

D11 Accuracy of Sensors

Table D1 gives an overview of the accuracies of the sensors used in the experimental fluidized bed heat exchangers (see also Section 22)

Table D1 Sensor accuracies in fluidized bed heat exchangers Parameter Maximum error Remark Coolant volume flow rate 16 lh 04 of full scale (4000 lh) Coolant temperatures at inlet and outlet 001 K ndash Ice slurry mass flow rate 6 kgh 01 of full scale (6000 kgh) Ice slurry volume flow rate 24 lh 04 of full scale (6000 lh) Ice slurry pressures at inlet and outlet 0015 bar 015 of full scale (10 bar) Ice slurry temperatures at inlet and outlet 001 K ndash

D12 Overall Heat Transfer Coefficient

The overall heat transfer coefficient in the experimental fluidized bed heat exchangers is calculated from (see also Equation C2)

( )pcool cool cool coolout coolin frcool cool uptakeinnero

o ln o ln

c V T T p V QQUA T A T

ρ minus minus ∆ minus= =

∆ ∆

ampamp ampamp (D1)

The energy contribution due to pressure drop and the heat uptake from the surroundings are small with respect to the heat transfer with the inner tube and are therefore neglected in this error analysis The error of the calculated overall heat transfer coefficient strongly depends on the difference between the inlet and outlet temperature of the coolant The absolute maximum error of this difference is 002 K which results in maximum relative errors between 13 and 67 for typical temperature differences between 03 and 16 K depending on the heat flux The average difference between the coolant temperatures at inlet and outlet is 07 K resulting in an average maximum relative error of 28

It can be shown that the maximum error in the logarithmic mean temperature difference ∆Tln is 001 K when the error in the coolant temperature difference is at its maximum Since values for the logarithmic mean temperature difference in the experiments vary between 14 to 67 K depending on the heat flux the maximum relative error of this parameter varies between 01 and 07 The average logarithmic mean temperature difference of all experiments is 28 K resulting in an average maximum relative error of 04

Appendix D

256

The presented maximum errors for the coolant temperature difference and the logarithmic mean temperature difference are combined with the accuracy of the coolant flow rate The magnetic flow meter used for the coolant is operated at full scale resulting in a maximum error of 04 Combining all maximum errors results in a maximum relative error of the overall heat transfer coefficient of 19 for high heat fluxes up to 79 for low heat fluxes These maximum relative errors correspond to maximum absolute errors of 30 and 120 Wm2K respectively for typical overall heat transfer coefficients of 1500 Wm2K The average heat flux of the presented experiments gives a maximum error of the overall heat transfer coefficient of 35 (50 Wm2K)

D13 Fluidized Bed Heat Transfer Coefficient

The fluidized bed heat transfer coefficient is deduced from the experimentally determined overall heat transfer coefficient the heat transfer coefficient in the annulus determined by a validated heat transfer model (see Appendix C) and the thermal resistance of the tube wall

iinner oinner oinner

i oinner o o w iinner

1 1 1 ln2

D D DD U Dα α λ

= minus minus

(D2)

Maximum errors for the overall heat transfer coefficient have been deduced above Calculated heat transfer coefficients for the coolant in the annulus vary from 3500 to 4400 Wm2K The maximum error of the heat transfer model is approximately 5 according to Appendix C Combining these two maximum errors results in maximum errors for the experimentally determined fluidized bed heat transfer coefficient of 12 for high heat fluxes up to 36 for low heat fluxes These maximum relative errors correspond to maximum absolute errors of 600 and 1800 Wm2K respectively for typical fluidized bed heat transfer coefficients of 5000 Wm2K The average maximum error of the fluidized bed heat transfer coefficient for all presented experiments is estimated at 18

D14 Difference between Wall and Equilibrium Temperature

The wall temperature in the fluidized bed that determines whether ice scaling occurs is located at the top of the heat exchanger where ice slurry leaves and coolant enters (see Section 23) The wall temperature at this location is determined from the inlet temperature of the coolant the outlet temperature of ice slurry and the ratio of the overall heat transfer coefficient and the fluidized bed heat transfer coefficient (see also Equation 24)

( )oinnerowout isout isout coolin

i iinner

DUT T T TDα

= minus minus (D3)

The maximum error of the ratio of heat transfer coefficients ranges from 9 for high heat fluxes up to 21 for low heat fluxes A typically value for this ratio is 03 and the temperature difference between ice slurry and coolant varies between 15 to 75 K depending on the heat flux Combining these values with Equation D3 and the maximum error of the local ice slurry temperature gives maximum absolute errors of the wall temperature ranging from 010 K for low heat fluxes up to 021 K for high heat fluxes

The equilibrium temperature at the outlet is calculated from the measured ice slurry inlet temperature and the heat balance (see Section 23) Since the difference between the equilibrium temperature at the outlet and the inlet temperature is only 02 K at maximum and

Accuracy of Heat Exchanger Measurements

257

the maximum error in the heat balance is 25 it can be shown that the maximum error of equilibrium temperature at the outlet is 002 K

A combination of the maximum errors of the wall and the equilibrium temperature results in a total maximum error for the difference between these values of 012 K (24) for low heat fluxes up to 023 K (9) for high heat fluxes

D15 Bed Voidage

The bed voidage in the fluidized bed is deduced from the pressures measured at inlet and outlet of the fluidized bed (see Equation 21)

( )( )liq p frliq-w1p gh pερ ε ρ∆ = + minus + ∆ (D4)

In all presented experiments the pressure drop caused by friction between the liquid and the wall is small compared to the total pressure drop Since its contribution is only 2 at maximum the accuracy of this contribution is neglected for the calculation of the maximum error of the bed voidage

( )( )liq p1p gh ερ ε ρprime∆ = + minus (D5)

The accuracy of the two pressure sensors is 0015 bar and the maximum error of the calculated pressure drop is therefore 003 bar For the applied heat exchangers and conditions with stainless steel particles and aqueous solutions as liquid it can be shown that the absolute maximum error of the bed voidage is 10 This means that a determined bed voidage of 800 ensures that the real bed voidage is between 790 and 810

D16 Average Upward Particle Velocity

The average upward particle velocity in circulating fluidized beds is deduced from the actual superficial velocity uscfb the experimentally determined bed voidage ε and the superficial velocity of a stationary fluidized bed with the same particles and bed voidage (see Equations 45 and 46)

scfb ssfbz

pu u Dv

εε

minus= (D6)

The superficial velocity of the circulating fluidized bed is deduced from the value obtained by a magnetic flow meter downstream of the heat exchanger However the flow rate through this sensor does not exactly equal the flow rate through the heat exchanger The cause for this deviation is that a small fraction of the flow from the outlet of the heat exchanger is carried by the particles through the downcomer towards the inlet of the heat exchanger The maximum error introduced by this phenomenon is estimated at 5

The models used to calculate the superficial velocity of a stationary fluidized bed with the same particles and bed voidage have a maximum error of 4 In the circulating fluidized bed experiments the superficial velocity was approximately 2 to 4 times higher than in stationary fluidized beds The absolute maximum error of the bed voidage is 10 as was shown above Application of these numbers in Equation D6 results in maximum absolute errors of 007 ms for upward particle velocities of 04 ms (18) up to 010 ms for 10 ms (10)

Appendix D

258

D2 Melting Heat Exchanger


Table D2 gives the accuracies of the sensors used in the melting heat exchanger

Table D2 Sensor accuracies in the melting heat exchanger Parameter Accuracy Remark Ethylene glycol solution flow rate 10 of rate ndash Ethylene glycol solution temperatures at inlet and outlet

001 K ndash

Ice slurry mass flow rate 6 kgh 01 of full scale (6000 kgh) Ice slurry pressures difference 0009 bar 015 of full scale (-3 to +3 bar) Ice slurry temperatures at inlet and outlet 001 K ndash


The overall heat transfer coefficient in the melting heat exchanger is calculated from (see Equation C11)

( )pEG EG EG EGout EGin frEG EG uptakeo

o ln o ln



∆ ∆

ampamp ampamp (D7)

The energy contribution due to pressure drop and the heat uptake from the surroundings are small with respect to the heat transfer with the inner tube and are therefore neglected in this error analysis The error of the calculated overall heat transfer coefficient strongly depends on the difference between inlet and outlet temperature of the ethylene glycol solution The maximum absolute error of this difference is 002 K which results in maximum relative errors between 09 and 25 for typical temperature differences between 08 and 22 K

It can be shown that the maximum error in the logarithmic mean temperature difference ∆Tln is 001 K when the error in the ethylene glycol solution temperature difference is at its maximum Since values for the logarithmic mean temperature difference in the experiments vary between 27 to 66 K depending on the heat flux the maximum relative error of this parameter is between 02 and 04

The presented errors for the coolant temperature difference and the logarithmic mean temperature difference are combined with the accuracy of the coolant flow rate The magnetic flow meter used for the coolant has a maximum error of 10 Combination of all these numbers results in a maximum relative error of the overall heat transfer coefficient of 21 for high heat fluxes up to 39 for low heat fluxes These maximum relative errors correspond to maximum absolute errors of 30 and 55 Wm2K respectively for typical overall heat transfer coefficients between 1000 and 1500 Wm2K

D23 Wall-to-liquid Heat Transfer Coefficient at Ice Slurry Side

The heat transfer coefficient at the ice slurry side is deduced from the experimentally determined overall heat transfer coefficient the annular heat transfer coefficient determined by a validated heat transfer model (see Appendix C) and the thermal resistance of the tube wall


259



1 1 1 ln2

D D DD U Dα α λ

= minus minus

(D8)

Maximum errors for the overall heat transfer coefficient have been deduced above Calculated heat transfer coefficients for the coolant in the annulus are typically about 3000 Wm2K The maximum error of this heat transfer model is approximately 5 according to Appendix C Combination of these numbers results in maximum relative errors for the heat transfer coefficient for melting ice slurry of 15 for high heat fluxes up to 22 for low heat fluxes These values correspond to maximum absolute errors between 400 Wm2K for heat transfer coefficients of 2000 Wm2K to 900 Wm2K for heat transfer coefficients of 5000 Wm2K for

D24 Degree of Superheating

The degree of superheating is defined as the difference between the measured temperature and the equilibrium temperature at the outlet of the melting heat exchanger (see Section 841)

sh liqmeas eq realT T T w∆ = minus (D9)

The equilibrium temperature at the outlet is deduced from the solute concentration in the solution which is calculated from the measured outlet temperature the enthalpy at the outlet and the total solute mass fraction (see Section 841) The enthalpy at the outlet is deduced from the heat balance and the enthalpy at the inlet whose error is assumed to be very small The error in the heat balance is 5 at maximum which results in maximum errors in the equilibrium temperature at the outlet of 004 K for the conditions used in the experiments Combination of this maximum error with the maximum error of the measured liquid temperature namely 001 K results in a maximum error for the degree of superheating of 005 K The latter value leads to relative errors of 10 and smaller

D25 Pressure Drop

The applied pressure difference sensor is able to measure pressure drops between ndash30 and +30 bar Its maximum error is 015 of its full scale which means a maximum absolute error of 0009 bar or 900 Pa The latter value leads to maximum relative errors of 4 for the presented experimental results

D3 Scraped Surface Heat Exchanger


Table D3 gives the accuracies of the sensors in the scraped surface heat exchanger

Table D3 Sensor accuracies in the scraped surface heat exchanger Parameter Accuracy Remark Coolant flow rate 8 lh 05 of full scale (1600 lh) Coolant temperatures at inlet and outlet 001 K ndash Ice slurry temperature 001 K ndash

Appendix D

260


The overall heat transfer coefficient in the scraped surface heat exchanger is calculated from (see Equation C34)

( )pcool cool cool coolout coolin frcool cool uptake

ln ln



∆ ∆

ampamp ampamp (D10)

The energy contribution due to pressure drop and the heat uptake from the surroundings are small with respect to the heat transfer with the inner tube and are therefore neglected in this error analysis The error of the calculated overall heat transfer coefficient strongly depends on the difference between the inlet and outlet temperature of the coolant The absolute maximum error of this temperature difference is 002 K which results in relative errors of 10 and smaller for the applied temperature differences

It can be shown that the maximum error in the logarithmic mean temperature difference ∆Tln is 001 K when the error in the coolant temperature difference is at its maximum Since values for the logarithmic mean temperature difference in the experiments vary between 3 to 5 K the relative error of this parameter is between 02 and 03

The presented relative errors for the coolant temperature difference and the logarithmic mean temperature difference are combined with the accuracy of the coolant flow rate The magnetic flow meter used for the coolant has a maximum error of 04 and is operated at about 65 of its full scale resulting in an actual error of 08 Combining all maximum errors results in a maximum relative error of the overall heat transfer coefficient of 11 which corresponds to a maximum absolute error of 200 Wm2K

D33 Scraped Surface Heat Transfer Coefficient

The scraped surface heat transfer coefficient is deduced from the experimentally determined overall heat transfer coefficient the heat transfer coefficient of the coolant underneath the plate determined by a heat transfer model (see Appendix C) and the thermal resistance of the plate (see also Equation 62)

plate

crys cool plate

1 1 1U

δα α λ

= minus minus (D11)

Maximum errors for the overall heat transfer coefficient have been deduced above Calculated heat transfer coefficients for the coolant are about 4300 Wm2K The maximum error of this heat transfer model is approximately 5 Combining these two maximum errors results in maximum errors for the experimentally determined scraped surface heat transfer coefficient of 36 which corresponds to a maximum absolute error of 1500 Wm2K


The minimum plate temperature in the scraped surface heat exchanger that determines ice scaling is determined from the inlet temperature of the coolant the average temperature of ice slurry and the ratio of the overall heat transfer coefficient and the scraped surface heat transfer coefficient (see also Equation 63)


261

( )platemin iscrys iscrys coolincrys

UT T T Tα

= minus minus (D12)

The maximum error of the ratio of the heat transfer coefficients is 18 A typical value for this ratio is 04 and the temperature difference between ice slurry and the coolant varies between 3 to 5 K depending on the heat flux Ice slurry in the bulk of the scraped surface heat exchanger is assumed to be in equilibrium and the equilibrium is therefore set at the measured ice slurry temperature (see Section 633) A combination of the maximum error of the wall temperature and this equilibrium temperature results in a total maximum error for the difference between these values of 027 K The latter value leads to relative errors of 15 and smaller

D4 Summary

Tables D4 and D5 give summaries of all relative and absolute maximum errors determined in this appendix for the three heat exchanger types

Table D4 Determined maximum relative errors of experimentally obtained parameters Parameter Heat exchanger type Fluidized bed Melting Scraped surfaceOverall heat transfer coefficient 19 to 79 21 to 39 11 Heat transfer coefficient ice slurry side 12 to 36 15 to 22 36 Difference between wall and equilibrium temperature

9 to 24 ndash 15

Bed voidage 14 ndash ndash Upward particle velocity 10 to 18 ndash ndash Pressure drop ndash 4 ndash Degree of superheating ndash 10 ndash

Table D5 Determined maximum absolute errors of experimentally obtained parameters Parameter Heat exchanger type Fluidized bed Melting Scraped surfaceOverall heat transfer coefficient (Wm2K)

30 to 120 30 to 55 200

Heat transfer coefficient ice slurry side (Wm2K)

600 to 1800 400 to 900 1500

Difference between wall and equilibrium temperature (K) 012 to 023 ndash 027

Bed voidage () 10 ndash ndash Upward particle velocity (ms) 007 to 010 ndash ndash Pressure drop (bar) ndash 0009 ndash Degree of superheating (K) ndash 005 ndash

Appendix D

262

Nomenclature

A Area (m2) Subscripts cp Specific heat (Jkg K) cool Coolant D Diameter (m) cfb Circulating fluidized bed g Gravity (ms2) crys Crystallizer h Height (m) EG Ethylene glycol solution ∆p Pressure drop (Pa) eq Equilibrium Qamp Heat (W) fr Friction T Temperature (degC) i Inside ∆Tln Logarithmic mean temperature in Inlet difference (K) inner Inner ∆Tsh Degree of superheating (K) is Ice slurry U Overall heat transfer coefficient liq Liquid (Wm2K) meas Measured us Superficial velocity (ms) min Minimum Vamp Volume flow (m3s) o Outside vz Upward particle velocity (ms) out Outlet w Solute mass fraction p Particle plate Plate Greek real Real α Heat transfer coefficient (Wm2K) sfb Stationary fluidized bed δ Thickness (m) uptake Uptake from surroundings ε Bed voidage w Wall λ Thermal conductivity (Wm K) ρ Density (kgm3)

xvii

Dankwoord

Tot besluit wil ik graag iedereen bedanken die een bijdrage heeft geleverd aan het tot stand komen van dit proefschrift

Allereerst bedank ik Carlos Infante Ferreira mijn dagelijkse begeleider voor al zijn ondersteuning tijdens mijn promotieonderzoek Zijn terugkoppeling op mijn resultaten en analyses maar ook zijn praktische oplossingen voor experimentele problemen hebben een enorme bijdrage geleverd aan dit promotieonderzoek Hij maakte tijd voor mij vrij als ik iets wilde bespreken zelfs in drukke onderwijsperioden Al mijn artikelen en hoofdstukken keek hij met de grootste precisie na Tenslotte wil ik hem ook bedanken voor de mogelijkheden die hij mij gaf om onderwijs te geven met name wat betreft het begeleiden van warmtepomp-groepen Carlos bedankt voor alles

Ik wil ook Geert-Jan Witkamp mijn promotor hartelijk danken voor al zijn suggesties en ideeeumln tijdens onze vele discussies Zijn expertise op het gebied van kristallisatie leverde veel nieuwe inzichten op wat betreft ijsslurries en zorgde ervoor dat we experimentele resultaten konden verklaren Henk van der Ree en Peter Janssens wil ik bedanken voor hun inspanningen bij de start van mijn promotieonderzoek en hun interesse gedurende het verloop ervan

Mijn collega-promovendus Jeroen Meewisse bedank ik voor de leuke samenwerking in de eerste twee jaar van mijn promotieonderzoek Hij realiseerde het grootste deel van de experimentele opstelling waardoor mijn deel van het onderzoek een vliegende start kende Verder maakte hij mij wegwijs binnen de wereld van de ijsslurries vooral tijdens onze bezoeken aan de diverse workshops

Ik bedank Dick Klaren en Koppe van der Meer voor al hun tips en suggesties op het gebied van wervelbed-warmtewisselaars Het idee van Dick Klaren om ijsslurrie te maken met deze warmtewisselaars was ruim tien jaar geleden het beginpunt van dit onderzoek De enorme praktische ervaring van Koppe van der Meer zorgde ervoor dat we metingen konden doen aan circulerende wervelbedden

Mijn promotieonderzoek werd gedeeltelijk gefinancierd door Senter NOVEM in het kader van het NECST programma Ik wil alle leden van de klankbordgroep bedanken voor hun bijdragen tijdens onze halfjaarlijkse bijeenkomsten Rob Jans (Coolsultancy Fri-jado) Richard Beissman (York Inham) Jan Gerritsen (Grenco) en Erik Hoogendoorn (GTI) In het bijzonder bedank ik onze contactpersoon bij Senter NOVEM Jos Reinders Verder dank ik al leden van de IIR Working Party on Ice Slurries onder leiding van Masahiro Kawaji Michael Kauffeld en Peter Egolf De goed georganiseerde lsquoIce Slurry Workshopsrsquo waren een grote stimulans voor dit onderzoek

