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SIMULATIONOF AREFRIGERANT EVAPORATOR

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J . S . van der Meer

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SIMULATIONOF AREFRIGERANT EVAPORATOR

J .S. van der Meer

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SIMULATIONOF AREFRIGERANT EVAPORATOR

Proefschriftter verkrijging van de graad van doctoraan de Technische Universiteit Delft,op gezag van de Rector Magnificus, prof.dr. J .M . Dirken,in het openbaar te verdedigen ten overstaan van een commissiedaartoe aangewezen door het College van Dekanenop 27 oktober 1987 te 14.00 uurdoorJ AKOB STEFANUS VAN DER MEER Prom i-.-pjcin1 ggeboren te Delft,Werktuigkundig Ingenieur

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Dit proefschrift is goedgekeurd door de promotorprof.ir. A.L. Stolk

dr.ir. S. Touberheeft als begeleider in hoge mate bijgedragenaan het totstandkomen van het proefschrift.Het College van Dekanen heeft hem als zodanig aangewezen.

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ContentsSamenvat t i ng iSummar y vConcl usi ons and r ecommendat i ons vi i iChapter 1 Introduction1. 1 Scope of t he i nvest i gat i on 11. 2 L i t er at ur e 21. 3 Concl us i ons f rom t he l i t erature 6Chapter 2 Modelling the evaporator2. 1 Evaporat or model l i ng 92. 2 Model equat i ons 10.2. 3 Si mpl i f yi ng t he model 112.1) Extendi ng t he model 132. 4. 1 The dynam c behavi our of t he evapor at i on r egi on 132. 4. 2 Tr ansport at i on t i mes i n t he evapor at i on r egi on 152. 4. 3 Ext endi ng t he model l i ng of t he boundary bet ween t heevapor at i on and t he superheat r egi on 162. 4. 4 Super heat r egi on, st eady si t uat i on 172. 4. 5 Super heat r egi on, dynam c si t uat i on 182. 5 Pressur e dr op 192. 5. 1 Pressure dr op evapor at i on r egi on 192. 5. 2 Pressur e dr op superheat r egi on 202. 6 Heat t r ansf er cor r el at i ons 212. 6. 1 Heat t r ansf er wat er si de 212. 6. 2 Heat t r ansf er super heat r egi on 212. 6. 3 Heat t r ansf er evapor at i on r egi on 212. 6. 4 Val i dat i on of t he heat t r ansf er cor r el at i on 232. 7 Model of t he suct i on pi pe 252. 8 L i qui d r ef r i ger ant i n t he suct i on pi pe 282. 8. 1 Fl ow pat t ern 282. 8. 2 The qual i t y of t he r ef r i ger ant l eavi ng t he evapor at or 292. 8. 3 The t emperat ur e behavi our of t he pi pe wal l atdi f f er ent super heat s 312. 8. 4 Li qui d r ef r i ger ant i n t he super heat ed vapour 31Chapter 3 Modelling the thermostaticexpansion valve3. 1 Why a t hermost at i c expansi on val ve 353. 2 Const r uct i on and act i on of a TEV 363. 3 Model l i ng t he TEV 373. 4 The equi l i br i um pr essur e of t he bul b cont ent s 373. 5 Di aphr agm and spri ngs 393. 6 The t hr ot t l e pr ocess 413. 6. 1 Thr ot t l i ng of a f l ow of boi l i ng or near l y boi l i ng l i qui d 41 3. 6. 2 I nf l uence of t he subcool i ng 423. 6. 3 Mass f l ow as a f unct i on of t he openi ng of t he val ve 423. 7 The t hr ot t l ed mass f l ow of r ef r i ger ant f or ot herexpansi on val ves 43

