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David Van Cauwenberge

steam cracking reactorsComputational Fluid Dynamics based design of finned

Academiejaar 2011-2012Faculteit Ingenieurswetenschappen en ArchitectuurVoorzitter: prof. dr. ir. Guy MarinVakgroep Chemische Proceskunde en Technische Chemie

Master in de ingenieurswetenschappen: chemische technologieMasterproef ingediend tot het behalen van de academische graad van

Begeleider: Carl SchietekatPromotor: prof. dr. ir. Kevin Van Geem

Computational Fluid Dynamics based design of finned

steam cracking reactor


Scriptie ingediend tot het behalen van de academische graad van Master in de

ingenieurswetenschappen: Chemische Technologie

Academiejaar: 2011-2012

Promotor: prof. dr. ir. K.M. Van Geem

Begeleider: ir. C. Schietekat

UNIVERSITEIT GENT

Faculteit Ingenieurswetenschappen en Architectuur

Vakgroep Chemische Proceskunde en Technische Chemie

Laboratorium voor Chemische Technologie

Directeur: prof. dr. ir. G.B. Marin

Abstract

The application of longitudinally and helicoidally finned tubes as steam cracker coils was studied

to evaluate the effect on product distribution and coke formation. An extensive parametric study

was performed to analyze the effect of the finned tube geometry on pressure drop and heat

transfer increase. The results were compared with bare tubes and optimal parameter values were

proposed. Finally 1D and 3D reactive simulations of an industrial propane cracker were performed

for finned tubes. Applying some of the optimal parameters showed considerable tube metal

temperature and run length improvements, although the loss in ethylene selectivity remains

limited to about 1wt%.

Keywords: steam cracking, coking, finned tubes, CFD, friction, heat transfer

FACULTEIT INGENIEURSWETENSCHAPPEN

EN ARCHITECTUUR

Laboratorium voor Chemische Technologie • Krijgslaan 281 S5, B-9000 Gent • www.lct.ugent.be

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Verklaring in verband met de toegankelijkheid van de scriptie

Ondergetekende, David Van Cauwenberge, afgestudeerd aan de UGent in het

academiejaar 2011-2012 en auteur van de scriptie met als titel: Computational Fluid

Dynamics based design of finned steam cracking reactors.

verklaart hierbij:

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de scriptie mag steeds ter beschikking gesteld worden van elke

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bronverwijzing

Gent,

(Handtekening)

Vakgroep Chemische Proceskunde en Technische Chemie


Directeur: Prof. Dr. Ir. Guy B. Marin

D

Computational Fluid Dynamics based design of

finned steam cracking reactors


Supervisor(s): Prof. Dr. Ir. Kevin Van Geem, Ir. Carl Schietekat

Abstract: The application of longitudinally and helicoidally

finned tubes as steam cracker coils was studied to evaluate the

effect on product distribution and coke formation. An extensive

parametric study was performed to analyze the effect of the

finned tube geometry on pressure drop and heat transfer

increase. The results were compared with bare tubes and optimal

parameter values were proposed. Finally 1D and 3D reactive

simulations of an industrial propane cracker were performed for

finned tubes. Applying some of the optimal parameters showed

considerable tube metal temperature and run length

improvements, although the loss in ethylene selectivity remains

limited to about 1wt%.

Keywords: CFD, friction, heat transfer, finned tubes, steam

cracking, coking

I. INTRODUCTION

Steam cracking of hydrocarbons is the predominant

commercial method for producing light olefins such as

ethylene, propylene and butadiene. Due to the formation of a

coke layer on the reactor wall, heat transfer from the furnace

to the process gas is reduced, resulting in a lower efficiency of

the furnace. Moreover the flow area is reduced and hence the

pressure drop increases. Decoking of industrial reactors is thus

inevitable. This is economically very undesirable as for about

two days production is halted. Much effort has been made to

reduce coking through the use of additives, metal surface

technologies and mechanical devices. In the category of

mechanical devices, the introduction of fins inside the coils is

a widely applied method to increase the heat transfer surface.

Because of this enhanced heating, lower tube metal

temperatures are obtained and coke reduction is significantly

lowered.

II. MODEL VALIDATION

A. Non-reactive Simulation Setup

A computational study on the heat transfer and pressure

drop characteristics of air flow through finned tubes was

performed. The commercial CFD packageAnsys FLUENT

13.0 was adopted. For the longitudinal fins, the applied

turbulence model was the RNG kε-model. The swirl flow

induced by helicoidally fined tubes required the use of the

more computationally demanding Reynolds Stress Model. For

solving the laminar boundary layer, FLUENT’s two-layer

wall-treatment with enhanced wall functions was applied.

Discretization was performed by use of the QUICK scheme.

Mesh refinement tests indicated that a high number of cells

were required for a good accuracy level. As such, the

computational domain was refined and limited to a single fin

that was extruded in the axial direction, applying a certain

twist angle for the helicoidal fins. Symmetry boundary

conditions were applied to the longitudinal fins, while the

helicoidal fins made use of rotationally periodic boundaries.

An outer tube skin temperature profile was set. The inlet

was specified as a constant mass flow inlet while the outlet

was taken to be at atmospheric pressure.

B. Results

The CFD model was validated by comparison with the

experimental data obtained by Albano et al. [1] for the

geometry shown in Figure 1. In these experiments, air was

heated from 300 to about 340 K using a jacket of condensing

steam. The CFD simulations were also compared with 1D-

simulations using Nusselt number and friction factor

correlations derived from this data by Vanden Eynde. [2]

Excellent agreement for both the longitudinally and

helicoidally finned tubes was obtained for the pressure drop,

with relative errors below 5%. The heating performance was

consistently underestimated by 2-3°C which implies a 10-20%

underestimation of the Nusselt number. This discrepancy for

heating characteristics can be assigned to large experimental

errors in the Albano et al. set-up due to inconsistent

temperature measurements, insufficient inlet section for flow

development and an unrealistically high Reynolds number of

160,000.

Figure 1: Cross-section of the geometry applied by Albano et al. [1]

III. PARAMETRIC STUDY

A. Influence of the Reynolds number

Next simulations of the Albano et al. geometry were

performed for Reynolds numbers between 50,000 and

130,000. A constant outer wall temperature of 100°C was

imposed while a sufficiently long adiabatic inlet section was

included to achieve fully developed flow at the finned tube

inlet. The results showed an almost equal Nusselt number for

both geometries, while the pressure drop was typically 25%

w

D = 36.8mm

e

OD = 50.8mm

e/D = 0.15

e/w = 0.37

α = 16°

Ω = 783mm²

Pitch = 143mm

higher for the helicoidal fins. Confirming previous studies,

these fins were simulated to have a decreased Reynolds

number dependency as well, indicating improved relative

performance at lower flow rates.

B. Influence of the fin height

The fin height-to-diameter ratio for both tube types was

varied from 0.02 to 0.2. The straight fin showed a perfectly

linear relationship between heat transfer, pressure drop and

increased internal surface, suggesting that the fin height does

not induce significant flow pattern changes. For the helicoidal

fins a steep increase in heat transfer was seen for increasing

fin height-to-diameter ratio up until an (e/D) value of 0.11,

after which the relative improvement diminished. This was

confirmed by plotting a temperature variation coefficient for

each of the geometries from which it was made clear that the

radial temperature uniformity significantly decreased at

height-to-diameter values above 0.11.

At increased Reynolds numbers, similar effects were seen,

although the flow uniformity improvements were much less

pronounced. This indicates a tendency towards so-called

“coring” flow regime where the air passes by the helicoidal

fins rather than flowing through them and inducing swirl flow,

which confirms the findings of Albano et al. [1] and Jensen

and Vlakancic. [3]

C. Influence of the number of fins

For fins with a fin height-to-diameter ratio of 0.15, the

number of fins was varied from 4 to 12 while for a lower

value of 0.04 a variation from 8 to 32 was studied. For both

series of experiments a linear trend was seen for the pressure

drop, while the heat transfer followed a subtle S-shape. It was

found that the fin height-to-width ratio is the most critical

parameter to be optimized rather than the number of fins. An

optimal value of 0.35 was found from simulations and showed

little dependency on the Reynolds number.

D. Influence of the helix angle

The helix angle of the helicoidally finned tubes was varied

from 0° (straight) to 49°. Although significant heating

improvements were determined for the higher helix angles,

the combination with tall fins caused excessive pressure

drops. Tubes with reduced fin height optimally benefited from

the high degree of swirl flow and excellent flow uniformity

was achieved for a moderate pressure drop. For the fin height

of the Albano setup an angle of 25° was seen to provide a

good trade-off between heating characteristics and pressure

drop.

E. Conclusions

For Reynolds numbers around and below 90,000, a tube

with a fin height-to-diameter ratio of 0.04, 45° helix angle and

24 fins performed significantly better than a longitudinally

finned or bare coil. Compared to a bare tube, a 35%

improvement in heating characteristics was seen at the cost of

a doubled pressure drop. At higher Reynolds number a tube

with e/D ratio of 0.11 suffered less from the coring effect than

the small fins and as such was able of achieving a 25%

improvement in heat transfer compared to a bare tube, at a

mere 56% increase in pressure drop.

IV. REACTIVE SIMULATIONS

Based on the non-reactive simulations, correlations were

derived for Nusselt number and friction factor of finned tubes.

These correlations were included in the COILSIM1D steam

cracker simulation program developed at the Laboratory for

Chemical Technology. The shooting method option was used

to adjust the heat flux and inlet pressure to achieve a certain

cracking severity and outlet pressure. These values were

chosen according to typical industrial conditions for

Millisecond propane cracking reactors. [4] Four different

reactor geometries were studied; a bare tube, an industrially

adopted helicoidally finned tube, a longitudinally finned tube

and a tube with small helicoidal fins. Table 1 shows an

overview of the simulation results at start-of-run.

Table 1: Start-of-run simulation results and process conditions for a

Millisecond propane cracking furnace.

Bare FAO_

Straight

FAO_

Helix

SmallFin

s

Inlet pressure

[bara] 2.26 2.38 2.56 2.65

Outlet pressure

[bara] 1.7 1.7 1.7 1.7

Maximal TMT

[K] 1298 1264 1243 1236

Outlet conversion

[wt%] 77.75 77.75 77.75 77.75

Ethylene yield

[wt%] 31.17 31.08 30.94 30.87

Coke yield [wt%] 0.019 0.022 0.017 0.013

Although the 1D-simulations were unable to take the

enhanced mixing properties into account, it is clear that

substantial lowering of the TMT can be achieved by use of

fins. The tube with small fins optimized from the cold flow

simulations, shows a 6°C improvement compared to the

industrially used tube. A run length simulation suggests

roughly 50% improved run length for straight fins and close to

a doubling of the run length for helicoidally finned tubes.

These results however assume retention of the original

geometry shape throughout the run, whereas in reality it can

be expected that the fin valleys will have a higher coking rate

and as such the shape might not be maintained.

V. CONCLUSIONS

In this work the application of finned tubes for steam

cracking reactors was studied. While an extensive parametric

study for non-reactive flow initially favored the use of

longitudinally finned coils, it was shown that a careful

selection of the helicoidal fin parameters at the specific

Reynolds number can provide increased performance.

Applying some of the optimal parameters to a 1D simulation

of a propane cracking Millisecond furnace showed

considerable TMT and run length improvements. It can be

expected that these will make up for the 1% loss of ethylene

selectivity that was simulated for the helicoidally finned coils.

In order to assess the run lengths on a more quantitative scale

however, it remains of primary importance to understand the

location of the coke formation and how this will influence the

tube geometries and enhanced heating characteristics over

time.

REFERENCES

[1] 1. J. V. Albano, K. M. Sundaram, M. J. Maddock, Applications of

extended surfaces in pyrolysis coils. Energy Progress, 1988. 8(3):

p. 9. [2] 2. Saegher, Johan J. De, Modellering van stroming, warmtetransport en

reactie in reactoren voor de thermische kraking van

koolwaterstoffen, in Laboratorium voor Petrochemische Techniek1994, Universiteit Gent.

[3] 3. Gregory J. Zdaniuk, Louay M. Chamra, Pedro J. Mago,

Experimental determination of heat transfer and friction in helically-finned tubes. Experimental Thermal and Fluid Science,

2008. 32: p. 15. [4] 4. Heynderickx, Geraldine J., Modellering en Simulatie van Huidige en

Nieuwe Technologieën voor de Thermische Kraking van

Koolwaterstoffen, in Laboratorium voor Petrochemische Techniek1993, Universiteit Gent: Faculteit van de Toegepaste

Wetenschappen.

Design van gevinde stoomkraak reactoren gebaseerd

op numerieke stromingsleer.


Promotor/Begeleider(s): Prof. Dr. Ir. Kevin Van Geem, Ir. Carl Schietekat

Abstract: De toepassing van longitudinaal of helisch gevinde

buizen als stoomkraak reactoren werd bestudeerd om het effect

op de productopbrengsten en cokesvorming te bestuderen. Een

uitgebreide parametrische studie werd uitgevoerd om allereerst

het effect van de gevinde buisgeometrie te bepalen op de drukval

en warmteoverdracht. De resultaten werden vergeleken met

cilindrische buizen en optimale parameterwaarden werden

vooropgesteld. Vervolgens werden 1D en 3D reactieve simulaties

uitgevoerd waarbij de gevinde buizen toegepast werden in een

industriële propaankraker. Door toepassing van enkele van deze

optimale parameters werd een aanzienlijk lagere

metaaltemperatuur verkregen met als gevolg een langere

productiecyclus, terwijl het verlies in ethyleenselectiviteit

beperkt bleef tot slechts 1 wt%.

Kernwoorden: Numerieke stromingsleer, frictie,

warmteoverdracht, gevinde buizen, stoomkraken, cokes

I. INTRODUCTIE

Stoomkraken van koolwaterstoffen is de meest gebruikte

methode voor productie van lichte olefinen zoals ethyleen,

propyleen en butadieen. Door de vorming van cokes op de

reactorwand wordt de warmteoverdracht echter bemoeilijkt,

wat leidt tot een lagere energie-efficiëntie van de oven.

Daarbij komt nog dat de doorstroomoppervlakte verkleint wat

de drukval doet toenemen. Decoken van industriële reactoren

is aldus onvermijdelijk. Economisch is dit uiteraard

ongewenst aangezien hierdoor de productie tot wel twee

dagen stil ligt. Aanzienlijke inspanningen zijn reeds gedaan

om cokesvorming tegen te gaan door middel van additieven,

metaaloppervlaktetechnologieën en geavanceerde

reactorgeometrieën. Binnen deze laatste categorie, is het

toevoegen van vinnen binnenin de reactor een frequent

toegepaste methode om de warmteuitwisselingsoppervlakte te

vergroten. Door deze verhoogde warmteoverdracht verkrijgt

men een lagere metaaltemperatuur en wordt de cokesvorming

aanzienlijk verminderd.

II. VALIDATIE VAN HET MODEL

A. Niet-reactieve simulatie methode

Een numerieke studie werd uitgevoerd rond de

eigenschappen van gevinde buizen op vlak van

warmteoverdracht en drukval. Hiervoor werd het commerciële

CFD-pakket Ansys FLUENT 13.0 gebruikt. Voor de

longitudinale vinnen werd als turbulentiemodel het RNG kε-

model aangewend. De wervelstroom geïnduceerd door de

helische vinnen echter vereiste het computationeel

veeleisende Reynolds Stress Model. De laminaire grenslaag

werd berekend door middel van FLUENTs two-layer wall-

treatment met aangepaste wandfuncties. De vergelijkingen

werden gediscretizeerd met behulp van het QUICK schema.

Tests indiceerden dat een groot aantal computationele cellen

vereist was voor een goede precisie. Aldus werd het

computationele domein sterk verfijnd en gelimiteerd tot één

enkele vin die in de axiale richting geëxtrudeerd werd, al dan

niet met een draaiingshoek voor de helische en longitudinale

vinnen respectievelijk. Vervolgens werden symmetrische

randvoorwaarden opgelegd voor de longitudinale vinnen,

terwijl de helische vinnen gebruik maakten van rotationeel

periodische randvoorwaarden.

De temperatuur aan de buitenwand van het metaal werd

vastgelegd volgens een bepaald profiel. Aan de inlaat werd

een vaste waarde voor het massadebiet opgelegd, terwijl de

uitlaat op atmosferische druk werd gespecifieerd.

B. Resultaten

Het CFD model werd gevalideerd door vergelijking met de

experimentele data van Albano et al. [1] voor de geometrie in

Figuur 1. Bij deze experimenten werd lucht opgewarmd van

300K tot ongeveer 340K door middel van een buismantel van

condenserende stoom. De CFD simulaties werden tevens

vergeleken met 1D-simulaties door gebruik te maken van de

correlaties voor het Nusselt getal en de frictiefactor afgeleid

uit deze data door Vanden Eynde [2]. Uitstekende

overeenkomst werd gezien voor zowel de longitudinaal als

helisch gevinde buizen voor de drukval, met relatieve

foutenmarges onder de 5%. De temperatuur werd consistent

onderschat met 2-3°C wat een onderschatting van 10-20% van

het Nusselt getal impliceert. Dit verschil kan toegeschreven

worden aan de grote experimentele fouten in de Albano et al.

opstelling door inconsistente temperatuurmetingen,

onvoldoende inlaatsectie voor stromingsontwikkeling en een

onrealistisch hoog Reynolds getal van 160,000.

Figuur 1:Radiale doorsnede van de Albano et al. geometrie. [1]

w

D = 36.8mm

e

OD = 50.8mm

e/D = 0.15

e/w = 0.37

α = 16°

Ω = 783mm²

Spoed = 143mm

III. PARAMETRISCHE STUDIE

A. Invloed van het Reynolds getal

Vervolgens werd deze geometrie bestudeerd voor typische

Reynoldsgetallen voor stroming in stoomkraakreactoren, d.i.

tussen 50,000 en 130,000. Hierbij werd de temperatuur aan de

buitenwand vastgelegd op 100°C, terwijl een voldoende lange

inlaatsectie zorgde voor een volledig ontwikkelde stroming

aan de reactorinlaat. De resultaten toonden een quasi gelijk

Nusselt getal voor beide geometrieën, terwijl de drukval

typisch 25% hoger lag voor de helische vinnen. In

overeenstemming met eerdere studies, toonden deze vinnen

ook een verlaagde afhankelijkheid van het Reynoldsgetal, wat

duidt op verhoogde prestaties bij lagere debieten.

B. Invloed van de vinhoogte

De vinhoogte/diameter verhouding werd gevarieerd tussen

0.02 en 0.2. De rechte vinnen vertoonden een perfect lineaire

relatie tussen warmteoverdracht, drukval en

warmteuitwisselingsoppervlakte, wat suggereert dat de

vinhoogte geen significante invloed heeft op het

stromingspatroon. Voor de helische vinnen werd een

aanzienlijke verhoging van de warmteoverdracht gezien voor

grotere vinhoogte/diameter verhoudingen, tot bij een waarde

van 0.11, waarna het relatieve effect afnam. Dit werd

bevestigd door het uitzetten van een temperatuur-

variatiecoëfficiënt waaruit duidelijk bleek dat de radiale

temperatuurgradiënten aanzienlijk groter werden vanaf een

vinhoogte/diameter verhouding boven de 0.11.

Bij hogere Reynoldsgetallen werd hetzelfde gezien, hoewel

de verhoogde stromingsuniformiteit minder significant was.

Dit duidt op een tendens naar zogenaamde “coring” van de

stroming, waarbij de lucht eerder over de vinnen stroomt dan

werkelijke wervelstroom te induceren, wat overeenkomt met

de bevindingen van Albano et al. [1] en Jensen en Vlakancic.

[3]

C. Invloed van het aantal vinnen

Voor vinnen met een vinhoogte/diameter verhouding van

0.15 werd het aantal vinnen gevarieerd van 4 tot 12, terwijl

voor een lagere verhouding van 0.04 een variatie van 8 tot 32

werd bestudeerd. For beide series van simulaties werd een

lineaire trend gezien voor de drukval, terwijl de

warmteoverdracht een subtiel S-profiel aannam. De

belangrijkste parameter in het optimaliseren van het aantal

vinnen, bleek de verhouding tussen vinhoogte en vinbreedte te

zijn. Een optimale, vrijwel Reynolds-onafhankelijke waarde

van 0.35 werd hiervoor afgeleid uit de simulaties.

D. Invloed van de helixhoek

The helixhoek van de helisch gevinde buizen werd

gevarieerd van 0° (rechte vinnen) tot 49°. Hoewel aanzienlijk

verbeterde warmteoverdracht werd vastgesteld voor de grotere

helixhoeken, liep de drukval eveneens erg hoog op in

combinatie met grote vinnen. Buizen met een kleinere

vinhoogte profiteerden veel meer van de sterke wervelstromen

en uitstekende stromingsuniformiteit werd gezien bij een

aanvaardbare drukval. Voor de vinhoogte uit de Albano

experimenten werd voor een hoek van 25° een goede balans

tussen warmteoverdracht en drukval gevonden.

E. Conclusies

Voor Reynoldsgetallen rond de 90,000 en lager, werden

aanzienlijk verbeterde eigenschappen vastgesteld voor een

buis met 24 vinnen met vinhoogte/diameter verhouding van

0.04 en een helixhoek van 45°. Ten opzichte van een

cilindrische buis werd een verbetering in de warmteoverdracht

gezien van 35%, ten koste van een verdubbeling in de

drukval. Bij hogere Reynoldsgetallen ondervond een buis met

vinhoogte/diameter verhouding van 0.11 minder last van het

“coring”-effect dan de kleine vinnen waardoor een verbetering

in warmteoverdracht van 25% werd bereikt ten koste van een

56% hogere drukval.

IV. REACTIEVE SIMULATIES

Correlaties voor het Nusselt getal en de frictie factor van

gevinde buizen werden afgeleid uit de niet-reactieve

simulatieresultaten. Deze correlaties werden vervolgens

gebruikt in het COILSIM1D simulatieprogramma ontwikkeld

aan het Laboratorium voor Chemische Technologie. Een

industriële Millisecond propaankraker werd bestudeerd. [4]

Vier verschillende reactorgeometrieën werden getest: een

cilindrische buis, een industrieel toegepast helisch gevinde

buis, een longitudinaal gevinde buis en een buis met kleine

helische vinnen. Tabel 1 toont een overzicht van de

simulatieresultaten bij het begin van de productiecyclus.