Naast Jeroen Meewisse waren ook andere promovendi binnen de afdeling Proces amp Energie actief op het gebied van ijskristallisatie Aan het begin van mijn onderzoek leverde Marius van der Gun veel onderzoeksideeeumln met name op gebied van ijsslurie opslag Raymond Vaessen Chrismono Himawan Robert Gaumlrtner Elif Genceli en Marcos Rodriguez hielden zich bezig met eutectische vrieskristallisatie (EFC) Al snel bleken er vele overeenkomsten te zijn in onderzoek vooral wat betreft ijsaankorsting De samenwerking tussen het EFC project en mijn onderzoek heb ik altijd als zeer nuttig ervaren

xviii

Een deel van dit promotieonderzoek is tot stand gekomen door de inzet van afstudeerders Vooral op experimenteel gebied hebben Inigo Celigueta-Azurmendi Lelia Olea Daniel Avram Bogdan Dolinski en Diana Lopez-Garcia ervoor gezorgd dat er veel werk is verzet waarvoor ik ze allen bedank

Een groot deel van de resultaten in dit proefschrift komt voort uit experimenten met verschillende opstellingen Mede door de goede werking van deze opstellingen heb ik een grote hoeveelheid metingen kunnen doen van hoge kwaliteit Mijn dank gaat hierbij in de eerste plaats uit naar de technici die de opstellingen bouwden en op verzoek wijzigden te weten Tjibbe van Dijk Danieumll van Baarle Jasper Ruijgrok Johan Boender en Henk de Niet In de tweede plaats wil ik Martin Verwaal Aad Vincenten en Rob Staal bedanken voor het verzorgen van de meet- en regeltechniek Tenslotte wil ik ook alle andere collegarsquos van de afdeling Proces amp Energie bedanken voor de gezellige tijd waarbij ik Duco Bosma Sam Berkhout en Jaap Keuvelaar nog expliciet wil noemen voor hun bijdrage aan dit onderzoek

Ik bedank Ilse Struik voor het prachtige ontwerp van de omslag van dit proefschrift

Tot slot bedank ik mijn ouders voor de uitstekende basis en de mogelijkheden die ze mij hebben gegeven En als allerlaatst bedank ik Ingeborg voor alle steun die ze mij gedurende de vier jaar van mijn promotieonderzoek heeft gegeven

xix

Curriculum Vitae

Pepijn Pronk was born on October 16th 1978 in Haarlem the Netherlands He attended secondary school at the Christelijk Atheneum Adriaen Pauw in Heemstede which was called Kaj Munk College after a merger in 1995 He graduated in 1996 and started his study Mechanical Engineering at Delft University of Technology in the same year As a part of his study he had an internship at SINTEF in Trondheim (Norway) where he worked on the evaporation of CO2 in micro channels He completed his study with honors in 2001 with a master thesis on the production of ice slurry with a fluidized bed heat exchanger This thesis was awarded as best master thesis in mechanical engineering at the Delft University of Technology in the academic year 2001-2002 From 2002 to 2006 he continued to work on this topic as PhD student at the same university in the Process amp Energy Department Currently Pepijn Pronk is employed by Corus where he works as researcher in the Research Development and Technology Department

Publications

Pronk P Infante Ferreira CA Witkamp GJ 2006 Influence of solute type and concentration on ice scaling in fluidized bed ice crystallizers Chemical Engineering Science vol61 pp4354-4362

Pronk P Infante Ferreira CA Witkamp GJ 2006 Prevention of crystallization fouling during eutectic freeze crystallization in fluidized bed heat exchangers submitted for publication in Chemical Engineering and Processing

Pronk P Infante Ferreira CA Witkamp GJ 2006 Particle impact measurements and analysis in stationary and circulating liquid-solid fluidized bed heat exchangers submitted for publication in International Journal of Heat and Mass Transfer

Pronk P Infante Ferreira CA Witkamp GJ 2006 Prevention of ice crystallization fouling in stationary and circulating liquid-solid fluidized bed heat exchangers submitted for publication in International Journal of Heat and Mass Transfer

Pronk P Infante Ferreira CA Witkamp GJ 2006 Superheating of ice slurry in melting heat exchangers submitted for publication in International Journal of Refrigeration


Pronk P Infante Ferreira CA Witkamp GJ 2005 A dynamic model of Ostwald ripening in ice suspensions Journal of Crystal Growth vol275 ppe1361-e1367

Pronk P Hansen TM Infante Ferreira CA Witkamp GJ 2005 Time-dependent behavior of different ice slurries during storage International Journal of Refrigeration vol28 pp27-36

xx

Pronk P Meewisse JW Kauffeld M 2005 Direct contact generators with immiscible liquid secondary refrigerant In Kauffeld M Kawaji M Egolf PW (Eds) Handbook on Ice Slurries Fundamentals and Engineering Paris International Institute of Refrigeration pp142-143

Pronk P Infante Ferreira CA Witkamp GJ 2005 Ice scaling prevention with a fluidized bed heat exchanger In Proceedings of the 16th International Symposium on Industrial Crystallization 11-14 September 2005 Dresden (Germany) pp849-854

Pronk P Infante Ferreira CA Rodriguez Pascual M Witkamp GJ 2005 Maximum temperature difference without ice-scaling in scraped surface crystallizers during eutectic freeze crystallization In Proceedings of the 16th International Symposium on Industrial Crystallization 11-14 September 2005 Dresden (Germany) pp1141-1146

Pronk P Infante Ferreira CA Witkamp GJ 2005 Circulating fluidized bed heat exchanger for ice slurry production In Proceedings of the IIR Conference on Thermophysical Properties and Transfer Processes of Refrigerants 29 August-1 September 2005 Vicenza (Italy) Paris International Institute of Refrigeration pp411-418

Pronk P Infante Ferreira CA Witkamp GJ 2005 Measuring particle-wall impacts in a fluidized bed heat exchanger In Proceedings of the IIR Conference on Thermophysical Properties and Transfer Processes of Refrigerants 29 August-1 September 2005 Vicenza (Italy) Paris International Institute of Refrigeration pp655-662

Pronk P Infante Ferreira CA 2005 De selectie van werkmedia voor indirecte koeling (Selection of coolants for secondary refrigeration) Koude amp Luchtbehandeling

Meewisse JW Pronk P Infante Ferreira CA 2005 Wervelbed-ijsslurrygenerator (Fluidized bed ice slurry generator) NPT Procestechnologie no4 August 2005

Pronk P Infante Ferreira CA Witkamp GJ 2004 Melting of Ice Slurry in a Tube-in-tube Heat Transfer Coil In Proceedings of the 6th IIR Gustav Lorentzen Conference on Natural Working Fluids 29 August-1 September 2004 Glasgow (UK) Paris International Institute of Refrigeration

Pronk P Meewisse JW Infante Ferreira CA Witkamp GJ 2003 Ice slurry production with a circulating fluidized bed heat exchanger In Proceedings of the 21st International Congress of Refrigeration 17-23 August 2003 Washington DC (USA) Paris International Institute of Refrigeration

Pronk P Meewisse JW Infante Ferreira CA Witkamp GJ 2002 Effects of long-term ice slurry storage on crystal size distribution In Proceedings of the 5th IIR Workshop on Ice Slurries 30-31 May 2002 Stockholm (Sweden) Paris International Institute of Refrigeration pp151-160

Pronk P Meewisse JW Infante Ferreira CA 2001 Heat transfer model for a fluidised bed ice slurry generator In Proceedings of the 4th IIR Workshop on Ice Slurries 12-13 November 2001 Osaka (Japan) Paris International Institute of Refrigeration pp185-194

Pronk P 2001 De invloed van koelmachineolie op de verdamping van CO2 in microkanalen (Influence of lubricating oil on the evaporation of refrigerants in micro channels) Koude amp Luchtbehandeling

Dit proefschrift is goedgekeurd door de promotor Prof dr GJ Witkamp

Toegevoegd promotor Drir CA Infante Ferreira

Samenstelling promotiecommissie Rector Magnificus voorzitter Profdr GJ Witkamp Technische Universiteit Delft promotor Drir CA Infante Ferreira Technische Universiteit Delft toegevoegd promotor Profdrdr-inghabil H Muumlller-Steinhagen Universitaumlt Stuttgart Profdr-ing M Kauffeld Karlsruhe University of Applied Sciences Profdrir PJAM Kerkhof Technische Universiteit Eindhoven Profir H van der Ree Technische Universiteit Delft drir JS van der Meer Bronswerk Heat Transfer BV

Dit onderzoek is gedeeltelijk gefinancierd door Novem in het kader van het BSE-NECST programma

ISBN 90-9020923-9

Copyright copy 2006 by P Pronk

All rights reserved

iii

Contents

Summary ix

Samenvatting xiii













iv

















v














vi











9 Conclusions 201

vii














viii








Dankwoord xvii


ix

Summary


Pepijn Pronk





x





xi





xii


xiii

Samenvatting


Pepijn Pronk




xiv





xv





xvi



1

1 Introduction







Chapter 1

2

-250

-200

-150

-100

-50

00

50


Ammonia

R407C

R404A

R134a

PropaneR

elat

ive

diff

eren

ce in

CO

P co

mpa

red

to a

mm

onia







Introduction

3







Chapter 1

4





12 Ice Slurry



Introduction

5



-200

-150

-100

-50

00


Free

zing

tem

pera

ture

(degC

)





Chapter 1

6


0

50

100

150

200

250

300

350

00 50 100 150 200 250Ice fraction (wt)

Rel

ativ

e pr

oper

ty c

hang

e

Density

Viscosity









Introduction

7








Chapter 1

8






Fluidized bed



Hot or cold fluid

Thermal boundary

layer

Fluidized bed

Inert particle

Hot or cold fluid

Deposit

Heat exchanger

wall




Introduction

9


Downcomer

Fluidized bed

Particle separation



Hot or cold fluid







Chapter 1

10




0 75 0 63h h0 0734 Nu Re Pr= (11)





Introduction

11






Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut

Salt

crystallization

crystallization

Ice




Chapter 1

12

14 Objectives




15 Thesis Outline



Introduction

13






Chapter 1

14

Nomenclature



Abbreviations


References








Introduction

15

















Chapter 1

16















Introduction

17







Chapter 1

18

19


21 Introduction







Chapter 2

20







1 1 1ln2

D D DU D Dα λ α

= + +

(23)


( )( )

sl wl oinnero

i iinnersl cooll

T T DUDT T α

minus=

minus (24)




21




fraction (wt)



(degC)


(mol)



50 160 -304 288 037 64 206 -396 372 037 76 247 -480 449 036


2

f H O

100 100expR 27315 27315

h M TyT

∆ = minus sdot +

(25)



Chapter 2

22




0

1000

2000

3000

4000

5000

6000

-300 0 300 600 900 1200 1500 1800 2100Time (s)

-60

-50

-40

-30

-20

-10

00

No ice scaling

Ice scaling

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Nucleation

Susp

ensi

on o

utle

t tem

pera

ture

(degC

)






23


00

05

10

15

20



Diff

eren

ce b

etw

een

wal

l and

eq

uilib

rium

tem

pera

ture

T -T

w (K

)




00

05

10

15

20

25

30

00 10 20 30 40 50 60 70

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)




MgSO4

NaCl



Chapter 2

24

24 Discussion


R Ggt (26)





( )iceint w

ice ice f

G T Th

λρ δ

= minus∆

(27)




( )2H Oliq

int bb ice liq

MkG x xx M

ρρ

= minus (29)


( )2

H Oliq

int bb ice liq b


x M dTρρ

asymp minus

(210)


25


2

155


liq H O iceb

27 10 ( ) w


ρ ρ δρ λ


(211)


( )2

H Oliq

w bb ice liq b

( )Mk dxG T T x

x M dTρρ

= minus

(212)

0

20

40

60

80

100


Perc

enta

ge o

f tot

al r

esis

tanc

e to

ice

grow

th

Surface integration

Mass transfer

Heat transfer





R G= (213)

Chapter 2

26


2

liq ice


( )MR dTT T x T x

k M dxρρ

∆ = minus = minus

(214)








13a


ReRe

ε=

minus and h p 1

Sh Sh εε

=minus

(217)


23

0 61 0 28s liq

0 281 15 D

uk

ρmicro

= (218)


2

H Oliq trans

ice liq bb

M Tdx RM dT x k

ρρ

∆minus =

(219)



27


23

2

028 liqice


087D

M dTT x RM dxu

micro ρρ

∆ = minus

(220)

00

02

04

06

08

10


MgSO4


NaClKNO3

KCl

Ice scaling

No ice scaling

y = 59610-6 x-1



0001020304050607080910


Diff

usio

n co

effic

ient

(10-9

m2 s

)


MgSO4

NaCl

D-glucose

EG

KNO3

KCl

NaCl

MgSO4




Chapter 2

28





~R Ef (221)




( )x 3

p

6 1f v

Dε

πminus

= (223)


29


34 sR c u= (224)


23

2

028 liq239 ice


M dTT c x uM dx

micro ρρ

∆ = minus

with 5 4087c c= (225)


00

10

20

30



∆T

tran

sm

eas (

K) D-glucose


MgSO4

NaCl

+25

-25


for ice scaling



Chapter 2

30

00

05

10

15

20

25

30


Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scla

ing

∆T

tran

s (K

)


MgSO4

NaCl

D-glucose

EG

KNO3

KCl

NaCl

MgSO4


al









31




25 Conclusions


Chapter 2

32

Nomenclature


Abbreviations



33

References
















Chapter 2

34









35


31 Introduction







Chapter 3

36









37





04 042p p

02p

125435E

Dv

ρυτ minus

=

with s p

s p

E EE

E E=

+ (32)




0406 2 12

max p p p2

E075741

F D vρυ

= minus (33)

Chapter 3

38

10

100

0001 0010D pv p

02 (m08s02)

τ (1

0-6 s

)


0002 0004 0006

80

60

4030

20




maxmax

s

FpA

= (34)




10

100

1000

10000

01 10 100 1000D p

2v p12 (10-6 m32s12)


pm

ax (1

03 Pa)


2vp12 for 2 3



39




21 694 020 32 760 032 43 798 038 727 022 790 033 826 041 762 024 825 037 866 047 794 027 860 041 897 053 827 031 895 047 934 061 862 035 930 053 963 068 897 040 960 060 932 045 962 051


scfbz slip p

uv v Dε

ε= minus (35)



825 045 017 825 087 061 831 082 048 825 054 029 855 105 075 864 091 051 825 077 056 895 058 013 894 114 069 859 101 077 895 078 034 885 124 097 895 097 056 895 050 012 895 127 090 895 066 029 895 088 054


ssfb p

slip p

u Dv D

εε

ε= (36)


Chapter 3

40

33 Results



-10

0

10

20

30

40

50

60

0 20 40 60 80 100Time (10-6 s)

Pres

sure

(10

3 Pa)

p max

τ

Threshold


0

10

20

30

40

0 10 20 30 40 50Contact time (10-6 s)

Freq

uenc

y (1

0 9 1

m2 s2 )


ε=895)


41





2

A rA r

ravgravg

exp2

f vy vvv π

= minus

(37)

00

10

20

30

40

000 005 010 015 020 025v r (ms)

y A (1

06 1m

3 )

Threshold


ε=895)



Chapter 3

42

ravg s010v u= (38)

000002004006008010012014016018020

65 70 75 80 85 90 95 100ε ()

v ra

vgu

ssf

b

2 mm 3 mm 4 mm




( ) A ravg 3p

6 1ff v

Dε

επ

minus= (39)


00

05

10

15

20

25

30

35

40

65 70 75 80 85 90 95 100ε ()

f = ( π

6) f

A D

p3 (v

r (1

- ε))

2 mm3 mm4 mmEq 312



43


3


223


= =int (310)


( ) 0f 1


13

1

0pb

111

g εε


(311)









Chapter 3

44

000

050

100

150

200

250

000 020 040 060 080 100v z (ms)

v ra

vgc

fbv

rav

gsf

b

2 mm3 mm4 mmEq 313




000

020

040

060

080

100

120

000 020 040 060 080 100v z (ms)

f Ac

fbf

As

fb

2 mm3 mm4 mmEq 314




45





2

pVV p

pavgpavg

exp2

vfy vvv π

= minus

(315)


53

V maxV max 8

5 max avg maxavg

exp2 2

f py pp pΓ

= minus =

53

V max

maxavg max avg

05596 exp2

f pp p

= minus

(316)

Chapter 3

46


( )5

32

max pVj max

maxavg maxavg

05596 exp2V

p r Dfy p dVp p

= minus int (317)


( )5

3

p

2 22max pV p


05596 exp sin2D


π π


int int int (318)


53

103

3V p 2 max


3516 exp2

f D py p l l dlp p


p

rlD

= (319)


3

2

16max


minus asymp minus


123





47

00

20

40

60

80

100

120

140

0 20 40 60 80 100p max (103 Pa)

y j p

max

32 (1

03 N1

2 m2 s)

Threshold








653


Chapter 3

48

00

05

10

15

20

25

30

35

40

000 020 040 060 080 100 120v pavg

12 (m12s12)

pm

axa

vg (1

03 Pa)

2 mm3 mm4 mmEq 322

-25

+25


the power 12


( )20 pavg

V 4p

11443

g vf

Dε

π πminus

= (324)



00

10

20

30

40

50

60

70

000 020 040 060 080 100 120v pavg (ms)

f Vd

p4 (g0

adj(1

- ε)2 ) (

ms

)

2 mm3 mm4 mmEq 324

-25

+25


velocity


49


( )20adj pavg

V 4p

15405

g vf

Dεminus

= (325)

34 Discussion






p-w A p-w r

0

J y j dvinfin

= int (326)


2


ravg0 ravg

2exp 22 3

f vJ m v dv f D vvv

π ρπ

infin = minus =

int (327)




Chapter 3

50




00

20

40

60

80

100

120

65 70 75 80 85 90 95 100ε ()

Impu

lse

J (N

m2 ) 2 mm

3 mm

4 mm


Energy of Impacts


p-w A p-w r

0

E y e dvinfin

= int (330)


2

2


ravg0 ravg

exp2 6

f vE m v dv f D vvv

π ρπ

infin = minus =

int (331)




51




000

002

004

006

008

010

012

014

016

65 70 75 80 85 90 95 100ε ()

Ene

rgy

E (J

m2 s)

2 mm

3 mm

4 mm








( ) ( )3



Chapter 3

52




lpf j lpf max

0

J y j dpinfin

= int (337)


lpf max lpf

0

2j pdt pτ

τπ

= =int with maxlpf

sin tp t p πτ

=

(338)


3

2

16max


2 exp pJ bp p dpa

τπ

infinminus

= minus int (339)


1 1

5 5

042

- -04 3p-p p p p p p

p

12922 3016 10E


= = sdot

(340)


16-2



lpf p-pτ τ= (342)


2

3

163 max

lpf p max max0


infinminusminus



53


( )1 23 33 16

lpf p0



= (344)


564





0

5

10

15

20

25

30

35

00 02 04 06 08 10v z (ms)

Impu

lse

J (N

m2 )


Pressure fronts

Total



Chapter 3

54

Energy of Impacts









lpf j lpf max

0

E y e dpinfin

= int (350)


22max lpf


ppe dtc c

τ τρ ρ

= =int with maxlpf

sin tp t p πτ

=

(351)


1

2

16max


exp2

pbE p dpc a

τρ



1

3

16p3 max



c aρ

infinminus



( )

43

13p3 16

lpfliq liq 0

586 10 expa bD

E x x dxcρ


a= (354)


55


1164

V p maxavglpf

liq liq

03061f D p

Ecρ

= (355)


1154

V p pavg5lpf

liq liq

9273 10f D v

Ecρ

= sdot (356)


( ) 165



000

005

010

015

020

025

00 02 04 06 08 10v z (ms)

Ene

rgy

E (J

m2 s)

Total




Chapter 3

56










57


35 Conclusions


Chapter 3

58

Nomenclature




59

Abbreviations


References














Chapter 3

60














61


41 Introduction






Chapter 4

62







1 1 1ln2

D D DU D Dα λ α

= + +

(42)


( )( )

sll wl oinnero

i iinnersll cooll

T T DUDT T α

minus=

minus (43)


63









(mm) () (ms) (mm) () (ms) (mm) () (ms) 21 718 017 32 763 026 43 808 037

758 020 792 029 839 042 789 022 813 032 874 047 827 026 847 035 906 052 859 029 939 059