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3- 7. 1 Model l i ng t he t hr ot t l e pr ocess 433. 7. 2 Met hods used i n l i t er at ur e 443. 7. 3 Concl usi ons about t hr ot t l i ng 483. 8 St eady st at e char act er i st i cs of t he TEV 493. 9 Dynam c pr oper t i es of t he TEV 513. 9. 1 Dynam c behavi our of t he TEV wi t hout t he bul b 523. 9. 2 Dynam c behavi our of t he bul b 52Chapt er 4 Validation of the water chiller model4. 1 Exper i ment al set up 574. 2 Val i dat i on of t he wat er chi l l er model f or st eady st at econdi t i ons 604. 2. 1 Measur ement s st eady st at e condi t i ons 604. 2. 2 Concl usi ons st eady st at e. val i dat i on 624. 3 Val i dat i on of t he wat er chi l l er model f or dynam c condi t i ons 634. 3. 1 Measur ement s dynam c condi t i ons 634. 3. 2 Concl usi ons dynam c measur ement s 64Chapter 5 Modelling an evaporator withpar al l el refrigerant circuits5 .1 P a r a l l e l c i r c u i t s 675.2 Mathemat ica l model of an eva po rato r wi th two p a r a l le lg roups o f c i r c u i t s 695. 2. 1 Model assumpt i ons 695. 2. 2 Mathemat i cal equat i ons 675. 3 Di st r i but i ng t he mass f l ows of r ef r i ger ant 715. 3. 1 Model f or t he di st r i but i on of the r ef r i ger ant 725. 4 Pr essur e dr op 735. 4. 1 Cor r el at i ons f or t he pr essure dr op 735. 4. 2 Cor r el at i ons f or t he pr essur e dr op i n t he t wophase f l ow accor di ng t o Br auer 745. 4. 3 I nf l uence of t he evapor at i on on t he pr essur e dr op 755. 4. 4 I nf l uence of t he bends on t he pr essur e dr op 755. 4. 5 I nf l uence of t he hei ght s of t he ci rcui t s 765. 4. 6 I nf l uence of a change i n f l ow t hr ough ar ea 765. 4. 7 I nf l uence of t he val ves 775. 5 St eady st at e model f or t he di st r i but i on of the r ef r i ger ant 775. 5. 1 Model l i ng t he two ci r cui t wat er chi l l er t est standf or t he val i dat i on of the di st r i but i on model 775. 5. 2 I nf l uence of t he subcool i ng on t he r ef r i ger ant 795. 6 About usi ng Br auer s cor r el at i on 805. 7 Model l i ng t he di st r i but or i n t he dynam c evapor at or model 815. 8 Model l i ng t he ai r cool er 835. 8. 1 Conf i gur at i on of t he pi pes 835. 8. 2 The f i ns of t he ai r cool er 845. 8. 3 Heat t r ansf er ai r s i de 855. 8. 4 Heat l eakage t hr ough t he f i ns 855. 9 Cor r el at i ons r ef r i ger ant s i de 875.-9.1 Pr essur e dr op r ef r i ger ant si de 875. 9. 2 Heat t r ansf er evaporat i on r egi on 885. 10 I nf l uence of t he col l ector on t he r ef r i ger ant f l ow t ot he suct i on pi pe 895. 11 I nt er pr et at i on of measur emenst on t he di st r i but or

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of t he ai r cool er 915.11. 1 Di st r i but i on of the r ef r i ger ant i n t he ai r cool er 915. 11. 2 About t he posi t i on of t he di st r i but or 945. 11. 3 I nf l uence of t he di st r i but i on of t he r ef r i ger ant 955. 12 Measur ement s on t he di st r i but i on of t he ai r f l ow 965.12. 1 Di st r i but i on of the ai r f l ow 965. 12. 2 I nf l uence of t he di st r i but i on of t he ai r f l ow 975. 12. 3 Frost ed cool er 98Chapter 6 Validation of the air cooler model6. 1 Ai r cool er t est st and 1016. 2 St eady st at e val i dat i on of t he ai r cool er 1016. 2. 1 Measur ement s st eadyst at e condi t i ons 1016. 2. 2 Concl usi ons st eady st at e val i dat i on 1046. 3 Dynam c val i dat i on of t he ai r cool er 1046. 3. 1 Measur ement s dynam c condi t i ons 1046. 3. 2 Concl usi ons dynam c val i dat i on 108Chapter 7 Using the steady state implementation7. 1 St ar t pr ogr am 1097. 2 Separ at e st eady st at e syst em 1097- 3 Exampl es of usi ng t he st eady st at e pr ogr am 1107. 4 Si mul at i on r esul t s wi t h a TEV wi t h i nt egr at i ng act i on 1117. 5 Si mul at i on r esul t s wi t hout i nt egr at i ng act i on of t he TEV 1137. 6 About usi ng a const ant m ni mum l engt h of t he super heat

r egi on as opt i mal set poi nt t o cont r ol an expansi on val ve 1157. 7 I nf l uence of t he super heat on t he COP 1167. 8 Concl usi ons 118Chapter 8 Using the dynamic model