Tabel 1: Start-of-run simulatieresultaten en procescondities voor een

Millisecond propaankraker.

Bare FAO

Straight

FAO

Helix

Small

Fins

Inlaatdruk [bara] 2.26 2.38 2.56 2.65

Uitlaatdruk [bara] 1.7 1.7 1.7 1.7

Maximale metaal-

temperatuur [K] 1298 1264 1243 1236

Conversie [wt%] 77.75 77.75 77.75 77.75

Ethyleen-opbrengst

[wt%] 31.17 31.08 30.94 30.87

Cokes-opbrengst

[wt%] 0.019 0.022 0.017 0.013

Hoewel de uniformiteitseffecten niet in rekening werden

gebracht in de 1D simulaties, is het duidelijk dat de

temperaturen in het metaal minder hoog zullen oplopen door

het gebruik van vinnen. De buis met de kleinere vinnen toont

een verdere verlaging van de metaaltemperatuur met 7°C ten

opzichte van de industrieel toegepaste buizen. Simulaties

waarbij de cokesvorming in rekening gebracht werd, duiden

op een 50% langere loopduur door gebruik van rechte vinnen

en een bijna verdubbeling voor de helisch gevinde buizen. In

deze simulaties werd echter verondersteld dat de vorm van de

buizen constant blijft doorheen de loopduur, terwijl in de

realiteit er meer cokes gevormd zullen worden in de

vinvalleien en de vorm aldus niet steeds behouden zal blijven.

V. CONCLUSIES

In het huidige werk werd het gebruik van gevinde buizen als

stoomkraakreactoren bestudeerd. Hoewel de uitgebreide

parametrische studie voor niet-reactieve stroming initieel de

longitudinaal gevinde buizen bevoordeelde, werd gezien dat

een nauwgezette keuze van de parameters van de helische

vinnen bij een specifiek Reynoldsgetal toch tot een beter

resultaat kan leiden. Toepassen van deze optimale parameters

in een 1D simulatie van een Millisecond propaankraker leidde

tot aanzienlijk verbeterde metaaltemperaturen en lengte van

de productiecycli. Hoewel een selectiviteitsverlies aan

ethyleen van 1% werd berekend voor de helisch gevinde

buizen, wordt verwacht dat dit goedgemaakt zal worden door

deze eigenschappen. Om een kwantitatieve evaluatie van de

lengte van de productiecycli te maken echter, blijft het van

primair belang om een grondiger begrip te krijgen rond de

locatie van de cokesvorming en hoe dit de buisgeometrie en

aangepaste warmteoverdracht zal beïnvloeden.

BIBLIOGRAFIE

1. J. V. Albano, K. M. Sundaram, M. J. Maddock, Applications of extended surfaces in pyrolysis coils. Energy Progress, 1988. 8(3): p. 9.

2. De Saegher, J. J., T. Detemmerman, and Gilbert Froment, Three

dimensional simulation of high severity internally finned cracking coils for olefins production. Revue de l'Institut Francais du Petrole, 1996.

51(2): p. 245-260.

3. Gregory J. Zdaniuk, Louay M. Chamra, Pedro J. Mago, Experimental determination of heat transfer and friction in helically-finned tubes.

Experimental Thermal and Fluid Science, 2008. 32: p. 15.

4. Heynderickx, Geraldine J., Modellering en Simulatie van Huidige en Nieuwe Technologieën voor de Thermische Kraking van

Koolwaterstoffen, in Laboratorium voor Petrochemische

Techniek1993, Universiteit Gent: Faculteit van de Toegepaste Wetenschappen.

Dankwoord

Dit eindwerk is tot stand gekomen met de hulp en steun van vele mensen. Via deze weg wil ik die

personen van harte bedanken.

Allereerst wens ik mijn promotor, prof. dr. Ir. Kevin Van Geem, samen met prof. dr. ir. Guy B. Marin, te

bedanken om me de kans te bieden dit onderwerp aan te vatten. Hierbij wil ik in het bijzonder Kevin

bedanken voor zijn begeleiding en feedback doorheen het jaar, alsook voor het scheppen van

uitdagende perspectieven in de vorm van een mogelijk doctoraat op dit onderwerp. Ondanks de niet

eenzijdig-positieve invloeden dat dit mogelijks had op mijn eindwerk, wil ik ook professor Marin

wederom bedanken voor de verrijkende ervaring die mij aangeboden werd door mijn eerste semester in

het buitenland te mogen doorbrengen.

De grootste dank gaat zonder twijfel uit naar mijn begeleider, Carl Schietekat. Zonder zijn kennis en

ervaring betreffende het onderwerp zou dit eindwerk nooit tot een goed einde gebracht zijn. Verder wil

ik Carl bedanken voor de constante aanmoedigingen en de verzekering dat het “allemaal wel slim komt”

als de resultaten eens wat minder geslaagd waren. Dank gaat verder ook uit naar Georges en Maarten

die steeds klaarstonden om alle mogelijke software-kwaaltjes te verhelpen.

I would also like to offer my gratitude to Amit for his expertise while dealing with all sorts of CFD issues

throughout the year.

Verder wil ik mijn medestudenten Cederik, Lieselot, Yumi, Maxime, Ben, Steven en Jonas bedanken voor

de aangename koffie-, middag-, avond- en nachtpauzes. In het bijzonder wens ik Lieselot, Yumi en Jeroen

te bedanken voor de uitstekende sfeer in ons kleine bureautje.

Ten slotte wil ik mijn ouders, broers en zus bedanken voor de nooit aflatende morele (en financiële)

steun gedurende mijn studieloopbaan. Als laatste wil ik mijn vriendin Roshanak van harte bedanken om

er altijd voor mij te zijn tijdens deze soms moeilijke maanden. Op één jaar tijd zowel een Erasmus als een

thesis doorstaan, toont toch nog maar eens hoe sterk onze relatie wel is…

Bedankt!


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Table of contents

Nomenclature ............................................................................................................................................ IV

Chapter 1 - Introduction ........................................................................................................................... 1

1.1 Steam cracking .............................................................................................................................. 1

1.1.1 General principles .................................................................................................................. 1

1.1.2 Coking .................................................................................................................................... 2

1.2 Problem description ...................................................................................................................... 3

1.3 Outline ........................................................................................................................................... 4

References ................................................................................................................................................. 5

Chapter 2 - Literature review .................................................................................................................. 6

2.1 Mechanical devices for coke reduction ......................................................................................... 6

2.2 Increased internal surface area ..................................................................................................... 7

2.2.1 Albano et al. ........................................................................................................................... 8

2.2.2 De Saegher et al. .................................................................................................................. 10

2.2.3 Other fin structures ............................................................................................................. 11

2.3 Enhanced mixing ......................................................................................................................... 13

2.3.1 Mixing Element Radiant Tube ............................................................................................. 13

2.3.2 Helical and Lemniscate Coils ............................................................................................... 15

2.3.3 SMall Amplitude Helical Tube ............................................................................................. 16

2.3.4 Coil inserts ........................................................................................................................... 18

References ............................................................................................................................................... 21

Chapter 3 - Computational study of pressure drop and heat transfer in finned tubes ............. 23

3.1 Mathematical formulation .......................................................................................................... 23

Governing equations ........................................................................................................... 23 3.1.1

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3.2 Turbulence modeling ................................................................................................................... 25

The k-ε model ...................................................................................................................... 26 3.2.1

Reynolds Stress Models (RSM) ............................................................................................ 28 3.2.2

Boundary conditions............................................................................................................ 29 3.2.3

3.3 Finite volume method ................................................................................................................. 31

3.4 Discretization schemes ................................................................................................................ 32

3.5 Meshing ....................................................................................................................................... 33

3.6 Non-reactive CFD model ............................................................................................................. 35

3.7 Model validation.......................................................................................................................... 36

Experimental data ............................................................................................................... 36 3.7.1

Full setup simulations .......................................................................................................... 39 3.7.2

Experimental setup shortcomings ....................................................................................... 43 3.7.3

3.8 Reynolds number dependency of friction factors and Nusselt numbers .................................... 44

3.9 Influence of fin height on pressure drop and heat transfer in finned tubes............................... 48

Constant Reynolds number ................................................................................................. 50 3.9.1

Influence of Reynolds number ............................................................................................ 57 3.9.2

3.10 Influence of pitch on pressure drop and heat transfer in helicoidally finned tubes ................... 61


Influence of the Reynolds Number...................................................................................... 68 3.10.2

3.11 Influence of number of fins on pressure drop and heat transfer in finned tubes ...................... 71


Influence of Reynolds number ............................................................................................ 77 3.11.2

3.12 Geometry optimization - Conclusions ......................................................................................... 79

References ............................................................................................................................................... 84

Chapter 4 - Simulation of reactive flow ............................................................................................... 85

4.1 Introduction ................................................................................................................................. 85

4.2 Reactor specifications ................................................................................................................. 86

4.2.1 The Kellog Millisecond reactor ............................................................................................ 86

4.2.2 Process conditions ............................................................................................................... 87

4.2.3 Base geometry ..................................................................................................................... 88

4.3 One-dimensional simulations using COILSIM1D ......................................................................... 89

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4.3.1 Introduction ......................................................................................................................... 89

4.3.2 Friction factor and Nusselt number correlations ................................................................ 91

4.3.3 Methodology ....................................................................................................................... 93

4.3.4 Results ................................................................................................................................. 93

4.3.5 Additional considerations .................................................................................................... 98

4.4 Three-dimensional FLUENT simulations ...................................................................................... 99

4.4.1 Reaction network ................................................................................................................ 99

4.4.2 Tube geometries ................................................................................................................ 100

4.4.3 Methodology ..................................................................................................................... 101

4.4.4 Results ............................................................................................................................... 101

References ............................................................................................................................................. 102

Chapter 5 - Conclusions and future work ......................................................................................... 103

5.1 Conclusions ................................................................................................................................ 103

5.2 Future work ............................................................................................................................... 105

References ............................................................................................................................................. 106

Annex A - Performed Simulations ...................................................................................................... 107

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Nomenclature Acronyms

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Nomenclature

Acronyms

TLE Transfer line exchanger

TMT Tube metal temperatures

MERT Mixing element Radiant Tube

CIP Coil inlet pressure [bara]

COP Coil outlet pressure [bara]

SMAHT Small Amplitude Helical Tube

IHT Intensified Heat Technology

SRT Short Residence Time

RANS Reynolds-Averaged Navier-Stokes

RNG Renormalization Group Methods

RSM Reynolds Stress Model

PDE Partial Differential Equation

QUICK Quadratic Upstream Interpolation for Convective Kinetics

CoV Coefficient of variation [-]

HC Hydrocarbon

FAO Fina Antwerp Olefins

SOR Start of run

EOR End of run

Nomenclature Roman symbols

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Roman symbols

Q Heat transfer [J/s]

T Temperature [K]

p Pressure [Pa]

A Surface area [m²]

Nu Nusselt number [-]

Re Reynolds number [-]

Pr Prandtl number [-]

j Colburn j-factor (Nu/RePr1/3) [-]

f Fanning friction factor [-]

De Dean number [-]

h Convection coefficient [J/sm²K]

ui Velocity in the i-direction [m/s]

t Time [s]

F Body forces [Pa.s]

e Internal energy [J/kg]

k Turbulent kinetic energy [J/kg]

l Characteristic length scale [m]

Cx Turbulence model constants [-]

u+ Dimensionless velocity [-]

y+ Dimensionless wall distance [-]

P (Wetted) perimeter [m]

Cp Specific heat capacity [J/kgK]

e Roughness height / Fin height [m]

D Diameter [m]

Nomenclature Greek symbols

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P Helicoidal pitch length [m]

w Fin width [m]

Greek symbols

ρ Density [kg/m³]

τij Shear stress [Pa.s]

µ Dynamic viscosity [Pa.s]

ν Kinematic viscosity [m²/s]

ε Turbulent kinetic energy dissipation rate [J/kg.s]

δij Kronecker-delta 0 or 1

κ von Kármán constant 0.42

φ Arbitrary conserved flow property [?]

λ Thermal conductivity [W/mK]

φm Mass flow rate [kg/s]

α Helix angle [°]

1 Introduction Steam cracking

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1 Introduction

1.1 Steam cracking .......................................................................................................................... 1

1.2 Problem description .................................................................................................................. 3

1.3 Outline ...................................................................................................................................... 4

References .................................................................................................................................................. 5

1.1 Steam cracking

1.1.1 General principles

Steam cracking of hydrocarbons is the predominant commercial method for producing light olefins such

as ethylene, propylene and butadiene. These low-molecular-weight olefins are widely used in the

manufacture of high volume polymeric materials and commercially important chemical intermediates.

Worldwide annual ethylene production capacity is around 148 x 106 tons with growth projections of 4%

per year [1, 2]. Depending on the feedstock used to produce the olefins, steam cracking can produce a

benzene-rich liquid by-product called pyrolysis gasoline. With an additional extraction process, benzene,

toluene and xylenes can be recovered [3]. In Europe this represents over 50% of the total benzene

production, while in the U.S. catalytic reforming is the most used method of production for these

aromatics [4]. Modern steam cracking plants form the core of a petrochemical process, producing

500,000 to 1,500,000 tons per year of ethylene, the main petrochemical building block [5].

A steam cracking plant consists of furnaces and a separation train. The furnace has a radiant section, a

convection section and a transfer line exchanger (TLE) and typically consists of a set of coils with an

1 Introduction Steam cracking

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internal diameter of 30-100mm and a length of 10-100m. In the convection section, feed and steam are

preheated up to approximately 600°C in order to recover the sensible heat contained in the flue gases

leaving the radiant section. In the radiant section the process gas temperature is increased to 820-900°C,

providing the required heat for the endothermic reactions. Under these conditions, the feedstock is

converted through free-radical reactions to the products. Ethylene yield is typically 25-30% for naphtha

crackers and over 50% for ethane crackers [1]. In a generalized and very simplified form, the complex

kinetics of cracking hydrocarbons can be summarized as a set of primary reactions leading to production

of olefins, hydrogen and methane, while secondary reactions lead to C4-C7 fractions and aromatics.

From these fundamental considerations, it can easily be understood that ethylene selectivity will be

favored by short residence times. As the secondary reactions are generally bimolecular reactions, these

will occur more prominently at higher hydrocarbon partial pressures [1, 6]. As such, increasing ethylene

selectivity is one of the reasons dilution steam is added to the feed-stock. Since this obviously leads to

higher energy requirements on the furnace, the steam-to-hydrocarbon mass ratio is usually limited from

0.3 for ethane to 0.7 for naphtha and heavier fractions [1, 5].

1.1.2 Coking

Of primary concern in all steam cracking process configurations is the formation of coke. When

hydrocarbon feedstocks are subjected to the heating conditions prevalent in a steam cracking furnace,

coke deposits form on the inner walls of the tubular cracking coils. This carbonaceous coke layer leads to

an increased pressure drop over the reactor which further leads to higher hydrocarbon partial pressures

and a loss of ethylene selectivity. Additionally, these coke deposits interfere with heat flow into the

reactant stream. To maintain the same cracking severity, this increased heat transfer resistance is

compensated by increasing the heat input from the furnace burners, leading to higher tube metal

temperatures (TMT) of up to 1100°C. Eventually either the metallurgic constraints of the coils or the

excessive pressure drop will force the operators to cease production and decoke the furnace. Typical

runlengths for industrial furnaces vary between 30-100 days, depending on cracking conditions and feed-

stock. The dilution steam lowers the partial pressures of high-boiling aromatics and tarry materials,

reducing their tendency to deposit and will even react with already deposited coke to form carbon

monoxide/dioxide and hydrogen [1]. Decoking is carried out by passing an air/steam mixture through the

coils at high temperature. The coke is thus removed by a combination of combustion and

erosion/spalling. For the latter case, some of this spalled coke can be in the form of large particles that

may plug the coils before or during decoking. As there is a tendency towards decreasing tube diameters,

1 Introduction Problem description

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this has become an even greater concern. Typically decoking will require operation to be interrupted for

12-48 hours, having a considerable adverse effect on the economics of the process.

Furthermore, coke formation will influence the service life of the reactor coils. In the radiant section of

the furnace, the tubes are heated with side wall burners and/or long-flame floor burners from opposite

sides. This causes each of the tubes to have two light sides, facing the burners, and dark sides which are

offset by a 90° angle. The mean tube metal temperature, i.e. the difference between the TMT on the

light side and the dark side, leads to internal stresses and therefore determines the service life of the

tubes [7]. This effect will further be enhanced by the insulating coke layer. Although the chromium-

nickel-steel alloys used have a high resistance to carburization, carbon will diffuse into the tube wall

possibly leading to carbon contents of 1% to 3%, associated with considerable embrittlement of the tube

material [7].

1.2 Problem description

In light of all the encountered problems, efforts are being made towards the development of

technologies to reduce coke formation. These technologies can be grouped according to three main

focuses: the use of additives, metal surface technologies and mechanical devices. As additives mainly

sulfur containing components have been investigated. While a general consensus exists on the beneficial

effect for the suppression of CO production, the reported effect on coke formation is contradictory [8, 9].

Besides sulfur-containing, components containing phosphor, silicon, alkali and alkaline earth metal salts

or tin and antimony have also been investigated [9, 10]. For metal surface technologies, much progress

has been made in high temperature alloys, low-coking alloys and (catalytic) coatings [11-13]. Finally, in

the category of mechanical devices, three-dimensional reactor configurations are used to improve the

heat transfer, which will form the main point of focus in the present work.

As decoking is generally initiated when the TMT reaches a certain temperature threshold, this point can

be delayed by improving the heating characteristics of the tube. This can be achieved by introducing

three-dimensional structures inside the reactor coils that increase the internal surface and/or promote

convection by improving the radial uniformity of the flow. Although these techniques have been widely

applied and studied for heat exchangers, the problem in steam cracking reactors is slightly more

sensitive because of the additional pressure drop these structures induce. This pressure drop will cause

prolonged residence times which in turn will lead to reduced ethylene selectivity.

1 Introduction Outline

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The presented problem as such consists of finding three-dimensional reactor structures that improve the

heat transfer, allowing increased run lengths, while limiting the pressure drop and loss of ethylene

selectivity.

1.3 Outline

The course that was followed in this Master’s Thesis consists firstly of a literature study on a number of

three-dimensional structures that have already been applied or show considerable promise for use in

steam cracking reactors.

In Chapter 3, a brief summary of the CFD basics is given, in order to have a better understanding of the

optimal model for simulating flow inside this type of tubes. Following this, the CFD model is validated by

comparison of the Ansys Fluent 13.0 simulation results with experimental data obtained for a given

geometry over a range of Reynolds numbers. Having done this, a parametric study will be performed for

the longitudinally and helicoidally finned coils. The influence of the fin height, the amount of fins and the

helix pitch angle is investigated for two different Reynolds numbers. Based upon the results obtained

from these simulations, optimal values for the specific parameters are proposed and assembled into a

few “optimized” geometries for which simulations were performed as well.

Having concluded the parametric study, it obviously remains of primary importance to evaluate the

effects on steam cracking of both improved heat transfer and additional pressure drop. This is covered in

Chapter 4 where the results of the parametric study allow derivation of correlations for the Nusselt

number and friction factors of these tubes. One-dimensional reactive simulation is then performed by

combining these obtained correlations with the extensive radical reaction network of the COILSIM1D

program. Using the built-in shooting method, it is possible to simulate the coking rates and run lengths

for the investigated finned tubes. Finally, three-dimensional simulations using a simplified molecular

reaction network are performed to directly assess any potential benefits provided by the enhanced

heating and mixing characteristics of the finned reactor coils.

1 Introduction References

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References

1. Zimmermann, Heinz and Roland Walzl, Ethylene, in Ullmann's Encyclopedia of Industrial

Chemistry2000, Wiley-VCH Verlag GmbH & Co. KGaA.

2. Plastemart. Overcapacity expected in ethylene uptil 2013. 2010 [cited 2012 May 3rd]; Available

from: http://www.plastemart.com/Plastic-Technical-

Article.asp?LiteratureID=1380&Paper=overcapacity-ethylene-demand-growth-2013.

3. SABIC. Pygas (Pyrolysis Gasoline). 2012 [cited 2012 May 3rd]; Available from:

http://www.sabic.com/me/en/productsandservices/chemicals/pygas.aspx.

4. Netzer, David, Benzene Supply Trends and Proposed Method for Enhanced Recovery, in 2005

World Petrochemical Conference2005: Houston, Texas.

5. J. Towfighi, R. Karimzadeh, SHAHAB-A PC-Based Software for Simulation of Steam Cracking

Furnaces (Ethane and Naphtha). Iranian Journal of Chemical Engineering, 2004. 1(2): p. 14.

6. Nicolantonio, Arthur Di, Pyrolysis furnace with an internally finned U-shaped radiant coil, E.

Chemical, Editor 2002: United States.

7. Peter Wolbert, Benno Ganser, Dietlinde Jakobi, Rolf Kirchheiner, Process and finned tube for the

thermal cracking of hydrocarbons, 2005: United States.

8. Wang, Jidong, Marie-Françoise Reyniers, and Guy B. Marin, Influence of Dimethyl Disulfide on

Coke Formation during Steam Cracking of Hydrocarbons. Industrial & Engineering Chemistry

Research, 2007. 46(Inconel 600): p. 15.

9. Jidong Wang, Marie-Françoise Reyniers, Kevin M. Van Geem and Guy B. Marin, Influence of

Silicon and Silicon/Sulfur-Containing Additives on Coke Formation during Steam Cracking of

Hydrocarbons. Ind. Eng. Chem. Res., 2008. 47: p. 15.

10. Wang, Jidong, Marie-Françoise Reyniers, and Guy B. Marin, The influence of phosphorus

containing compounds on steam cracking of n-hexane. Journal of Analytical and Applied

Pyrolysis, 2006. 77(2): p. 133-148.