820 075 061 816 081 060 836 084 051 855 100 083 852 105 081 863 103 066 888 122 101 875 128 103 887 126 086


scfbz slip

uv v

ε= minus (45)

Chapter 4

64


ssfbslip p

uv Dε

ε= (46)





0

1000

2000

3000

4000

5000

6000

-300 0 300 600 900 1200 1500 1800Time (s)

-60

-50

-40

-30

-20

-10

00No ice scaling

Ice scaling

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Nucleation

Susp

ensi

on o

utle

t tem

pera

ture

(degC

)





65





00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

2 mm 3 mm 4 mm

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

No ice scaling

Ice scaling

for

ice

scal

ing

∆T

tran

s (K

)




Chapter 4

66




00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

2 mm 3 mm 4 mm 043 061

083

101

056060

081 103

041051 066

086

SFB 2 mm

SFB 3 mm

SFB 4 mm

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)






67


0

1000

2000

3000

4000

5000

6000

70 75 80 85 90 95 100ε ()


eat t

rans

fer

coef

ficie

nt (W

m 2 K

)





layer d r

layer

ddtδ ϕ ϕ

ρminus

= (47)


R Ggt (48)

Chapter 4

68



R G= (49)


( )2H Oliq

w bb ice liq

MkG x xx M

ρρ

= minus (410)


( )2

H Oliq

w bb ice liq b

Mk dxG T T xx M dT

ρρ

= minus

(411)


( )


H Oliq -1

propb ice liq b

1 0216 KM dxc

x M dTρρ

= =

(412)


( )( )( )033 0 33 -033 0 33 0 67p pb p

p








69


e p-wR c E= (415)



( )

13

1

0adjpb

1max 3 1

1g

εε


(416)



00

20

40

60

80

100

120

140

000 002 004 006 008 010 012Total energy (Jm2s)

Rem

oval

rat

e (1

0 -6

ms

)

2 mm3 mm4 mmEq 417




j p-wR c J= (418)

Chapter 4

70







transsfbprop

1 1415 10 286 10

c g u g uT


∆ = sdot = sdot (421)

00

20

40

60

80

100

120

140


Rem

oval

rat

e (1

0 -6

ms

)

2 mm3 mm4 mmEq 420





71

00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)

2 mm 3 mm 4 mm











Chapter 4

72





00

20

40

60

80


2 mm3 mm4 mmEq 427

Rem

oval

rat

e ca

used

by

liqui

d pr

essu

re fr

onts

(10-6

ms

)







73


( ) ( )( ) ( )2


1286 10 1 068 exp 109 481 10

gT u v v v




00

05

10

15

20

25

00 05 10 15 20 25


∆T

tran

sm

eas (

K)

+20

-20



45 Discussion



Chapter 4

74








75


00

05

10

15

20


Pressure fronts

Total

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)





Chapter 4

76


46 Conclusions



77

Nomenclature





Chapter 4

78

References


















79





Chapter 4

80

81


51 Introduction





521 Introduction



Chapter 5

82







83











Chapter 5

84

Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


Ice + salt

Ice line


0degC

T eut

0 w eut


Boiling line for p2

Boiling line for p1



process




85




Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point

S

aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut


Ice +



process



Chapter 5

86





Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut


A

B





87






(Ham et al 1998)


Chapter 5

88








89


-66-58

-43-39-29-21-18-15-15-12

-272

-78-105-106

-156-168

-181-187-190

-362-336

-287-280

-264-212-200-190

38

233390

403190

427214

396

342398

286260

381424

197197

322225

272245

215180

10459

12766

119

-40 -30 -20 -10 0 10 20 30 40 50






Chapter 5

90











91





Chapter 5

92





(wt) Tsat

(degC) Fluidized

bed us

(ms) qamp






93

0

5

10

15

20

0 1800 3600 5400 7200 9000Time (s)

Susp

ensi

on te

mpe

ratu

re a

t he

at e

xcha

nger

inle

t (degC

)

0

2000

4000

6000

8000

salt nucleation

with fluidized bed


steady state Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)








Chapter 5

94


5

10

15

20

25

0 1800 3600 5400 7200 9000Time (s)

Susp

ensi

on te

mpe

ratu

re a

t he

at e

xcha

nger

inle

t (degC

)

0

1000

2000

3000

4000

salt nucleation

with fluidized bed


steady state Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)



543 Discussion





95






(wt) Teut


(wt) us

(ms) 102 037 KNO3 104 -29 KNO3 106 037




Chapter 5

96




00

05

10

15

20

25

30

00 50 100 150 200

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)


MgSO4

KNO3

Eutectic

Eutectic

Fouling

No fouling


MgSO4 solutions






97

-35

-30

-25

-20

-15

0 900 1800 2700 3600 4500 5400Time (s)

0

2000

4000

6000



Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Susp

ensio

n te

mpe

ratu

re a

t he

at e

xcha

nger

out

let (

degC)




-35

-30

-25

-20

-15

0 300 600 900 1200 1500 1800Time (s)

0

2000

4000

6000


Ice nucleation

Salt nucleation

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Susp

ensio

n te

mpe

ratu

re a

t he

at e

xcha

nger

out

let (

degC)


Chapter 5

98

00

05

10

15

20

25

30

00 50 100 150 200

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)


MgSO4

KNO3



554 Discussion



R Ggt (51)



99

0

20

40

60

80

100


Perc

enta

ge o

f tot

al r

esis

tanc

e to

ice

grow

th

Surface integration

Mass transfer

Heat transfer




( ) ( )2 2

H O H Oliq liq



ρ ρρ ρ

= minus asymp minus

(52)



Chapter 5

100










101


component wadd

(wt) wKNO3 (wt)

Tfr or Teut (degC)

Type of crystals









Chapter 5

102

00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling



00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling






103





and 58 wt KNO3



00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling



Chapter 5

104

564 Discussion









105








Chapter 5

106



57 Conclusions



107

Nomenclature


Abbreviations


References






Chapter 5

108


















109



Chapter 5

110

111


61 Introduction




Chapter 6

112









113







Chapter 6

114







(Gladis et al 1996)



115




631 Introduction





Chapter 6

116








T T T TT

T T T T


minus minus (61)



117

plate

crys plate cool

1 1 1U

δα λ α

= + + (62)


( )( )

iscrys platemin

crysiscrys coolin

T T UT T α

minus=

minus ( 63)









Chapter 6

118


-80

-70

-60

-50

-40

-30

-20

-10

00

0 1200 2400 3600 4800 6000Time (s)

Tem

pera

ture

(degC

)

T iscrys

T platemin

T coolin

Ice nucleation


during experiment 3


0

1000

2000

3000

4000

5000

6000

0 1200 2400 3600 4800 6000Time (s)

00

01

02

03

04

05

06Uα crys

Torque

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Tor

que

(Nm

)

Ice nucleation



119




00

05

10

15

20

25

30

35

40


Tis

cry

s-Tpl

ate

min

(K)


No ice scaling

Ice scaling

-50

-40

-30

-20

-10

00



No ice scaling

Ice scaling

Tpl

ate

min

(degC

)


without ice scaling



R Ggt (64)


Chapter 6

120

( )liq eq

eq crys plateminice

dwkG T w Tw dT

ρρ

= minus minus

(65)


( )liq eq

iscrys plateminice

dwkG T Tw dT

ρρ

= minus minus

(66)


eqice


dTwT T T Rk dw

ρρ

∆ = minus = minus

(67)






121


00

05

10

15

20

25

30

35

40


∆T

tran

s (K

)




0

5

10

15

20

25


Hea

t flu

x (k

Wm

2 )

Ice scaling




Scraperblades

Orbitalrods

No ice scaling








Chapter 6

122







0 75 063


liq 1D

Nuα ελ ε

=minus

and ( )

liq s ph

liq 1u D

Reρ

micro ε=

minus (68)




123

0

2000

4000

6000

8000

70 80 90 100Bed voidage ()

2 mm3 mm4 mmH

eat t

rans

fer

coef

ficie

nt (W

m 2 K

)

0

2000

4000

6000

8000

00 50 100 150 200Scraper passes (1s)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Re-Pr Eq611

Re-Pr Eq610







liq liq pliq

4 c Nα λ ρπ

= (69)



0 5 025


liq scrscr

liq

NDRe

ρmicro

= ( 610)

Chapter 6

124


0 5 033


liq scrscr

liq

NDRe

ρmicro

= and scrscr

liq

DNu αλ

= (611)








125

0

2000

4000

6000

8000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

NaCl

EGD-glucose

0

2000

4000

6000

8000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

NaCl

EG D-glucose




Eq 610



0

2000

4000

6000

8000

0 5 10 15 20 25 30Ice fraction (wt)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K

)

T fr= ndash20degC

T fr= ndash10degC

T fr= ndash5degC



Chapter 6

126











127

1

10

100

1000


Inve

stm

ent c

osts

(keuro)


1

10

100

1000


Inve

stm

ent c

osts

(keuro)

STHESSHE

FBHE


trendline


exchangers





Chapter 6

128

0

5

10

15

20

25


Hea

t flu

x (k

Wm

2 )SSHE

FBHE

0

100

200

300

400

500


Inve

stm

ent c

osts

(eurok

W)

SSHE

FBHE -5degC

FBHE -10degC

FBHE -2degC









129








( )( )p is

he tube

1gpA D


= ( 616)


( )( )p is s tubepd

he he

14

g u DW pVA A


amp amp (617)



he he he pump pump

14

g u DW WQA A A

ρ ρ ε

η η

minus minus= = =

amp ampamp ( 618)




14

g u DWWA A

ρ ρ ε

η η η

minus minus= =

ampamp ( 619)


Chapter 6

130



Comparison






000

005

010

015

020


Scraper blades

Orbital rods

Fluidized bed

Rel

ativ

e ad

ditio

nal p

ower



131





net add

cyclecomp

Q QCOPW

+=amp amp

amp ( 621)

-25

-20

-15

-10

-5

0



Fluidized bed

Eva

pora

tion

tem

pera

ture

(degC

)

00

01

02

03

04

05

06



Fluidized bed

Rel

ativ

e co

mpr

esso

r po

wer




Chapter 6

132



net

totalcomp add

QCOPW W

=+

amp

amp amp (622)


00

05

10

15

20

25

30

35


Scraper blades

Orbital rods

Fluidized bed

CO

P


removal mechanisms





133

0

50

100

150

200

250


Rel

ativ

e an

nual

cos

ts (euro

kW

) 100 kW


Fluidized bed

0

50

100

150

200

250


Rel

ativ

e an

nual

cos

ts (euro

kW

) 1 MW


Fluidized bed


system


system


67 Conclusions



Chapter 6

134

Nomenclature



References




135

















Chapter 6

136















137














Chapter 6

138












139


71 Introduction







Chapter 7

140







141




721 Attrition


00

01

02

03

04

05


Mas

s fr

actio

n (-

)

(a)

00

01

02

03

04

05


Mas

s fr

actio

n (-

)

(b)



Chapter 7

142


722 Agglomeration





Theory


32V

Am


γ γ∆ = ∆ + = ∆ + (723)


143






( ) ( ) sol

0liq 0liq s ssol


ψψ infin infin

infin

∆ = +

(726)


( ) ( )


T T

T T


infin infin


∆∆ = + = ∆ = ∆ = ∆int int (727)


( )3

2V fA

m

-B L hG T T B LV T

γinfininfin

∆∆ = + (728)


( ) 0d G

dL∆

= (729)


A

V ice f

2( ) 1-3

BT L TB h L

γρinfin

= ∆

(730)

Chapter 7

144







145

00020406081012141618


Num

ber

dens

ity (1

06 1

m) Initial

After 1 hr

After 2 hrs

After 3 hrs

0

50

100

150

200

250


Ave

rage

dia

met

er (micro

m)

10

15

223342








Chapter 7

146

0

100

200

300

400

500

600


Ave

rage

cry

stal

siz

e (micro

m)





724 Conclusions





147








Chapter 7

148

-70

-60

-50

-40

-30

-20

-10

00

-2 -1 0 1 2Time (hours)

Tem

pera

ture

(degC

)



Seeding

∆T maxsuper

24




p

Feret

4 AD

π= (731)


FeretDΓP

π= (732)


733 Results



149









a b

c d



Chapter 7

150


00

01

02

03

04


Num

ber

frac

tion

(10 4 1

m) 0 h

2 h6 h22 h

00

02

04

06

08

10


Cum

ulat

ive

num

ber

frac

tion

(-)

0 h2 h6 h22 h



experiment 2



0

100

200

300

400

500

0 4 8 12 16 20 24Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)





151

080

085

090

095

100

0 4 8 12 16 20 24Time (hours)

Ave

rage

cry

stal

rou

ndne

ss (-





0

100

200

300

400

500

0 4 8 12 16 20 24Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)

400 rpm750 rpm

080

085

090

095

100

0 4 8 12 16 20 24Time (hours)

Ave

rgae

cry

stal

rou

ndne

ss (-

)

400 rpm750 rpm






Chapter 7

152




0

100

200

300

400

500

0 10 20 30 40 50Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)



solutions





153

0

100

200

300

400

500

0 20 40 60 80 100Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm




homogeneous storage

735 Discussion






Chapter 7

154



( )Ai b

V ice f

-3

=∆

BG T TB h

αρ

(734)



3 3liq liq

2 1 3 for lt10

D DNu Pr


= +

(735)


( )2 2

liqAdsi H Ob H Oi

V ice

-3BG k w wB

ρρ

= (736)


2

ddsi

H Ob1-kk

w= (737)


0207 0173 4liq equiv 036 mix

3liq tank

2 047D DSh Sc

Dξ ρ

micro

= + (738)



155

( )2 2

2

b i H Ob H OiH O

- - dTT T w wdw

= (739)


( )int i i-=

rG k T T (740)


( )155-3 i i27 10 -=G T T (741)



-Tb by

2

2

155


A d liq H O


B k dwρ ρρ α

∆ = minus minus +

(742)



Chapter 7

156

10E-11

10E-10

10E-09

10E-08

0 5 10 15 20w soluteb (wt)

G (m

s)






10E-11

10E-10

10E-09

10E-08

0 5 10 15 20w soluteb (wt)

G (m

s)

00 Wkg01 Wkg10 Wkg





157


10E-12

10E-11

10E-10

10E-09

10E-08

0 5 10 15 20 25 30w soluteb (wt)

G (m

s)



stirring



Chapter 7

158

10E-12

10E-11

10E-10

10E-09

10E-08

-120 -100 -80 -60 -40 -20 00T freeze (degC)

G (m

s)



without stirring

736 Conclusions








159


G L t n L tn L tt L

partpart=

part part (743)


tρ φ φ ρpart

+ =part

(746)


ρ φpart=

part (747)



part (748)


3ice V

tot 0

( )L

L

B n L L dLm

ρφ=infin

=

= int (749)


2icetot A

0

( )L

L

A B n L L dL=infin

=

= int (750)




Chapter 7

160


ice f ice solV

liq d sol

1 13

BG T Th w dTB

k dwρ ρ

α ρ

= minus ∆ +

(751)


A

V ice lat

21-3

BT TB h L

γρinfin

= ∆

(730)


0173 4liq equiv 025

3liq

2 13D

Nu Prξ ρ

micro

= +

(735)


0207 0253 4liq equiv 036 mix

3liq tank

2 047D DSh Sc

Dξ ρ

micro

= + (738)



( )155-3 27 10 -G T T= (741)



161


-15

-10

-05

00

05


Cry

stal

gro

wth

rat

e (1

0 -7 m

s)

G heat

G surf G mass







Tank volume (l)

Time (h)


Chapter 7

162




0

100

200

300

400

500

600

0 5 10 15 20 25Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)






163

0

50

100

150

200

250

300

00 10 20 30 40 50 60Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)

8 wt φ =1

86 wt φ =0142

130 wt φ =0142

15 wt φ =1

190 wt φ =0132

369 wt φ =0122




00102030405060708090

100


Num

ber

frac

tion

(10 3 1

m) 5


00

10

20

30

40

50


Num

ber

frac

tion

(10 3 1






chloride


Chapter 7

164


0

100

200

300

400

500

600

700

0 20 40 60 80 100Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)




744 Discussion





165

0

100

200

300

400

500

600

700

0 5 10 15 20 25Time (hours)

Ave

rage

cry

stal

siz

e (m

m)


HD =015 HD =020 HD =025HD =030






( ) ( )isgin

tot


t L mpartpart

= +part part

amp (752)


Chapter 7

166


0

100

200

300

400

500

600

700

0 20 40 60 80 100Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)



glycol (PG)

745 Conclusions


75 Conclusions



167

Nomenclature






Chapter 7

168

Abbreviations


References














169
















Chapter 7

170
















171


81 Introduction







821 Flow Patterns


Chapter 8

172





822 Rheology


823 Pressure Drop



173









Chapter 8

174

825 Superheating




loop



175











Chapter 8

176








177


833 Data Reduction







1 1 1ln2

D D DU D Dα λ α

= + +

(82)


Chapter 8

178






-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

00

50

100

150

200

250

300

350

400

Ice

frac

tion

(wt

)

Tfr

T inmeas

T outmeas

T coriomeas

ineqinφ




ineqin 0ineqin

ineqin

w ww

φminus

= (83)


179





Enthalpy at Inlet






( )he rest


0t Q Q

h t h t dtm

+= = + int

amp amp (87)


( )he rest


0tn t

n

Q Q th t h t

m

= ∆

=

+ ∆= = + sum

amp amp (88)


Chapter 8

180

-800

-700

-600

-500

-400

-300

-200

-100

00

0 600 1200 1800 2400 3000 3600Time (s)

Ent

halp

y (k

Jkg

)

h isineqin

h isinreal


rest

( 0 W)Q =amp





end


0end is

0tn t

n

m Q tQ h t t h tt m

= ∆

=

∆ = = minus = +

sum

ampamp (810)


Enthalpy at Outlet


is


Qh hm

= +amp

amp (811)


181








-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

0

5

10

15

20

25

30

35

40Ic

e fr

actio

n (w

t)

T inmeas

T outmeas

inreal

outreal

φφ


experiment 1



Chapter 8

182


-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

0

5

10

15

20

25

30

35

40

Ice

frac

tion

(wt

)

T outmeas

T outeq

outrealφ

∆Tsh








exchanger


183


meas eqsh

w-liq sh w eq

T TTT T T T

ζminus∆

= =∆ + ∆ minus

(816)



( )( )

oinnerw is o

EG is i iinner

DT T UT T Dα

minus=

minus (817)



00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)


00

02

04

06

08

10


Rel

ativ

e su

perh

eatin

g ζ






Chapter 8

184



00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)


00

02

04

06

08


Rel

ativ

e su

perh

eatin

g ζ









185

00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)


00

02

04

06

08

10


Rel

ativ

e su

perh

eatin

g ζ






846 Discussion







Chapter 8

186
















ice ice ice

is is

m A Gm m


amp

amp amp (827)


187




ice3

2 ice Feret

mNc Dρ


m m D xπφ φρ= = ∆ (829)


eq liqA

eqice V f

liq cr

3T TBG

dTB hwk dw

ρρ α

minus=

∆minus +

(830)


eq liqA

ice V eqcrf

cr f liq

31

T TBGB dTh w

k h dwρ α

α ρ

minus=

∆minus + ∆

(831)


1 1 1 23 3 3 3

1 23 3


cr D D DNu Pr c


= = = (832)


1 2

3 3

2 23 3

eq liqcrA

ice V f pliq liq eq

f liq

31

D

T TBGB h c w dT

dwh

αρ λ

ρ

minus=

∆ minus + ∆

(833)


Chapter 8

188

00

10

20

30

40

50

60

70


Con

trib

utio

n to

cry

stal

gro

wth

re

sist

ance

rel

ativ

e to

hea

t tra

nsfe

r

Total

Mass transfer

Heat transfer



1 2

3 3

2 23 3



f liq

121

D


dwh

φρ απφρ λ

ρ

minus∆∆ =

∆ minus + ∆

amp

(834)