1 Li qui d sensi ng expansi on val ve 1191. 1 Wor ki ng of t he expansi on val ve 1191. 2 Li qui d sensi ng expansi on val ve 1201. 3 Si mul at i on LSEV and TEV 1211. 4 Concl usi ons r el at i nf t o t he LSEV 1212 Ti me const ant of t he bul b 121Chapter 9 Conclusions

9. 1 Model l i ng 1279. 1. 1 About t he model of t he TEV 1289. 1. 2 About t he di st r i but i on of t he r ef r i ger ant 1299. 1. 3 About t he t r ansf er r ed heat 1309. 2 I nf l uences on t he st abi l i t y 1319. 3 Abi l i t y and usef ul ness of t he model 1339. 4 Cont r ol of t he super heat 134Appendix Compressor and condenserA. 1 Model l i ng of ot her component s of t he cycl e 135A. 2 Compr essor model 135A. 2. 1 Open compr essor 135

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A .2 .2 H e r m e t i c c o m p r e s so r s 137A.3 Co nden ser model 138A . 3 . 1 H ea t t r a n s f e r a r e a s 139A .3 .2 D yn am ic e q u a t i o n s o f t h e c o n d e n se r 140A .4 I m p l em e n t e d v e r s i o n s o f t h e e v a p o r a t o r m o d e l 142Nomenclature 143L i t e r a t u r e 14 5C u rr i cu l u m v i t a e 152

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Samenvat t i ngDoel en onder wer p van het onder zoek.Het voornaamst e doel van het ver r i cht e onder zoek i s geweest het ver kri j genvan een hul pm ddel dat bi j het ont werpen en het opt i mal i zer en van eencompressi e- koel machi ne gebr ui kt kan wor den, speci aal met het oog op hetdynam sche gedr ag. Di t hul pm ddel i s een comput ermodel gewor den.Gekozen i s voor de ont wi kkel i ng van mat hemat i sche model l en van component envan koel syst emen, di e geschi kt zi j n om met behul p van de comput er hetver l oop van de r el evant e pr ocesvar i abel en i n het t i j dsdomei n t e voors pel l en.Omdat sl echt s een ger i nge hoeveel hei d i nf or mat i e ui t de l i t er at uur di r ectt oe t e passen was en ook ui t gebr ei d exper i ment eel onderzoek noodzakel i j k wasom bet r ouwbare model l en t e ver kr i j gen, i s de st udi e beper kt t ot de vol gendebasi scomponent en van een compressi e- koel machi ne of - war m epomp:- een zui ger compr essor ,- een hori zont al e shel l - and- t ube wat er gekoel de condensor ,- een smoor or gaan,- een dr oge ver damper met di r ect e i nspui t i ng.De meest e aandacht werd hi er bi j geschonken aan de verdamper of wel de koel er ,met de bi j behor ende r egel kr i ng voor de voedi ng. Veel pr obl emen metbet r ekki ng t ot de dynam ca bl i j ken namel i j k hi er ui t voor t t e v l oei en,t er wi j l het pr eci eze mechani sme van de i nst abi l i t ei t van deze r egel kri ng totnog t oe onbekend was. Daar om i s er met een l i t er at uur st udi e gepoogd een zocompl eet mogel i j k over zi cht t e ver kr i j gen van de el ement ai r e ei genschappenvan de verdamper en het smoor or gaan, zodat di t i n model l en verwer kt konwor den. Aanvul l end waren hi erbi j ui t gebrei de met i ngen aan deze component envan de cycl us noodzakel i j k.De hi erui t r esul t er ende eer st e ver si es van de model l en wer den ver bet er d enver f i j nd naar aanl ei di ng van exper i ment en aan t wee speci f i eke t echni scheui t voeri ngen: een 2 kW wat er koel er en een 10 kW l ucht koel er , bei de metgebr ui k van R- 12 al s koudem ddel , en met een t her most at i sch expansi e vent i el( TEV) al s smoor orgaan.Bi j het model l er en van de, pi j pvor m ge, ver damper i s speci al e aandachtgeschonken aan de mogel i j khei d van de aanwezi ghei d van onverdampt vl oei baarkoudem ddel i n de over ver hi t t e damp aan de ui t l aat van de ver damper , en hetst or ende ef f ect hi er van op de st abi l i t ei t van de r egel kr i ng. Met bet r ekki ngt ot di t ver schi j nsel i s ook een ver damper model ont wi kkel d met par al l el l ekoudem ddel ci r cui t s, di e zi ch onder l i ng ver schi l l end kunnen gedr agen. Det est opst el l i ng van de wat er koel er i s met het oog hi er op aangepast , engebr ui kt voor best uder i ng van het mechani sme van de ver del i ng van hetkoudem ddel over deze par al l el l e ver damper ci r cui t s. De l ucht koel er was,zoal s gebr ui kel i j k, ui t paral l el e c i r cui t s opgebouwd.Model vor m ng.Behal ve een dynam sche ver si e van de model l en van de t e si mul eren pr ocessenwer d er ook een st at i sche ver si e ont wi kkel d. Hi er mee was het mogel i j kst at i sche st ar t waarden t e ber ekenen voor de pr ocesvar i abel en, al sui t gangspunt voor dynam sche si mul at i e. Aanvankel i j k wer d zo' n st ar t modelni et nodi g geacht omdat ook met r am ngen kon wor den gewer kt . Onder gegevenst at i onai r e condi t i es moet i mmer s de dynam sche si mul at i e i n de st at i schecondi t i es ui t monden. Een af zonder l i j k st at i sch model bl eek echt er bi j zondernut t i g om r ekent i j d bi j dynam sche si mul at i es t e besparen. Bovendi en kan hetzel f st andi g gebr ui kt worden al s hul pm ddel bi j het ont wer pen vankoel sys t emen.