11. Györffy, Michael, MERT Technology Update: X-MERT, in AlCHE: Ethylene Producers

Meeting2009: Tampa Bay.

12. Kubota, Alloy Data Sheet, KHR 45A, 1999.

13. Zhou, Jianxin, Zhiyuan Wang, Xiaojian Luan, and Hong Xu, Anti-coking property of the SiO2/S

coating during light naphtha steam cracking in a pilot plant setup. Journal of Analytical and

Applied Pyrolysis, 2011. 90(1): p. 7-12.

http://www.plastemart.com/Plastic-Technical-Article.asp?LiteratureID=1380&Paper=overcapacity-ethylene-demand-growth-2013

http://www.plastemart.com/Plastic-Technical-Article.asp?LiteratureID=1380&Paper=overcapacity-ethylene-demand-growth-2013

http://www.sabic.com/me/en/productsandservices/chemicals/pygas.aspx

2 Literature review Mechanical devices for coke reduction

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2 Literature review Mechanical devices for coke reduction

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2 Literature review

2.1 Mechanical devices for coke reduction ......................................................................................... 6

2.2 Increased internal surface area ..................................................................................................... 7

2.2.1 Albano et al. ......................................................................................................................... 8

2.2.2 De Saegher et al. ................................................................................................................ 10

2.2.3 Other fin structures ........................................................................................................... 11

2.3 Enhanced mixing .......................................................................................................................... 13

2.3.1 Mixing Element Radiant Tube ............................................................................................ 13

2.3.2 Helical and Lemniscate Coils .............................................................................................. 15

2.3.3 SMall Amplitude Helical Tube ............................................................................................ 16

2.3.4 Coil inserts ......................................................................................................................... 18

References ........................................................................................................................................... 21

2.1 Mechanical devices for coke reduction

The focus of this work will lie in the development of three-dimensional reactor configurations. Therefore

an overview will be given on previously investigated and applied methods in steam crackers. In general

the mechanical devices can be divided in two classes based on the physical reason behind the increased

heat transfer. Heat transfer in its most basic form can be written as:

Q = A.U.ΔT (1)

2 Literature review Increased internal surface area

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, with Q being the transferred amount of heat, A the contact area, U the overall heat transfer coefficient

(including all convection and conduction contributions) and ΔT the difference in temperature between a

solid surface and the bulk of a fluid. It is easy to understand that increasing the heat transfer area will

have a direct effect. This can be achieved by decreasing the pipe diameter, which has been a main trend

over the previous decades, but which also is limited by the occurrence of pipe plugging during the

decoking phase as explained above. Devices that increase the internal surface area by means of fin-like

structures will represent a first type of reactor configuration used in order to reduce coke formation.

Secondly, the U-factor can be increased to increase heat transfer. This overall heat transfer coefficient is

greatly influenced by the measure of flow turbulence. Mixing will be greater at higher Reynolds numbers

and for more complex flow patterns but both of these will lead to greater pressure drops, which in turn

lead to reduced selectivity to ethylene [1]. Finding three-dimensional structures that achieve this

improved mixing while limiting the extra head loss will constitute the second type of reactor

configurations. It may be clear that for some mechanical devices an increase in heat transfer is achieved

by a combination of both mechanisms.

2.2 Increased internal surface area

Fins constitute a commonly used method for increasing internal surface area. In the case of steam

cracking, both helically and longitudinally finned tubes have been studied and applied industrially. As

shown in Figure 1 from Stone & Webster for straight finned tubes, a linear relationship exists between

the ratio of heat transfer improvement and the ratio of surface increase [2].


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Figure 1: Heat transfer and surface increase relation for longitudinally finned tubes [2].

2.2.1 Albano et al.

A study by Albano et al. from the Lummus Technology Division compares the pressure drops and heat

transfer coefficients of straight and helicoidally finned tubes with those of circular tubes [3]. Remarkable

about their tube geometry is the use of relatively high fins of 5.4mm, leading to a greater internal surface

area but a strongly modified velocity field compared to flow in a circular tube as well. A drawing of the

cross section and dimensions of the adopted tubes is shown in Figure 2.

STRAIGHT

FIN SPIRAL

FIN

d0 [mm] 50.8 50.8

d1 [mm] 36.8 36.9

d2 [mm] 26.0 26.1

t [mm] 7.0 7.0

Mean Fin Height [mm] 5.4 5.4

Pitch of Helix [mm] -- 406.4

Open Area of Cross. Sec (A), [mm²] 774.2 779.4

Average Diameter [mm] 31.4 31.5

Inside Perimeter (P) [mm] 138.0 136.0

Hydraulic Diameter (4A/P) [mm] 22.4 22.9

Figure 2: Tube geometry used in the study by Albano et al. [3]

Although Figure 3 shows the Colburn j-factors (Nu/RePr1/3) of both types of finned tubes to be

respectively around 20% and 40% lower, this loss is offset by the 44% increase in internal surface area.

Applying these values, Albano and coworkers conclude that the straight finned tubes show a 20%


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increase in heat transfer, while the helicoidally finned show a decrease of approximately 10%. This latter

behavior is attributed to a greater tendency for the air to bypass the fins in the spiral tubes.

Figure 3: Influence of the Reynolds number on the j-factor for straight and spiral fins [3].

Pressure drop measurements for unheated air flow were also performed. Calculated friction factors for

these experiments can be seen in Figure 4. These were shown to be much greater for the spiral fins

compared to smooth circular or longitudinally finned tubes. The helicoidally finned tubes also exhibited a

decreased sensitivity to the Reynolds number. This behavior is similar to that of very rough tubes. The

Reynolds dependency of the straight fin was similar to the smooth circular tube but with lower friction

factors. This proved consistent with the thermal data and showed good agreement with the Chilton-

Colburn analogy which relates the friction factor and Nusselt number as f/2 = Nu/RePr1/3.


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Figure 4: Influence on the Reynolds number on the Darcy friction factor for straight and spiral fins [3].

2.2.2 De Saegher et al.

De Saegher et al. evaluated both straight and helicoidally finned tubes using a three dimensional reactor

model to simulate thermal cracking in an industrial propane cracker. The geometry included eight fins

with a height of 4mm while the pitch was similar to the Albano case with a value of 0.4m [4].

Contradictorily to the conclusions of Albano et al., they do simulate a more efficient heat transfer for the

tubes with helical fins. This is attributed to more intensive mixing as can also be seen from the much

more pronounced temperature gradients over the cross section of the longitudinally finned tubes (see

Figure 5). Similar to Albano et al., they simulate much higher pressure drops for the helically finned

tubes.

Figure 5: Isotherms in a cross section of a tube with helicoidal (l) and longitudinal (r) fins [4].


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A pyrolysis reaction model for a propane feed was also imposed. As can be seen from Figure 6, the

propane conversion was higher for the helicoidally finned tube because of the longer residence time due

to the induced swirl flow and higher inlet pressures. Ethylene yield however was calculated to be lower

than for the longitudinal fins because of the reduced selectivity at the start of the reactor where

pressures are higher.

Figure 6: Simulated product yields [wt%] for a propane feed [4].

Furthermore a coke formation rate equation was included which showed the circumferentially averaged

coking rate to be substantially lower for the helicoidal fins. This follows expectations as the improved

mixing leads to lower tube skin temperatures.

2.2.3 Other fin structures

A different type of helicoidally finned tubes is more recently patented by Sumitomo Metal Industries [5].

Unlike the previously discussed geometries, the invention consists of a tube with only 3 or 4 spiral ribs of

a more triangular or trapezoidal shape with rounded edges as seen in Figure 7. The fin characteristics

consist of a fin height between 10% and 20% of the inner diameter and a fin height-to-width ratio of 0.25

to 1. In the patent, few details are released concerning the practical opportunities for pyrolysis reactions.

A thorough parametric study of the heat transfer possibilities based on air flow experiments for the tube

is enclosed however, suggesting that the optimal angle between the helical fins and the tube axis is

around 25-35° [5]. This is almost twice the value used in the Albano et al. study. It is furthermore claimed

that the sharper angle of the triangular shape offers a greater increase in inner surface area than the


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gentle curve of the “concavo-convex” shape previously discussed, while not significantly disturbing the

flow pattern.

Figure 7: Cross section of the Sumitomo helicoidally finned tube with 3 ribs [5].

Figure 8: Parametric study of the influence of the rib height and height-to-width ratio on the gas outlet temperature

for different helix inclination angles of a finned tube with 3 ribs [5].

Figure 8 plots the average temperature and average temperature deviation for different tube

geometries. A higher value of the temperature deviation implies higher radial non-uniformity of gas

temperature and will thus be undesirable for the applicability of the tube as a steam cracking reactor. It

can clearly be seen that sharper and higher ribs offer better and more uniform heating characteristics.

Although the study recognizes this to be beneficial for pyrolysis reactions, it fails to mention the pressure

drops for each of these configurations and the effect these would have on selectivity.

2 Literature review Enhanced mixing

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Extensive parametric studies have also been performed on tubes with non-rounded ribs, often used in

heat exchangers [6]. Although the majority of the data is for liquid flow instead of gaseous, some

interesting conclusions have been drawn from these experiments. A study by Jensen and Vlakanic for

example showed the existence of two types of flow in helicoidally finned tubes [7]. The first type of flow

is said to occur inside tubes with few tall fins and relatively small helix angles (less than 30°). In this type

of flow, the fluid follows the space in between the fins and true swirl flow is generated. The second type

of flow takes place in tubes with more and shorter fins and at higher helix angles. According to the

authors, this second type of flow is prone to having high fluid velocities in the center of the tube while

the fluid in the regions between the small fins stagnate and possibly relaminarize. This phenomenon is

called coring and obviously has a negative effect on the heating characteristics of these pipes. Because of

the existence of these different regimes, it is said to be difficult to provide correlations for flow inside

helicoidally finned tubes, valid over a wide range of geometries [6].

2.3 Enhanced mixing

A second class of three-dimensional structures focuses on improved mixing. This enhanced mixing leads

to a more effective and homogeneous heating of the process gas. As has previously been shown from

both two- and three-dimensional simulations, large radial concentration and temperature gradients exist

in industrial crackers [8, 9]. Local temperature or coke precursor concentration peaks can lead to high

coking rates. A more uniform radial profile will limit these occurrences, as well as prevent over- or under-

cracking and consequently maximizing proper cracking gas volume.

2.3.1 Mixing Element Radiant Tube

One of the most successful examples of three-dimensional reactors is the Mixing Element Radiant Tube

(MERT), patented by Kubota and widely installed in industrial crackers since 1996 [10]. These coils

consist of a centrifugally cast cracking tube with a spiral mixing element protruded inside of it, as shown

in Figure 9. Kubota states that, depending on the mixing element specifications and the application, heat

transfer coefficients up to 20-50% higher than for a bare tube can be expected whilst only increasing the

internal surface area by 2%. Pressure drops on the other hand are reported to be 2-3.5 times higher than

for a bare tube. It was proven that the angle of the element was vital to its effect, as low angles lead to

flow stagnation behind the element. A certain angle threshold value was required to achieve the desired

swirl flow.


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Figure 9: MERT-profile originally patented by Kubota in 1996 [10].

Pilot plant tests with various feedstocks were performed, proving ethylene yields to be 1-4% higher than

for bare tubes. Although these yield improvements are significant, the fact that the pressure drop over

the pilot plant reactor was negligible and that the flow regime was laminar rather than turbulent, should

also be taken into account. For commercial furnaces, a higher pressure drop and turbulent flow can be

expected, which probably deteriorates the overall yield effect of the MERT. As the gradual coke

formation worsens this problem, this effectively leads to an extra limitation on the run length for an

industrial cracker. A typical value for the maximal coil inlet pressure (CIP) is around 1.2 bars above the

outlet pressure. Although the MERT succeeds in lowering the TMT, the CIP limitation is typically reached

long before the TMT limitation, prohibiting substantially longer run lengths.

Over time, Kubota progressively improved the MERT technology, developing the “Slit MERT” [11]. These

new coils are similar to the previous profile, except for the fact that the element is applied intermittently

as shown in Figure 10 (a). The volume fraction of the element is reduced, but since the alignment of the

segments is maintained, the swirl mixing effect continues throughout the length of the tube.

Figure 10: Pictures of Slit MERT (a) and X-MERT profiles (b) [11].

The latest version of this technology was named X-MERT and is said to even further reduce the friction

factor while maintaining the same improved heat transfer properties [11, 12]. This is achieved by

decreasing the element height as compared to the Slit MERT while increasing the number of slits from 4

(a) (b)


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to 6 per turn and narrowing the pitch between subsequent elements. CFD simulations show a similar

positive effect on the heat transfer coefficient compared to the normal MERT, while lowering the friction

factor by 30%. Because of this reduced pressure drop, the X-MERT succeeds in reaching both the CIP-

and TMT-limitation after the same amount of time, effectively lengthening runs. These results were

confirmed for commercial furnaces. With feed rates increased by 20%, run lengths of up to 100 days

were achieved for furnaces with traditional runlengths of 70 days [11].

2.3.2 Helical and Lemniscate Coils

An entirely different use of helixes is having the centerline of the tube itself follow a helical path. Helical

coil heat exchangers are already widely used in industrial applications such as power generation, nuclear

industry, food industry, etc. Due to the curvature effect, the fluid streams faster in the outer side of the

pipe than on the inner side, inducing vortex-like secondary flows. Numerous studies towards

understanding the flow pattern in these kinds of tubes have been performed [13-15], although none

including reactive, turbulent gas flow in curved tubes.

Figure 11: General structure of a helical (a) and a lemniscate (b) coil [14].

The flow inside a helical tube is generally described by the Dean number, defined as:

(

)

(2)

with D referring to the inner diameter of the tube and R the radius of curvature by the path of the

channel. The Dean number is therefore the product of the Reynolds number and the square root of the

curvature ratio. The ratio of the tube radius to the radius of the helical centerline is known as the aspect

ratio. For helical-tube reactors, Austin and Seader showed experimentally that for Dean numbers of

about 500 and aspect ratios of 0.1, fully developed curved-tube flow occurred at about 180° around the


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turn [15]. If the flow direction is then changed, as in a lemniscate tube (Figure 11 (b)), the flow crosses

from one side of the tube to the other at the intersection of the lemniscate lobes, resulting in even

greater uniformity. Slominski and Seader also performed a computational study including the aqueous

saponification reaction of ethyl acetate with sodium hydroxide. From this study it was seen that the

conversion for the lemniscate tube very nearly approximated that of an ideal plug flow reactor (no radial

concentration gradients) [14]. They concluded that a tube with curvature in different directions could

prove an effective means of enhancing conversion in tubular reactors.

The main disadvantage towards use as steam cracking reactors is that the shape of these coils makes

radiative heating in a gas-fired furnace problematic. It would be impossible to apply this kind of tubes in

existing furnaces without a total redesign of the steam cracker radiation section.

2.3.3 SMall Amplitude Helical Tube

The Small Amplitude Helical Tube (SMAHT) or Swirl Flow Tube (SFT) is a recent technology patented by

Technip for which the centerline follows a helical path as well. The term “small amplitude” refers to the

amplitude of the helical path being equal to or smaller than the radius of the tube.

Figure 12: General principle and main parameters of the SMAHT [16].

Because of this, the tube is more or less straight allowing it to be heated in standard furnaces unlike the

previously discussed helical tubes [16]. The approach is based on biological fluid mechanics within blood

vessels where it is seen that helical stents reduce stagnation zones compared to clinical arterial bypass

grafts. This led to less instances of intimal hyperplasia which is promoted by regions with low wall shear

[17]. The main advantage of these tubes for pyrolysis reaction is the high degree of swirl flow that is

induced. This can be described as a rotation of the flow about the main axis of the pipe, which in this


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case is helical itself. The net flow field can therefore be considered as a primary axial and a secondary

rotating flow that rotates about this helical centerline. Caro et al. studied numerically the performance

of SMAHT in laminar liquid flows [17]. Their CFD results are visualized on Figure 13, depicting the

position of differently colored rings of tracer particles as they progress through the tube. Within half a

turn, considerable mixing can be seen. It is further claimed in the study that mixing continues, although

slightly diminished, in a straight tube further downstream.

Figure 13: Visualization of the SMAHT‘s mixing effects by tracking of differently colored rings of particles as they

progress through the tube [17].

Even though, because of the small amplitude of the helix, a lumen exists in the center of the tube where

the fluid could potentially follow a straight path, it has been found that it generally has a swirl

component [18]. With higher Reynolds numbers, smaller relative amplitudes may be used whilst swirl

flow is induced to a satisfactory extent. Likewise the helix angle can be optimized according to the

conditions. Generally, for a given Reynolds number, the helix angle and relative amplitude will be chosen

to be as low as required to produce satisfactory swirl.

Typically, swirl flow induces higher wall shear stresses and therefore a higher pressure drop. This

increased wall shear however also promotes thinner boundary layers leading to improved heat transfer

coefficients [16]. These assumptions were validated by Caro et al. using CFD simulations for 4 different

tubes with varying curvatures. The heat transfer coefficient was calculated to be 40-70% higher than for

a straight tube, with higher values coinciding with greater curvatures (larger helix angles and/or relative

amplitudes) as shown in Figure 14 (a). To illustrate the improved heating and mixing even better, a

temperature-modified coefficient of variation was introduced:


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√∑( )

(3)

, in which: T, the temperature at a sample point on a plane

Tav, the average temperature calculated over the cross-sectional plane

n is the number of sample points taken.

Figure 14: Heat transfer coefficients (a) and temperature-based coefficients of variation (b) for different SMAHTs

(curvature C > B > A) [16].

Although no reactive simulations were performed, it was concluded from this quantification that the

SMAHT should provide a better olefin yield and reduce coke formation by means of improved mixing and

enhanced heat transfer.

2.3.4 Coil inserts

An entirely different approach is used by the Lummus Technology division in cooperation with Sinopec.

Their Intensified Heat Transfer Technology (IHT) is based on the use of radiant coil inserts at certain

locations in the tube (see Figure 15) [19]. The main advantage of this technique is that the inserts can be

readily installed into both new and existing reactor tubes. The coil inserts have a twisted (100-360°)

baffle integrated within their inner surface and have the same diameter and metallurgy as the radiant

coil. The connection between the baffle and the coil surface is rounded in order to minimize eddy

formation at this location and reduce flow resistance.

a) b)


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Figure 15: Intensified Heat Transfer Technology with twisted baffle: picture (a) and schematic drawing (b) [19].

By strategic placement, these inserts create turbulence in the process fluid, thus reducing the boundary

layer and improving mixing and heat transfer while limiting the added pressure drop as much as possible.

The additional pressure drop compared to a bare tube accounts for only 15-20%, which is considerably

lower than for any of the other techniques previously discussed. This is obviously because the total

length of all the inserts in a given tube-pass is only a small fraction of the entire furnace tube length,

typically in the range of 5-20%.

A CFD analysis confirmed the beneficial effect on the heat transfer and uniformity of the temperature

profile while only simulating a friction increase of 15%. Through plotting of the tangential velocity the

swirl flow can be clearly visualized (see Figure 16). The helical effect of the insert on the flow tends to

fade away with distance, allowing careful evaluation of the optimum locations for the inserts. A distance

equal to 10-15 times the reactor inner diameter proved to be a good tradeoff between swirl flow

intensity and pressure loss.

Figure 16: CFD analysis: Velocity x-component in the x=0 plane (a); Flow path lines colored by value of x-velocity (b)

[19].

a) b)

a) b)


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In order to further prove the benefits of the IHT for pyrolysis reactions, a kinetic scheme was also

devised to estimate the coke formation at the tube surface. The model assumed the coking rate to be

first order with respect to butadiene. Although the total amount of coke-precursor was about the same

with or without the inserts, the stronger radial mixing distributed it more evenly through the cross-

section. This lower butadiene concentration near the wall, along with a TMT that was 25°C lower than

for a bare, resulted in 47% less coke generated on the surface. This difference in coke build-up rate and

TMT, translates into a theoretical run length that is approximately doubled using the inserts.

A commercial test in a SRT-IV furnace cracking light naphtha proved successful as well. The configuration

with the inserts allowed operation at 107% load, using the same feedstock. At comparable propylene-to-

ethylene ratio, the run length was 85 days compared to the original 55 days. When operated at 100%

load, run length could even be increased up to 105 days. Commercial tests also show that yields do not

deteriorate in spite of the 20% pressure drop increase. The reason stated for this is that the inserts

flatten the cross-sectional temperature profile, making it unnecessary to over-crack near the wall to get

the same average yield. It can be assumed however that these differences in selectivity will be small and

hard to measure in an industrial setting. Currently over 50 furnaces in China use this type of inserts with

run lengths typically being extended by a factor of 1.2 to 2 times [19]. A crucial weakness of the IHT that

was not mentioned in the study, is that spalled coke can build up on top of an insert. This could lead to a

local hot spot for further coke formation causing tube blockage at the insert, leading to advanced need

for decoking.

2 Literature review References

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References

1. Nicolantonio, Arthur Di, Pyrolysis furnace with an internally finned U-shaped radiant coil, E.

Chemical, Editor 2002: United States.

2. David J. Brown, Stone & Webster, Inc., Internally Finned Radiant Coils: a Valuable Tool for

Improving Ethylene Plant Economics, in 6th EMEA Petrochemicals Technology Conference2004:

London, UK.

3. J. V. Albano, K. M. Sundaram, M. J. Maddock, Applications of extended surfaces in pyrolysis

coils. Energy Progress, 1988. 8(3): p. 9.

4. De Saegher, J. J., T. Detemmerman, and Gilbert Froment, Three dimensional simulation of high

severity internally finned cracking coils for olefins production. Revue de l'Institut Francais du

Petrole, 1996. 51(2): p. 245-260.

5. Higuchi, Junichi, Metal Tube for Pyrolysis Reaction, 2012, Sumitomo Metal Industries: United

States.

6. Gregory J. Zdaniuk, Louay M. Chamra, Pedro J. Mago, Experimental determination of heat

transfer and friction in helically-finned tubes. Experimental Thermal and Fluid Science, 2008. 32:

p. 15.