( )

1 23 3

2 23 3




c B D dwhλρ α

ρ φ α ρ


(835)





189



( )

1 23 3

2 23 3


is f liq

1Dc w dTDT c T T

dwhλρ

ρ φ ρ


with V2 i3

1 A iinner cr

12Bccc B D

αα

= (836)




00

05

10

15

20

000 001 002 003 004 005

∆T

shm

eas (

K) 1

2 34

56

7

8

9

10

-25

+25

(m K)( )1 2

3 3

2 23 3


is f liq

1Dc w dTD T T

dwhλρ

ρ φ ρ

minus + minus ∆



Chapter 8

190


847 Conclusions





0

1000

2000

3000

4000

5000

6000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)





191






measliq

predliq

αα



measis

predis

αα




Chapter 8

192

08

10

12

14

16

18

20



Hea

t tra

nsfe

r fa

ctor

Ψliq

08

10

12

14

16

18

20



Hea

t tra

nsfe

r fa

ctor

Ψis









193

08

10

12

14

16

18

20


Hea

t tra

nsfe

r fa

ctor

Ψis


08

10

12

14

16

18

20


Hea

t tra

nsfe

r fa

ctor

Ψis






854 Conclusions





0 404liq liq2


1 42 for 67001 with 0 112 for 67002


ρminus

minus

= lt∆ = = ge (841)


Chapter 8

194

000

020

040

060

080

100

120

140


Pres

sure

dro

p (b

ar)





measliq

predliq

pp

∆Π =



measis

predis

pp

∆Π =






195

08

10

12

14

16



Pres

sure

dro

p fa

ctor

Πliq

08

10

12

14

16



Pres

sure

dro

p fa

ctor

Πis




08

10

12

14

16


Pres

sure

dro

p fa

ctor

Πis


08

10

12

14

16


Pres

sure

dro

p fa

ctor

Πis






Chapter 8

196

863 Conclusions


87 Conclusions




197

Nomenclature




Chapter 8

198

References














199














Chapter 8

200




201

9 Conclusions







Chapter 9

202








Conclusions

203


Overall Conclusions



Chapter 9

204

205







Tem

pera

ture

Aqueous solution

Eutectic point



Ice + solid solute

Ice line

Solubility line

0degC

T eut

0 wt w eut




5i

eq ii 0

T C w=


Appendix A

206

5i

eq ii 0

w C T=





( ) ( )( )

5 3i j

ij m mi 0 j 0

f C w w T T= =





( ) ( ) ( )( )5 3

i j3ij m m

i 0 j 0




A14 Enthalpy





2

diss


T

T




207




0degC

T



2 2

2 2 3H O pH O

0degC

42163 1495 1925 10T



3i

diss diss ii 1

h w T C w=



m

diss diss m

psol psol psol TT T

T T T



m

diss

psol T

T

c w T dTint ( )diss

0

psol m mmT T

c w T T d T Tminus


( ) ( )( ) ( )

diss 5 3i j

ij m m mi 0 j 00

mT T


= =


( ) ( )

5 3i j+1

ij m diss mi 0 j 0

1j+1

C w w T T= =


sumsum (A14)

( )( )5

ii ij diss m m

i 0 c j C T T w w

=


Appendix A

208


m

psol T

T

c w T dTint ( ) ( )( ) ( )m 5 3

i jij m m m

i 0 j 00

T T


= =


( ) ( )

5 3i j+1

ij m mi 0 j 0

1j+1

C w w T T= =


sumsum (A17)


( ) ( )( )

5 4i k

ik m mi 0 k 0

h C w w T T= =





5i

0 ii 1

D wT C w=



D constant273 15T

micro=

+ (A20)


0

00

273 15D D273 15

wT T wT wTwT T

micromicro

+= +

(A21)


209




CAS number 50-99-7



-100

-50

00

50

100

150

200

250


Tem

pera

ture

(degC

)

Aqueous solution


Ice linedextrose


Solubility line






Appendix A

210








211

A22 Ethanol (C2H6O)


CAS number 64-17-5




-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

) Aqueous solution


Ice line






Appendix A

212







1Melinder (1997)




213



CAS number 107-21-1




-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

) Aqueous solution


Ice line






Appendix A

214







1Melinder (1997)




215



CAS number 57-55-6




-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

) Aqueous solution


Ice line






Appendix A

216







1Melinder (1997)




217








-100

-50

00

50

100

150

200

250


Tem

pera

ture

(degC

)

Aqueous solution


Ice + MgSO412H2O


aqueoussolution +

MgSO47H2O


Eutectic point









Appendix A

218













219


Other name -





-150

-100-50

0050

100150

200250

300


Tem

pera

ture

(degC

) Aqueous solution


Ice line

Ice + KClH2O


Eutectic point

Solubility line

aq sol + KClH2O








Appendix A

220













221


Other name -

CAS number 590-29-4



-450-400-350-300-250-200-150-100-500050

100


Tem

pera

ture

(degC

) Aqueous solution


Ice line





Appendix A

222










223


Other name -





-100

-50

00

50

100

150

200

250

300


Tem

pera

ture

(degC

)

Aqueous solution


Ice line

Ice + KNO3


Eutectic point

Solubility line








Appendix A

224











225







-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

)

Aqueous solution


Ice line

Ice + NaCl2H2O


Eutectic point









Appendix A

226











227

Nomenclature


References











Appendix A

228

















229



B11 Density






B13 Enthalpy



and T in (degC)(B3)

B14 Specific Heat





B21 Density



Appendix B

230


( )is

ice liq

11-

ρφ ρ φ ρ

=+

(B6)




( )( )


liq ice liq ice

2 2

2

λ λ ξ λ λλ λ

λ λ ξ λ λ


(B7)



B23 Enthalpy




B24 Specific Heat


p

hcT

part=

part (B9)



0degC 0degC

0degC 1 0degCT T


= + + minus +

int int (B10)



231



( ) is


10degC 0degC





(B11)



( ) ( )is



T Tφ φ φ


int (B12)


( ) ( )ice



Tφ φ


int (B13)








Appendix B

232

Nomenclature


References









233






C11 Dimensions






bed heat exchanger

Appendix C

234



( ) ( )

2 2out in out in




amp ampamp (C1)


( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C2)


2frcool

cool hyd

12

p Lf uDρ

∆= with

hyd


hyd

52300 10DRele le (C3)





235

-50

0

50

100

150


Hea

t upt

ake

from

sur

roun

ding

s (W

)c uptake=35 WK







inner

ooinner ln

QUA T

=∆

amp (C5)



o o ss i iinner

ln1 1 12

D D D DU Dα λ α

= + + (C6)

Appendix C

236


hyd hyd

23

iouter

oinner

086D D

DNu Nu

D

=

in which (C7)

( )( )

hyd

hyd

23

hyd

2 13

10008 1

1 12 7 18

D

D

f Re Pr DNu

Lf Pr


21 82log 1 64Df (Re )

minus= minus (C8)





( )

( )iinner

23

iinner

23

10008 11 12 7 1

8

i innerD

D

f Re Pr DNu

Lf Pr


21 82log 1 64Df (Re )

minus= minus (C9)



237

0

500

1000

1500

2000


Pred

icte

d U

o (W

m2 K

)

+5

-5



0

1000

2000

3000

4000

5000

6000


Pred

icte

d α

i (W

m2 K

)

+5

-5




Appendix C

238


C21 Dimensions





bed heat exchanger



( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C10)



239

-50

0

50

100

150

200

250


Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=55 WK







Appendix C

240

0

500

1000

1500

2000


Pred

icte

d U

o (W

m2 K

)

+5

-5



0

1000

2000

3000

4000

5000

6000


Pred

icte

d α

i (W

m2 K

)

+5

-5




241





coil

C31 Dimensions





( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C11)


2fr

EGEG hyd

12

p Lf uD

∆=

ρ with

hyd

hyd

0 5hyd 0 25

0 25c

0 3164 1 0 095

D

D

Df ReRe D

= +

(C12)


Appendix C

242


-10

0

10

20

30


Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=095 WK





iinner

0 45iinner

critc

2300 1 8 6

D

DRe

D

= +

(C13)




243





1

iinner iinner

0 331



2

iinner iinner

0 332




3

hyd hyd

0 333


hyd2300DRe gt (C18)





oinnerss

o o i iinner

1 1 1 DR

U Dα α= + + (C19)

Appendix C

244



ss

ln2

D D DR

λ= (C20)


3 6 2

hyd iinner

hyd oinnerss 0 33


1r c r D D

D DR



3 6 2

hyd iinner


EG 3 EG NaCl 2 NaCl

1 r c r D D

U D U DU R



Z AX BY= + in which

3

hyd

o hydo ss 0 33

3 EG EG

11 r D

U DZ U R A X


2

iinner

o oinner0 33

2 NaCl NaCl

1 and r D

U DB Y

c Re Prλ= =

(C23)


( ) ( )AX Y Z

B

=

(C24)




245



iinner iinner



hyd hyd


hyd2300DRe gt (C26)


Appendix C

246

0

500

1000

1500

2000

2500


Pred

icte

d U

o (W

m2 K

)

+5

-5





iinner

ssi oinner o o

1 1 1DR

D Uα α

= minus minus

(C27)


iinner iinner





247

00

50

100

150

200

250

0 2000 4000 6000 8000Re D iinner

Nu

Pr -0

33

iinner iinner






2frpred

iinner

12

Lp f uD

ρ∆ = (C29)


iinner frmeas22

D pf

u Lρ∆

= (C30)


4


Appendix C

248

000

001

002

003

004

005

006

007

0 5000 10000 15000 20000Re Diinner

Fric

tion

fact

or f



iinner



iinner




0

50

100

150

200

250


Pred

icte

d ∆

p (k

Pa)

+5

-5



249





C41 Dimensions





Appendix C

250

( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C34)


-20

0

20

40

60

80

100


Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=151 WK





plate

SSHE ln

QU

A T=

∆

amp with


tank coolin

tank coolout

ln

T T T TT

T TT T


minus minus

(C35)


ss

scr cool

1 1 1RU α α

= + + with platess

ss

Rδλ

= (C36)


5

hydpath hydpath

0 335




251


plate plate

0 5 0 336

D DNu c Re Pr= with

plate

2plate

D

NDRe

ρmicro

= (C38)




hydpath hydpath

0 699 0 330 0507 D DNu Re Pr= for


plate plate

0 5 0 330 997 D DNu Re Pr= with

plate

2plate

D

NDRe

ρmicro

= (C40)


0

250

500

750

1000

1250

1500


Pred

icte

d U

(Wm

2 K)

+5

-5


Appendix C

252

Nomenclature


References






253




Appendix C

254

255










o ln o ln



∆ ∆

ampamp ampamp (D1)



Appendix D

256






1 1 1 ln2

D D DD U Dα α λ

= minus minus

(D2)





i iinner

DUT T T TDα

= minus minus (D3)




257



D15 Bed Voidage








scfb ssfbz

pu u Dv

εε

minus= (D6)



Appendix D

258





001 K ndash





o ln o ln



∆ ∆

ampamp ampamp (D7)







259



1 1 1 ln2

D D DD U Dα α λ

= minus minus

(D8)






D25 Pressure Drop






Appendix D

260




ln ln



∆ ∆

ampamp ampamp (D10)






plate

crys cool plate

1 1 1U

δα α λ

= minus minus (D11)





261


UT T T Tα

= minus minus (D12)


D4 Summary



9 to 24 ndash 15



30 to 120 30 to 55 200


600 to 1800 400 to 900 1500



Appendix D

262

Nomenclature


xvii

Dankwoord








xviii





xix

Curriculum Vitae


Publications









xx













iii

Contents

Summary ix

Samenvatting xiii













iv

















v














vi











9 Conclusions 201

vii














viii








Dankwoord xvii


ix

Summary


Pepijn Pronk





x





xi





xii


xiii

Samenvatting


Pepijn Pronk




xiv





xv





xvi



1

1 Introduction







Chapter 1

2

-250

-200

-150

-100

-50

00

50


Ammonia

R407C

R404A

R134a

PropaneR

elat

ive

diff

eren

ce in

CO

P co

mpa

red

to a

mm

onia







Introduction

3







Chapter 1

4





12 Ice Slurry



Introduction

5



-200

-150

-100

-50

00


Free

zing

tem

pera

ture

(degC

)





Chapter 1

6


0

50

100

150

200

250

300

350

00 50 100 150 200 250Ice fraction (wt)

Rel

ativ

e pr

oper

ty c

hang

e

Density

Viscosity









Introduction

7








Chapter 1

8






Fluidized bed



Hot or cold fluid

Thermal boundary

layer

Fluidized bed

Inert particle

Hot or cold fluid

Deposit

Heat exchanger

wall




Introduction

9


Downcomer

Fluidized bed

Particle separation



Hot or cold fluid







Chapter 1

10




0 75 0 63h h0 0734 Nu Re Pr= (11)





Introduction

11






Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut

Salt

crystallization

crystallization

Ice




Chapter 1

12

14 Objectives




15 Thesis Outline



Introduction

13






Chapter 1

14

Nomenclature



Abbreviations


References








Introduction

15

















Chapter 1

16















Introduction

17







Chapter 1

18

19


21 Introduction







Chapter 2

20







1 1 1ln2

D D DU D Dα λ α

= + +

(23)


( )( )

sl wl oinnero

i iinnersl cooll

T T DUDT T α

minus=

minus (24)




21




fraction (wt)



(degC)


(mol)



50 160 -304 288 037 64 206 -396 372 037 76 247 -480 449 036


2

f H O

100 100expR 27315 27315

h M TyT

∆ = minus sdot +

(25)



Chapter 2

22




0

1000

2000

3000

4000

5000

6000

-300 0 300 600 900 1200 1500 1800 2100Time (s)

-60

-50

-40

-30

-20

-10

00

No ice scaling

Ice scaling

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Nucleation

Susp

ensi

on o

utle

t tem

pera

ture

(degC

)






23


00

05

10

15

20



Diff

eren

ce b

etw

een

wal

l and

eq

uilib

rium

tem

pera

ture

T -T

w (K

)




00

05

10

15

20

25

30

00 10 20 30 40 50 60 70

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)




MgSO4

NaCl



Chapter 2

24

24 Discussion


R Ggt (26)





( )iceint w

ice ice f

G T Th

λρ δ

= minus∆

(27)




( )2H Oliq

int bb ice liq

MkG x xx M

ρρ

= minus (29)


( )2

H Oliq

int bb ice liq b


x M dTρρ

asymp minus

(210)


25


2

155


liq H O iceb

27 10 ( ) w


ρ ρ δρ λ


(211)


( )2

H Oliq

w bb ice liq b

( )Mk dxG T T x

x M dTρρ

= minus

(212)

0

20

40

60

80

100


Perc

enta

ge o

f tot

al r

esis

tanc

e to

ice

grow

th

Surface integration

Mass transfer

Heat transfer





R G= (213)

Chapter 2

26


2

liq ice


( )MR dTT T x T x

k M dxρρ

∆ = minus = minus

(214)








13a


ReRe

ε=

minus and h p 1

Sh Sh εε

=minus

(217)


23

0 61 0 28s liq

0 281 15 D

uk

ρmicro

= (218)


2

H Oliq trans

ice liq bb

M Tdx RM dT x k

ρρ

∆minus =

(219)



27


23

2

028 liqice


087D

M dTT x RM dxu

micro ρρ

∆ = minus

(220)

00

02

04

06

08

10


MgSO4


NaClKNO3

KCl

Ice scaling

No ice scaling

y = 59610-6 x-1



0001020304050607080910


Diff

usio

n co

effic

ient

(10-9

m2 s

)


MgSO4

NaCl

D-glucose

EG

KNO3

KCl

NaCl

MgSO4




Chapter 2

28





~R Ef (221)




( )x 3

p

6 1f v

Dε

πminus

= (223)


29


34 sR c u= (224)


23

2

028 liq239 ice


M dTT c x uM dx

micro ρρ

∆ = minus

with 5 4087c c= (225)


00

10

20

30



∆T

tran

sm

eas (

K) D-glucose


MgSO4

NaCl

+25

-25


for ice scaling



Chapter 2

30

00

05

10

15

20

25

30


Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scla

ing

∆T

tran

s (K

)


MgSO4

NaCl

D-glucose

EG

KNO3

KCl

NaCl

MgSO4


al









31




25 Conclusions


Chapter 2

32

Nomenclature


Abbreviations



33

References
















Chapter 2

34









35


31 Introduction







Chapter 3

36









37





04 042p p

02p

125435E

Dv

ρυτ minus

=

with s p

s p

E EE

E E=

+ (32)




0406 2 12

max p p p2

E075741

F D vρυ

= minus (33)

Chapter 3

38

10

100

0001 0010D pv p

02 (m08s02)

τ (1

0-6 s

)


0002 0004 0006

80

60

4030

20




maxmax

s

FpA

= (34)




10

100

1000

10000

01 10 100 1000D p

2v p12 (10-6 m32s12)


pm

ax (1

03 Pa)


2vp12 for 2 3



39




21 694 020 32 760 032 43 798 038 727 022 790 033 826 041 762 024 825 037 866 047 794 027 860 041 897 053 827 031 895 047 934 061 862 035 930 053 963 068 897 040 960 060 932 045 962 051


scfbz slip p

uv v Dε

ε= minus (35)



825 045 017 825 087 061 831 082 048 825 054 029 855 105 075 864 091 051 825 077 056 895 058 013 894 114 069 859 101 077 895 078 034 885 124 097 895 097 056 895 050 012 895 127 090 895 066 029 895 088 054


ssfb p

slip p

u Dv D

εε

ε= (36)


Chapter 3

40

33 Results



-10

0

10

20

30

40

50

60

0 20 40 60 80 100Time (10-6 s)

Pres

sure

(10

3 Pa)

p max

τ

Threshold


0

10

20

30

40

0 10 20 30 40 50Contact time (10-6 s)

Freq

uenc

y (1

0 9 1

m2 s2 )


ε=895)


41





2

A rA r

ravgravg

exp2

f vy vvv π

= minus

(37)

00

10

20

30

40

000 005 010 015 020 025v r (ms)

y A (1

06 1m

3 )

Threshold


ε=895)



Chapter 3

42

ravg s010v u= (38)

000002004006008010012014016018020

65 70 75 80 85 90 95 100ε ()

v ra

vgu

ssf

b

2 mm 3 mm 4 mm




( ) A ravg 3p

6 1ff v

Dε

επ

minus= (39)


00

05

10

15

20

25

30

35

40

65 70 75 80 85 90 95 100ε ()

f = ( π

6) f

A D

p3 (v

r (1

- ε))

2 mm3 mm4 mmEq 312



43


3


223


= =int (310)


( ) 0f 1


13

1

0pb

111

g εε


(311)









Chapter 3

44

000

050

100

150

200

250

000 020 040 060 080 100v z (ms)

v ra

vgc

fbv

rav

gsf

b

2 mm3 mm4 mmEq 313




000

020

040

060

080

100

120

000 020 040 060 080 100v z (ms)

f Ac

fbf

As

fb

2 mm3 mm4 mmEq 314




45





2

pVV p

pavgpavg

exp2

vfy vvv π

= minus

(315)


53

V maxV max 8

5 max avg maxavg

exp2 2

f py pp pΓ

= minus =

53

V max

maxavg max avg

05596 exp2

f pp p

= minus

(316)

Chapter 3

46


( )5

32

max pVj max

maxavg maxavg

05596 exp2V

p r Dfy p dVp p

= minus int (317)


( )5

3

p

2 22max pV p


05596 exp sin2D


π π


int int int (318)


53

103

3V p 2 max


3516 exp2

f D py p l l dlp p


p

rlD

= (319)


3

2

16max


minus asymp minus


123





47

00

20

40

60

80

100

120

140

0 20 40 60 80 100p max (103 Pa)

y j p

max

32 (1

03 N1

2 m2 s)