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i iUi t de i n de l i t er at uur gevonden ver damper model l en di e op l i neai r er egel t heor i e ber ust en, kan geconcl udeer d wor den dat l i neai r e model l enaant r ekkel i j k zi j n door de mogel i j khei d, i n het f r equent i edomei n, een goedover zi cht t e ver kr i j gen van het dynam sche gedr ag van het t e onder zoeken,gel i near i seer de, syst eem Deze met hode i s echt er m nder aant r ekkel i j k bi jeen appar aat al s de gekozen dr oge ver damper , waar bi j het nog ni et bekend i swel ke van de, meest al ni et l i neai r e, ei genschappen wer kel i j k van bel angz i j n . Daar om i s de nadr uk gel egd op het ont wi kkel en van st r uct uur model l enwaar i n, i n het t i j dsdomei n, de noodzakel i j ke ni et - l i neai r e ei genschappenvoor de si mul at i e van het dynam sche gedr ag opgenomen kunnen wor den.De voornaamst e model ver onder st el l i ngen zi j n:- Het model voor de t oest and van het koudem ddel i n de ver damper i sgespl i t st i n deel syst emen: - de damp en de vl oei st of i n hetver dampi ngsgebi ed en - de damp i n het overver hi t i ngs- gebi ed. Voor desi mul at i e van de commerci l e l ucht koel er ( Hel pman LEX- 18) , waar i n hetover ver hi t t i ngsgebi ed ui t t wee rui m el i j k geschei den del en kan best aan, wer ddeze mogel i j khei d t ot spl i t sen ook i n het model doorgevoer d. Af hankel i j k vande hoeveel hei d vl oei baar koudem ddel i n het ver damper model kan de gr enst ussen ver dampi ngsgebi ed en oververhi t t i ngsgebi ed var i r en, zodat devol um na ( en dus de pi j pl engt en) van bei de gebi eden var i abel zi j n. Di t i sweer van i nvl oed op de groot t e van de war m eoverdragende opper vl akken en dedr ukval .De toest and van het koudem ddel wor dt wel i swaar voor de ener gi e- en voor demassabal ans ai s homogeen beschouwd, maar een aant al ef f ect en di e ni et i n eenhomogeen model weer t e geven zi j n, worden daar naast i n r ekeni ng gebr acht . Debel angr i j kst e z i j n: - de dr ukval i n bei de del en, - de temper at uur gr adi nt i nhet over ver hi t t i ngsgebi ed, i .v.m de war m eover dr acht , - de aanwezi ghei d vanonver dampt koudem ddel i n het overver hi t t i ngsdeel .De met al en const r uct i e i s anal oog met het koudem ddel i n, t wee of dr i e,del en van var i abel e l engt e gespl i t st . Daar naast i s er nog een dynam schmodel van de zui gl ei di ng waar op de sensor van het TEV i s bevest i gd.- Een rel at i ef eenvoudi g mechani sme, dat voor namel i j k op empi r i e ber ust ,dr aagt zor g voor het ver r ekenen van de i nvl oed van de l oopt i j den i n hetver dampi ngsgebi ed i n het model . Pl aat saf hankel i j ke beschr i j vi ng van de hi eropt r edende processen zou kenni s ei sen van de t weef asen- st r om ng, i n hetbi j zonder van de l ocal e voi d- f r act i on of van de l ocal e sl i pf act or . Hetgecompl i ceer de kar akt er van deze st r om ng, speci aal gedur ende de ni et -st at i onai r e condi t i es, ver hi nder t de ber ekeni ng van een meer gedet ai l l eer det heor et i sche beschri j vi ng van het ver dampi ngsgebi ed.Daar naast di enen, i n zowel de st at i sche al s de dynam sche ver si e, decor r el at i es voor dr ukval en warm eover dr acht gecorr i geer d t e worden voor despeci f i eke conf i gur at i e van de gesi mul eerde ver damper s, omdat de i n del i t er at uur beschi kbare cor r el at i es ont wi kkel d zi j n aan de hand van met i ngenaan speci f i eke, r echt e pi j pen. Met i ngen z i j n daar om noodzakel i j k, ni etal l een wanneer het verdampi ngsgebi ed al s een bl ok i s gemodel l eer d maar ookwanneer het , ondanks het hi er boven genoemde bezwaar van de onbekendhei d metde st r om ngspat r onen, i n meer del en opgedeel d zou zi j n.- Voor het over ver hi t t i ngsgebi ed i s de massabal ans van het koudem ddelbeschouwd al s quasi st at i sch wegens de ger i nge mass a van de damp.De ener gi ebal ans houdt r ekeni ng met pl aat s- af f i ankel i j ke condi t i es en wor dthi er voor gest el d door de anal yt i sche opl ossi ng van de par t i l edi f f er ent i aal ver gel i j ki ng di e di t gebi ed beschr i j f t voor st at i schecondi t i es. Voor de dynam sche ef f ect en i s aan deze opl ossi ng een cor r ect i et oegevoegd. Deze cor r ect i e i s , voor al l e i nvl oeds- gr oot heden, ui t gevoer d