7. M.K. Jensen, A. Vlakancic, Experimental investigation of turbulent heat transfer and fluid flow in

internally finned tubes. International Journal of Heat and Mass Transfer, 1999. 42: p. 9.

8. Van Geem, K. M., G. J. Heynderickx, and G. B. Marin, Effect of radial temperature profiles on

yields in steam cracking. AIChE Journal, 2004. 50(1): p. 173-183.

9. Guihua Hu et al., Kevin Van Geem, Comprehensive CFD simulation of product yields and coking

rates for a floor and wall fired naphtha cracking furnace. Industrial & Engineering Chemistry

Research, 2011: p. 39.

10. Torigoe, T., Mixing Element Radiant Tube (MERT) Improves Cracking Furnace Performance, K.

Corporation, Editor 2001.



12. Hamada, Masahiro Inui; Kaoru, Cracking Tubes Having Helical Fins, 2009, Kubota Organisation:

United States.

13. J.S. Jayakumar, S.M. Mahajani, J.C. Mandal, K.N. Iyer, P.K. Vijayan, CFD Analysis of single-

phase flows inside helically coiled tubes. Computers and Chemical Engineering, 2010. 34: p. 17.

14. Seader, Charles G. Slominski; Warren D. Seider; J.D., Helical and Lemniscate Tubular Reactors.

Industrial & Engineering Chemistry Research, 2011.

2 Literature review References

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15. Austin, L.R.; Seader, J.D., Entry Region for Steady Viscous Flow in Coiled Circular Pipes.

AIChE Journal, 1974. 20: p. 3.

16. W. Tallis, C. Caro, C. Dang, A novel approach to ethylene furnace coil design, in 18th Annual

Ethylene Producers’ Conference2006: Orlando, FL.

17. Colin G. Caro, Nick J. Cheshire and Nick Watkins, Preliminary comparative study of small

amplitude helical and conventional ePTFE arteriovenous shunts in pigs. Journal of the Royal

Society Interface, 2005. 2: p. 6.

18. Caro, Colin Gerald, Olefin production furnace with a helical tube, T.F. S.A.S., Editor 2005.

19. Carrillo, Alejandro, Intensified Heat Transfer Technology – CFD Analysis to Explain How and

Why IHT Increases Runlength in Commercial Furnaces, in AIChE and EPC 2010 Spring National

Meeting2010: San Antonio, TX.

3 Computational study of pressure drop and heat transfer in finned tubes Mathematical formulation

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3 Computational study of pressure drop and heat transfer in finned

tubes

3.1 Mathematical formulation ........................................................................................................... 23

3.2 Turbulence modeling ................................................................................................................... 25

3.3 Finite volume method .................................................................................................................. 31

3.4 Discretization schemes ................................................................................................................ 32

3.5 Meshing........................................................................................................................................ 33

3.6 Model validation .......................................................................................................................... 36

3.7 Reynolds number dependency of friction factors and Nusselt numbers .................................... 44

3.8 Influence of fin height on pressure drop and heat transfer in finned tubes ............................... 48

3.9 Influence of pitch on pressure drop and heat transfer in helicoidally finned tubes ................... 61

3.10 Influence of number of fins on pressure drop and heat transfer in finned tubes ....................... 71

3.11 Geometry optimization - Conclusions ......................................................................................... 79

References ................................................................................................................................................ 84

3.1 Mathematical formulation

Governing equations 3.1.1

In this paragraph an overview of the model equations is presented, based on “Computational Fluid

Dynamics for Chemical Engineers” by Bengt Andersson (2011) [1], “An Introduction to Computational

3 Computational study of pressure drop and heat transfer in finned tubes

Mathematical formulation

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Fluid Dynamics” by H.K. Versteeg (1995) [2] and some lectures from the University of Queensland by M.

Macrossan (2008) [3]. The governing equations of fluid flow represent mathematical formulations of the

laws of conservation.

Continuity 0

u

t

(1)

Momentum Fτu

ij pDt

D

(2)

Energy Φqu

t

Q

Dt

De)(

(3)

Where ρ is the fluid density, u is the fluid velocity vector, τij is the viscous stress tensor, p is pressure, F

are the body forces, e is the internal energy, Q is the heat source term, t is time, is the dissipation

term and q is the heat loss by conduction.

A more useful form of the conservation laws is obtained by introducing a suitable model for the

unknown viscous stresses τij. In a Newtonian fluid the viscous stresses are proportional to the local strain

rate. In three-dimensional flow, the local strain rate is composed of the linear deformation rate and the

volumetric deformation rate. The rate of linear deformation of a fluid element has nine components in

three dimensions, six of which are independent in isotropic fluids such as gasses, while the volumetric

deformation is given by the divergence of the velocity vector. The three-dimensional form of Newton’s

law of viscosity for compressible flows involves two constants of proportionality: the dynamic viscosity µ

which relates stresses to linear deformations and a second viscosity λ to relate stresses to the volumetric

deformation. The nine viscous stress components are then given by:

u

i

iii

x

u2

i

j

j

ijiij

x

u

x

u (4)

In practice the effect of the second viscosity is small. For gases a good working approximation can be

obtained by taking the value λ=-2/3 µ. Substitution of the above shear stresses into the momentum

equation (2) yields the three Navier-Stokes equations:


Turbulence modeling

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iij

l

l

i

j

j

i

ji

ji

j

i Fx

u

x

u

x

u

xx

puu

xu

t

3

2 (5)

Along with p = p(ρ,T) and e= e(ρ,T), Eq. (1), (3) and (5) amount to 7 equations with 7 unknowns. With an

equal number of equations and unknown functions this system is mathematically closed, i.e. it can be

solved provided that suitable initial and boundary conditions and supplied.

3.2 Turbulence modeling

As the Reynolds number in steam cracking reactors is between 30,000 and 120,000 , the flow inside the

coils is highly turbulent. In this regime, the motion has unsteady fluctuations around a time-averaged

value, even with constant steady boundary conditions imposed. The velocity and other flow properties

vary in a random and chaotic way. Because of this random nature, computations based on a complete

description of the motion of all the fluid particles become impossible. Even in flows where the mean

velocities and temperatures vary in only one or two space dimensions, turbulent fluctuations always

have a three-dimensional spatial character. These observed rotational flow structures are called

turbulent eddies and exist on a wide range of length and time scales. Particles of fluid which are initially

separated by a long distance can be brought close together by the eddying motions of the turbulent

flow, leading to much more effective exchange of heat, mass and momentum.

Although it is obvious that these eddies should be included in the calculation of the mean flow

characteristics, present day computing power comes nowhere near the computational requirements for

direct solution of the time-dependent Navier-Stokes equations for practical engineering applications.

Luckily, for most applications interest lies with the mean flow characteristics which can still be obtained

by a careful consideration of the additional turbulence influences. Typically this is achieved by

decomposing the velocity into a steady mean value ̅ with a fluctuating component u’(t) superimposed

on it. Symbolically this implies substituting u(t) = ̅ + u’(t) in Eq.(5), thus obtaining the so-called Reynolds-

averaged Navier-Stokes equations (RANS):

''

3

2ji

j

iij

i

i

i

j

j

i

ji

ji

j

i uux

Fx

u

x

u

x

u

xx

puu

xu

t

(6)


Turbulence modeling

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By performing this time-averaging, the equations become easier but a great deal of information is lost as

well. As a result, an additional tensor of stresses is generated, characterizing the transfer of momentum

by turbulence. These stresses are called the Reynolds stresses: ''

ji

t

ij uu . Since the tensor is

symmetric, this adds six additional unknowns to the momentum equation. It is the main task of

turbulence modeling to develop computational methods of sufficient accuracy and generality to predict

the Reynolds stresses and thus the additional scalar transport terms.

The k-ε model 3.2.1

The Boussinesq approximation

One way to achieve closure for these additional unknowns is by relating them to the dependent variables

they are meant to transport. A simple approximation is to express the Reynolds stress tensor in terms of

the mean velocity itself. This is the basis of the Boussinesq approximation, which proposes that the

transport of momentum by turbulence is a diffusive process. As such, the Reynolds stresses can be

modeled using an eddy viscosity which is the turbulent analog to molecular viscosity.

ij

i

it

i

j

j

itji

t

ij

x

uk

x

u

x

uuu

3

2'' (7)

Regardless of the approach used to determine this turbulent viscosity, there are several limitations with

the Boussinesq approximation as it is based on the assumption that eddies behave like molecules. First

of all, the size of eddies is comparable in size to the scale of the flow, much larger than molecules.

Furthermore molecules participate in a lot of collisions because their mean free path is short. This

implies that they have a lot of opportunities to reach local equilibrium with regards to momentum

whereas the mean free path of eddies is of comparable scale to the scale of the flow. By introducing the

turbulent viscosity factor, it is also assumed that the turbulence is isotropic, although it is known that

turbulence is always a three-dimensional occurrence and considerable anisotropy is present in some

applications. Despite these shortcomings, the Boussinesq approximation is one of the cornerstones in

several turbulence models as sufficiently accurate results can be obtained with it for most engineering

applications while the cost of more elaborate turbulence models is significantly higher.

Turbulent kinetic energy and dissipation rate


Turbulence modeling

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As part of quantitative turbulence modeling, this eddy viscosity, t , must be determined. When it comes

to turbulence modeling based on the RANS-equations and the eddy viscosity concept, the turbulence

model can be seen as the set of equations that are needed to determine this viscosity. Similar to kinetic

theory of gases the viscosity is proportional to velocity multiplied by distance. The turbulent viscosity

models are based on an appropriate velocity, u, and length scale, l, describing the local turbulent

viscosity, t . As the dimension of viscosity is [m²/s], the product of these two scales gives the right

dimension, that is:

ulCt (8)

In this expression u and l are the characteristic scales for the large turbulent eddies and C a

proportionality constant.

As it takes two quantities to characterize the length and velocity scales of turbulent flows, the most

successful models to determine these scales consist of two or more transport equations. A

straightforward approach to model the scales is to solve the turbulent kinetic energy equation for the

velocity scale and the l-equation for the length scale. This approach is called a k-l model. More often

however the second transport equation describes transport of another property than the length scale,

provided it remains possible to explicitly determine the length scale from this property.

The most commonly used variable is the energy dissipation rate ε. The length scale can then be obtained

by multiplying the turbulent velocity, k , with the lifetime of the turbulent eddies /k . The turbulent

viscosity is thus given by:

223

21 k

Ck

kCt (9)

After careful modeling of the turbulent kinetic energy production, dissipation and transport terms, the

equation for k and ε is obtained as:


Turbulence modeling

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j

t

jj

i

t

ij

j

j

j

kt

jj

i

t

ij

j

j

xxkC

x

u

kC

xu

t

x

k

xx

u

x

ku

t

k

/

/

2

21

(10)

The five closure coefficients in the k-ε model are assumed to be universal and constant in the so-called

standard k-ε model:

09.0C 44.11 C 92.12 C 00.1k 30.1 (11)

Although it has certain shortcomings, the standard k-ε model is the most widely used and validated

turbulence model. Excellent performance can be expected in confined flows where the Reynolds shear

stresses are most important. In swirling and unconfined flows however, the model fails to describe the

effects of streamline curvature effects on turbulence.

The RNG k- ε model enhances the dissipation equation by adding an additional source term. In regions

with large strain rate, the additional term results in smaller destruction of ε, hence augmenting ε and

reducing k which in effect reduces the effective viscosity. This makes the RNG model more responsive to

the effects of rapid strain and streamline curvature, making it especially useful for modeling of swirling

flows.

Reynolds Stress Models (RSM) 3.2.2

Turbulence models based on the Boussinesq-approximation are inaccurate for flows with sudden

changes in the mean strain rate. Abandoning the isotropic eddy viscosity concept, the RSM closes the

RANS equations via solving transport equations for the Reynolds stresses and for the energy dissipation

rate. In these transport equations however, the viscous dissipation, the pressure-strain correlation and

the transport terms of the different Reynolds stresses need to be modeled. This leads to the problem of

providing proper closure approximations to the 22 extra unknowns. As the 7 additional PDE’s are

strongly coupled, this not only makes computation much more expensive but also makes it susceptible to

numerical instability. However, the natural approach in which non-local and history effects are

accounted for by means of the stress transport models, leads to significantly improved performance

under complex flow conditions.


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Boundary conditions 3.2.3

For solving viscous steady flow problems, boundary conditions on all solid walls and fluid boundaries are

equally important as the differential equations. In a sense, the process of solving a field problem, such as

fluid flow, is nothing more than the extrapolation of a set of data defined on a boundary surface into the

domain interior. Additionally, boundary conditions can be introduced to simplify the computational

domain e.g. symmetry.

The inlet boundary can be defined by either a velocity or pressure inlet boundary condition. For a

velocity condition, an average or custom profile velocity or mass flow can be set. The pressure inlet

boundary condition can be useful when the inlet pressure is known without knowledge of the flow rate

or even the flow direction.

The standard outlet boundary condition is the zero diffusion flux condition, which means that the

conditions of the outflow plane are extrapolated from within the domain and all gradients in the flow

direction are set to be zero. For flow outlets the default condition is a pressure outlet boundary

condition. This often results in a better rate of convergence when backflow occurs during iteration.

The usual boundary condition for velocity at the walls is the ‘no-slip condition’, setting the velocity

difference between the wall and the fluid to zero. When solving the energy equations, walls can be

either considered insulated or a specific boundary condition such as fixed heat flux, fixed temperature,

etc. may be set.

Wall treatment

For highly turbulent flow the no-slip condition is still valid but the grid resolution is often too coarse to

specify the condition as rapid variation of the flow variables occurs within this boundary layer. In this

case wall functions are used to “bridge” the solution variables at the near-wall cells and the

corresponding quantities on the wall.

As the boundary layer consists of several sub-layers, it is common practice to express the physical extent

of these sub-layers in terms of wall variables. Using the wall friction velocity , a dimensionless velocity

u+, a dimensionless wall distance y+ and a characteristic wall length scale l* can be introduced:


Turbulence modeling

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√ (12)

(13)

(14)

(15)

Using these scaled variables, the following classification of the inner region of the boundary layer can be

defined:

i. Viscous sub-layer 0 < y+ < 5

ii. Buffer sub-layer 5 < y+ < 30

iii. Fully turbulent sub-layer 30 < y+ < 400

In the viscous sub layer the velocity varies linearly with y+ whereas in the turbulent sub-layer it

approaches the so-called logarithmic law of the wall or simply log-law, as shown in Figure 1.

Figure 1: The law of the wall.

In these equations κ is the von Kármán constant and is equal to 0.42 while E is an empirical constant that

is typically taken fixed at 9.793. Reynolds’ analogy between momentum and energy transport gives a

similar logarithmic law for mean temperature.

𝑢 1

𝜅ln 𝐸𝑦

𝑢 𝑦


Finite volume method

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This is the “standard wall function” used in Fluent and is applicable when the first grid point adjacent to

the wall lies within the logarithmic region. Because this takes away the need to resolve the viscosity

affected near-wall region, the use of the log-law saves considerable computational resources.

In the case of more complex flow patterns however, improved modeling can be achieved using a two-

layer zonal approach, solving the governing equations all the way to the wall. This obviously requires a

very fine near wall grid resolution (y+ 1) and large computation power. Additionally, Fluent also offers a

third near-wall formulation that can be used with coarse meshes as well as fine meshes. This “Enhanced

wall treatment” combines the two-layer model with enhanced wall functions by blending linear and

logarithmic laws-of-the-wall.

3.3 Finite volume method

As finite difference is most suited for Cartesian problems and finite element does not have local

conservation as a main property, the finite volume method is used in most commercial CFD packages. To

solve the equations numerically with the finite volume method, the entire computational domain is

divided into small sub-volumes, so called cells. The partial derivatives are then reformulated at each cell

into a set of linear algebraic equations, which are then solved numerically in an iterative manner. This is

done by integrating the general transport equation over a control volume, in this case the computational

cell:

In this general transport equation for the property φ, Γ is a diffusion coefficient while Sφ represents the

source terms inside the control volume dV.

The next step is to reformulate Eq. (16) into an algebraic form. In the present work only steady state

problems are considered so the accumulation term will be zero. The convective term represents the net

flux of φ transported out of the cell by convection. As flow can only enter or leave the cell through any of

its faces, this can be rewritten as:

........

)()(

vcvc jjvc j

j

vc

dVSdVxx

dVx

udV

t

(16)


Discretization schemes

Confidential - 32 -

btnsew

vc j

jAuAuAuAuAuAudV

x

u)()()()()()(

)(

..

(17)

Here the indices w, e, s, n, b, t refer to the six faces of the control volume, as illustrated in Figure 2. The

signs are chosen in order to obtain a negative flux when u is positive leaving the control volume.

Figure 2: A three-dimensional cell and neighboring nodes.

A similar approach can be used for the diffusive term, while the source term can be evaluated into a

single cell mean value. These equations can now be solved algebraically, provided the face values of φ, Γ

and uj are known, as well as the gradient of φ at the faces.

3.4 Discretization schemes

The most straightforward way of defining the face values of all the variables is to take the average of the

values of the two cells connected to the face. This is called the central differencing scheme. In cases with

strong convection however, faces should be more influenced by the upstream cell than by the

downstream cell, as a consequence of the flow direction. Schemes that let face values be dependent

only on upstream conditions are called upwind schemes. A first order upwind simply takes the face value

between two cells equal to the nearest upstream cell value. This scheme succeeds in transporting data

along the flow direction, while still being bounded. Boundedness means that the face value will be


Meshing

Confidential - 33 -

neither larger nor smaller than any of the values that are used to calculate it. Although the first order

upwind scheme shines in its simplicity and stability, it cannot be used to obtain quantitative results, as it

overestimates the transport of entities in the flow direction and often gives rise to numerical diffusion.

Higher order schemes will predict values by making assumptions based on the upstream gradients. This

improves accuracy by being less diffusive but has a major drawback in the fact that it is unbounded,

which can cause numerical problems. The Quadratic Upstream Interpolation for Convective Kinetics

(QUICK) combines the strengths of both the upwind schemes and of the central differencing by using a

three-point upstream quadratic interpolation. For the western and eastern faces respectively:

WWPWw 8

1

8

3

8

6 WEPe

8

1

8

3

8

6 (18)

It is proven that this scheme is third order accurate. [1, 4] Although it is also unbounded, it provides

better accuracy than the second-order scheme for rotating and swirling flows and as such will be the

scheme of choice in the present work.

3.5 Meshing

Meshing was performed by first establishing a proper triangular 2D mesh of the inlet surface. A

boundary layer of 0.005mm thickness and growth rate of 1.5 was also added at the fluid–metal interface.

From previous mesh tests, these values proved to be sufficient to achieve y+ values smaller than 1 for all

Reynolds numbers. The acquired 2D mesh was then extruded straight for the longitudinal fins and

twisted for the helicoidally finned tubes. In this manner, the final mesh was built from slightly skewed

triangular prisms with a boundary layer consisting of rectangular prisms.

In order to check the mesh density required to properly model the swirling flow in the helicoidally finned

tubes, a mesh dependency test was performed. Initially, calculations were performed on the entire cross

section of the tube. The applied CFD model was the FLUENT Reynolds Stress Model with enhanced wall

treatment. Both in the axial direction and over the radial profile mesh refinement was performed, for

which the results can be seen in Table 1.


Meshing

Confidential - 34 -

Table 1: Simulated pressure drops over a helicoidally finned tube at different mesh densities.

ID Axial size

[mm]

Radial size

[mm]

Number of

cells/m

Pressure

drop [Pa]

Error [-]

Axial1 4 1,2 617540 7971 6%

Axial2 3 1,2 822286 7365 -2% Experimental

pressure drop

7526 Pa

Axial3 2 1,2 1203000 6822 -9%

MeshDens1 3 1,8 496615 8106 8%

MeshDens2 3 1,5 621613 7814 4%

MeshDens3 3 1,2 822286 7365 -2%

MeshDens4 3 0,8 1374982 6870 -9%

It can clearly be seen that even at a mesh density of over 1,000,000 cells/m tube, the calculated pressure

drop still did not settle for a fixed value. From these mesh tests on the full cross section of the tube, it

was concluded that even the densest mesh would not be sufficient to properly model the complex flow

induced by the helicoidally finned tube. The fact that the pressure drop was calculated to be lower than

the experimental value can be contributed to the tubes in the experiments having a certain roughness

while ideal smooth tubes are used in the simulations.

Further mesh refinement was achieved by limiting the computational domain to a single fin, effectively

simulating 1/8th of the initial volume. This was done by extruding the 2D single fin cross-sectional mesh

across the required pitch, while meshing each of the radial boundaries in a periodic manner and applying

periodic boundary conditions.


Non-reactive CFD model

Confidential - 35 -

Figure 3: Mesh used in the present work.

Using this approach, a mesh consisting of cells of 2mm in the axial direction and maximum 0.6mm in the

radial direction was found to provide satisfying results. Further mesh refinement with a factor 2 only

offered a 1.5% improvement in accuracy, which was not considered to be worth the added

computational cost. The mesh that was predominantly used in the present work is shown in Figure 3 and

required approximately 500.000 cells/meter tube for the fluid section and 300.000 cells/meter tube for

the metal section.

3.6 Non-reactive CFD model

A full summary of the simulation setup for both the longitudinally and helicoidally finned coils is

presented in Table 2.

Table 2: Ansys Fluent simulation setup

Longitudinal fins Helicoidal fins

Turbulence model kε-RNG kε-RNG for first 1000 iterations,

then Reynolds Stress Model

Wall treatment Two-layer with enhanced wall functions

Discretization scheme 1st order for first 1500 iterations, then QUICK


Model validation

Confidential - 36 -

Residuals convergence criteria Energy: 10-8 – Others: 10-5

Inlet boundary condition Fixed mass flow rate - Fixed total temperature

Inlet turbulence settings Turbulent intensity: 8% – Length scale: Hydraulic diameter / 10

Outlet boundary condition Fixed pressure: 1 bara

Wall boundary conditions Adiabatic inlet section followed by outer wall temperature profile

Radial boundary conditions Symmetry Rotationally periodic

Air density Ideal gas (Mw = 28.966 g/mol)

Air thermal conductivity Piecewise-linear function of temperature

Air specific Heat Piecewise-linear function of temperature

Air viscosity Piecewise-linear function of temperature

Metal thermal conductivity Constant: λ = 20 W/mK

3.7 Model validation

Experimental data 3.7.1

The experimental results from the study by Albano et al. [5] were used in order to validate the applied

model in the present work.