Threshold








653


Chapter 3

48

00

05

10

15

20

25

30

35

40

000 020 040 060 080 100 120v pavg

12 (m12s12)

pm

axa

vg (1

03 Pa)

2 mm3 mm4 mmEq 322

-25

+25


the power 12


( )20 pavg

V 4p

11443

g vf

Dε

π πminus

= (324)



00

10

20

30

40

50

60

70

000 020 040 060 080 100 120v pavg (ms)

f Vd

p4 (g0

adj(1

- ε)2 ) (

ms

)

2 mm3 mm4 mmEq 324

-25

+25


velocity


49


( )20adj pavg

V 4p

15405

g vf

Dεminus

= (325)

34 Discussion






p-w A p-w r

0

J y j dvinfin

= int (326)


2


ravg0 ravg

2exp 22 3

f vJ m v dv f D vvv

π ρπ

infin = minus =

int (327)




Chapter 3

50




00

20

40

60

80

100

120

65 70 75 80 85 90 95 100ε ()

Impu

lse

J (N

m2 ) 2 mm

3 mm

4 mm


Energy of Impacts


p-w A p-w r

0

E y e dvinfin

= int (330)


2

2


ravg0 ravg

exp2 6

f vE m v dv f D vvv

π ρπ

infin = minus =

int (331)




51




000

002

004

006

008

010

012

014

016

65 70 75 80 85 90 95 100ε ()

Ene

rgy

E (J

m2 s)

2 mm

3 mm

4 mm








( ) ( )3



Chapter 3

52




lpf j lpf max

0

J y j dpinfin

= int (337)


lpf max lpf

0

2j pdt pτ

τπ

= =int with maxlpf

sin tp t p πτ

=

(338)


3

2

16max


2 exp pJ bp p dpa

τπ

infinminus

= minus int (339)


1 1

5 5

042

- -04 3p-p p p p p p

p

12922 3016 10E


= = sdot

(340)


16-2



lpf p-pτ τ= (342)


2

3

163 max

lpf p max max0


infinminusminus



53


( )1 23 33 16

lpf p0



= (344)


564





0

5

10

15

20

25

30

35

00 02 04 06 08 10v z (ms)

Impu

lse

J (N

m2 )


Pressure fronts

Total



Chapter 3

54

Energy of Impacts









lpf j lpf max

0

E y e dpinfin

= int (350)


22max lpf


ppe dtc c

τ τρ ρ

= =int with maxlpf

sin tp t p πτ

=

(351)


1

2

16max


exp2

pbE p dpc a

τρ



1

3

16p3 max



c aρ

infinminus



( )

43

13p3 16

lpfliq liq 0

586 10 expa bD

E x x dxcρ


a= (354)


55


1164

V p maxavglpf

liq liq

03061f D p

Ecρ

= (355)


1154

V p pavg5lpf

liq liq

9273 10f D v

Ecρ

= sdot (356)


( ) 165



000

005

010

015

020

025

00 02 04 06 08 10v z (ms)

Ene

rgy

E (J

m2 s)

Total




Chapter 3

56










57


35 Conclusions


Chapter 3

58

Nomenclature




59

Abbreviations


References














Chapter 3

60














61


41 Introduction






Chapter 4

62







1 1 1ln2

D D DU D Dα λ α

= + +

(42)


( )( )

sll wl oinnero

i iinnersll cooll

T T DUDT T α

minus=

minus (43)


63









(mm) () (ms) (mm) () (ms) (mm) () (ms) 21 718 017 32 763 026 43 808 037

758 020 792 029 839 042 789 022 813 032 874 047 827 026 847 035 906 052 859 029 939 059



820 075 061 816 081 060 836 084 051 855 100 083 852 105 081 863 103 066 888 122 101 875 128 103 887 126 086


scfbz slip

uv v

ε= minus (45)

Chapter 4

64


ssfbslip p

uv Dε

ε= (46)





0

1000

2000

3000

4000

5000

6000

-300 0 300 600 900 1200 1500 1800Time (s)

-60

-50

-40

-30

-20

-10

00No ice scaling

Ice scaling

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Nucleation

Susp

ensi

on o

utle

t tem

pera

ture

(degC

)





65





00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

2 mm 3 mm 4 mm

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

No ice scaling

Ice scaling

for

ice

scal

ing

∆T

tran

s (K

)




Chapter 4

66




00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

2 mm 3 mm 4 mm 043 061

083

101

056060

081 103

041051 066

086

SFB 2 mm

SFB 3 mm

SFB 4 mm

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)






67


0

1000

2000

3000

4000

5000

6000

70 75 80 85 90 95 100ε ()


eat t

rans

fer

coef

ficie

nt (W

m 2 K

)





layer d r

layer

ddtδ ϕ ϕ

ρminus

= (47)


R Ggt (48)

Chapter 4

68



R G= (49)


( )2H Oliq

w bb ice liq

MkG x xx M

ρρ

= minus (410)


( )2

H Oliq

w bb ice liq b

Mk dxG T T xx M dT

ρρ

= minus

(411)


( )


H Oliq -1

propb ice liq b

1 0216 KM dxc

x M dTρρ

= =

(412)


( )( )( )033 0 33 -033 0 33 0 67p pb p

p








69


e p-wR c E= (415)



( )

13

1

0adjpb

1max 3 1

1g

εε


(416)



00

20

40

60

80

100

120

140

000 002 004 006 008 010 012Total energy (Jm2s)

Rem

oval

rat

e (1

0 -6

ms

)

2 mm3 mm4 mmEq 417




j p-wR c J= (418)

Chapter 4

70







transsfbprop

1 1415 10 286 10

c g u g uT


∆ = sdot = sdot (421)

00

20

40

60

80

100

120

140


Rem

oval

rat

e (1

0 -6

ms

)

2 mm3 mm4 mmEq 420





71

00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)

2 mm 3 mm 4 mm











Chapter 4

72





00

20

40

60

80


2 mm3 mm4 mmEq 427

Rem

oval

rat

e ca

used

by

liqui

d pr

essu

re fr

onts

(10-6

ms

)







73


( ) ( )( ) ( )2


1286 10 1 068 exp 109 481 10

gT u v v v




00

05

10

15

20

25

00 05 10 15 20 25


∆T

tran

sm

eas (

K)

+20

-20



45 Discussion



Chapter 4

74








75


00

05

10

15

20


Pressure fronts

Total

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)





Chapter 4

76


46 Conclusions



77

Nomenclature





Chapter 4

78

References


















79





Chapter 4

80

81


51 Introduction





521 Introduction



Chapter 5

82







83











Chapter 5

84

Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


Ice + salt

Ice line


0degC

T eut

0 w eut


Boiling line for p2

Boiling line for p1



process




85




Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point

S

aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut


Ice +



process



Chapter 5

86





Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut


A

B





87






(Ham et al 1998)


Chapter 5

88








89


-66-58

-43-39-29-21-18-15-15-12

-272

-78-105-106

-156-168

-181-187-190

-362-336

-287-280

-264-212-200-190

38

233390

403190

427214

396

342398

286260

381424

197197

322225

272245

215180

10459

12766

119

-40 -30 -20 -10 0 10 20 30 40 50






Chapter 5

90











91





Chapter 5

92





(wt) Tsat

(degC) Fluidized

bed us

(ms) qamp






93

0

5

10

15

20

0 1800 3600 5400 7200 9000Time (s)

Susp

ensi

on te

mpe

ratu

re a

t he

at e

xcha

nger

inle

t (degC

)

0

2000

4000

6000

8000

salt nucleation

with fluidized bed


steady state Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)








Chapter 5

94


5

10

15

20

25

0 1800 3600 5400 7200 9000Time (s)

Susp

ensi

on te

mpe

ratu

re a

t he

at e

xcha

nger

inle

t (degC

)

0

1000

2000

3000

4000

salt nucleation

with fluidized bed


steady state Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)



543 Discussion





95






(wt) Teut


(wt) us

(ms) 102 037 KNO3 104 -29 KNO3 106 037




Chapter 5

96




00

05

10

15

20

25

30

00 50 100 150 200

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)


MgSO4

KNO3

Eutectic

Eutectic

Fouling

No fouling


MgSO4 solutions






97

-35

-30

-25

-20

-15

0 900 1800 2700 3600 4500 5400Time (s)

0

2000

4000

6000



Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Susp

ensio

n te

mpe

ratu

re a

t he

at e

xcha

nger

out

let (

degC)




-35

-30

-25

-20

-15

0 300 600 900 1200 1500 1800Time (s)

0

2000

4000

6000


Ice nucleation

Salt nucleation

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Susp

ensio

n te

mpe

ratu

re a

t he

at e

xcha

nger

out

let (

degC)


Chapter 5

98

00

05

10

15

20

25

30

00 50 100 150 200

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)


MgSO4

KNO3



554 Discussion



R Ggt (51)



99

0

20

40

60

80

100


Perc

enta

ge o

f tot

al r

esis

tanc

e to

ice

grow

th

Surface integration

Mass transfer

Heat transfer




( ) ( )2 2

H O H Oliq liq



ρ ρρ ρ

= minus asymp minus

(52)



Chapter 5

100










101


component wadd

(wt) wKNO3 (wt)

Tfr or Teut (degC)

Type of crystals









Chapter 5

102

00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling



00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling






103





and 58 wt KNO3



00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling



Chapter 5

104

564 Discussion









105








Chapter 5

106



57 Conclusions



107

Nomenclature


Abbreviations


References






Chapter 5

108


















109



Chapter 5

110

111


61 Introduction




Chapter 6

112









113







Chapter 6

114







(Gladis et al 1996)



115




631 Introduction





Chapter 6

116








T T T TT

T T T T


minus minus (61)



117

plate

crys plate cool

1 1 1U

δα λ α

= + + (62)


( )( )

iscrys platemin

crysiscrys coolin

T T UT T α

minus=

minus ( 63)









Chapter 6

118


-80

-70

-60

-50

-40

-30

-20

-10

00

0 1200 2400 3600 4800 6000Time (s)

Tem

pera

ture

(degC

)

T iscrys

T platemin

T coolin

Ice nucleation


during experiment 3


0

1000

2000

3000

4000

5000

6000

0 1200 2400 3600 4800 6000Time (s)

00

01

02

03

04

05

06Uα crys

Torque

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Tor

que

(Nm

)

Ice nucleation



119




00

05

10

15

20

25

30

35

40


Tis

cry

s-Tpl

ate

min

(K)


No ice scaling

Ice scaling

-50

-40

-30

-20

-10

00



No ice scaling

Ice scaling

Tpl

ate

min

(degC

)


without ice scaling



R Ggt (64)


Chapter 6

120

( )liq eq

eq crys plateminice

dwkG T w Tw dT

ρρ

= minus minus

(65)


( )liq eq

iscrys plateminice

dwkG T Tw dT

ρρ

= minus minus

(66)


eqice


dTwT T T Rk dw

ρρ

∆ = minus = minus

(67)






121


00

05

10

15

20

25

30

35

40


∆T

tran

s (K

)




0

5

10

15

20

25


Hea

t flu

x (k

Wm

2 )

Ice scaling




Scraperblades

Orbitalrods

No ice scaling








Chapter 6

122







0 75 063


liq 1D

Nuα ελ ε

=minus

and ( )

liq s ph

liq 1u D

Reρ

micro ε=

minus (68)




123

0

2000

4000

6000

8000

70 80 90 100Bed voidage ()

2 mm3 mm4 mmH

eat t

rans

fer

coef

ficie

nt (W

m 2 K

)

0

2000

4000

6000

8000

00 50 100 150 200Scraper passes (1s)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Re-Pr Eq611

Re-Pr Eq610







liq liq pliq

4 c Nα λ ρπ

= (69)



0 5 025


liq scrscr

liq

NDRe

ρmicro

= ( 610)

Chapter 6

124


0 5 033


liq scrscr

liq

NDRe

ρmicro

= and scrscr

liq

DNu αλ

= (611)








125

0

2000

4000

6000

8000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

NaCl

EGD-glucose

0

2000

4000

6000

8000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

NaCl

EG D-glucose




Eq 610



0

2000

4000

6000

8000

0 5 10 15 20 25 30Ice fraction (wt)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K

)

T fr= ndash20degC

T fr= ndash10degC

T fr= ndash5degC



Chapter 6

126











127

1

10

100

1000


Inve

stm

ent c

osts

(keuro)


1

10

100

1000


Inve

stm

ent c

osts

(keuro)

STHESSHE

FBHE


trendline


exchangers





Chapter 6

128

0

5

10

15

20

25


Hea

t flu

x (k

Wm

2 )SSHE

FBHE

0

100

200

300

400

500


Inve

stm

ent c

osts

(eurok

W)

SSHE

FBHE -5degC

FBHE -10degC

FBHE -2degC









129








( )( )p is

he tube

1gpA D


= ( 616)


( )( )p is s tubepd

he he

14

g u DW pVA A


amp amp (617)



he he he pump pump

14

g u DW WQA A A

ρ ρ ε

η η

minus minus= = =

amp ampamp ( 618)




14

g u DWWA A

ρ ρ ε

η η η

minus minus= =

ampamp ( 619)


Chapter 6

130



Comparison






000

005

010

015

020


Scraper blades

Orbital rods

Fluidized bed

Rel

ativ

e ad

ditio

nal p

ower



131





net add

cyclecomp

Q QCOPW

+=amp amp

amp ( 621)

-25

-20

-15

-10

-5

0



Fluidized bed

Eva

pora

tion

tem

pera

ture

(degC

)

00

01

02

03

04

05

06



Fluidized bed

Rel

ativ

e co

mpr

esso

r po

wer




Chapter 6

132



net

totalcomp add

QCOPW W

=+

amp

amp amp (622)


00

05

10

15

20

25

30

35


Scraper blades

Orbital rods

Fluidized bed

CO

P


removal mechanisms





133

0

50

100

150

200

250


Rel

ativ

e an

nual

cos

ts (euro

kW

) 100 kW


Fluidized bed

0

50

100

150

200

250


Rel

ativ

e an

nual

cos

ts (euro

kW

) 1 MW


Fluidized bed


system


system


67 Conclusions



Chapter 6

134

Nomenclature



References




135

















Chapter 6

136















137














Chapter 6

138












139


71 Introduction







Chapter 7

140







141




721 Attrition


00

01

02

03

04

05


Mas

s fr

actio

n (-

)

(a)

00

01

02

03

04

05


Mas

s fr

actio

n (-

)

(b)



Chapter 7

142


722 Agglomeration





Theory


32V

Am


γ γ∆ = ∆ + = ∆ + (723)


143






( ) ( ) sol

0liq 0liq s ssol


ψψ infin infin

infin

∆ = +

(726)


( ) ( )


T T

T T


infin infin


∆∆ = + = ∆ = ∆ = ∆int int (727)


( )3

2V fA

m

-B L hG T T B LV T

γinfininfin

∆∆ = + (728)


( ) 0d G

dL∆

= (729)


A

V ice f

2( ) 1-3

BT L TB h L

γρinfin

= ∆

(730)

Chapter 7

144







145

00020406081012141618


Num

ber

dens

ity (1

06 1

m) Initial

After 1 hr

After 2 hrs

After 3 hrs

0

50

100

150

200

250


Ave

rage

dia

met

er (micro

m)

10

15

223342








Chapter 7

146

0

100

200

300

400

500

600


Ave

rage

cry

stal

siz

e (micro

m)





724 Conclusions





147








Chapter 7

148

-70

-60

-50

-40

-30

-20

-10

00

-2 -1 0 1 2Time (hours)

Tem

pera

ture

(degC

)



Seeding

∆T maxsuper

24




p

Feret

4 AD

π= (731)


FeretDΓP

π= (732)


733 Results



149









a b

c d



Chapter 7

150


00

01

02

03

04


Num

ber

frac

tion

(10 4 1

m) 0 h

2 h6 h22 h

00

02

04

06

08

10


Cum

ulat

ive

num

ber

frac

tion

(-)

0 h2 h6 h22 h



experiment 2



0

100

200

300

400

500

0 4 8 12 16 20 24Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)





151

080

085

090

095

100

0 4 8 12 16 20 24Time (hours)

Ave

rage

cry

stal

rou

ndne

ss (-





0

100

200

300

400

500

0 4 8 12 16 20 24Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)

400 rpm750 rpm

080

085

090

095

100

0 4 8 12 16 20 24Time (hours)

Ave

rgae

cry

stal

rou

ndne

ss (-

)

400 rpm750 rpm






Chapter 7

152




0

100

200

300

400

500

0 10 20 30 40 50Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)



solutions





153

0

100

200

300

400

500

0 20 40 60 80 100Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm




homogeneous storage

735 Discussion






Chapter 7

154



( )Ai b

V ice f

-3

=∆

BG T TB h

αρ

(734)



3 3liq liq

2 1 3 for lt10

D DNu Pr


= +

(735)


( )2 2

liqAdsi H Ob H Oi

V ice

-3BG k w wB

ρρ

= (736)


2

ddsi

H Ob1-kk

w= (737)


0207 0173 4liq equiv 036 mix

3liq tank

2 047D DSh Sc

Dξ ρ

micro

= + (738)



155

( )2 2

2

b i H Ob H OiH O

- - dTT T w wdw

= (739)


( )int i i-=

rG k T T (740)


( )155-3 i i27 10 -=G T T (741)



-Tb by

2

2

155


A d liq H O


B k dwρ ρρ α

∆ = minus minus +

(742)



Chapter 7

156

10E-11

10E-10

10E-09

10E-08

0 5 10 15 20w soluteb (wt)

G (m

s)






10E-11

10E-10

10E-09

10E-08

0 5 10 15 20w soluteb (wt)

G (m

s)

00 Wkg01 Wkg10 Wkg





157


10E-12

10E-11

10E-10

10E-09

10E-08

0 5 10 15 20 25 30w soluteb (wt)

G (m

s)



stirring



Chapter 7

158

10E-12

10E-11

10E-10

10E-09

10E-08

-120 -100 -80 -60 -40 -20 00T freeze (degC)

G (m

s)



without stirring

736 Conclusions








159


G L t n L tn L tt L

partpart=

part part (743)


tρ φ φ ρpart

+ =part

(746)


ρ φpart=

part (747)



part (748)


3ice V

tot 0

( )L

L

B n L L dLm

ρφ=infin

=

= int (749)


2icetot A

0

( )L

L

A B n L L dL=infin

=

= int (750)




Chapter 7

160


ice f ice solV

liq d sol

1 13

BG T Th w dTB

k dwρ ρ

α ρ

= minus ∆ +

(751)


A

V ice lat

21-3

BT TB h L

γρinfin

= ∆

(730)


0173 4liq equiv 025

3liq

2 13D

Nu Prξ ρ

micro

= +

(735)


0207 0253 4liq equiv 036 mix

3liq tank

2 047D DSh Sc

Dξ ρ

micro

= + (738)



( )155-3 27 10 -G T T= (741)



161


-15

-10

-05

00

05


Cry

stal

gro

wth

rat

e (1

0 -7 m

s)

G heat

G surf G mass







Tank volume (l)

Time (h)


Chapter 7

162




0

100

200

300

400

500

600

0 5 10 15 20 25Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)






163

0

50

100

150

200

250

300

00 10 20 30 40 50 60Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)

8 wt φ =1

86 wt φ =0142

130 wt φ =0142

15 wt φ =1

190 wt φ =0132

369 wt φ =0122




00102030405060708090

100


Num

ber

frac

tion

(10 3 1

m) 5


00

10

20

30

40

50


Num

ber

frac

tion

(10 3 1






chloride


Chapter 7

164


0

100

200

300

400

500

600

700

0 20 40 60 80 100Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)




744 Discussion





165

0

100

200

300

400

500

600

700

0 5 10 15 20 25Time (hours)

Ave

rage

cry

stal

siz

e (m

m)


HD =015 HD =020 HD =025HD =030






( ) ( )isgin

tot


t L mpartpart

= +part part

amp (752)