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i i ivol gens de dynam sche anal yti sche opl ossi ng van de ver gel i j ki ng voor hetgeval dat de ver dampi ngst emper at uur de i nvl oedsgroot hei d zou zi j n.- De bi j het onder zoek gebr ui kt e smoor or ganen war en t her most at i scheexpansi event i el en (TEV), het geen de gebr ui kel i j ke keuze i s i n combi nat i e meteen dr oge ver damper . De model l er i ng van een smoor or gaan van di t t ype ver ei stspeci f i eke empi r i sche gegevens, di e ni et ver kr egen kunnen wor den ui tcat al ogi van commerci eel beschi kbare component en. Daar om waren ui t gebr ei demet i ngen van het vent i el hui s, de t emperat uur voel er en het smoor pr ocesnoodzakel i j k, om gegevens t e ver kri j gen voor ver schei dene wer kgebi eden. Hetdynam sche gedr ag van het TEV, dat al l een van de t emperat uur sensoraf hankel i j k i s , bl eek beschr even t e kunnen wor den met een eer st e-ordesysteemHet model kan aangepast worden voor het gebrui k van ander e t ypen sensor en.Zo i s i n deze st udi e het model van een " i deal e" sensor bepr oef d, di e ni etgebaseer d i s op de over ver hi t t i ng van de damp, maar op de kwal i t ei t er van( het massa aandeel vl oei st of i n de koudem ddel st r oom . Aanget oond i s dat dei nst el l i ng van het smoor or gaan dan geen cor r ect i es nodi g heef t bi jver ander i ng van het wer kgebi ed, zoal s bi j een TEV wel het geval i s.Een der gel i j ke sensor i s echt er nog ni et beschi kbaar .- De compr essor kon beschr even worden al s quasi - st at i sch omdat de snel hei dwaar mee de processen hi er gepaard gaan, van een hoger e or de van gr oot t e i sdan di e bi j de over i ge pr ocessen van een koel cycl us.Om bi j de val i dat i emet i ngen aan de ver damper de i nvl oeden van bui t enaf t ever m nder en, wer d de ver damper t en opzi cht e van zul ke i nvl oeden zoveelmogel i j k af gescher md. Zo waren de ei genschappen van de compressor ni et vanbel ang vanwege een t ussen de compr essor en de ver damper gepl aat st er est r i ct i e, waar i n het koudem ddel met super kri t i sche snel hei d st r oomde. Depr ocescondi t i es na deze r est r i ct i e hadden daar om geen i nvl oed op de gr oot t evan de massast r oom koudem ddel di e de ver damper ver l i et .- Om de ver damper ook aan de i nt r ede van zi j n omgevi ng af t e scher men, wer dde condensor gedur ende de val i dat i emet i ngen van de ver damper op const ant edr uk ger egel d, t er wi j l de onder koel i ng met een apar t e warm e- wi ssel aar wer dger egel d. De condensor kon daar door aanvankel i j k op eenvoudi ge wi j zebeschr even wor den, namel i j k door het TEV van een koudem ddel st r oom bi jconst ant e pr ocescondi t i es t e voor zi en.Bi j de l at er e model l er i ng van de condensor zi j n, evenal s bi j di e van dever damper , de massa' s i n t wee gebi eden gespl i t st .- De val i dat i emet i ngen wer den aan een ni et ber i j pende l ucht koel er ver r i cht ,om de gecompl i ceer de pr ocessen bi j zul k een ber i j pi ng bui t en beschouwi ng t ekunnen l at en. Om de ber i j pi ng t e voor komen wer d met een t weede l ucht koel erde l ucht i n de koel r ui m e gedr oogd.- De ei genschappen van het koudem ddel ( R- 12) z i j n, vanwege de rekent i j d bi jeen dynam sche s i mul at i e, beschr even i n het wer kgebi ed met behul p vanpol ynomen vol gens get abel l eer de waarden ui t de l i t er at uur ( [ A2] en [V1] ) ,i n pl aat s van gebr ui k t e maken van st andaar d pakket t en van st of gegevens.