The experimental equipment of the Albano et al. study is shown on Figure 4. The installation consists of a

finned tube, surrounded by a steam jacket which can be used for heating. A radial cross section of the

finned tube is shown in Figure 5. The hydraulic diameter (4A/P) of this geometry is 21.9mm. The pitch for

the helicoidally finned tube is 40.64cm. The mass flow of air is measured at the inlet by a calibrated

diaphragm. The outlet of the tube is connected to a barrel which is open to the atmosphere.


Model validation

Confidential - 37 -

Thermocouples measure the air and tube wall temperatures at 4 different axial locations (A-D in Figure

4).

Figure 4: Experimental installation used by Albano et al. (1988) [6]

Figure 5: Radial cross section of the finned tube used by Albano et al.


Model validation

Confidential - 38 -

Using this equipment, both longitudinally and helicoidally finned tubes were tested. The data covered a

Reynolds number range of 60,000 to 120,000 based on hydraulic diameter, which is comparable to

typical commercial steam cracking reactor operating conditions. A heat transfer rate was computed from

the mass flow rate of the air, and the temperature rise:

(19)

Using this and the axial mean temperature difference between the wall temperature and the air

temperature, an average inside convection heat transfer coefficient was determined.

(20)

Similarly for the pressure drop data, a mean friction coefficient was calculated.

(

)

(21)

From the obtained data, the following correlations for the Nusselt number and Darcy friction factor were

derived by Vanden Eynde (1989) [6] for helicoidally finned tubes:

1 1 (22)

1 (23)

And for longitudinally finned tubes:

(24)

(25)

As the tube parameters such as the fin height, number of fins and pitch length do not explicitly appear in

these correlations, the applicability range is most likely limited to the applied geometry.


Model validation

Confidential - 39 -

Full setup simulations 3.7.2

In a primary stage, a single experiment for both the helicoidally and longitudinally finned tubes was

compared to a one-dimensional simulation and a three-dimensional CFD simulation. The one-

dimensional simulation made use of Eq. (22)-(25) to calculate heat transfer and friction coefficients. The

experiments were performed for air mass flows of respectively 0.107 and 0.103 kg/s, which correspond

to an inlet Reynolds number of approximately 160.000. It is important to note that the experiments did

not involve a sufficiently long inlet section to filter out entrance effects. In the performed CFD

simulations a small inlet section of 0.2m length was included, as the exact value of the experimental inlet

section is unknown. Furthermore, the temperatures measured on the outside of the tube were flawed

due to steam condensation, leaving only the inner wall temperatures as reliable data. For both the 1D

and CFD simulation, this inner wall temperature profile was imposed, without taking conduction through

the metal into account. As a result of this, the temperatures in the peaks and valleys were assumed to be

equal, whereas in reality they differed by 1-2°C [6]. The applied CFD model was the k-ε model with

enhanced wall functions, as this had previously shown to accurately calculate non-curved flow at a

limited computational cost. The applied discretization scheme was the QUICK scheme. The results for the

longitudinally finned tube can be seen in Figure 6 and Figure 7.

Figure 6: Simulated and experimental pressure drop for a longitudinally finned tube.

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6 7

Pre

ssu

re [

bar

g]

z [m]

1D

3D

Experimental


Model validation

Confidential - 40 -

From Figure 6 the pressure drop appears to be simulated very accurately by both the 1D (rel error =

1.6%) and CFD (rel error = 3.2%) simulations. As only the pressure drop over the entire pipe was

measured, the experimental pressure was plotted as a straight line, although it can be expected that this

should actually follow a similar profile as the simulated pressure because of flow expansion and

acceleration.

The temperature plots on Figure 7 show a slightly different behavior for both the 1D and CFD

simulations. It appears that the three-dimensional simulations fails to properly model the strong inlet

effects, leading to a temperature difference of almost 3°C after a few metres. Further downstream

however the behavior is similar to that of the experiments, leading to final temperature difference of

2°C. Interesting to note is the distinct curve of the 1D simulation. Even though the correlations are fitted

to the experimental data, it can be seen that there is a relatively large temperature difference of 3.6°C at

the outlet. From these simulations, it would seem that Eq. (24) overestimates the Nusselt number by

approximately 20%.

Figure 7: Simulated and experimental temperatures in the center of a longitudinally finned tube with imposed inner wall temperature profile.

0

20

40

60

80

100

0 1 2 3 4 5 6 7

Tem

per

atu

re [

°C]

z [m]

1D

3D

Experimental

Inner Wall


Model validation

Confidential - 41 -

A similar method was followed for the helicoidally finned tubes. This time however, the Reynolds Stress

Model was used to properly account for the non-isotropic turbulence properties in the swirling flow.

Discretization was again done by use of the QUICK scheme. It is important to note that the inlet

temperature was lower in this experiment and the imposed inner wall temperature profile differed as

well. Because of these important differences, it is difficult to compare the different tubes from this data

and it should solely be used as a means of model validation. The results for the helicoidally finned tubes

can be seen in Figure 8 and Figure 9.

Figure 8: Simulated and experimental pressure drop for a helicoidally finned tube.

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6 7

Pre

ssu

re [

bar

g]

z [m]

1D

3D

Experimental


Model validation

Confidential - 42 -

Figure 9: Simulated and experimental temperatures in the center of a helicoidally finned tube with imposed inner wall temperature profile.

As with the longitudinally finned tube, the pressure drop is calculated accurately by both simulations.

The relative errors for the 1D and 3D simulations account for respectively 1.3% and 4.9%. In this case as

well, the profile for the experimental pressure drop should be curved but was plotted as a straight line

because only two data points were available.

The temperature results seem to be more accurate than for the longitudinally finned tube. Near the start

of the tube, where entrance effects are strong, there appears to occur very efficient heat transfer which

is not properly modeled in the CFD simulation. Further downstream however, the simulated

temperatures approach the experimental values within a 2.8°C margin. This time, the correlation fits

very well with the experimental data as the temperature difference at the outlet amounts to only 0.6°C.

Using the known tube metal temperatures and the simulated heat fluxes and temperature at the center

of the tube, a convection coefficient was calculated over the length of the tube. Again it needs to be

emphasized that the tube metal temperature profile is different for the two tubes and no direct

comparison should be made based on these results. It is however interesting to see the axial profile

shown in Figure 10.

0

20

40

60

80

100

0 1 2 3 4 5 6 7

Tem

per

atu

re [

°C]

z [m]

1D

3D

Experimental

Inner Wall


Model validation

Confidential - 43 -

Figure 10: Simulated convection coefficient over the length of a finned tube as in the Albano experiments.

As the Reynolds number barely changes when a gas is heated, the correlations (22) and (24) predict a

more or less constant value of the convection coefficient. This does not appear to be the case for the

simulated convection coefficient which shows especially great fluctuations in the first few meters. The

initially high convection coefficient is caused by an undeveloped flow and the high velocities near the

wall. As the flow develops, the convection coefficient drops, before the increasing turbulence causes it to

rise again. The most important conclusion that can be drawn from these plots however, is that the

assumption of a constant convection coefficient is flawed and the correlations of Albano et al. are simply

averaged coefficients over the experimental 7m installation. This is clear proof that one- or two-

dimensional models are not sufficient to properly simulate the performance of finned tubes and a three-

dimensional model will need to be applied.

Experimental setup shortcomings 3.7.3

The experimental setup used by Albano et al. clearly showed a number of shortcomings. First, there was

no sufficient inlet section to allow flow development. Second, the experimental conditions for the two

types of tubes were quite distinct from one another. The inlet temperature and the wall temperature


Reynolds number dependency of friction factors and Nusselt numbers

Confidential - 44 -

profile, as well as the mass flow rate, were different in the two experiments. Finally, the Reynolds

number that corresponds with these mass flow rates of around 0.1kg/s is over 160,000 and lies outside

the typical working range of steam cracking reactors. Upon plotting of the tangential velocity in the

helicoidally finned tube, it appeared as if the induced swirl flow remained limited to the interfin region

and did not efficiently spread further inwards. This may be caused by the high flow rates as well.

3.8 Reynolds number dependency of friction factors and

Nusselt numbers

As was explained above, the experimental setup used by Albano et al. had certain shortcomings, making

direct comparison with CFD results impossible. Therefore CFD simulations were performed on the same

tube geometry while cancelling out these existing flaws. A mass-weighted temperature and pressure

were calculated after 4m and at the outlet at 6m, providing an adiabatic inlet section of 4m for flow

development. Only the last two meters of the tube were heated for as to avoid asymptotic heating

leading to an underestimation of the Nusselt numbers. Both preliminary simulations and typical entrance

length correlations confirm this to be more than sufficient to cancel out any entrance effects. In order to

obtain the Nusselt number, a constant outer wall temperature of 100°C was imposed. The tube material

was taken similar to the Incoloy 800H used by Albano et al., with a fixed conductivity of 20 W/mK [7]. For

the friction factors calculations, either the entire tube was taken to be adiabatic or no metal section was

included at all. Simulations were performed at Reynolds numbers ranging from 50,000 to 130,000, based

on the hydraulic diameter of the finned tube. The obtained results can be seen in Figure 11 and Figure

12, where they are compared to the correlations of Vanden Eynde and those of a bare tube (Eq. (26) and

Eq. (27)). The bare tube was chosen with an equal cross-sectional area and mass flow, in essence equal

space-time.

Dittus-Boelter equation: (26)

( ⁄ )

( ⁄ )

(27)



Confidential - 45 -

1

ln ( 1 11ln

)

Surprisingly, the heat transfer coefficient simulations show little difference between the helicoidally and

longitudinally finned tubes. The data does however agree with the previously discussed full-setup

simulations, where the correlation for the straight fins proved to overestimate the heat transfer

coefficient by around 20%. Furthermore, because the Nusselt number is also linearly dependent on the

hydraulic diameter, which is considerably smaller for a finned tube, these correlations propose a higher

heat transfer coefficient for a longitudinally finned tube compared to a bare tube. As the straight fins do

not significantly alter the flow pattern, this would imply fin efficiency greater than 100%, which is highly

unlikely. The simulated different sensitivity to the Reynolds number however, concurs with the

conclusions drawn by Albano et al. [5] The Nusselt number and friction factor are less Reynolds number

dependent for helicoidally finned tubes which is similar behavior to that of very rough tubes.

Figure 11: Simulated Nusselt numbers for both helicoidally and longitudinally finned tubes.

0

50

100

150

200

250

300

40000 60000 80000 100000 120000 140000

Nu

sse

lt n

um

be

r

Reynolds number

Straight CFD Helical CFD Straight correlation

Helical correlation Bare correlation



Confidential - 46 -

Figure 12: Simulated Fanning friction factors for both helicoidally and longitudinally finned tubes.

Excellent agreement is obtained for the friction factor calculations. Important to note is that a roughness

factor was introduced for the simulation results to provide better comparison with the experimental

data. It was assumed that the roughness relative influence on the friction factor is equal for a bare tube

as for a finned tube. As such, the roughness height was fitted to the data to a value of 1.6x10-5m, which

is a typical value for tubes of this type. The simulations clearly confirm the conclusions drawn by Albano

et al. and De Saegher that friction factors of helicoidally finned tubes are significantly higher [5, 6].

The performed simulations apparently conclude equal or better performance of the longitudinally finned

tubes. Albano et al. attributed this to an increased tendency of the air to bypass the fins in the case of

helicoidal fins [5]. This would imply lower velocity inside the fins and a higher velocity in the center of

the tube. The performed simulations confirm this effect, as shown in Figure 13.

0.003

0.0035

0.004

0.0045

0.005

0.0055

0.006

40000 60000 80000 100000 120000 140000

Fan

nin

g fr

icti

on

fact

or

Reynolds number

Straight CFD Helical CFD Straight correlation

Helical correlation Bare correlation



Confidential - 47 -

Figure 13: Radial velocity profile at Re = 90,000 for air flow in an adiabatic tube.

De Saegher denied this as the main reason, instead attributing the lower heat transfer to a region of

lower turbulence inside the helicoidal fins [6]. This could explain a thicker boundary layer and

consequential lowered heat transfer. The simulations in the present work however do not confirm these

findings. In Figure 14(a), the ratio of the turbulent viscosity to the molecular viscosity is plotted along the

length of the fin, at a distance of 0.5mm from the wall. From this plot, it can be seen that there is only a

small region where the turbulent viscosity inside the helicoidal fin is lower than for the longitudinal fin.

In general, the existence of swirl flow will create additional turbulence. This effect is even clearer in the

center of the tube, as can be seen from the radial turbulence profile on Figure 14(b).

0

10

20

30

40

50

60

70

80

90

0 0.005 0.01 0.015 0.02

Vel

oci

ty m

agn

itu

de

[m/s

]

Radial position [m]

Longitudinal Fins

Helicoidal Fins


Influence of fin height on pressure drop and heat transfer in finned tubes

Confidential - 48 -

3.9 Influence of fin height on pressure drop and heat transfer

in finned tubes

Having validated the model by comparison with the experimental data from Albano et al., a more

thorough study was performed in order to assess the possibilities of the two types of finned tube.

Although the straight fins seemed to perform better both experimentally and simulated, one can still

expect the increased turbulence in the center of helicoidally finned tubes to improve mixing, giving rise

to more uniform temperature and concentration profiles. As the fins discussed up until now all had a

relatively large fin height, a number of simulations with a smaller fin were performed.

An important consideration for this study is of course the basis of comparison for the different fin

heights. As the fin height is reduced, typically the flow cross section area of the tube will become larger.

Working with a same mass flow under these circumstances would provide a flawed basis of comparison,

as the space times would be higher, obviously leading to increased heating of the gas. Since the focus in

the Albano et al. experiments lied with the influence of the Reynolds number, adjusting the mass flow to

0

10

20

30

40

50

-0.005 0 0.005

Turb

ule

nt

visc

osi

ty r

atio

[-]

x [m]

Peak Pea Valley

Figure 14: Ratio of turbulent to molecular viscosity along the length of the fin (a) and radial profile at the outlet (b).

(a) (b)



Confidential - 49 -

obtain an equal Reynolds number would seem like a possible outcome. Using lower fins however also

increases the hydraulic diameter, which further increases the Reynolds number. In order to obtain the

same Reynolds number, the mass flow would have to be lowered, while the tube cross-sectional area

increases. It is clear that this would not provide a good basis of comparison. It was thus concluded that

the most appropriate means of comparison would be to use a Reynolds number based on the equivalent

diameter. This equivalent diameter is calculated as the diameter of a circular tube with equal cross-

sectional area as the original tube used in the model validation section.

Instead of adjusting the mass flow rate for each of the finned profiles however, in the present work we

have opted to scale the entire geometry while keeping the mass flow rate constant. Doing so, the

Reynolds number (based on the equivalent diameter) is preserved, allowing evaluation of any enhanced

mixing properties. By scaling the entire geometry by a certain fraction however, the tube metal thickness

as well would be altered. In the present work, the minimum metal thickness (i.e. at the valleys) was fixed

at 7mm in order to comply with any structural stability constraints and to avoid great differences in

conductional resistance. A detailed overview of the studied geometries is given in Table 3, where Tube

F2 coincides with the geometry used by Albano et al.

Table 3: Fin height study: tube geometries.

Tube ID F1 F2 F3 F4 F5 F6 F7 F8 F9

Outer diameter D [mm] 39.0 36.8 36.0 35.3 34.6 33.9 33.2 32.6 32.0

Metal thickness [mm] 7 7 7 7 7 7 7 7 7

Fin Height e [mm] 7.6 5.4 4.6 3.9 3.2 2.5 1.8 1.2 0.6

e/D [-] 0.196 0.147 0.128 0.110 0.092 0.073 0.055 0.037 0.018

Helicoidal fin pitch [mm] 406.4 406.4 406.4 406.4 406.4 406.4 406.4 406.4 406.4

Inner surface [m²/m] 0.175 0.143 0.132 0.123 0.115 0.109 0.105 0.102 0.100

Inner surface increase

compared to bare [%]

77% 44% 33% 24% 16% 10% 6% 2% 1%



Confidential - 50 -

Cross-sectional area

[mm²]

783 783 783 783 783 783 783 783 783

Hydraulic diameter [mm] 17.9 21.9 23.7 25.5 27.1 28.6 29.9 30.8 31.4

Constant Reynolds number 3.9.1

Initially the study was performed at an air mass flow of 215kg/h (0.00747kg/s for 1/8th of the tube). This

coincides with an inlet Reynolds number of 90,000 based on the hydraulic diameter of the original

Albano et al. geometry and is a typical value for steam cracking furnaces as well. As previously

discussed, the actual Reynolds number may differ strongly depending on the fin height, but this proved

to be the best basis of comparison. A few of these geometries can be seen in Figure 15 along with the

simulated velocity profile at the outlet for helicoidally finned tubes. It can clearly be seen that the

velocity inside the fin is lower for the tubes with very high fins.



Confidential - 51 -

Although from the increased velocities in the center of the tube compared to a bare tube, one could

expect lower temperatures in that region as well, it is seen that this is not necessarily the case. This is

because swirl flow occurs, causing a significant tangential velocity component. This in turn causes

improved mixing towards the center. The temperatures at the outlet for the helicoidally finned tubes can

be seen in Figure 16.

Figure 15: Velocity magnitude [m/s] profile at the outlet of helicoidally finned tubes with different fin heights.

F1

F2

F3

F4

F5

F6

F8

Bare



Confidential - 52 -

It is clear that each of the tubes perform better than a standard circular tube without fins. Even for

similar average temperatures (Bare vs. Tube F8), the radial temperature gradient is much less

pronounced. Upon using very large fins such as is the case for Tube F1, the air inside the fin is heated

very strongly but when compared to slightly smaller fins, no significant improvement is achieved for the

temperature in the center of the tube. The very strong swirl flow inside the fin does not appear to spread

efficiently towards the center, limiting the mixing effect. The geometry used by Albano et al., Tube F2,

Figure 16: Temperature [°C] profile at the outlet of helicoidally finned tubes with different fin heights.

F1

F2

F3

F4

F5

F6

F8

Bare



Confidential - 53 -

appears to have over-designed fins as well when compared to Tube F3. This can be concluded as the bulk

temperature is slightly lower while obviously the pressure drop will be higher. The pressure drops for

both the longitudinally finned and helicoidally finned tube simulations can be seen in Figure 17.

Figure 17: Average pressure drop for tubes with different fin height-to-diameter ratios.

As could be predicted, the pressure drop for the helicoidally finned tubes is consistently higher than for

the longitudinal fins. Comparing with the results for a bare tube of equal cross-section however (e/D =

0), the pressure drop lies only about 40% higher. This is relatively low considering the values

encountered in the literature study for similar three-dimensional structures such as the MERT (1.8-3.5

times higher) [8, 9] and SMAHT coils (1.4-3 times higher. [10, 11]

Because of the difference in hydraulic diameters, it is clear that the Nusselt number would not be a good

basis of comparison to analyze the heating characteristics of each of the tubes. The heat transfer

coefficient does not suffer from this problem, but also fails to point out the real beneficial effects of the

fins, as the surface increase is the main reason for improved heat transfer. As such, in the present work it

was chosen to simply make a comparison based on the actual heat exchanged at the air-metal interface.

Although these values will be much higher for reactive flow at high temperatures, it can be assumed that

the mechanics of heat transfer will remain the same and this will merely alter the driving force. The

transferred heat per axial meter for each of the tubes is plotted in Figure 18.

0

500

1000

1500

2000

2500

3000

3500

0 0.05 0.1 0.15 0.2 0.25

Pre

ssu

re d

rop

[P

a/m

]

e/D ratio [-]

Longitudinal

Helicoidal



Confidential - 54 -

It is clear that the fins offer improved heat transfer. At a fin ratio of 0.11, the heat transfer is

approximately 12% higher for the helicoidally finned tube and 8% higher for the longitudinally finned

tube. It is interesting to note the similar S-shaped course of the pressure drop and heat transfer in

function of the fin height. These graphs clearly agree with the Chilton-Colburn analogy which states a

linear relationship between the friction factor and Nusselt number.

Figure 18: Average heat transfer for tubes with different fin height-to-diameter ratios.

To study whether or not the increased heat transfer is merely caused by the increased internal surface

area, the ratio of heat transfer in the finned tubes compared to the bare tube was plotted against the

increase of internal surface area. In Figure 19 it can clearly be seen that the longitudinal fins follow a

perfectly linear course, confirming the findings of Brown et al [12]. The helicoidally finned tubes however

were not studied in the before mentioned article, and it is clear that they exhibit a substantially different

behavior. Interesting is the appearance of a local bump around a perimeter ratio of 1.3-1.4, which

corresponds to an e/D ratio of around 0.12.

800

900

1000

1100

1200

1300

0 0.05 0.1 0.15 0.2 0.25

Q [

W/m

]

e/D ratio [-]

Longitudinal

Helicoidal



Confidential - 55 -

Figure 19: Influence of the wetted perimeter on heat transfer characteristics.

The reason for this can be attributed to a number of things. First of all it is obvious from the previously

considered velocity and temperature profiles that the larger fins generate a strong swirl flow component

that greatly improves heating inside the fin. For very high fins however, it is clear that a second heat

transfer resistance appears: the transfer of heat from within the fin towards the center of the flow. As

such, it can be assumed that there is a certain “optimal” e/D-ratio for which the increased surface leads

to increased heat transfer, while yet effectively spreading the swirl flow towards the center of the tube

and as such lowering the heat transfer resistance at the peaks of the fins. As a visualization of the two

heat transfer resistances, the radial temperature profile at the outlet of the tube was plotted for a

variety of fin heights. The result is presented in

Figure 20.