Chapter 7

166


0

100

200

300

400

500

600

700

0 20 40 60 80 100Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)



glycol (PG)

745 Conclusions


75 Conclusions



167

Nomenclature






Chapter 7

168

Abbreviations


References














169
















Chapter 7

170
















171


81 Introduction







821 Flow Patterns


Chapter 8

172





822 Rheology


823 Pressure Drop



173









Chapter 8

174

825 Superheating




loop



175











Chapter 8

176








177


833 Data Reduction







1 1 1ln2

D D DU D Dα λ α

= + +

(82)


Chapter 8

178






-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

00

50

100

150

200

250

300

350

400

Ice

frac

tion

(wt

)

Tfr

T inmeas

T outmeas

T coriomeas

ineqinφ




ineqin 0ineqin

ineqin

w ww

φminus

= (83)


179





Enthalpy at Inlet






( )he rest


0t Q Q

h t h t dtm

+= = + int

amp amp (87)


( )he rest


0tn t

n

Q Q th t h t

m

= ∆

=

+ ∆= = + sum

amp amp (88)


Chapter 8

180

-800

-700

-600

-500

-400

-300

-200

-100

00

0 600 1200 1800 2400 3000 3600Time (s)

Ent

halp

y (k

Jkg

)

h isineqin

h isinreal


rest

( 0 W)Q =amp





end


0end is

0tn t

n

m Q tQ h t t h tt m

= ∆

=

∆ = = minus = +

sum

ampamp (810)


Enthalpy at Outlet


is


Qh hm

= +amp

amp (811)


181








-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

0

5

10

15

20

25

30

35

40Ic

e fr

actio

n (w

t)

T inmeas

T outmeas

inreal

outreal

φφ


experiment 1



Chapter 8

182


-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

0

5

10

15

20

25

30

35

40

Ice

frac

tion

(wt

)

T outmeas

T outeq

outrealφ

∆Tsh








exchanger


183


meas eqsh

w-liq sh w eq

T TTT T T T

ζminus∆

= =∆ + ∆ minus

(816)



( )( )

oinnerw is o

EG is i iinner

DT T UT T Dα

minus=

minus (817)



00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)


00

02

04

06

08

10


Rel

ativ

e su

perh

eatin

g ζ






Chapter 8

184



00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)


00

02

04

06

08


Rel

ativ

e su

perh

eatin

g ζ









185

00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)


00

02

04

06

08

10


Rel

ativ

e su

perh

eatin

g ζ






846 Discussion







Chapter 8

186
















ice ice ice

is is

m A Gm m


amp

amp amp (827)


187




ice3

2 ice Feret

mNc Dρ


m m D xπφ φρ= = ∆ (829)


eq liqA

eqice V f

liq cr

3T TBG

dTB hwk dw

ρρ α

minus=

∆minus +

(830)


eq liqA

ice V eqcrf

cr f liq

31

T TBGB dTh w

k h dwρ α

α ρ

minus=

∆minus + ∆

(831)


1 1 1 23 3 3 3

1 23 3


cr D D DNu Pr c


= = = (832)


1 2

3 3

2 23 3

eq liqcrA

ice V f pliq liq eq

f liq

31

D

T TBGB h c w dT

dwh

αρ λ

ρ

minus=

∆ minus + ∆

(833)


Chapter 8

188

00

10

20

30

40

50

60

70


Con

trib

utio

n to

cry

stal

gro

wth

re

sist

ance

rel

ativ

e to

hea

t tra

nsfe

r

Total

Mass transfer

Heat transfer



1 2

3 3

2 23 3



f liq

121

D


dwh

φρ απφρ λ

ρ

minus∆∆ =

∆ minus + ∆

amp

(834)


( )

1 23 3

2 23 3




c B D dwhλρ α

ρ φ α ρ


(835)





189



( )

1 23 3

2 23 3


is f liq

1Dc w dTDT c T T

dwhλρ

ρ φ ρ


with V2 i3

1 A iinner cr

12Bccc B D

αα

= (836)




00

05

10

15

20

000 001 002 003 004 005

∆T

shm

eas (

K) 1

2 34

56

7

8

9

10

-25

+25

(m K)( )1 2

3 3

2 23 3


is f liq

1Dc w dTD T T

dwhλρ

ρ φ ρ

minus + minus ∆



Chapter 8

190


847 Conclusions





0

1000

2000

3000

4000

5000

6000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)





191






measliq

predliq

αα



measis

predis

αα




Chapter 8

192

08

10

12

14

16

18

20



Hea

t tra

nsfe

r fa

ctor

Ψliq

08

10

12

14

16

18

20



Hea

t tra

nsfe

r fa

ctor

Ψis









193

08

10

12

14

16

18

20


Hea

t tra

nsfe

r fa

ctor

Ψis


08

10

12

14

16

18

20


Hea

t tra

nsfe

r fa

ctor

Ψis






854 Conclusions





0 404liq liq2


1 42 for 67001 with 0 112 for 67002


ρminus

minus

= lt∆ = = ge (841)


Chapter 8

194

000

020

040

060

080

100

120

140


Pres

sure

dro

p (b

ar)





measliq

predliq

pp

∆Π =



measis

predis

pp

∆Π =






195

08

10

12

14

16



Pres

sure

dro

p fa

ctor

Πliq

08

10

12

14

16



Pres

sure

dro

p fa

ctor

Πis




08

10

12

14

16


Pres

sure

dro

p fa

ctor

Πis


08

10

12

14

16


Pres

sure

dro

p fa

ctor

Πis






Chapter 8

196

863 Conclusions


87 Conclusions




197

Nomenclature




Chapter 8

198

References














199














Chapter 8

200




201

9 Conclusions







Chapter 9

202








Conclusions

203


Overall Conclusions



Chapter 9

204

205







Tem

pera

ture

Aqueous solution

Eutectic point



Ice + solid solute

Ice line

Solubility line

0degC

T eut

0 wt w eut




5i

eq ii 0

T C w=


Appendix A

206

5i

eq ii 0

w C T=





( ) ( )( )

5 3i j

ij m mi 0 j 0

f C w w T T= =





( ) ( ) ( )( )5 3

i j3ij m m

i 0 j 0




A14 Enthalpy





2

diss


T

T




207




0degC

T



2 2

2 2 3H O pH O

0degC

42163 1495 1925 10T



3i

diss diss ii 1

h w T C w=



m

diss diss m

psol psol psol TT T

T T T



m

diss

psol T

T

c w T dTint ( )diss

0

psol m mmT T

c w T T d T Tminus


( ) ( )( ) ( )

diss 5 3i j

ij m m mi 0 j 00

mT T


= =


( ) ( )

5 3i j+1

ij m diss mi 0 j 0

1j+1

C w w T T= =


sumsum (A14)

( )( )5

ii ij diss m m

i 0 c j C T T w w

=


Appendix A

208


m

psol T

T

c w T dTint ( ) ( )( ) ( )m 5 3

i jij m m m

i 0 j 00

T T


= =


( ) ( )

5 3i j+1

ij m mi 0 j 0

1j+1

C w w T T= =


sumsum (A17)


( ) ( )( )

5 4i k

ik m mi 0 k 0

h C w w T T= =





5i

0 ii 1

D wT C w=



D constant273 15T

micro=

+ (A20)


0

00

273 15D D273 15

wT T wT wTwT T

micromicro

+= +

(A21)


209




CAS number 50-99-7



-100

-50

00

50

100

150

200

250


Tem

pera

ture

(degC

)

Aqueous solution


Ice linedextrose


Solubility line






Appendix A

210








211

A22 Ethanol (C2H6O)


CAS number 64-17-5




-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

) Aqueous solution


Ice line






Appendix A

212







1Melinder (1997)




213



CAS number 107-21-1




-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

) Aqueous solution


Ice line






Appendix A

214







1Melinder (1997)




215



CAS number 57-55-6




-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

) Aqueous solution


Ice line






Appendix A

216







1Melinder (1997)




217








-100

-50

00

50

100

150

200

250


Tem

pera

ture

(degC

)

Aqueous solution


Ice + MgSO412H2O


aqueoussolution +

MgSO47H2O


Eutectic point









Appendix A

218













219


Other name -





-150

-100-50

0050

100150

200250

300


Tem

pera

ture

(degC

) Aqueous solution


Ice line

Ice + KClH2O


Eutectic point

Solubility line

aq sol + KClH2O








Appendix A

220













221


Other name -

CAS number 590-29-4



-450-400-350-300-250-200-150-100-500050

100


Tem

pera

ture

(degC

) Aqueous solution


Ice line





Appendix A

222










223


Other name -





-100

-50

00

50

100

150

200

250

300


Tem

pera

ture

(degC

)

Aqueous solution


Ice line

Ice + KNO3


Eutectic point

Solubility line








Appendix A

224











225







-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

)

Aqueous solution


Ice line

Ice + NaCl2H2O


Eutectic point









Appendix A

226











227

Nomenclature


References











Appendix A

228

















229



B11 Density






B13 Enthalpy



and T in (degC)(B3)

B14 Specific Heat





B21 Density



Appendix B

230


( )is

ice liq

11-

ρφ ρ φ ρ

=+

(B6)




( )( )


liq ice liq ice

2 2

2

λ λ ξ λ λλ λ

λ λ ξ λ λ


(B7)



B23 Enthalpy




B24 Specific Heat


p

hcT

part=

part (B9)



0degC 0degC

0degC 1 0degCT T


= + + minus +

int int (B10)



231



( ) is


10degC 0degC





(B11)



( ) ( )is



T Tφ φ φ


int (B12)


( ) ( )ice



Tφ φ


int (B13)








Appendix B

232

Nomenclature


References









233






C11 Dimensions






bed heat exchanger

Appendix C

234



( ) ( )

2 2out in out in




amp ampamp (C1)


( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C2)


2frcool

cool hyd

12

p Lf uDρ

∆= with

hyd


hyd

52300 10DRele le (C3)





235

-50

0

50

100

150


Hea

t upt

ake

from

sur

roun

ding

s (W

)c uptake=35 WK







inner

ooinner ln

QUA T

=∆

amp (C5)



o o ss i iinner

ln1 1 12

D D D DU Dα λ α

= + + (C6)

Appendix C

236


hyd hyd

23

iouter

oinner

086D D

DNu Nu

D

=

in which (C7)

( )( )

hyd

hyd

23

hyd

2 13

10008 1

1 12 7 18

D

D

f Re Pr DNu

Lf Pr


21 82log 1 64Df (Re )

minus= minus (C8)





( )

( )iinner

23

iinner

23

10008 11 12 7 1

8

i innerD

D

f Re Pr DNu

Lf Pr


21 82log 1 64Df (Re )

minus= minus (C9)



237

0

500

1000

1500

2000


Pred

icte

d U

o (W

m2 K

)

+5

-5



0

1000

2000

3000

4000

5000

6000


Pred

icte

d α

i (W

m2 K

)

+5

-5




Appendix C

238


C21 Dimensions





bed heat exchanger



( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C10)



239

-50

0

50

100

150

200

250


Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=55 WK







Appendix C

240

0

500

1000

1500

2000


Pred

icte

d U

o (W

m2 K

)

+5

-5



0

1000

2000

3000

4000

5000

6000


Pred

icte

d α

i (W

m2 K

)

+5

-5




241





coil

C31 Dimensions





( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C11)


2fr

EGEG hyd

12

p Lf uD

∆=

ρ with

hyd

hyd

0 5hyd 0 25

0 25c

0 3164 1 0 095

D

D

Df ReRe D

= +

(C12)


Appendix C

242


-10

0

10

20

30


Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=095 WK





iinner

0 45iinner

critc

2300 1 8 6

D

DRe

D

= +

(C13)




243





1

iinner iinner

0 331



2

iinner iinner

0 332




3

hyd hyd

0 333


hyd2300DRe gt (C18)





oinnerss

o o i iinner

1 1 1 DR

U Dα α= + + (C19)

Appendix C

244



ss

ln2

D D DR

λ= (C20)


3 6 2

hyd iinner

hyd oinnerss 0 33


1r c r D D

D DR



3 6 2

hyd iinner


EG 3 EG NaCl 2 NaCl

1 r c r D D

U D U DU R



Z AX BY= + in which

3

hyd

o hydo ss 0 33

3 EG EG

11 r D

U DZ U R A X


2

iinner

o oinner0 33

2 NaCl NaCl

1 and r D

U DB Y

c Re Prλ= =

(C23)


( ) ( )AX Y Z

B

=

(C24)




245



iinner iinner



hyd hyd


hyd2300DRe gt (C26)


Appendix C

246

0

500

1000

1500

2000

2500


Pred

icte

d U

o (W

m2 K

)

+5

-5





iinner

ssi oinner o o

1 1 1DR

D Uα α

= minus minus

(C27)


iinner iinner





247

00

50

100

150

200

250

0 2000 4000 6000 8000Re D iinner

Nu

Pr -0

33

iinner iinner






2frpred

iinner

12

Lp f uD

ρ∆ = (C29)


iinner frmeas22

D pf

u Lρ∆

= (C30)


4


Appendix C

248

000

001

002

003

004

005

006

007

0 5000 10000 15000 20000Re Diinner

Fric

tion

fact

or f



iinner



iinner




0

50

100

150

200

250


Pred

icte

d ∆

p (k

Pa)

+5

-5



249





C41 Dimensions





Appendix C

250

( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C34)


-20

0

20

40

60

80

100


Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=151 WK





plate

SSHE ln

QU

A T=

∆

amp with


tank coolin

tank coolout

ln

T T T TT

T TT T


minus minus

(C35)


ss

scr cool

1 1 1RU α α

= + + with platess

ss

Rδλ

= (C36)


5

hydpath hydpath

0 335




251


plate plate

0 5 0 336

D DNu c Re Pr= with

plate

2plate

D

NDRe

ρmicro

= (C38)




hydpath hydpath

0 699 0 330 0507 D DNu Re Pr= for


plate plate

0 5 0 330 997 D DNu Re Pr= with

plate

2plate

D

NDRe

ρmicro

= (C40)


0

250

500

750

1000

1250

1500


Pred

icte

d U

(Wm

2 K)

+5

-5


Appendix C

252

Nomenclature


References






253




Appendix C

254

255










o ln o ln



∆ ∆

ampamp ampamp (D1)



Appendix D

256






1 1 1 ln2

D D DD U Dα α λ

= minus minus

(D2)





i iinner

DUT T T TDα

= minus minus (D3)




257



D15 Bed Voidage








scfb ssfbz

pu u Dv

εε

minus= (D6)



Appendix D

258





001 K ndash





o ln o ln



∆ ∆

ampamp ampamp (D7)







259



1 1 1 ln2

D D DD U Dα α λ

= minus minus

(D8)






D25 Pressure Drop






Appendix D

260




ln ln



∆ ∆

ampamp ampamp (D10)






plate

crys cool plate

1 1 1U

δα α λ

= minus minus (D11)





261


UT T T Tα

= minus minus (D12)


D4 Summary



9 to 24 ndash 15



30 to 120 30 to 55 200


600 to 1800 400 to 900 1500



Appendix D

262

Nomenclature


xvii

Dankwoord








xviii





xix

Curriculum Vitae


Publications









xx













iv

















v














vi











9 Conclusions 201

vii














viii








Dankwoord xvii


ix

Summary


Pepijn Pronk





x





xi





xii


xiii

Samenvatting


Pepijn Pronk




xiv





xv





xvi



1

1 Introduction







Chapter 1

2

-250

-200

-150

-100

-50

00

50


Ammonia

R407C

R404A

R134a

PropaneR

elat

ive

diff

eren

ce in

CO

P co

mpa

red

to a

mm

onia







Introduction

3







Chapter 1

4





12 Ice Slurry



Introduction

5



-200

-150

-100

-50

00


Free

zing

tem

pera

ture

(degC

)





Chapter 1

6


0

50

100

150

200

250

300

350

00 50 100 150 200 250Ice fraction (wt)

Rel

ativ

e pr

oper

ty c

hang

e

Density

Viscosity









Introduction

7








Chapter 1

8






Fluidized bed



Hot or cold fluid

Thermal boundary

layer

Fluidized bed

Inert particle

Hot or cold fluid

Deposit

Heat exchanger

wall




Introduction

9


Downcomer

Fluidized bed

Particle separation



Hot or cold fluid







Chapter 1

10




0 75 0 63h h0 0734 Nu Re Pr= (11)





Introduction

11






Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut

Salt

crystallization

crystallization

Ice




Chapter 1

12

14 Objectives




15 Thesis Outline



Introduction

13






Chapter 1

14

Nomenclature



Abbreviations


References








Introduction

15

















Chapter 1

16















Introduction

17







Chapter 1

18

19


21 Introduction







Chapter 2

20







1 1 1ln2

D D DU D Dα λ α

= + +

(23)


( )( )

sl wl oinnero

i iinnersl cooll

T T DUDT T α

minus=

minus (24)




21




fraction (wt)



(degC)


(mol)



50 160 -304 288 037 64 206 -396 372 037 76 247 -480 449 036


2

f H O

100 100expR 27315 27315

h M TyT

∆ = minus sdot +

(25)



Chapter 2

22




0

1000

2000

3000

4000

5000

6000

-300 0 300 600 900 1200 1500 1800 2100Time (s)

-60

-50

-40

-30

-20

-10

00

No ice scaling

Ice scaling

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Nucleation

Susp

ensi

on o

utle

t tem

pera

ture

(degC

)






23


00

05

10

15

20



Diff

eren

ce b

etw

een

wal

l and

eq

uilib

rium

tem

pera

ture

T -T

w (K

)




00

05

10

15

20

25

30

00 10 20 30 40 50 60 70

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)




MgSO4

NaCl



Chapter 2

24

24 Discussion


R Ggt (26)





( )iceint w

ice ice f

G T Th

λρ δ

= minus∆

(27)




( )2H Oliq

int bb ice liq

MkG x xx M

ρρ

= minus (29)


( )2

H Oliq

int bb ice liq b


x M dTρρ

asymp minus

(210)


25


2

155


liq H O iceb

27 10 ( ) w


ρ ρ δρ λ


(211)


( )2

H Oliq

w bb ice liq b

( )Mk dxG T T x

x M dTρρ

= minus

(212)

0

20

40

60

80

100


Perc

enta

ge o

f tot

al r

esis

tanc

e to

ice

grow

th

Surface integration

Mass transfer

Heat transfer





R G= (213)

Chapter 2

26


2

liq ice


( )MR dTT T x T x

k M dxρρ

∆ = minus = minus

(214)








13a


ReRe

ε=

minus and h p 1

Sh Sh εε

=minus

(217)


23

0 61 0 28s liq

0 281 15 D

uk

ρmicro

= (218)


2

H Oliq trans

ice liq bb

M Tdx RM dT x k

ρρ

∆minus =

(219)



27


23

2

028 liqice


087D

M dTT x RM dxu

micro ρρ

∆ = minus

(220)

00

02

04

06

08

10


MgSO4


NaClKNO3

KCl

Ice scaling

No ice scaling

y = 59610-6 x-1



0001020304050607080910


Diff

usio

n co

effic

ient

(10-9

m2 s

)


MgSO4

NaCl

D-glucose

EG

KNO3

KCl

NaCl

MgSO4




Chapter 2

28





~R Ef (221)




( )x 3

p

6 1f v

Dε

πminus

= (223)


29


34 sR c u= (224)


23

2

028 liq239 ice


M dTT c x uM dx

micro ρρ

∆ = minus

with 5 4087c c= (225)


00

10

20

30



∆T

tran

sm

eas (

K) D-glucose


MgSO4

NaCl

+25

-25


for ice scaling



Chapter 2

30

00

05

10

15

20

25

30


Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scla

ing

∆T

tran

s (K

)