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V

Summar yPur pose and scope of t he i nvest i gat i on.The mai n pur pose of t he i nvest i gat i on was t o obt ai n a t ool f or t he desi gnand t he opt i m zat i on of t he compr essor r ef r i ger at i on cycl e, especi al l y wi t hr espect t o t he dynam c behavi our . Thi s t ool has become a comput er model .The way chosen has been t he devel opment of mat hemat i cal model s of t hecomponent s of a ref r i ger at i ng syst em sui t abl e t o pr edi ct wi t h t he comput ert he behavi our of t he r el evant pr ocess var i abl es i n t he t i me domai n.As onl y l i t t l e mat er i al coul d be ext r acted di r ect l y f r om the l i t er at ur e andext ensi ve exper i ment al val i dat i on was envi saged t o pr oduce r el i abl e model s,t hi s st udy was l i m t ed t o t he f ol l owi ng basi c component s of a compr essi onr ef r i ger at or or heat pump:- a r eci pr ocat i ng compr essor ,- a hor i zont al shel l and t ube wat er cool ed condenser,- an expansi on val ve, and- a di r ect f eed dr y evapor at or .Most at t ent i on was pai d t o the dry evapor at or , or t he cool er , and i t s l i qui df eed cont r ol l oop. Many pr obl ems concer ni ng t he dynam c behavi our areor i gi nat ed her e whi l e t he exact mechani sm of f or i nst ance t he i nst abi l i t y oft hi s cont r ol l oop was st i l l unknown. Consequent l y, compl et eness was ai med ati n t he st udy of the l i t er at ur e i n order t o f i nd basi c dat a f or t heconst r uct i on of t he evaporat or and expansi on val ve model s. Al so t he ownmeasur ement s on speci mens t o obt ai n t he necess ar y empi r i cal i nf ormat i on hadt o be ext ensi ve.The r esul t i ng f i r st ver si ons of t he model s have been i mpr oved and ref i nedwi t h t he ai d of exper i ment s on t wo speci f i c cases: a 2 kW wat er chi l l er anda 10 kW ai r cool er , bot h usi ng R- 12 as r ef r i ger ant , and wi t h a ther most at i cexpansi on val ve ( TEV) as expansi on devi ce.W t h t he model l i ng of t he, t ubul ar , evapor at or speci al at t ent i on has beenpai d t o t he poss i bi l i t y of the presence of l i qui d ref r i ger ant i n t hesuper heat ed vapour at t he out l et of t he evapor at or , and t o t he possi bl enegat i ve ef f ect of t hi s on the s tabi l i t y of t he cont r ol l oop. W t h respectt o t hi s phenomenon an evapor at or model wi t h par al l el r ef r i ger ant ci r cui t shas been devel oped al so. The wat er chi l l er t est st and has, or i gi nal l y wi t h asi ngl e r ef r i ger ant c i r cui t , has been r e- ar r anged t o st udy t he pr ocesses oft he di s t r i but i on of t he r ef r i ger ant . The ai r cool er was , as usual ,const r uct ed wi t h para l l el c i r cui t s .Descr i pt i on of t he model :I n addi t i on t o t he dynam c ver si on of t he model s of t he pr ocesses t o besi mul at ed, a st eady st at e ver si on has been devel oped. W t h t hi s ver si on i ti s possi bl e t o cal cul at e val ues of t he pr ocess var i abl es i n st eadycondi t i ons, t o use f or t he star t of a dynam c s i mul at i on. F i r st such a star tpr ogr am was not t hought t o be necessar y because s t ar t i ng a dynam csi mul at i on wi t h est i mat ed val ues woul d resul t i n st eady condi t i ons t oo. Asepar at e pr ogr am however pr oved t o be usef ul t o save cal cul at i on t i me f ordynam c si mul at i ons. Mor eover i t can be used separ at el y as a usef ul t ool i ndesi gn pr act i ce.Fr om t he l i t er at ur e r el at i ng t o evapor at or model s based on l i near cont r olt heor y, i t coul d be concl uded t hat t he l i near appr oach i s at t r act i ve by i t spossi bi l i t y, usi ng t he f r equency domai n, t o obt ai n a good i nsi ght i n t hedynam c pr oper t i es of a l i near i zed system Thi s met hod however i s l essat t r act i ve i n the case of t he chosen dry evaporat or , i n whi ch case i t was