1

1.1

1.2

1.3

1 1.2 1.4 1.6 1.8 2

Hea

t tr

ansf

er r

atio

[-]

Wetted perimeter ratio [-]

Helicoidal

Longitudinal



Confidential - 56 -

Figure 20: Radial temperature profile at the outlet of helicoidally finned tubes with different fin height-to-diameter ratios.

It can be seen that for the tallest fins, the air within the fin is heated very strongly because of the large

internal surface increase. This heat however does not appear to be spread efficienty towards the center

of the tube, as there is almost no difference in bulk air temperature for all of the larger fins. These

considerations are interesting for unreactive heating, but are even more relevant in the case of reactive

flow. As greater temperature uniformity often goes coupled with greater concentration uniformity, a

flatter profile could provide double benefits to the steam cracking reactions. In order to quantify the

radial uniformity in one number, a coefficient of variation (CoV) was introduced. This is a widely applied

method within the mixing industry as a measure of the uniformity of a fluid mixture. In the current work

the CoV was calculated using the discrete temperatures from the computational cells at the tube outlet:

e/D = 0.196

e/D = 0.147

e/D = 0.128

e/D = 0.092

e/D = 0.073

e/D = 0.018

Bare



Confidential - 57 -

√∑

(16)

The result of this approach can be seen in Figure 21. As lower values of the CoV point towards greater

uniformity, it is obvious that the helicoidal fins perform better than longitudinally finned or bare (e/D =

0) tubes. Interestingly, the influence of the fin height remains limited for both types of tubes up until a

certain e/D value. At this point, the inwards transfer of heat coming from the fin valleys starts to get

limited by an increased resistance as the flow gets more and more isolated inside the fins. It appears that

the transition point lies at a fin height/diameter ratio of 0.12. It is clear that the geometry previously

used by Albano et al. (e/D = 0.147) has overdesigned fins and as such only provides limited uniformity

improvements compared to the case of a bare tube.

Figure 21: Temperature-based coefficient of variation for tubes with different fin height-to-diameter ratios.

Influence of Reynolds number 3.9.2

All of the previous calculations were done at an equal cross-sectional area and mass flow. As previously

shown in 3.8, the Nusselt number and friction factor are considerably influenced by the Reynolds

0

0.005

0.01

0.015

0.02

0.025

0 0.05 0.1 0.15 0.2 0.25

Co

effi

cien

t o

f va

riat

ion

e/D ratio [-]

Helicoidal

Longitudinal



Confidential - 58 -

number and as such the optimal fin height for helicoidally finned tubes may be dependent on the

Reynolds number as well. In order to study this, the same simulations were performed at a mass flow of

311kg/h, which corresponds to a Reynolds number of 130,000 based on the hydraulic diameter of the

Albano et al. geometry (Tube ID F2). No changes were made to the scaling or meshing methods from the

previous study. The pressure drop and heat transfer characteristics are shown in Figure 22.

Figure 22: Average pressure drop (a) and heat transfer (b) for tubes with different fin height-to-diameter ratios at Reynolds = 130,000.

Although perhaps slightly less pronounced, there Is still a definite non-linearity in the fin height

dependency, leading to assume that there is an optimal fin height. Plotting the heat transfer

improvement as function of the increase of internal surface area, this becomes even more obvious as is

shown in Figure 23.

0

1000

2000

3000

4000

5000

6000

7000

0 0.05 0.1 0.15 0.2 0.25

Pre

ssu

re d

rop

[P

a/m

]

e/D ratio [-]

1200

1300

1400

1500

1600

1700

0 0.05 0.1 0.15 0.2 0.25

Hea

t tr

ansf

er [

W/m

]

e/D ratio [-]



Confidential - 59 -

Figure 23: Influence of the wetted perimeter on heat transfer characteristics at Reynolds = 130,000.

Although the cut-off is slightly less sharp for the higher Reynolds number, there is still a significant bend

in the curve for an e/D ratio of 1.2, coinciding with a wetted perimeter ratio of around 1.3.

Again this optimal e/D ratio can be better illustrated by looking at the radial temperature profile for each

of the fin sizes. It is also interesting to compare these profiles, shown in Figure 24, with those previously

acquired for a lower Reynolds number, on

Figure 20. The taller fins again each have a region where the flow is trapped inside the fin and the local

temperature is high. The bulk temperature however remains more or less the same over the entire range

of e/D from 0.2 to 0.1, as was seen for the case with Reynolds = 90,000 as well. The heat transfer

improvement is slightly lower than originally, only accounting for a 6°C temperature rise in the bulk

compared to a bare tube instead of almost 10°C for a lower Reynolds number. This can be explained by

the fact that the tangential velocity component now makes up a lower fraction of the total velocity

magnitude inside the fin and as such the relative increase in wall friction is lower. This could be

1

1.05

1.1

1.15

1.2

1.25

1 1.2 1.4 1.6 1.8 2

Hea

t tr

ansf

er r

atio

[-]

Wetted perimeter ratio [-]

Helicoidal - Reynolds = 90k

Longitudinal - Reynolds = 90k




Confidential - 60 -

concluded from Figure 23 as well, where the heat transfer improvement typically was about 1-2% lower

than for a lower flow rate.

Figure 24: Radial temperature profile at the outlet of helicoidally finned tubes with different fin height-to-diameter ratios at Reynolds = 130,000.

A coefficient of variation was introduced on the same basis as previously, leading to the profile seen on

Figure 25. Judging from the results for the bare tube (e/D = 0) and the helicoidal fins, it appears that all

coefficients are slightly higher for an increased Reynolds number. This is easily understood as the

increased velocity leads to lower residence time and less time for the heated air at the wall to

diffuse/mix in the radial direction. This will lead to a less uniform temperature profile. The fin height

influence does not appear to have changed, with fin heights below 0.13 leading to greater uniformity

than for the bare fin. Any higher and the swirl flow effect is lost due to the increased tendency of the air

to get trapped inside the fins. In any case, it can be concluded that the uniformity of the helicoidally


Influence of pitch on pressure drop and heat transfer in helicoidally finned tubes

Confidential - 61 -

finned coils will consistently be greater than for the longitudinally finned coils or a coil without fins (e/D

= 0).

Figure 25: Temperature-based coefficient of variation for tubes with different fin height-to-diameter ratios at Reynolds = 130,000.

3.10 Influence of pitch on pressure drop and heat transfer in

helicoidally finned tubes

The next parameters that were investigated are the helix pitch P and helix angle α. The definition of the

two can be seen on Figure 26. The formula linking the two parameters is given by:

n (

)

(17)

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.05 0.1 0.15 0.2 0.25

Co

effi

cien

t o

f va

riat

ion

[-]

e/D ratio [-]


Longitudinal - Reynolds = 90k


Bare - Reynolds = 90k

Bare - Reynolds = 130k



Confidential - 62 -

Figure 26: Conceptual structure of a helicoidally finned tube with a helix angle α.

As it can easily be understood that the influence of the helix angle will be greatly influenced by the fin

height, the study was performed for e/D ratios of both 0.147 (Albano et al. geometry) and 0.037 (Tube

F8). The tube geometry for the latter case was again scaled to achieve an equal cross-sectional area for

both fin heights. No additional scaling was needed between the individual simulations as this time the

helix angle did not have such a drastic influence on space-time. The geometries studied in these

simulations are listed in Table 4.

Table 4: Helicoidal fin pitch length study: Tube geometries

Tube ID F2P1 F2P2 F2P3 F2P4 F2P5 F2P6 F8P2 F8P3 F8P4 F8P6

Diameter [mm] 36.8 36.8 36.8 36.8 36.8 36.8 32.6 32.6 32.6 32.6

Fin Height [mm] 5.4 5.4 5.4 5.4 5.4 5.4 1.2 1.2 1.2 1.2

e/D [-] 0.147 0.147 0.147 0.147 0.147 0.147 0.037 0.037 0.037 0.037

Helicoidal fin pitch

[mm] 1626 812.8 406.4 203.2 135.5 101.6 812.8 406.4 203.2 101.6

Helix angle α [°] 4.1 8.1 15.9 29.6 40.5 48.7 7.2 14.2 26.8 45.2


[mm²] 783 783 783 783 783 783 783 783 783 783



Confidential - 63 -

Achieving convergence for these geometries was often problematic. Extruding the 2D mesh produced

cells with a high skewness for the larger helix angles, often causing numerical errors. A possible solution

is extruding the 2D mesh along smaller steps in the axial direction, reducing cell skewness. This however

drastically leads to an increased number of cells, unacceptable for current computational power.

Nevertheless, residuals for all simulations dropped down to 0.001 or lower, where any remaining

fluctuations were filtered out by averaging over a large amount of iterations in which no significant flow

field changes occured.


The resulting temperature profiles for a mass flow of 215kg/h and a fin height-to-diameter ratio of 0.147

are plotted in Figure 27. There appears to be a substantial difference in temperature uniformity for

different values of the helix pitch. In general, both the average temperature and the temperature

uniformity will be higher for a shorter helix pitch. The straight fin slightly deviates from this trend but this

can be explained by a number of considerations. First of all, the simulations of longitudinally finned

tubes make use of the kε-model equations as opposed to the RSM equations used in the simulation of

helicoidally finned tubes, so 1-on-1 quantitative comparison is difficult. Furthermore, it was previously

shown that the enhanced heat transfer is influenced by two effects. On the one hand longitudinal fins

have better heat transfer at the wall because there is less stagnation inside the fins, while on the other

hand the helicoidal fins typically enhance mixing and reduce temperature gradients in the cross-section.

If for large values of the helix pitch the first effect would be more prominent than the latter, it is not

entirely unlikely that the straight fins do perform better than the helicoidal ones with large pitches.

Hydraulic diameter

[mm] 21.9 21.9 21.9 21.9 21.9 21.9 30.8 30.8 30.8 30.8



Confidential - 64 -

The general trend however remains that the average temperature is higher for a shorter helix pitch. This

can be attributed to the fact that a large helix angle will introduce a very strong swirl component in the

flow. While not directly altering the axial velocity, this will greatly increase the total velocity magnitude

both inside and outside the fin, which in turn will reduce the boundary layer thickness because of the

increased wall shear. As this swirl flow component also increases the residence time, it is easy to

understand that there will be more heat transfer and the flow average temperature will be higher. The

improved uniformity however cannot directly be explained from these considerations. Previously, in the

1626

813

203

136

101

Bare

Straight

Figure 27: Temperature [°C] profile at the outlet of helicoidally finned tubes with different helix pitch lengths [mm] for an e/D ratio of 0.147.

406



Confidential - 65 -

part concerning the fin height, it was concluded that the geometry used by Albano et al. had an

overdesigned fin, causing the flow to be slightly “trapped” inside the fin and as such prohibiting efficient

heat transfer towards the center of the tube. From these simulations however, it would appear as if the

trapping effect merely depends on the degree of swirl flow that is induced. As the helix angle increases,

the temperature between the fins becomes more and more uniform. Upon consideration of the

increased tangential velocity however, it could be expected that the “trapping” inside the fin would be

stronger, as stated by Jensen and Vlakanic. [13] This is seen to not be the case as at a relatively high helix

angle of 48.7° the temperature profile is even more uniform than for the lower values.

Similar calculations were performed for a tube with smaller fins. The temperature profiles can be seen in

Figure 28.

Figure 28: Temperature [°C] profile at the outlet of helicoidally finned tubes with different fin helix angles for a e/D ratio of 0.037.

Despite the significantly shorter fin, the effect of the helicoidal pitch is still very apparent. Again the low-

pitched helicoidal fin appears to perform even slightly worse than a straight fin. At higher values of the

pitch however, the temperature profile is significantly flattened, indicating that even the small fins are

capable of inducing swirl flow and improved mixing in the center of the tube.

P2

P3 P4

P6



Confidential - 66 -

Figure 29: Radial temperature profile at the outlet of helicoidally finned tubes with different fin helix angles for e/D ratios of 0.147 (a) and 0.037 (b).

Upon consideration of Figure 29, a reevaluation of the previous study on the influence of the fin height

can be performed. It can be concluded that the smaller fins do consistently have a lower heat transfer

than the taller fins, due to the lower increase in internal surface area, but yet they are capable of

providing the same or even improved uniformity benefits. They have the significant advantage however

of causing a much lower pressure drop. The results of these calculations can be seen in Figure 30 and

Figure 31.

Figure 30: Average pressure drop for helicoidally finned tubes with different helix angles.

0

1000

2000

3000

4000

5000

0.00 20.00 40.00 60.00

Pre

ssu

re D

rop

[P

a/m

]

Helix angle [°]

e/D = 0.147

e/D = 0.0367

Inter-fin

(a) (b)



Confidential - 67 -

Figure 31: Average heat transfer for helicoidally finned tubes with different helix angles.

From the previous considerations, the main influence of the helicoidal pitch appears to be an

improvement of the radial mixing. This can be illustrated even more clearly when plotting the

temperature-based coefficient of variation that was previously introduced. Figure 32 shows these results

for the two sets of calculations.

Figure 32: Temperature-based coefficient of variation for helicoidally finned tubes with different helix angles.

800

900

1000

1100

1200

1300

1400

1500

0.00 20.00 40.00 60.00

Q [

W/m

]

Helix angle [°]

e/D = 0.147

e/D = 0.0367

0

0.005

0.01

0.015

0.02

0.025

0.00 20.00 40.00 60.00Co

effi

cien

t o

f va

riat

ion

[-]

Helix angle [°]

e/D = 0.147

e/D = 0.0367



Confidential - 68 -

The obtained graph confirms the significant improvements in terms of radial mixing. It is also clear that

not only do the small fins achieve a similar swirl flow effect but they also do not suffer from local

stagnation zones inside the fins. Because of this double effect, they provide even greater radial mixing

benefits, while from Figure 30 it could be seen that the pressure drop is significantly lower as well. The

sole problem with these fins lies in the fact that the increase in internal surface area is small as well.

Opportunities to solve this by having a greater amount of fins will be discussed further on.

Influence of the Reynolds Number 3.10.2

In order to see whether these conclusions are applicable to all Reynolds numbers, the simulations were

repeated for a mass flow of 311kg/h. Given the difficulty in achieving convergence for these calculations,

no pitch lengths greater than the 406.4mm originally used by Albano et al. were considered. The heat

transfer and pressure drop results can be seen in Figure 33 and Figure 34.

Figure 33: Average pressure drop for helicoidally finned tubes with different helix angles at Reynolds = 130,000.

0

2000

4000

6000

8000

10000

0.00 20.00 40.00 60.00

Pre

ssu

re D

rop

[P

a/m

]

Helix angle [°]

e/D = 0.147

e/D = 0.0367



Confidential - 69 -

Figure 34: Average heat transfer for helicoidally finned tubes with different helix angles at Reynolds = 130,000.

Although only a limited amount of cases were studied, the results appear quite similar to those obtained

for a Reynolds number of 90,000. Interestingly, the tube with small fins and a helix angle of 26.8° again

shows superior heating characteristics than the one with helix angle 14.2°, while the additional pressure

drop is very small. This may point towards a very beneficial combination of the fin height and pitch

values and should further be studied.

The radial temperature profiles can be seen in Figure 35.

Figure 35: Radial temperature profile at the outlet of helicoidally finned tubes with different fin helix angles for e/D ratios of 0.147 (a) and 0.037 (b) at Reynolds = 130,000.

1200

1300

1400

1500

1600

1700

1800

1900

0.00 20.00 40.00 60.00

Q [

W/m

]

Helix angle [°]

e/D = 0.147

e/D = 0.0367



Confidential - 70 -

Although the general shape of the temperature profiles is maintained, the temperature difference

between the tubes is lowered. At a Reynolds number of 90,000 increasing the pitch length from

101.6mm to 406.4mm resulted in a 10°C lower bulk temperature for both fin heights as can be seen on

Figure 29. At a Reynolds number of 130,000 however, this difference amounts to barely 5°C for the small

fins, while the taller fins maintain an 8°C temperature difference. This indicates that at high flow rates,

the air is more likely to bypass the small fins when the pitch length is small. As the effect on the taller fins

is less pronounced, this does confirm the coring effect described by Jensen and Vlakanic [13] which was

previously not seen at a Reynolds number of 90,000.

The coefficients of variation are shown in Figure 36. Although only consisting of a limited number of data

points there is still a clear difference in the behavior of the different fins. The positive unifying effect of

the small fins stays maintained at higher mass flows, while this does not appear to be the case for the

taller fins as can be seen from the increase in the coefficient of variation for the cases with an e/D of

0.147. Nevertheless, this figure shows a slight trend change for the small fins as well, proving what was

previously concluded from the radial temperature profiles.

Figure 36: Coefficients of variation for helicoidally finned with different helix angles and Reynolds numbers.

0

0.005

0.01

0.015

0.02

0.025

0.00 10.00 20.00 30.00 40.00 50.00 60.00

Co

effi

cien

t o

f va

riat

ion

[-]

Helix angle [°]

e/D = 0.147 - Re = 90k

e/D = 0.0367 - Re = 90k

e/D = 0.147 - Re = 130k

e/D = 0.0367 - Re = 130k


Influence of number of fins on pressure drop and heat transfer in finned tubes

Confidential - 71 -

3.11 Influence of number of fins on pressure drop and heat

transfer in finned tubes

Finally the influence of the number of fins was studied. For this only 1/nth of the tube was simulated,

with n being the number of fins. The radial mesh was slightly refined for the more narrow fins to provide

sufficient cells in the angular direction. Similar to the previously performed parametric studies, the entire

tube geometry was scaled in order to keep the cross-sectional flow area constant. It was also again

assumed that the fin height would have a considerable influence on the optimal number of fins and as

such calculations were performed for both large (e/D = 0.147) and smaller (e/D = 0.037) fins. The fin

width was calculated as the perimeter of a circle with equal diameter divided by the number of fins. An

overview of the studied geometries can be seen in Table 5.

Table 5: Number of fins study: tube geometries.

Tube ID 4F2 6F2 8F2 10F2 12F2 8F8 12F8 16F8 24F8 32F8

Diameter [mm] 36.3 36.6 36.8 36.9 36.9 32.6 32.7 32.7 32.8 32.8

Number of fins 4 6 8 10 12 8 12 16 24 32

Fin Height [mm] 5.3 5.4 5.4 5.4 5.4 1.2 1.2 1.2 1.2 1.2

e/D [-] 0.147 0.147 0.147 0.147 0.147 0.037 0.037 0.037 0.037 0.037

Fin height/width ratio

[-] 0.19 0.28 0.37 0.47 0.56 0.09 0.14 0.19 0.28 0.37

Inner surface increase

compared to bare [%] 11% 26% 44% 66% 90% 2% 5% 10% 21% 36%


[mm²] 783 783 783 783 783 783 783 783 783 783

Hydraulic diameter

[mm] 28.4 25.2 21.9 19.0 16.6 30.8 29.9 28.8 26.1 23.2



Confidential - 72 -


Pressure drop and heat transfer results for the tubes with large fins are shown in Figure 37 and Figure

38.

Figure 37: Average pressure drop for tubes with a varying amount of 5.4mm high fins.

Figure 38: Average heat transfer for tubes with a varying amount of 5.4mm high fins.

From these plots it can be seen that for a relatively large fin, the pressure drop has an almost linear

dependency on the number of fins, while the heat transfer curve follows an upward trend with negative

0

500

1000

1500

2000

2500

3000

3500

4 6 8 10 12

Pre

ssu

re d

rop

[P

a/m

]

Number of fins

Helicoidal - e/D = 0.147

Longitudinal - e/D = 0.147

1000

1100

1200

1300

4 6 8 10 12

Q [

W/m

]

Number of fins





Confidential - 73 -

second derivative. Upon qualitative consideration of these trends, it would appear that the optimal

number of fins is somewhere around 8-10, as at this point the increase in heat transfer rate starts to

flatten out. These values for the number of fins are the values most often encountered in the literature

as well.

This can be confirmed by looking at the temperature profiles inside the helicoidally finned tubes, which

are shown in Figure 39. As the fins get more narrow, there is more and more stagnation inside the fin,

leading to increased temperatures in these regions as well. Although the tubes with only 4 fins have a

more uniform temperature profile, actual heat transfer improvement is small because of the limited

increase of internal surface. The flow velocity inside the fin and the fin surface appear to be the decisive

factors when altering the number of fins, which also explains why there is little difference between the

trend of the longitudinal and the helicoidal fins respectively.

Figure 39: Temperature [°C] profile at the outlet of helicoidally finned tubes with different numbers of fins.

Figure 40 shows the radial temperature profile at the outlet for the helicoidally finned tubes, further

confirming the previously discussed findings. Although the behavior near the wall appears to be quite

6

4

8

10

12



Confidential - 74 -

distinct for all of the tubes, this can easily be explained by further consideration of Figure 39. The radial

line connecting the center of the tube with the fin valley simply lies closer to the walls as the fin width

decreases, leading to increased temperature. In general, it can be concluded that the number of fins will

not significantly alter the flow pattern.

Figure 40: Radial temperature profile at the outlet of helicoidally finned tubes with a varying number of 5.4mm high fins.

Similar calculations were also performed on tubes with much smaller fins (see Table 5, Tube IDs ending

on F8). Figure 41 and Figure 42 show the results for these geometries, where it is clear that this time the

effect of the helicoidal fins is quite distinct from that of the longitudinal fins.



Confidential - 75 -

Figure 41: Average pressure drop for tubes with a varying number of 1.2mm high fins.

Figure 42: Average heat transfer for tubes with a varying amount of 1.2mm high fins.

Increasing the amount of helicoidal fins will considerably increase wall shear, leading to both increased

heat transfer and increased pressure drop. From this data, one can assume an optimal number of these

smaller fins to be around 24-32. A radial temperature plot of the flow inside the tubes confirms these

findings, as shown in Figure 43.

0

500

1000

1500

2000

2500

3000

0 10 20 30

Pre

ssu

re d

rop

[P

a/m

]

Number of fins



1000

1100

1200

1300

0 10 20 30

Q [

W/m

]

Number of fins





Confidential - 76 -

Figure 43: Radial temperature profile at the outlet of helicoidally finned tubes with varying number of 1.2mm high fins.

Increasing the amount of fins does not appear to significantly alter the temperature gradients inside the

tube, while the increased internal surface area will lead to a higher average temperature.