MgSO4

NaCl

D-glucose

EG

KNO3

KCl

NaCl

MgSO4


al









31




25 Conclusions


Chapter 2

32

Nomenclature


Abbreviations



33

References
















Chapter 2

34









35


31 Introduction







Chapter 3

36









37





04 042p p

02p

125435E

Dv

ρυτ minus

=

with s p

s p

E EE

E E=

+ (32)




0406 2 12

max p p p2

E075741

F D vρυ

= minus (33)

Chapter 3

38

10

100

0001 0010D pv p

02 (m08s02)

τ (1

0-6 s

)


0002 0004 0006

80

60

4030

20




maxmax

s

FpA

= (34)




10

100

1000

10000

01 10 100 1000D p

2v p12 (10-6 m32s12)


pm

ax (1

03 Pa)


2vp12 for 2 3



39




21 694 020 32 760 032 43 798 038 727 022 790 033 826 041 762 024 825 037 866 047 794 027 860 041 897 053 827 031 895 047 934 061 862 035 930 053 963 068 897 040 960 060 932 045 962 051


scfbz slip p

uv v Dε

ε= minus (35)



825 045 017 825 087 061 831 082 048 825 054 029 855 105 075 864 091 051 825 077 056 895 058 013 894 114 069 859 101 077 895 078 034 885 124 097 895 097 056 895 050 012 895 127 090 895 066 029 895 088 054


ssfb p

slip p

u Dv D

εε

ε= (36)


Chapter 3

40

33 Results



-10

0

10

20

30

40

50

60

0 20 40 60 80 100Time (10-6 s)

Pres

sure

(10

3 Pa)

p max

τ

Threshold


0

10

20

30

40

0 10 20 30 40 50Contact time (10-6 s)

Freq

uenc

y (1

0 9 1

m2 s2 )


ε=895)


41





2

A rA r

ravgravg

exp2

f vy vvv π

= minus

(37)

00

10

20

30

40

000 005 010 015 020 025v r (ms)

y A (1

06 1m

3 )

Threshold


ε=895)



Chapter 3

42

ravg s010v u= (38)

000002004006008010012014016018020

65 70 75 80 85 90 95 100ε ()

v ra

vgu

ssf

b

2 mm 3 mm 4 mm




( ) A ravg 3p

6 1ff v

Dε

επ

minus= (39)


00

05

10

15

20

25

30

35

40

65 70 75 80 85 90 95 100ε ()

f = ( π

6) f

A D

p3 (v

r (1

- ε))

2 mm3 mm4 mmEq 312



43


3


223


= =int (310)


( ) 0f 1


13

1

0pb

111

g εε


(311)









Chapter 3

44

000

050

100

150

200

250

000 020 040 060 080 100v z (ms)

v ra

vgc

fbv

rav

gsf

b

2 mm3 mm4 mmEq 313




000

020

040

060

080

100

120

000 020 040 060 080 100v z (ms)

f Ac

fbf

As

fb

2 mm3 mm4 mmEq 314




45





2

pVV p

pavgpavg

exp2

vfy vvv π

= minus

(315)


53

V maxV max 8

5 max avg maxavg

exp2 2

f py pp pΓ

= minus =

53

V max

maxavg max avg

05596 exp2

f pp p

= minus

(316)

Chapter 3

46


( )5

32

max pVj max

maxavg maxavg

05596 exp2V

p r Dfy p dVp p

= minus int (317)


( )5

3

p

2 22max pV p


05596 exp sin2D


π π


int int int (318)


53

103

3V p 2 max


3516 exp2

f D py p l l dlp p


p

rlD

= (319)


3

2

16max


minus asymp minus


123





47

00

20

40

60

80

100

120

140

0 20 40 60 80 100p max (103 Pa)

y j p

max

32 (1

03 N1

2 m2 s)

Threshold








653


Chapter 3

48

00

05

10

15

20

25

30

35

40

000 020 040 060 080 100 120v pavg

12 (m12s12)

pm

axa

vg (1

03 Pa)

2 mm3 mm4 mmEq 322

-25

+25


the power 12


( )20 pavg

V 4p

11443

g vf

Dε

π πminus

= (324)



00

10

20

30

40

50

60

70

000 020 040 060 080 100 120v pavg (ms)

f Vd

p4 (g0

adj(1

- ε)2 ) (

ms

)

2 mm3 mm4 mmEq 324

-25

+25


velocity


49


( )20adj pavg

V 4p

15405

g vf

Dεminus

= (325)

34 Discussion






p-w A p-w r

0

J y j dvinfin

= int (326)


2


ravg0 ravg

2exp 22 3

f vJ m v dv f D vvv

π ρπ

infin = minus =

int (327)




Chapter 3

50




00

20

40

60

80

100

120

65 70 75 80 85 90 95 100ε ()

Impu

lse

J (N

m2 ) 2 mm

3 mm

4 mm


Energy of Impacts


p-w A p-w r

0

E y e dvinfin

= int (330)


2

2


ravg0 ravg

exp2 6

f vE m v dv f D vvv

π ρπ

infin = minus =

int (331)




51




000

002

004

006

008

010

012

014

016

65 70 75 80 85 90 95 100ε ()

Ene

rgy

E (J

m2 s)

2 mm

3 mm

4 mm








( ) ( )3



Chapter 3

52




lpf j lpf max

0

J y j dpinfin

= int (337)


lpf max lpf

0

2j pdt pτ

τπ

= =int with maxlpf

sin tp t p πτ

=

(338)


3

2

16max


2 exp pJ bp p dpa

τπ

infinminus

= minus int (339)


1 1

5 5

042

- -04 3p-p p p p p p

p

12922 3016 10E


= = sdot

(340)


16-2



lpf p-pτ τ= (342)


2

3

163 max

lpf p max max0


infinminusminus



53


( )1 23 33 16

lpf p0



= (344)


564





0

5

10

15

20

25

30

35

00 02 04 06 08 10v z (ms)

Impu

lse

J (N

m2 )


Pressure fronts

Total



Chapter 3

54

Energy of Impacts









lpf j lpf max

0

E y e dpinfin

= int (350)


22max lpf


ppe dtc c

τ τρ ρ

= =int with maxlpf

sin tp t p πτ

=

(351)


1

2

16max


exp2

pbE p dpc a

τρ



1

3

16p3 max



c aρ

infinminus



( )

43

13p3 16

lpfliq liq 0

586 10 expa bD

E x x dxcρ


a= (354)


55


1164

V p maxavglpf

liq liq

03061f D p

Ecρ

= (355)


1154

V p pavg5lpf

liq liq

9273 10f D v

Ecρ

= sdot (356)


( ) 165



000

005

010

015

020

025

00 02 04 06 08 10v z (ms)

Ene

rgy

E (J

m2 s)

Total




Chapter 3

56










57


35 Conclusions


Chapter 3

58

Nomenclature




59

Abbreviations


References














Chapter 3

60














61


41 Introduction






Chapter 4

62







1 1 1ln2

D D DU D Dα λ α

= + +

(42)


( )( )

sll wl oinnero

i iinnersll cooll

T T DUDT T α

minus=

minus (43)


63









(mm) () (ms) (mm) () (ms) (mm) () (ms) 21 718 017 32 763 026 43 808 037

758 020 792 029 839 042 789 022 813 032 874 047 827 026 847 035 906 052 859 029 939 059



820 075 061 816 081 060 836 084 051 855 100 083 852 105 081 863 103 066 888 122 101 875 128 103 887 126 086


scfbz slip

uv v

ε= minus (45)

Chapter 4

64


ssfbslip p

uv Dε

ε= (46)





0

1000

2000

3000

4000

5000

6000

-300 0 300 600 900 1200 1500 1800Time (s)

-60

-50

-40

-30

-20

-10

00No ice scaling

Ice scaling

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Nucleation

Susp

ensi

on o

utle

t tem

pera

ture

(degC

)





65





00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

2 mm 3 mm 4 mm

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

No ice scaling

Ice scaling

for

ice

scal

ing

∆T

tran

s (K

)




Chapter 4

66




00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

2 mm 3 mm 4 mm 043 061

083

101

056060

081 103

041051 066

086

SFB 2 mm

SFB 3 mm

SFB 4 mm

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)






67


0

1000

2000

3000

4000

5000

6000

70 75 80 85 90 95 100ε ()


eat t

rans

fer

coef

ficie

nt (W

m 2 K

)





layer d r

layer

ddtδ ϕ ϕ

ρminus

= (47)


R Ggt (48)

Chapter 4

68



R G= (49)


( )2H Oliq

w bb ice liq

MkG x xx M

ρρ

= minus (410)


( )2

H Oliq

w bb ice liq b

Mk dxG T T xx M dT

ρρ

= minus

(411)


( )


H Oliq -1

propb ice liq b

1 0216 KM dxc

x M dTρρ

= =

(412)


( )( )( )033 0 33 -033 0 33 0 67p pb p

p








69


e p-wR c E= (415)



( )

13

1

0adjpb

1max 3 1

1g

εε


(416)



00

20

40

60

80

100

120

140

000 002 004 006 008 010 012Total energy (Jm2s)

Rem

oval

rat

e (1

0 -6

ms

)

2 mm3 mm4 mmEq 417




j p-wR c J= (418)

Chapter 4

70







transsfbprop

1 1415 10 286 10

c g u g uT


∆ = sdot = sdot (421)

00

20

40

60

80

100

120

140


Rem

oval

rat

e (1

0 -6

ms

)

2 mm3 mm4 mmEq 420





71

00

05

10

15

20

25

70 75 80 85 90 95 100ε ()

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)

2 mm 3 mm 4 mm











Chapter 4

72





00

20

40

60

80


2 mm3 mm4 mmEq 427

Rem

oval

rat

e ca

used

by

liqui

d pr

essu

re fr

onts

(10-6

ms

)







73


( ) ( )( ) ( )2


1286 10 1 068 exp 109 481 10

gT u v v v




00

05

10

15

20

25

00 05 10 15 20 25


∆T

tran

sm

eas (

K)

+20

-20



45 Discussion



Chapter 4

74








75


00

05

10

15

20


Pressure fronts

Total

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

scal

ing

∆T

tran

s (K

)





Chapter 4

76


46 Conclusions



77

Nomenclature





Chapter 4

78

References


















79





Chapter 4

80

81


51 Introduction





521 Introduction



Chapter 5

82







83











Chapter 5

84

Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


Ice + salt

Ice line


0degC

T eut

0 w eut


Boiling line for p2

Boiling line for p1



process




85




Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point

S

aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut


Ice +



process



Chapter 5

86





Salt concentration

Tem

pera

ture

Aqueous solution

Eutectic point


aqueous solution

Ice + salt

Ice line


0degC

T eut

0 w eut


A

B





87






(Ham et al 1998)


Chapter 5

88








89


-66-58

-43-39-29-21-18-15-15-12

-272

-78-105-106

-156-168

-181-187-190

-362-336

-287-280

-264-212-200-190

38

233390

403190

427214

396

342398

286260

381424

197197

322225

272245

215180

10459

12766

119

-40 -30 -20 -10 0 10 20 30 40 50






Chapter 5

90











91





Chapter 5

92





(wt) Tsat

(degC) Fluidized

bed us

(ms) qamp






93

0

5

10

15

20

0 1800 3600 5400 7200 9000Time (s)

Susp

ensi

on te

mpe

ratu

re a

t he

at e

xcha

nger

inle

t (degC

)

0

2000

4000

6000

8000

salt nucleation

with fluidized bed


steady state Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)








Chapter 5

94


5

10

15

20

25

0 1800 3600 5400 7200 9000Time (s)

Susp

ensi

on te

mpe

ratu

re a

t he

at e

xcha

nger

inle

t (degC

)

0

1000

2000

3000

4000

salt nucleation

with fluidized bed


steady state Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)



543 Discussion





95






(wt) Teut


(wt) us

(ms) 102 037 KNO3 104 -29 KNO3 106 037




Chapter 5

96




00

05

10

15

20

25

30

00 50 100 150 200

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

ice

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)


MgSO4

KNO3

Eutectic

Eutectic

Fouling

No fouling


MgSO4 solutions






97

-35

-30

-25

-20

-15

0 900 1800 2700 3600 4500 5400Time (s)

0

2000

4000

6000



Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Susp

ensio

n te

mpe

ratu

re a

t he

at e

xcha

nger

out

let (

degC)




-35

-30

-25

-20

-15

0 300 600 900 1200 1500 1800Time (s)

0

2000

4000

6000


Ice nucleation

Salt nucleation

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Susp

ensio

n te

mpe

ratu

re a

t he

at e

xcha

nger

out

let (

degC)


Chapter 5

98

00

05

10

15

20

25

30

00 50 100 150 200

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)


MgSO4

KNO3



554 Discussion



R Ggt (51)



99

0

20

40

60

80

100


Perc

enta

ge o

f tot

al r

esis

tanc

e to

ice

grow

th

Surface integration

Mass transfer

Heat transfer




( ) ( )2 2

H O H Oliq liq



ρ ρρ ρ

= minus asymp minus

(52)



Chapter 5

100










101


component wadd

(wt) wKNO3 (wt)

Tfr or Teut (degC)

Type of crystals









Chapter 5

102

00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling



00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling






103





and 58 wt KNO3



00

05

10

15

20

00 20 40 60 80 100 120

Tra

nsiti

on te

mpe

ratu

re d

iffer

ence

for

crys

talli

zatio

n fo

ulin

g ∆

Ttr

ans (K

)



Ice scaling

No ice scaling



Chapter 5

104

564 Discussion









105








Chapter 5

106



57 Conclusions



107

Nomenclature


Abbreviations


References






Chapter 5

108


















109



Chapter 5

110

111


61 Introduction




Chapter 6

112









113







Chapter 6

114







(Gladis et al 1996)



115




631 Introduction





Chapter 6

116








T T T TT

T T T T


minus minus (61)



117

plate

crys plate cool

1 1 1U

δα λ α

= + + (62)


( )( )

iscrys platemin

crysiscrys coolin

T T UT T α

minus=

minus ( 63)









Chapter 6

118


-80

-70

-60

-50

-40

-30

-20

-10

00

0 1200 2400 3600 4800 6000Time (s)

Tem

pera

ture

(degC

)

T iscrys

T platemin

T coolin

Ice nucleation


during experiment 3


0

1000

2000

3000

4000

5000

6000

0 1200 2400 3600 4800 6000Time (s)

00

01

02

03

04

05

06Uα crys

Torque

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Tor

que

(Nm

)

Ice nucleation



119




00

05

10

15

20

25

30

35

40


Tis

cry

s-Tpl

ate

min

(K)


No ice scaling

Ice scaling

-50

-40

-30

-20

-10

00



No ice scaling

Ice scaling

Tpl

ate

min

(degC

)


without ice scaling



R Ggt (64)


Chapter 6

120

( )liq eq

eq crys plateminice

dwkG T w Tw dT

ρρ

= minus minus

(65)


( )liq eq

iscrys plateminice

dwkG T Tw dT

ρρ

= minus minus

(66)


eqice


dTwT T T Rk dw

ρρ

∆ = minus = minus

(67)






121


00

05

10

15

20

25

30

35

40


∆T

tran

s (K

)




0

5

10

15

20

25


Hea

t flu

x (k

Wm

2 )

Ice scaling




Scraperblades

Orbitalrods

No ice scaling








Chapter 6

122







0 75 063


liq 1D

Nuα ελ ε

=minus

and ( )

liq s ph

liq 1u D

Reρ

micro ε=

minus (68)




123

0

2000

4000

6000

8000

70 80 90 100Bed voidage ()

2 mm3 mm4 mmH

eat t

rans

fer

coef

ficie

nt (W

m 2 K

)

0

2000

4000

6000

8000

00 50 100 150 200Scraper passes (1s)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

Re-Pr Eq611

Re-Pr Eq610







liq liq pliq

4 c Nα λ ρπ

= (69)



0 5 025


liq scrscr

liq

NDRe

ρmicro

= ( 610)

Chapter 6

124


0 5 033


liq scrscr

liq

NDRe

ρmicro

= and scrscr

liq

DNu αλ

= (611)








125

0

2000

4000

6000

8000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

NaCl

EGD-glucose

0

2000

4000

6000

8000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)

NaCl

EG D-glucose




Eq 610



0

2000

4000

6000

8000

0 5 10 15 20 25 30Ice fraction (wt)

Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K

)

T fr= ndash20degC

T fr= ndash10degC

T fr= ndash5degC



Chapter 6

126











127

1

10

100

1000


Inve

stm

ent c

osts

(keuro)


1

10

100

1000


Inve

stm

ent c

osts

(keuro)

STHESSHE

FBHE


trendline


exchangers





Chapter 6

128

0

5

10

15

20

25


Hea

t flu

x (k

Wm

2 )SSHE

FBHE

0

100

200

300

400

500


Inve

stm

ent c

osts

(eurok

W)

SSHE

FBHE -5degC

FBHE -10degC

FBHE -2degC









129








( )( )p is

he tube

1gpA D


= ( 616)


( )( )p is s tubepd

he he

14

g u DW pVA A


amp amp (617)



he he he pump pump

14

g u DW WQA A A

ρ ρ ε

η η

minus minus= = =

amp ampamp ( 618)




14

g u DWWA A

ρ ρ ε

η η η

minus minus= =

ampamp ( 619)


Chapter 6

130



Comparison






000

005

010

015

020


Scraper blades

Orbital rods

Fluidized bed

Rel

ativ

e ad

ditio

nal p

ower



131





net add

cyclecomp

Q QCOPW

+=amp amp

amp ( 621)

-25

-20

-15

-10

-5

0



Fluidized bed

Eva

pora

tion

tem

pera

ture

(degC

)

00

01

02

03

04

05

06



Fluidized bed

Rel

ativ

e co

mpr

esso

r po

wer




Chapter 6

132



net

totalcomp add

QCOPW W

=+

amp

amp amp (622)


00

05

10

15

20

25

30

35


Scraper blades

Orbital rods

Fluidized bed

CO

P


removal mechanisms





133

0

50

100

150

200

250


Rel

ativ

e an

nual

cos

ts (euro

kW

) 100 kW


Fluidized bed

0

50

100

150

200

250


Rel

ativ

e an

nual

cos

ts (euro

kW

) 1 MW


Fluidized bed


system


system


67 Conclusions



Chapter 6

134

Nomenclature



References




135

















Chapter 6

136















137














Chapter 6

138












139


71 Introduction







Chapter 7

140







141




721 Attrition


00

01

02

03

04

05


Mas

s fr

actio

n (-

)

(a)

00

01

02

03

04

05


Mas

s fr

actio

n (-

)

(b)



Chapter 7

142


722 Agglomeration





Theory


32V

Am


γ γ∆ = ∆ + = ∆ + (723)


143






( ) ( ) sol

0liq 0liq s ssol


ψψ infin infin

infin

∆ = +

(726)


( ) ( )


T T

T T


infin infin


∆∆ = + = ∆ = ∆ = ∆int int (727)


( )3

2V fA

m

-B L hG T T B LV T

γinfininfin

∆∆ = + (728)


( ) 0d G

dL∆

= (729)


A

V ice f

2( ) 1-3

BT L TB h L

γρinfin

= ∆

(730)

Chapter 7

144







145

00020406081012141618


Num

ber

dens

ity (1

06 1

m) Initial

After 1 hr

After 2 hrs

After 3 hrs

0

50

100

150

200

250


Ave

rage

dia

met

er (micro

m)

10

15

223342








Chapter 7

146

0

100

200

300

400

500

600


Ave

rage

cry

stal

siz

e (micro

m)





724 Conclusions





147








Chapter 7

148

-70

-60

-50

-40

-30

-20

-10

00

-2 -1 0 1 2Time (hours)

Tem

pera

ture

(degC

)



Seeding

∆T maxsuper

24




p

Feret

4 AD

π= (731)


FeretDΓP

π= (732)


733 Results



149









a b

c d



Chapter 7

150


00

01

02

03

04


Num

ber

frac

tion

(10 4 1

m) 0 h

2 h6 h22 h

00

02

04

06

08

10


Cum

ulat

ive

num

ber

frac

tion

(-)

0 h2 h6 h22 h



experiment 2



0

100

200

300

400

500

0 4 8 12 16 20 24Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)





151

080

085

090

095

100

0 4 8 12 16 20 24Time (hours)

Ave

rage

cry

stal

rou

ndne

ss (-





0

100

200

300

400

500

0 4 8 12 16 20 24Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)

400 rpm750 rpm

080

085

090

095

100

0 4 8 12 16 20 24Time (hours)

Ave

rgae

cry

stal

rou

ndne

ss (-

)

400 rpm750 rpm






Chapter 7

152




0

100

200

300

400

500

0 10 20 30 40 50Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm

)



solutions





153

0

100

200

300

400

500

0 20 40 60 80 100Time (hours)

Ave

rage

Fer

et d

iam

eter

(microm




homogeneous storage

735 Discussion






Chapter 7

154



( )Ai b

V ice f

-3

=∆

BG T TB h

αρ

(734)



3 3liq liq

2 1 3 for lt10

D DNu Pr


= +

(735)


( )2 2

liqAdsi H Ob H Oi

V ice

-3BG k w wB

ρρ

= (736)


2

ddsi

H Ob1-kk

w= (737)


0207 0173 4liq equiv 036 mix

3liq tank

2 047D DSh Sc

Dξ ρ

micro

= + (738)



155

( )2 2

2

b i H Ob H OiH O

- - dTT T w wdw

= (739)


( )int i i-=

rG k T T (740)


( )155-3 i i27 10 -=G T T (741)



-Tb by

2

2

155


A d liq H O


B k dwρ ρρ α

∆ = minus minus +

(742)



Chapter 7

156

10E-11

10E-10

10E-09

10E-08

0 5 10 15 20w soluteb (wt)

G (m

s)






10E-11

10E-10

10E-09

10E-08

0 5 10 15 20w soluteb (wt)

G (m

s)

00 Wkg01 Wkg10 Wkg





157


10E-12

10E-11

10E-10

10E-09

10E-08

0 5 10 15 20 25 30w soluteb (wt)

G (m

s)



stirring



Chapter 7

158

10E-12

10E-11

10E-10

10E-09

10E-08

-120 -100 -80 -60 -40 -20 00T freeze (degC)

G (m

s)



without stirring

736 Conclusions








159


G L t n L tn L tt L

partpart=

part part (743)


tρ φ φ ρpart

+ =part

(746)


ρ φpart=

part (747)



part (748)


3ice V

tot 0

( )L

L

B n L L dLm

ρφ=infin

=

= int (749)


2icetot A

0

( )L

L

A B n L L dL=infin

=

= int (750)




Chapter 7

160


ice f ice solV

liq d sol

1 13

BG T Th w dTB

k dwρ ρ

α ρ

= minus ∆ +

(751)


A

V ice lat

21-3

BT TB h L

γρinfin

= ∆

(730)


0173 4liq equiv 025

3liq

2 13D

Nu Prξ ρ

micro

= +

(735)


0207 0253 4liq equiv 036 mix

3liq tank

2 047D DSh Sc

Dξ ρ

micro

= + (738)



( )155-3 27 10 -G T T= (741)



161


-15

-10

-05

00

05


Cry

stal

gro

wth

rat

e (1

0 -7 m

s)

G heat

G surf G mass







Tank volume (l)

Time (h)


Chapter 7

162




0

100

200

300

400

500

600

0 5 10 15 20 25Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)






163

0

50

100

150

200

250

300

00 10 20 30 40 50 60Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)

8 wt φ =1

86 wt φ =0142

130 wt φ =0142

15 wt φ =1

190 wt φ =0132

369 wt φ =0122




00102030405060708090

100


Num

ber

frac

tion

(10 3 1

m) 5


00

10

20

30

40

50


Num

ber

frac

tion

(10 3 1






chloride


Chapter 7

164


0

100

200

300

400

500

600

700

0 20 40 60 80 100Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)




744 Discussion





165

0

100

200

300

400

500

600

700

0 5 10 15 20 25Time (hours)

Ave

rage

cry

stal

siz

e (m

m)


HD =015 HD =020 HD =025HD =030






( ) ( )isgin

tot


t L mpartpart

= +part part

amp (752)


Chapter 7

166


0

100

200

300

400

500

600

700

0 20 40 60 80 100Time (hours)

Ave

rage

cry

stal

siz

e (micro

m)



glycol (PG)

745 Conclusions


75 Conclusions



167

Nomenclature






Chapter 7

168

Abbreviations


References














169
















Chapter 7

170
















171


81 Introduction







821 Flow Patterns


Chapter 8

172





822 Rheology


823 Pressure Drop



173









Chapter 8

174

825 Superheating




loop



175











Chapter 8

176








177


833 Data Reduction







1 1 1ln2

D D DU D Dα λ α

= + +

(82)


Chapter 8

178






-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

00

50

100

150

200

250

300

350

400

Ice

frac

tion

(wt

)

Tfr

T inmeas

T outmeas

T coriomeas

ineqinφ




ineqin 0ineqin

ineqin

w ww

φminus

= (83)


179





Enthalpy at Inlet






( )he rest


0t Q Q

h t h t dtm

+= = + int

amp amp (87)


( )he rest


0tn t

n

Q Q th t h t

m

= ∆

=

+ ∆= = + sum

amp amp (88)


Chapter 8

180

-800

-700

-600

-500

-400

-300

-200

-100

00

0 600 1200 1800 2400 3000 3600Time (s)

Ent

halp

y (k

Jkg

)

h isineqin

h isinreal


rest

( 0 W)Q =amp





end


0end is

0tn t

n

m Q tQ h t t h tt m

= ∆

=

∆ = = minus = +

sum

ampamp (810)


Enthalpy at Outlet


is


Qh hm

= +amp

amp (811)


181








-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

0

5

10

15

20

25

30

35

40Ic

e fr

actio

n (w

t)

T inmeas

T outmeas

inreal

outreal

φφ


experiment 1



Chapter 8

182


-60

-50

-40

-30

-20

-10

00

10

20

0 600 1200 1800 2400 3000 3600Time (s)

Tem

pera

ture

(degC

)

0

5

10

15

20

25

30

35

40

Ice

frac

tion

(wt

)

T outmeas

T outeq

outrealφ

∆Tsh








exchanger


183


meas eqsh

w-liq sh w eq

T TTT T T T

ζminus∆

= =∆ + ∆ minus

(816)



( )( )

oinnerw is o

EG is i iinner

DT T UT T Dα

minus=

minus (817)



00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)


00

02

04

06

08

10


Rel

ativ

e su

perh

eatin

g ζ






Chapter 8

184



00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)


00

02

04

06

08


Rel

ativ

e su

perh

eatin

g ζ









185

00

10

20

30

40

50


Deg

ree

of s

uper

heat

ing

(K)


00

02

04

06

08

10


Rel

ativ

e su

perh

eatin

g ζ






846 Discussion







Chapter 8

186
















ice ice ice

is is

m A Gm m


amp

amp amp (827)


187




ice3

2 ice Feret

mNc Dρ


m m D xπφ φρ= = ∆ (829)


eq liqA

eqice V f

liq cr

3T TBG

dTB hwk dw

ρρ α

minus=

∆minus +

(830)


eq liqA

ice V eqcrf

cr f liq

31

T TBGB dTh w

k h dwρ α

α ρ

minus=

∆minus + ∆

(831)


1 1 1 23 3 3 3

1 23 3


cr D D DNu Pr c


= = = (832)


1 2

3 3

2 23 3

eq liqcrA

ice V f pliq liq eq

f liq

31

D

T TBGB h c w dT

dwh

αρ λ

ρ

minus=

∆ minus + ∆

(833)


Chapter 8

188

00

10

20

30

40

50

60

70


Con

trib

utio

n to

cry

stal

gro

wth

re

sist

ance

rel

ativ

e to

hea

t tra

nsfe

r

Total

Mass transfer

Heat transfer



1 2

3 3

2 23 3



f liq

121

D


dwh

φρ απφρ λ

ρ

minus∆∆ =

∆ minus + ∆

amp

(834)


( )

1 23 3

2 23 3




c B D dwhλρ α

ρ φ α ρ


(835)





189



( )

1 23 3

2 23 3


is f liq

1Dc w dTDT c T T

dwhλρ

ρ φ ρ


with V2 i3

1 A iinner cr

12Bccc B D

αα

= (836)




00

05

10

15

20

000 001 002 003 004 005

∆T

shm

eas (

K) 1

2 34

56

7

8

9

10

-25

+25

(m K)( )1 2

3 3

2 23 3


is f liq

1Dc w dTD T T

dwhλρ

ρ φ ρ

minus + minus ∆



Chapter 8

190


847 Conclusions





0

1000

2000

3000

4000

5000

6000


Hea

t tra

nsfe

r co

effic

ient

(Wm

2 K)





191






measliq

predliq

αα



measis

predis

αα




Chapter 8

192

08

10

12

14

16

18

20



Hea

t tra

nsfe

r fa

ctor

Ψliq

08

10

12

14

16

18

20



Hea

t tra

nsfe

r fa

ctor

Ψis









193

08

10

12

14

16

18

20


Hea

t tra

nsfe

r fa

ctor

Ψis


08

10

12

14

16

18

20


Hea

t tra

nsfe

r fa

ctor

Ψis






854 Conclusions





0 404liq liq2


1 42 for 67001 with 0 112 for 67002


ρminus

minus

= lt∆ = = ge (841)


Chapter 8

194

000

020

040

060

080

100

120

140


Pres

sure

dro

p (b

ar)





measliq

predliq

pp

∆Π =



measis

predis

pp

∆Π =






195

08

10

12

14

16



Pres

sure

dro

p fa

ctor

Πliq

08

10

12

14

16



Pres

sure

dro

p fa

ctor

Πis




08

10

12

14

16


Pres

sure

dro

p fa

ctor

Πis


08

10

12

14

16


Pres

sure

dro

p fa

ctor

Πis






Chapter 8

196

863 Conclusions


87 Conclusions




197

Nomenclature




Chapter 8

198

References














199














Chapter 8

200




201

9 Conclusions







Chapter 9

202








Conclusions

203


Overall Conclusions



Chapter 9

204

205







Tem

pera

ture

Aqueous solution

Eutectic point



Ice + solid solute

Ice line

Solubility line

0degC

T eut

0 wt w eut




5i

eq ii 0

T C w=


Appendix A

206

5i

eq ii 0

w C T=





( ) ( )( )

5 3i j

ij m mi 0 j 0

f C w w T T= =





( ) ( ) ( )( )5 3

i j3ij m m

i 0 j 0




A14 Enthalpy





2

diss


T

T




207




0degC

T



2 2

2 2 3H O pH O

0degC

42163 1495 1925 10T



3i

diss diss ii 1

h w T C w=



m

diss diss m

psol psol psol TT T

T T T



m

diss

psol T

T

c w T dTint ( )diss

0

psol m mmT T

c w T T d T Tminus


( ) ( )( ) ( )

diss 5 3i j

ij m m mi 0 j 00

mT T


= =


( ) ( )

5 3i j+1

ij m diss mi 0 j 0

1j+1

C w w T T= =


sumsum (A14)

( )( )5

ii ij diss m m

i 0 c j C T T w w

=


Appendix A

208


m

psol T

T

c w T dTint ( ) ( )( ) ( )m 5 3

i jij m m m

i 0 j 00

T T


= =


( ) ( )

5 3i j+1

ij m mi 0 j 0

1j+1

C w w T T= =


sumsum (A17)


( ) ( )( )

5 4i k

ik m mi 0 k 0

h C w w T T= =





5i

0 ii 1

D wT C w=



D constant273 15T

micro=

+ (A20)


0

00

273 15D D273 15

wT T wT wTwT T

micromicro

+= +

(A21)


209




CAS number 50-99-7



-100

-50

00

50

100

150

200

250


Tem

pera

ture

(degC

)

Aqueous solution


Ice linedextrose


Solubility line






Appendix A

210








211

A22 Ethanol (C2H6O)


CAS number 64-17-5




-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

) Aqueous solution


Ice line






Appendix A

212







1Melinder (1997)




213



CAS number 107-21-1




-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

) Aqueous solution


Ice line






Appendix A

214







1Melinder (1997)




215



CAS number 57-55-6




-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

) Aqueous solution


Ice line






Appendix A

216







1Melinder (1997)




217








-100

-50

00

50

100

150

200

250


Tem

pera

ture

(degC

)

Aqueous solution


Ice + MgSO412H2O


aqueoussolution +

MgSO47H2O


Eutectic point









Appendix A

218













219


Other name -





-150

-100-50

0050

100150

200250

300


Tem

pera

ture

(degC

) Aqueous solution


Ice line

Ice + KClH2O


Eutectic point

Solubility line

aq sol + KClH2O








Appendix A

220













221


Other name -

CAS number 590-29-4



-450-400-350-300-250-200-150-100-500050

100


Tem

pera

ture

(degC

) Aqueous solution


Ice line





Appendix A

222










223


Other name -





-100

-50

00

50

100

150

200

250

300


Tem

pera

ture

(degC

)

Aqueous solution


Ice line

Ice + KNO3


Eutectic point

Solubility line








Appendix A

224











225







-250

-200

-150

-100

-50

00

50


Tem

pera

ture

(degC

)

Aqueous solution


Ice line

Ice + NaCl2H2O


Eutectic point









Appendix A

226











227

Nomenclature


References











Appendix A

228

















229



B11 Density






B13 Enthalpy



and T in (degC)(B3)

B14 Specific Heat





B21 Density



Appendix B

230


( )is

ice liq

11-

ρφ ρ φ ρ

=+

(B6)




( )( )


liq ice liq ice

2 2

2

λ λ ξ λ λλ λ

λ λ ξ λ λ


(B7)



B23 Enthalpy




B24 Specific Heat


p

hcT

part=

part (B9)



0degC 0degC

0degC 1 0degCT T


= + + minus +

int int (B10)



231



( ) is


10degC 0degC





(B11)



( ) ( )is



T Tφ φ φ


int (B12)


( ) ( )ice



Tφ φ


int (B13)








Appendix B

232

Nomenclature


References









233






C11 Dimensions






bed heat exchanger

Appendix C

234



( ) ( )

2 2out in out in




amp ampamp (C1)


( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C2)


2frcool

cool hyd

12

p Lf uDρ

∆= with

hyd


hyd

52300 10DRele le (C3)





235

-50

0

50

100

150


Hea

t upt

ake

from

sur

roun

ding

s (W

)c uptake=35 WK







inner

ooinner ln

QUA T

=∆

amp (C5)



o o ss i iinner

ln1 1 12

D D D DU Dα λ α

= + + (C6)

Appendix C

236


hyd hyd

23

iouter

oinner

086D D

DNu Nu

D

=

in which (C7)

( )( )

hyd

hyd

23

hyd

2 13

10008 1

1 12 7 18

D

D

f Re Pr DNu

Lf Pr


21 82log 1 64Df (Re )

minus= minus (C8)





( )

( )iinner

23

iinner

23

10008 11 12 7 1

8

i innerD

D

f Re Pr DNu

Lf Pr


21 82log 1 64Df (Re )

minus= minus (C9)



237

0

500

1000

1500

2000


Pred

icte

d U

o (W

m2 K

)

+5

-5



0

1000

2000

3000

4000

5000

6000


Pred

icte

d α

i (W

m2 K

)

+5

-5




Appendix C

238


C21 Dimensions





bed heat exchanger



( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C10)



239

-50

0

50

100

150

200

250


Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=55 WK







Appendix C

240

0

500

1000

1500

2000


Pred

icte

d U

o (W

m2 K

)

+5

-5



0

1000

2000

3000

4000

5000

6000


Pred

icte

d α

i (W

m2 K

)

+5

-5




241





coil

C31 Dimensions





( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C11)


2fr

EGEG hyd

12

p Lf uD

∆=

ρ with

hyd

hyd

0 5hyd 0 25

0 25c

0 3164 1 0 095

D

D

Df ReRe D

= +

(C12)


Appendix C

242


-10

0

10

20

30


Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=095 WK





iinner

0 45iinner

critc

2300 1 8 6

D

DRe

D

= +

(C13)




243





1

iinner iinner

0 331



2

iinner iinner

0 332




3

hyd hyd

0 333


hyd2300DRe gt (C18)





oinnerss

o o i iinner

1 1 1 DR

U Dα α= + + (C19)

Appendix C

244



ss

ln2

D D DR

λ= (C20)


3 6 2

hyd iinner

hyd oinnerss 0 33


1r c r D D

D DR



3 6 2

hyd iinner


EG 3 EG NaCl 2 NaCl

1 r c r D D

U D U DU R



Z AX BY= + in which

3

hyd

o hydo ss 0 33

3 EG EG

11 r D

U DZ U R A X


2

iinner

o oinner0 33

2 NaCl NaCl

1 and r D

U DB Y

c Re Prλ= =

(C23)


( ) ( )AX Y Z

B

=

(C24)




245



iinner iinner



hyd hyd


hyd2300DRe gt (C26)


Appendix C

246

0

500

1000

1500

2000

2500


Pred

icte

d U

o (W

m2 K

)

+5

-5





iinner

ssi oinner o o

1 1 1DR

D Uα α

= minus minus

(C27)


iinner iinner





247

00

50

100

150

200

250

0 2000 4000 6000 8000Re D iinner

Nu

Pr -0

33

iinner iinner






2frpred

iinner

12

Lp f uD

ρ∆ = (C29)


iinner frmeas22

D pf

u Lρ∆

= (C30)


4


Appendix C

248

000

001

002

003

004

005

006

007

0 5000 10000 15000 20000Re Diinner

Fric

tion

fact

or f



iinner



iinner




0

50

100

150

200

250


Pred

icte

d ∆

p (k

Pa)

+5

-5



249





C41 Dimensions





Appendix C

250

( ) fr


pm c T T Q Qρ

∆minus minus = +

amp ampamp (C34)


-20

0

20

40

60

80

100


Hea

t upt

ake

from

sur

roun

ding

s (W

)

c uptake=151 WK





plate

SSHE ln

QU

A T=

∆

amp with


tank coolin

tank coolout

ln

T T T TT

T TT T


minus minus

(C35)


ss

scr cool

1 1 1RU α α

= + + with platess

ss

Rδλ

= (C36)


5

hydpath hydpath

0 335




251


plate plate

0 5 0 336

D DNu c Re Pr= with

plate

2plate

D

NDRe

ρmicro

= (C38)




hydpath hydpath

0 699 0 330 0507 D DNu Re Pr= for


plate plate

0 5 0 330 997 D DNu Re Pr= with

plate

2plate

D

NDRe

ρmicro

= (C40)


0

250

500

750

1000

1250

1500


Pred

icte

d U

(Wm

2 K)

+5

-5


Appendix C

252

Nomenclature


References






253




Appendix C

254

255










o ln o ln



∆ ∆

ampamp ampamp (D1)



Appendix D

256






1 1 1 ln2

D D DD U Dα α λ

= minus minus

(D2)





i iinner

DUT T T TDα

= minus minus (D3)




257



D15 Bed Voidage








scfb ssfbz

pu u Dv

εε

minus= (D6)



Appendix D

258





001 K ndash





o ln o ln



∆ ∆

ampamp ampamp (D7)







259



1 1 1 ln2

D D DD U Dα α λ

= minus minus

(D8)






D25 Pressure Drop






Appendix D

260




ln ln



∆ ∆

ampamp ampamp (D10)






plate

crys cool plate

1 1 1U

δα α λ

= minus minus (D11)





261


UT T T Tα

= minus minus (D12)


D4 Summary



9 to 24 ndash 15



30 to 120 30 to 55 200


600 to 1800 400 to 900 1500



Appendix D

262

Nomenclature


xvii

Dankwoord








xviii





xix

Curriculum Vitae


Publications









xx













Fluidized Bed Heat Exchangers to Prevent Fouling in Ice ...

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