Interestingly, the tubes with the optimal number of fins appear to have around the same height-to-width

fin ratio for both large and smaller fins. From this it can be concluded that the predominant decisive

factor in determining the optimal number of fins is the fin height-to-width ratio and not so much the

diameter or fin height. Although for a Reynolds number of 90,000 the optimal value of this ratio is

around 0.3-0.4, it is not unlikely for this to be otherwise when working at different flow rates.

Upon consideration of these conclusions, the results can now be plotted in a much more comprehensive

manner using the fin height-to-width ratio, as shown in Figure 44.



Confidential - 77 -

Figure 44: Fin height-to-width ratio dependency of heat transfer for finned tubes.

Influence of Reynolds number 3.11.2

As was the case for the other studies as well, the helicoidal fin simulations were repeated for a mass flow

of 311kg/h, which coincides with a Reynolds number of 130,000 for the tube with 8 fins. The results are

shown in Figure 45 and Figure 46.

1000

1100

1200

1300

0 0.1 0.2 0.3 0.4 0.5 0.6








Confidential - 78 -

Figure 45: Fin height-to-width ratio dependency of pressure drop for finned tubes at Reynolds = 130,000.

Figure 46: Fin height-to-width ratio dependency of heat transfer for finned tubes at Reynolds = 130,000.

Figure 46 shows a remarkably good performance of the small fins as the pressure drop is clearly lower

while the heat transfer is improved compared to the taller fins. It is important to again emphasize

however that for the small-finned tubes with the highest height-to-width ratio the computational

0

1000

2000

3000

4000

5000

6000

7000

0 0.1 0.2 0.3 0.4 0.5 0.6

Pre

ssu

re d

rop

[P

a/m

]




1200

1300

1400

1500

1600

1700

0 0.1 0.2 0.3 0.4 0.5 0.6

Q [

W/m

]





Geometry optimization - Conclusions

Confidential - 79 -

domain became very small because only 1/24th or 1/32nd of the tube was simulated. Because of this it is

possible that the periodic boundary conditions are slightly unreliable as the width of the computational

domain often was limited to just 1 or 2 cells.

3.12 Geometry optimization - Conclusions

The entire parametric study was performed in the absence of reactive species but yet some conclusions

can be drawn towards the applications in steam cracking reactors. As previously discussed, the

predominant factors to be influenced by application of fins are the product selectivities and the

reduction of coke formation. As such, in order to draw conclusions from the performed calculations, the

two main parameters to check for are the heat transfer improvement and the additional pressure drop

compared to a bare tube. A plot summarizing all of the obtained data is presented in Figure 47 and

Figure 48.

Figure 47: Simulated heat transfer and pressure drop ratios for a variety of finned tubes at Reynolds = 90,000.

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1 1.5 2 2.5

Hea

t tr

ansf

er r

atio

[-]

Pressure drop ratio [-]

H_Number of Fins: e/D = 0.147


H_Pitch: e/D = 0.037


H_Fin Height

L_Fin Height

L_Number of Fins: e/D = 0.037




Confidential - 80 -

Figure 48: Simulated heat transfer and pressure drop ratios for a variety of finned tubes at Reynolds = 130,000.

A first interesting observation is the almost perfectly linear relationship between pressure drop and heat

transfer for all of the longitudinally finned coils. This suggests that neither the fin height, nor the number

of fins, nor a combination of the two can improve the heating characteristics beyond that linear

relationship. As pressure drop typically follows a linear relationship with wetted perimeter, this also

confirms the study of Brown et al. [12]

Unlike the longitudinal fins, it was made clear throughout the parametric study and on these plots as

well, that the helicoidal fins do have certain optimal parameter values. For the tall fins an optimal e/D

ratio was found to be around 0.12, while further on it was seen that not just the fin height but mostly the

height-to-width ratio was of primary importance. A value of 0.3-0.4 turned out to be optimal for both tall

and short fins. A significant increase in both pressure drop and heat transfer is seen for the higher helix

angle values. The latter was seen to primarily be caused by improved radial temperature uniformity.

Upon consideration of these values it is clear that none of the cases studied so far make use of all the

optimal parameters and as such none of the geometries performs better than the quasi-linear

relationship between heat transfer and pressure drop seen in Figure 47. Because of this, three additional

geometries were tested to see if a certain combination of optimal parameters might lead to a helicoidally

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1 1.5 2 2.5

Hea

t tr

ansf

er r

atio

[-]






H_Fin Height



Confidential - 81 -

finned tube that actually outperforms the longitudinally finned tubes in both aspects. These geometries

are listed in Table 6.

Table 6: Optimized geometries

Tube ID 24F8P6 24F8P4 10F4P4

Diameter [mm] 32.8 32.8 35.4

Number of fins 24 24 10

Fin Height [mm] 1.2 1.2 3.9

e/D [-] 0.037 0.037 0.11

Fin height/width ratio [-] 0.28 0.28 0.35

Helicoidal fin pitch [mm] 101.6 203.2 203.2

Helix angle α [°] 45.4 26.9 28.7

Inner surface increase compared to bare [%] 21% 21% 37%

Cross-sectional area [mm²] 783 783 783

Hydraulic diameter [mm] 26.1 26.1 23.1

From the radial temperature profiles seen in Figure 49, it is very clear that these geometries provide

considerable improvements over the use of a bare tube. The tube with taller fins (10F4P4) offers a

slightly higher mass-weighted average temperature than the one with the smaller fins (24F8P4) and the

same pitch, but the uniformity appears to be worse. The best performance is obviously achieved by use

of the 24F8P6 but the very short pitch length also makes this the tube with the highest pressure drop,

despite the very small fins used. An overview of the pressure drop and heating characteristics is provided

in Table 7.



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Figure 49: Radial outlet temperature profiles for the optimized helicoidally finned tubes.

Table 7: Pressure drop and heat transfer results for the optimized geometries.

Tube ID 24F8P6 24F8P4 10F4P4

Pressure drop [Pa/m] 3402 2547 2893

Heat transfer [W/m] 1398 1250 1275

All three tubes appear to perform significantly better than any of the previously studied geometries. This

can be seen by introducing the new data points on the previous summarizing graph, as shown in Figure

50.



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Figure 50: Simulated heat transfer and pressure drop ratios including the optimized geometries.

Another decisive aspect for reactive flow will be the flow uniformity, reducing temperature and

concentration spikes and as such limiting unwanted reactions from occurring. The coefficients of

variation for these geometries were calculated as well and turned out to be in full accordance with the

previously obtained values for similar geometries.

It is clear that the parametric study has provided us with the necessary insights to select optimized

geometries that offer better heating characteristics than any of the typical tubes. Whether or not these

tubes will perform better as steam cracking reactors still depends on the relative importance of on the

one hand the run length improvements due to improved heat transfer and on the other hand the

selectivity losses due to increased pressure drops. This issue will be examined in the following chapter.

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1 1.5 2 2.5 3

Hea

t tr

ansf

er r

atio

[-]






H_Fin Height

L_Fin Height



24F8P6

10F4P4

24F8P4


References

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References

1. Bengt Andersson, Ronnie Andersson, Love Hakansson, Mikael Mortensen, Rahman Sudiyo,

Berend van Wachem, Computational Fluid Dynamics for Chemical Engineers. 7th ed2011,

Gothenburg, Sweden.

2. H. K. Versteeg, W. Malalasekera, An introduction to computational fluid dynamics - The

finite volume method1995: Longman.

3. Macrossan, Dr. Michael. Practical Turbulence Modelling in Fluent. 2008; Available from:

http://www.mech.uq.edu.au/courses/mech4480/turb2.pdf.

4. Leonard, B.P., Order of accuracy of QUICK and related convection-diffusion schemes. Appl.

Math. Modelling, 1995. 19(November): p. 14.



6. Saegher, Johan J. De, Modellering van stroming, warmtetransport en reactie in reactoren voor

de thermische kraking van koolwaterstoffen, in Laboratorium voor Petrochemische

Techniek1994, Universiteit Gent.

7. Corporation, Special Metals, Incoloy alloy 800, 2004.

8. Torigoe, T., Mixing Element Radiant Tube (MERT) Improves Cracking Furnace Performance,

K. Corporation, Editor 2001.



10. W. Tallis, C. Caro, C. Dang, A novel approach to ethylene furnace coil design, in 18th Annual

Ethylene Producers’ Conference2006: Orlando, FL.

11. A.N. Cookson, D.J. Doorly, S.J. Sherwin, Mixing Through Stirring of Steady Flow in Small

Amplitude Helical Pipes. 2008.

12. David J. Brown, Stone & Webster, Inc., Internally Finned Radiant Coils: a Valuable Tool for

Improving Ethylene Plant Economics, in 6th EMEA Petrochemicals Technology

Conference2004: London, UK.

13. Gregory J. Zdaniuk, Louay M. Chamra, Pedro J. Mago, Experimental determination of heat

transfer and friction in helically-finned tubes. Experimental Thermal and Fluid Science, 2008.

32: p. 15.

http://www.mech.uq.edu.au/courses/mech4480/turb2.pdf

4 Simulation of reactive flow Introduction

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4 Simulation of reactive flow

4.1 Introduction ................................................................................................................................. 85

4.2 Reactor specifications .................................................................................................................. 86

4.3 One-dimensional simulations using COILSIM1D .......................................................................... 89

4.4 Three-dimensional FLUENT simulations ...................................................................................... 99

References .............................................................................................................................................. 102

4.1 Introduction

In the previous chapter an extensive study was performed on the heating characteristics of finned tubes

for unreactive air flow. Although a number of optimal geometries were identified, it still remains to be

seen what the actual influence of these geometries will be on product selectivity and coking rate in

steam cracking reactors. The improved heat transfer will allow the reactor to run at a lower metal

temperature, which will lead to reduced coking and increased runlengths, having a direct economic

impact. The higher pressure drop however will lead to reduced selectivity to olefins. Finding a balance

between these two aspects is decisive.

The detailed steam cracking chemistry however is extensive and requires an enormous amount of

compounds to be considered. Although computing capacity has drastically increased over the past

decades, computational fluid dynamics software remains unable of simulating networks of this

complexity for practical engineering geometries. Because of these considerations, a double approach

was followed in order to provide both a qualitative and quantitative analysis.

4 Simulation of reactive flow Reactor specifications

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The first method makes use of the COILSIM1D program, developed at the Laboratory for Chemical

Technology. Although this program makes use of a 1-dimensional reactor model, it is capable of

performing these simulations using a reaction network with over 700 compounds. Additionally, it

contains two coking models, allowing an indication of the coking performance of the tubes. Run length

simulations can be performed as well to simulate the influence of the tube performance on the decoking

frequency. To take into account the heating characteristics of the finned coils, the code was altered to

include friction factor and Nusselt number correlations constructed from the data gathered in the

previous chapter.

The second method consists of 3D simulations using Ansys FLUENT 13.0 which was used in the previous

chapter as well. Using a simplified molecular reaction network, full reactor simulations were performed.

As computation time for these simulations ran well over 400 hours on 12 cores in order to achieve

convergence, only a limited amount of geometries were considered.

These two methods were applied to an industrial propane cracker which makes use of a so-called

Millisecond reactor.

4.2 Reactor specifications

4.2.1 The Kellog Millisecond reactor

As a reactor type the Kellogg Millisecond reactor was chosen. This design was based on the series of

experiments conducted by M.W. Kellog’s R&D Center, to determine the effects of temperature,

residence time and hydrocarbon partial pressures on the olefin yields of various feedstocks [1]. At a

given cracking temperature and hydrocarbon pressure, it was seen that the optimal residence time was

in the range of 0.05 – 0.1 seconds, which is the range in which commercial Millisecond furnaces operate.

To accommodate this requirement, the furnace differs from conventional cracking furnaces in a number

of ways. The cracking coils are made of a large number (typically 100-200) of small diameter single-pass

tubes, in contrast to conventional coils that employ slightly larger tubes and employ return bends for

multiple passes. A conceptual sketch of the Millisecond furnace design is shown in Figure 1.


Confidential - 87 -

Figure 1: Kellogg Millisecond furnace design [2].

Although the Millisecond furnace succeeds in achieving the highest ethylene yields of all commercial

types of furnaces, it also has the shortest run length [3, 4]. As very intense heating is required to obtain

sufficient conversion with such a low space time, the tube metal temperatures for this kind of furnace is

typically higher than for conventional furnaces. These high temperatures lead to increased coking rates,

which further hampers the heat transfer. Eventually the tube metal temperature constraints are reached

and the furnace needs to be decoked. Although conventional furnaces often run for over 50 days, the

run length of a Millisecond furnace can be as low as 1- 1.5 weeks.

4.2.2 Process conditions

The Millisecond furnace was simulated under typical industrial conditions. An overview of these

conditions is provided in Table 1. Though typically a propane steam-cracking feed contains a number of

other compounds such as ethane, propylene and butane as well, a feed of 100% purity in propane was

assumed.

Table 1: Millisecond furnace operating conditions.

Hydrocarbon flow rate [kg/h/reactor] 118.5

Steam flow rate [kg/h/reactor] 38.69


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Steam dilution [kg H2O/kg HC] 0.326

Coil inlet temperature [K] 903.65

Coil outlet pressure [bara] 1.7

As a fully-coupled reactor-furnace simulation would require several reactor simulations, requiring

months of calculation time, a heat flux profile was applied to the outer wall of the reactor. This heat flux

profile was taken from a full furnace simulation where the energy boundary condition applied to the

reactor tubes is the industrially measured temperature profile. The heat flux profile is shown in Figure 2.

The highest heat flux values are obtained at 1 meter axial coordinate as at this height combustion of the

fuel gas is strongest.

Figure 2: Heat flux profile applied to the outer tube wall.

4.2.3 Base geometry

Although a variety of tube geometries was studied, all of them were scaled according to the geometry of

the tubes originally used in the Kellogg cracking furnace at Fina Antwerp Olefins, Antwerp. This geometry

largely resembles the one used in the Albano et al. study but with slightly lower fin heights. The main

properties are presented in Table 2.

0

20000

40000

60000

80000

100000

120000

0 2 4 6 8 10 12

Hea

t fl

ux

[W/m

²]

Axial reactor coordinate [m]

4 Simulation of reactive flow One-dimensional simulations using COILSIM1D

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Table 2: Base tube geometry applied in the Millisecond furnace.

Coil length [mm] 10518

Number of fins [-] 8

Helix pitch [mm] 406

Outer diameter [mm] 48.3

Metal thickness [mm] 6.75

Fin height [mm] 4.8

Cross sectional area [mm²] 715.7

Equivalent circular inner diameter [mm] 30.2

Wetted perimeter [mm] 131.5

Other geometries were scaled to have the same cross-sectional area while the heat flux profile was

adjusted according to the outer diameter to maintain the same total heat input.

4.3 One-dimensional simulations using COILSIM1D

4.3.1 Introduction

COILSIM1D is developed at the Laboratory for Chemical Technology to simulate steam cracking of

hydrocarbons in a tubular reactor. The reaction network is a radical scheme consisting of both a

monomolecular µ network and a β network.

The model equations are based on a 1-dimensional plug flow reactor model, in which no radial gradients

are assumed, except for the temperature in a very thin film close to the wall in which all resistance to

heat transfer is located. The model equations contain the continuity equations for the different species,

an energy balance and a momentum equation. These equations are integrated along the reactor coil,

finally resulting in the species, pressure and temperature profiles.


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To allow for simulation of the run length of industrial steam cracking coils the fundamental simulation

model COILSIM1D incorporates two coking models. The coking model of Plehiers et al. (1992) is

developed for predicting coking rates for steam cracking of light hydrocarbon feedstocks. The model of

Reyniers et al. (1994) allows simulation of the coking rate for heavier feedstocks ranging from light

naphtha fractions to heavy condensates. Both coking models account for the free radical mechanism or

so-called asymptotic coking only. The contributions of the catalytic coking and droplets condensation/tar

deposition mechanism to the total amount of coke formed during the complete run length are assumed

to be negligible.

The program allows simulations to be set up in two ways. The user can either set a gas temperature,

heat flux or wall temperature profile along the length of the reactor or simply specify the coil outlet

conditions. The latter is much more attractive as for industrial applications the inlet pressure and

especially the heat flux profile is not easily accessible. These parameters can however be substituted by

more easily accessible process conditions. The inlet pressure condition can be replaced in a very

straightforward manner by setting the outlet pressure. The heat flux profile however is typically not

constant over the length of the reactor and needs careful consideration. Fortunately, the heat flux

profile has been studied extensively and as such the program includes several typical industrial profile

shapes and also allows the specification of a custom profile shape. In this work the profile shape as

shown in Figure 2 is used. The original two-point boundary value problem is now translated in a

boundary condition problem that can be solved using the iterative shooting method. This technique

reformulates the problem of the form of an initial value problem with initial conditions chosen to

approximate the boundary condition at the other endpoint:

( ( ))

( ) (1)

( )

In these equations s is the vector of parameters so that the solution to the initial value problem, ( ),

agrees with the solution of the original two-point boundary value problem. To determine the correct

initial values, the objective function F is considered:

( ) ( ) (2)


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, where are the desired boundary values at endpoint b. Typically the Newton-Raphson method is then

used to find the root for this problem. As this requires the evaluation of the unknown Jacobian matrix

( ), COILSIM1D uses Broyden’s method to approximate the inverse of the Jacobian. The method is

then applied iteratively until the allowed deviation from the target endpoint value is attained. A number

of parameters or severity indices can be used to define this boundary condition at the endpoint,

including the coil outlet temperature, the propylene/ethylene ratio, specific compound conversions and

yield maximization.

4.3.2 Friction factor and Nusselt number correlations

Although COILSIM1D contains a few correlations for finned tubes, these are typically for a specific type

and size of the fin and are not universally applicable. New correlations were derived from the data

obtained throughout the parametric study discussed in the previous chapter to allow COILSIM1D to

properly account for the influence of the different fin parameters. The program code was then modified

to include these correlations. For longitudinally finned coils the correlations are given by:

(

)

(

)

(3)

(

)

(

)

(4)

And for the helicoidally finned tubes:

( ) (

)

(

)

(5)

( ) (

)

(

)

(6)

In these equations, α is the helix angle, e represents for the fin height, D is the diameter of the tube

(measured from fin valley to fin valley) and w is the fin width, calculated as:


Confidential - 92 -

Although based on a relatively small amount of data, close approximation to the simulation data is

achieved. The relations between the simulated and correlated values for the Fanning friction factor and

Nusselt number of both types of finned coils are shown in Figure 3 and Figure 4.

Figure 3: Relation between simulated and correlated values for the Fanning friction factor and the Nusselt number for longitudinally finned coils.

Figure 4: Relation between simulated and correlated values for the Fanning friction factor and the Nusselt number for helicoidally finned coils.

For the bare tube friction factor, correlation (5) is encoded in the program while the Nusselt number is

calculated from the Dittus-Boelter correlation (7):

(

( )

)

(7)

(8)

R² = 0.9628

0.003

0.0035

0.004

0.0045

0.003 0.0035 0.004 0.0045

Ff, c

orr

[-]

Ff, sim [-]

R² = 0.9982

0

50

100

150

200

250

0 50 100 150 200 250

Nu

, co

rr [

-]

Nu, sim [-]

R² = 0.8842

0.003

0.004

0.005

0.006

0.007

0.008

0.003 0.005 0.007 0.009

Ff, c

orr

[-]

Ff, sim [-]

R² = 0.9708

0

50

100

150

200

250

300

0 100 200 300

Nu

, co

rr [

-]

Nu, sim [-]


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4.3.3 Methodology

The coking model was slightly rewritten as well to include the effects of the increased heat transfer

surface by the adoption of fins. Although typically the highest rate of coke formation would be in the fin

valley, it is impossible to take this into account in a 1D simulation. As such, it was elected to keep the

(e/D) and (e/w) parameters constant, indicating a slightly increased tendency of the coke to form inside

the fin valley while keeping the geometry shape constant for simplicity’s sake.

The boundary conditions were chosen equal to the ones applied in the three-dimensional simulations. As

the heat flux is automatically scaled in the shooting method to reach the desired endpoint value, the

shape of the heat flux profile shown in Figure 2 was taken as a basis. Propane conversion was chosen as

severity index. From the work of G.J. Heynderickx, it was seen that this type of reactors typically achieves

conversions of around 83% [3]. It is important to note however that this value is measured not at the

outlet of the reactor but rather at the end of the transfer line heat exchanger in which a non-negligible

amount of reaction still occurs. Heynderickx acknowledges this fact and calculated the conversion at the

outlet of the reactor to be 77.75% [3]. As only the reactor section was simulated using the COILSIM1D

program, this value was chosen as target severity. The outlet pressure was set to 1.7bara, which is a

typical value for industrial crackers.

4.3.4 Results

The start-of-run (SOR) yields for each of the tubes are shown in Table 3.

Table 3: Simulated process parameters and product yields at SOR for various reactor geometries.

Compound Bare FAO Straight FAO Helix Small Fins

Inlet pressure [bara] 2.26 2.38 2.56 2.65

Outlet temperature [K] 1171.4 1170.6 1169.6 1169.1

Yields [wt%] Hydrogen 1.50 1.49 1.47 1.47

Methane 16.88 16.97 17.08 17.13

Ethyne 0.35 0.34 0.33 0.33

Ethylene 31.17 31.08 30.94 30.87

Ethane 2.73 2.73 2.75 2.76

Propyne 0.78 0.77 0.75 0.75

Propadiene 0.18 0.18 0.18 0.17

Propylene 20.10 20.08 20.09 20.10

Propane 22.25 22.25 22.25 22.25

1,3-Butadiene 0.91 0.92 0.93 0.94


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1-Butene 0.60 0.60 0.60 0.60

2-Butene 0.20 0.20 0.21 0.21

iso-Butene 0.14 0.14 0.14 0.14

1,3-Pentadiene 0.15 0.15 0.16 0.16

1,4-Pentadiene 0.10 0.10 0.10 0.10

1,3-Cyclopentadiene 1.02 1.02 1.02 1.02

methyl-1,3-Cyclopentadiene 0.10 0.10 0.11 0.11

Benzene 0.40 0.42 0.44 0.45

Toluene 0.10 0.10 0.11 0.11

The selectivity towards ethylene is lower, confirming the general trends described in the literature. This

amounts to a considerable 1% lower ethylene yield when comparing a bare tube with the tube with

small fins and short pitch length. Higher mass fractions of the heavier components are obtained as the

increased pressure drop leads to higher hydrocarbon partial pressures, promoting bimolecular reactions.

Also the yield of components typically formed through recombination reactions such as methane and

ethane increases with increased pressure drop.

After 9 days however a considerable layer of coke was deposited, leading to slightly altered product

yields. These are shown in Table 4.

Table 4: Simulated product yields [%w] after 9 days for various reactor geometries.

Compound Bare FAO Straight FAO Helix Small Fins

Inlet pressure [bara] 3.44 3.05 3.13 3.23

Outlet temperature [K] 1190.3 1185.0 1180.3 1178.8

Yields [wt%]

Hydrogen 1.46 1.45 1.44 1.43

Methane 17.02 17.13 17.24 17.29

Ethyne 0.37 0.35 0.33 0.32

Ethylene 30.74 30.63 30.52 30.44

Ethane 2.92 2.91 2.91 2.92

Propyne 0.78 0.76 0.74 0.73

Propadiene 0.19 0.18 0.18 0.17

Propylene 20.21 20.20 20.17 20.19

Propane 22.25 22.25 22.25 22.25

1,3-Butadiene 0.94 0.96 0.97 0.98

1-Butene 0.63 0.63 0.63 0.63

2-Butene 0.21 0.21 0.21 0.21

iso-Butene 0.14 0.15 0.14 0.15

1,3-Pentadiene 0.16 0.16 0.17 0.17

1,4-Pentadiene 0.10 0.10 0.11 0.11

1,3-Cyclopentadiene 0.96 0.97 0.98 0.98


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methyl-1,3-Cyclopentadiene 0.10 0.10 0.11 0.11

Benzene 0.38 0.41 0.44 0.45

Toluene 0.09 0.09 0.10 0.10

It is clear that the coke layer leads to reduced ethylene selectivity. While this is the case for all the coils,

this drop appears to be more severe for the bare and longitudinally finned tubes. The evolution of the

ethylene selectivity is shown in Figure 5.

Figure 5: Evolution of ethylene yield in function of the run time.

The reason for this drop in ethylene selectivity is made clear by plotting the coil inlet pressure (CIP) as a

function of run time, as presented in Figure 6.

30.3

30.4

30.5

30.6

30.7

30.8

30.9

31

31.1

31.2

0 2 4 6 8 10 12

Eth

ylen

e y

ield

[%

w]

Run time [days]

FAO Helix

FAO Straight

Small Fins

Bare


Confidential - 96 -

Figure 6: Evolution of the coil inlet pressure in function of the run time for a COP of 1.7bara.

As the inlet pressure becomes higher, the hydrocarbon partial pressure will rise as well, leading to

increased occurrence of the recombination reactions and as such lower ethylene yields. It can be seen

that the coil inlet pressure for the bare coil even becomes higher than that of a finned tube after a

certain run time. This can be explained upon consideration of the maximal thickness of the coke layer as

a function of run time, shown in Figure 7.

Figure 7: Evolution of the coke layer thickness as function of the run time.

1.7

2.2

2.7

3.2

3.7

4.2

0 2 4 6 8 10 12

Co

il in

let

pre

ssu

re [

bar

a]

Run time [days]

FAO Helix

FAO Straight

Small Fins

Bare

0

1

2

3

4

5

0 2 4 6 8 10 12

Max

co

ke la

yer

thic

kne

ss [

mm

]

Run time [days]

FAO Helix

FAO Straight

Small Fins

Bare


Confidential - 97 -

It is clear that the coke layer grows considerably faster for the bare tube. This can be seen from the

coking rate on Figure 8 as well.

Figure 8: Total coking rate across the length of the reactor at SOR conditions.

On this figure, the coking rate is already multiplied by the wetted perimeter to plot the total rate of coke

formation at a certain axial distance and to provide a more realistic comparison between the tubes.

From all the figures considered so far, it is clear that the helicoidally finned tube with the smaller fin

height and short pitch length has considerably improved coking characteristics. Although the ethylene

yield loss is non-negligible at the start of the run, it is likely that the increased run length can make up for

that. Figure 9 shows the evolution of the maximum tube metal temperature which is typically a crucial

factor in deciding when to decoke a coil.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8 10 12

Co

kin

g ra

te [

g/m

/h]

Axial distance [m]

FAO Helix

FAO Straight

Small Fins

Bare


Confidential - 98 -

Figure 9: Evolution of the maximal tube metal temperature as a function of the run time for different

geometries.

4.3.5 Additional considerations

In the current simulations the assumption was made that the shape of the tube would remain

maintained. A more realistic assumption however would be that the fin valleys have a higher coking rate

due to the higher metal temperatures and the increased concentration of reactive species. Because of

this, the enhanced heat transfer surface will shrink faster than presently simulated and the positive

effects on the flow mixing properties will not be maintained either.

In order to get a quantitative result, it was assumed that all of the formed coke of Figure 7 was formed

inside the fins, and as such the helicoidally finned coil with the small fins would show similar coking rates

as a bare coil after around 5 days. Following this reasoning, the longitudinally and helicoidally finned FAO

coils would do the same after a run length of respectively 14 and 18 days. In light of the linear profile of

the maximal tube metal temperatures as seen in Figure 9, the finned coils would have an equal TMT

slope after those initial days. Assuming a linear change while the coke inside the fins is still building up,

the following TMT profiles are obtained:

y = 4.0162x + 968.76 y = 5.2792x + 989.53

y = 3.4788x + 962.45

y = 5.3634x + 1023.2

940

960

980

1000

1020

1040

1060

1080

1100

0 5 10 15

Max

TM

T [°

C]

Run time [days] FAO Helix FAO Straight Small Fins Bare

4 Simulation of reactive flow Three-dimensional FLUENT simulations

Confidential - 99 -

Figure 10: Evolution of the maximal TMTs with realistic coking assumptions.

Although these assumptions are very strict by ignoring beneficial geometry effects beyond the first few

days, it is clear that the run length improvement is considerable. Assuming a decoking length of around

12 hours, which is on the low side for a Millisecond furnace, a doubling of the run length by adopting the

‘Small Fins reactor’ would lead to 1.7% less time spent decoking. This leads to an overall increase in

ethylene production of 0.7% by applying these helicoidally finned tubes. Based on the profiles shown, it

can however be questioned whether the use of small fins is justified, given the fact that the positive

effects of the enhanced geometry might disappear quickly due to coking inside the fins. This requires a

further evaluation of the local coke formation rates and how these will influence the geometry shape

over time.

4.4 Three-dimensional FLUENT simulations

4.4.1 Reaction network

Given the high computational requirements for simulating reactive flow, a simplified molecular reaction

network was used in the three-dimensional simulations. The network was generated by K.M. Sundaram

and consists of the following 10 components and 9 reactions: [5]

C3H8 -> C2H4 + CH4

C3H8 <-> C3H6 + H2

940

960

980

1000

1020

1040

1060

1080

1100

1120

0 5 10 15 20 25 30

TMT

[°C

]

Run time [days]

FAO Helix

FAO Straight

Small Fins

Bare


Confidential - 100 -

C3H8 + C2H4 -> C2H6 + C3H6

2 C3H6 -> 3 C2H4

4 C3H6 -> C6 + 6 CH4

C3H6 <-> C2H2 + CH4

C3H6 + C2H6 -> C4H8-1 + CH4

C2H6 <-> C2H4 + H2

C2H4 + C2H2 -> C4H6

In this network C6 represents the C5+ fraction, mainly benzene in propane cracking. The hydrogen

content in the C6 compound is neglected. For propane cracking, the C5+ weight yield varies from 3 to 6%

depending mainly upon the cracking severity and steam dilution [5].

4.4.2 Tube geometries

The performed full reactor simulations made use of 4 distinct types of tubes. First, a bare non-finned

tube was simulated as a basis of comparison. Second, the industrially used helicoidally finned reactor

was simulated. To have a better understanding of the effects of the increased pressure drop and the

enhanced heat transfer induced by the helicoidal fins, a similar geometry but with straight fins was

studied thirdly. Finally an “optimal” tube was elected from the parametric study, which should offer even

better heating characteristics at a moderate increase of the pressure drop. The geometry specifications

can be found in Table 5.

Table 5: Reactor geometries studied using Ansys FLUENT.

Reactor ID Bare FAO Helix FAO Straight Small Fins

Coil length [mm] 10556 10556 10556 10500

Adiabatic inlet section [mm] 444 444 444 500

Number of fins [-] 8 8 8 24

Helix pitch [mm] -- 406 -- 150



Outer diameter [mm] 43.7 48.3 48.3 44.8

Metal thickness [mm] 6.75 6.75 6.75 6.75

Fin height [mm] -- 4.8 4.8 1.15

Cross sectional area [mm²] 715.7 715.7 715.7 715.7

Equivalent circular inner diameter [mm] 30.2 30.2 30.2 30.2

Wetted perimeter [mm] 94.8 131.5 131.5 114.9

4.4.3 Methodology

The tubes were meshed using the same meshing scheme as the one in the previous chapter which was

proven to be sufficient to simulate an accurate pressure drop and heat transfer. For the studied

geometries, this led to a mesh consisting of about 8 milllion cells.

The turbulence models were chosen in the same manner as in the previous chapter. The bare and

longitudinally finned tubes were simulated using the RNG kε-model while the helicoidally finned reactors

were simulated with the more computationally demanding Reynolds Stress Model. The QUICK scheme

was again chosen as discretization scheme for all of the performed simulations.

As the heat flux profile was taken from a full furnace simulation for a certain outer tube diameter, the

values were divided by the relative outer diameters to ensure the same amount total heat input was

transferred in each of the different cases.

The applied boundary conditions include those listed in Table 1, more specifically the inlet temperature

and mass flow and the outlet pressure.

4.4.4 Results

4 Simulation of reactive flow References


References

1. Aly, Sherif, Ethylene from naphtha by Millisecond SM cracking with front-end demethanization -

Aspen Model Documentation. 2000.

2. Scott, Tom, SCORE Features for Millisecond Furnaces: The Borealis Furnace Revamp Project,

in Furnace Technology Conference, KBR, Editor 2009: Dubai, U.A.E.

3. Heynderickx, Geraldine J., Modellering en Simulatie van Huidige en Nieuwe Technologieën voor

de Thermische Kraking van Koolwaterstoffen, in Laboratorium voor Petrochemische

Techniek1993, Universiteit Gent: Faculteit van de Toegepaste Wetenschappen.

4. Ramin Karimzadeh, Amin Hematian, Mohammad Reza Omidkhah, The Effect of Coil

Configuration on Run Length of Thermal Cracking Reactors. International Journal of Chemical

Reactor Engineering, 2007. 5(A118): p. 17.

5. Sundaram, K.M., Kinetic Modeling of Thermal Cracking as a basis for Reactor Simulation, in

Laboratorium voor Petrochemische Techniek1977, Universiteit Gent.

5 Conclusions and future work Conclusions


5 Conclusions and future work

5.1 Conclusions ................................................................................................................................ 103

5.2 Future work ................................................................................................................................ 105

5.1 Conclusions

In this study, the effects of both longitudinally and helicoidally finned tubes for steam cracking

applications was investigated.

In chapter two, a literature review was performed on a number of recent advances in three-dimensional

structures for enhanced mixing, as well as existent and commercially applied technologies.

Chapter 3 describes the non-reactive simulations performed in this work. First a grid independency study

was performed. It was seen that an axial and radial cell length of 2mm and 0.6mm respectively gave grid

independent results. A typical simulation setup contained about 800.000 cells per meter reactor.

Doubling the number of cells only resulted in a 1.5% accuracy improvement. The model was validated

against a limited amount of experimental data points retrieved from Albano et al. [1] General agreement

was seen to be satisfactory, with relative errors below 5% for the friction factors, while the Nusselt

number was simulated with respectively 23% and 3% relative error for the longitudinally and helicoidally

finned tubes. After model validation, a parametric study was elaborated where the effect of the

geometry parameters on pressure drop and heat transfer was analyzed. From this study it was made

clear that all of the longitudinally finned tubes follow a linear relationship between heat transfer

increase and heat transfer area. Neither fin height, nor amount of fins influenced this relationship as the

5 Conclusions and future work Conclusions


linear relationship is maintained up until a wetted perimeter ratio of 1.5-1.6, after which further surface

increase shows reduced benefits.

The helicoidal fins on the other hand were found to have optimal parameters, of which the fin height-to-

width ratio appears to be of primary importance. From the parametric study, it was shown that the

optimal value for this relationship lies around 0.35. Upon assessing the mixing properties of variable fin

heights for this value it was seen that a larger number of small fins induce even stronger swirl flow and

improved mixing inside the tube than the 8-10 tall fins typically used. At higher Reynolds numbers

however, this effect considerably weakens and flow coring can occur, as the fluid no longer follows the

small fins but bypasses them.

Shortening the pitch length and thus increasing the helix angle leads to a significant increase in wall

shear and as a result much higher heat transfer and pressure drop. Small fins provide great benefits at

these short pitch lengths while still only causing a moderate increase in pressure drop. Although the

additional pressure drop is significant, it appears that the optimal helix angle for the tall-finned tubes is

around 30° instead of the 16° angle of the geometry adopted by Albano et al.

From the findings of the parametrical study three new optimized geometries were assembled that each

showed significantly improved heating characteristics from the previously seen linear relationship for

longitudinally finned tubes. At moderate Reynolds numbers (i.e. below 90,000) a tube with short pitch

length and a large number of small fins (fin height-to-diameter ratio around 0.04) offered a 35%

increased heat transfer over a bare tube at the cost of a slightly less than doubled pressure drop. At

higher Reynolds numbers a tube with relatively tall fins (fin height-to-diameter ratio of 0.11)

outperformed the bare tube by 24% whilst increasing the pressure drop by a factor of 1.55. Comparing

these values with the industrially applied MERT and X-MERT technology which both provide a 40%

improvement of heat transfer while multiplying the pressure drop by respectively 3 and 2.1 [2, 3], it can

be concluded that the presently studied geometries show similar performance.

In chapter 4, correlations were derived from the data of the parametric study. These correlations were

added to the in-house developed COILSIM1D software which simulated an 11% decreased coking rate for

the tube with tall helicoidal fins and a decrease of over 28% for the tube with small fins and a short helix

pitch length. These 1D simulations obviously neglect the increased mixing and assume a radially uniform

coke deposition. Three-dimensional simulations however predict higher temperatures and hence higher

coke deposition in the fin valleys. Nevertheless, a considerably increased run length can be expected.

5 Conclusions and future work Future work


The cost of the additional pressure drop was calculated to be a maximal loss in ethylene selectivity of 1%

at start of run conditions. Assuming the fins retain their original shape however, the CIP of the bare tube

rises faster than that of the finned coils. Averaged over the entire run length, this may eventually even

lead to a selectivity gain for these reactors.

As the three-dimensional simulations using Fluent applied a heat flux profile to the outer wall, the main

difference between these simulations lies in the increased gas temperature and hence improved

conversion for the finned reactors. The achieved conversion increase compared to bare was between

XXX% and XXX%, with the higher value corresponding to the optimized helicoidally finned tube. Although

the reaction network was greatly simplified, the yields were close to the values obtained through 1D plug

flow simulations. An ethylene selectivity loss of XXX% was measured for the optimized reactor. Although

non-negligible, it can be assumed that the increased run length will make up for this.

5.2 Future work

Although the heat transfer improvements have been confirmed in the present work, it remains uncertain

how fin valleys will fill up with coke and how well the heat transfer and the improved flow pattern will be

preserved as a consequence of this. The use of dynamic meshing to model the influence of coke

formation on the fin structure would provide significantly more insights into the flow pattern changes

over time and is an area that requires further examination.

A significant problem in the evaluation of the present work was also the lack of experimental data for

this type of structures. If the change in product yields and TMT evolution over time were known from

e.g. pilot plant experiments, this could already provide a significant indication on the influence of the

cokes and how to best model this for future CFD simulations.

In order to obtain more accurate results for the CFD simulations, it would also be advised to incorporate

a radical reaction network instead of the presently applied molecular network. This however would

greatly increase the computational cost and, given the high reactivity of these species, significantly

decrease the stability of the calculations due to increase stiffness of the set of governing equations.

Furthermore it would be interesting to incorporate the oven and burners in the simulations, as it is not

unlikely that the shape of the reactor might influence the heat flux. Also it was previously noted that real

5 Conclusions and future work References


reactor tubes always have a significant temperature difference between their light and dark side due to

the burners at either side of the reactor.

Finally, in the present work only a Millisecond reactor was investigated. As these typically run at higher

Reynolds numbers while applying more intense heating, further studies are necessary to analyze the

influence of finned tubes for other industrial reactors. As it was seen that helicoidally finned tubes have a

lower Reynolds number dependency on the Nusselt number, it can be assumed that the relative

improvement might be greater for these reactors.

References



2. Torigoe, T., Mixing Element Radiant Tube (MERT) Improves Cracking Furnace Performance, K.

Corporation, Editor 2001.



Annex A – Performed Simulations Mesh Tests


A Performed Simulations

Mesh Tests

Full geometry

CFDfiles/djvcauwe/MasterThesis/MeshTests/Full/R70

CFDfiles/djvcauwe/MasterThesis/MeshTests/Full/R90

Boundary Layer tests

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/BL1

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/BL1_RSM



CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/BL3_RSM




CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/FC1

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/FC4

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/F1




CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/FF1

Annex A – Performed Simulations Full Albano Setup


CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/FF3

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/FFC4

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/FFC4_RSM

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/FFF4

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/1C1

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/1BL1

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/1F1

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/1F1_RSM

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/1FF1

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/1FFF1

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/Rot_test

CFDfiles/djvcauwe/MasterThesis/MeshTests/BL/Rot_test_RSM

Single Fin Tests

CFDfiles/djvcauwe/MasterThesis/MeshTests/SF/Q_Albano_N2_RSM

CFDfiles/djvcauwe/MasterThesis/MeshTests/SF/Q_Albano_N3_RSM

CFDfiles/djvcauwe/MasterThesis/MeshTests/SF/Q_Albano_N_RSM

CFDfiles/djvcauwe/MasterThesis/MeshTests/SF/Q_Albano_F_RSM

CFDfiles/djvcauwe/MasterThesis/MeshTests/SF/Q_Albano_FF_RSM

Full Albano Setup

CFDfiles/djvcauwe/MasterThesis/Albano_Full/Helix

CFDfiles/djvcauwe/MasterThesis/Albano_Full/Straight

Albano geometry – Friction factors

CFDfiles/djvcauwe/MasterThesis/Albano_Cold/Helix_R50

CFDfiles/djvcauwe/MasterThesis/Albano_Cold/Helix _R70




Annex A – Performed Simulations Albano geometry – Heated flow


CFDfiles/djvcauwe/MasterThesis/Albano_Cold/Straight_R50





Albano geometry – Heated flow

CFDfiles/djvcauwe/MasterThesis/Albano_Hot/Tests/Albano_S2

CFDfiles/djvcauwe/MasterThesis/Albano_Hot/Tests/Albano_S2

CFDfiles/djvcauwe/MasterThesis/Albano_Hot/Helix_R50





CFDfiles/djvcauwe/MasterThesis/Albano_Hot/Straight_R50





Bare tube

CFDfiles/djvcauwe/MasterThesis/Bare/R50





Parametric study – Fin Height

CFDfiles/djvcauwe/MasterThesis/Fin_Height/HF4


Annex A – Performed Simulations Parametric study – Pitch



CFDfiles/djvcauwe/MasterThesis/Fin_Height/HF0.5

CFDfiles/djvcauwe/MasterThesis/Fin_Height/HF1.5




CFDfiles/djvcauwe/MasterThesis/Fin_Height/HF6_R130

CFDfiles/djvcauwe/MasterThesis/Fin_Height/HF0.5_R130

CFDfiles/djvcauwe/MasterThesis/Fin_Height/HF1.5_R130




CFDfiles/djvcauwe/MasterThesis/Fin_Height/SF1




Parametric study – Pitch

CFDfiles/djvcauwe/MasterThesis/Pitch/HP1

CFDfiles/djvcauwe/MasterThesis/Pitch/HP1.5




CFDfiles/djvcauwe/MasterThesis/Pitch/HP1_R130

CFDfiles/djvcauwe/MasterThesis/Pitch/HP1.5_R130

CFDfiles/djvcauwe/MasterThesis/Pitch/HP2_R130

CFDfiles/djvcauwe/MasterThesis/Pitch/HF3P1



CFDfiles/djvcauwe/MasterThesis/Pitch/HF3P1_R130


Annex A – Performed Simulations Parametric study – Number of fins



Parametric study – Number of fins

CFDfiles/djvcauwe/MasterThesis/Num_Fin/H4Base




CFDfiles/djvcauwe/MasterThesis/Num_Fin/H4Base_R130




CFDfiles/djvcauwe/MasterThesis/Num_Fin/H12F3


CFDfiles/djvcauwe/MasterThesis/Num_Fin/H16F3n



CFDfiles/djvcauwe/MasterThesis/Num_Fin/H12F3_R130




CFDfiles/djvcauwe/MasterThesis/Num_Fin/S4Base




CFDfiles/djvcauwe/MasterThesis/Num_Fin/S12F3




Parametric study – Optimized geometries

CFDfiles/djvcauwe/MasterThesis/Optimized/H24F3P1

Annex A – Performed Simulations Reactive simulations


CFDfiles/djvcauwe/MasterThesis/Optimized/H24F3P1_R130





Reactive simulations

CFDfiles/djvcauwe/MasterThesis/Reactive/FAO

CFDfiles/djvcauwe/MasterThesis/Reactive/FAO_Straight

CFDfiles/djvcauwe/MasterThesis/Reactive/Bare

CFDfiles/djvcauwe/MasterThesis/Reactive/SmallFins

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