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viunknown whi ch of t he, most l y non l i near char act er i st i cs, were r eal l y ofi nf l uence. Ther ef or e t he st r ess was l ai d on bui l di ng st r uct ur e based model swhi ch non- l i near phenomena t ake pl ace. I t was a pr i or i unknown whi ch oft hese phenomena had t o be t aken i nt o account . Theref or e i t was deci ded t omake use of st r uct ur e based model s whi ch coul d cont ai n t he i nevi t abl y nonl i near equat i ons f or t he si mul at i on of t he dynam c behavi our of speci f i cequi pment i n t he t i me domai n.The most i mpor t ant model assumpt i ons ar e:- The model descr i bi ng t he r ef r i gerant i n t he evapor ator model has beenspl i t up i n l umps: t he evapor at i on r egi on and t he super heat r egi on. For t hesi mul at i on of t he commerci al ai r cool er ( a Hel pman LEX- 18) , wher e t hesuper heat r egi on coul d consi st of t wo separ at ed par t s due t o t he speci alconst r uct i on, t he possi bi l i t y of an extr a super heat r egi on has beenmodel l ed. Accor di ng t o the amount of l i qui d mass i n t he evapor at or , t heboundar y of t hese r egi ons coul d var y cont i nuousl y and so coul d t he vol umesand t he pi pe l engt hes of t hese regi ons. Thi s i nf l uences t he si ze of t he heatt r ansf er areas and t he pr essure dr op.The r ef r i ger ant has been assumed homogeneous f or t he ener gy and t he massbal ance, but some ef f ect s whi ch cannot be descr i bed wi t h a homogeneous modelar e descri bed separ at el y: - t he pr essur e dr op i n bot h par t s, - t het emper at ur e gr adi ent i n the super heat r egi on, because of t he heat t r ansf er,and - t he pr esence of unevapor at ed r ef r i gerant i n the superheat ar ea.The met al const r uct i on was spl i t up i n l umps l i ke the r ef r i ger ant r egi ons i nt wo or t hr ee par t s. Al so t he suct i on pi pe on whi ch t he sensor of t he TEV hasbeen c l amped, has been model l ed dynam cal l y.- A r at her si mpl e mechani sm mai nl y based upon empi r i cs, corr ect s t he modelf or t he i nf l uence of t he tr anspor t at i on t i mes i n the evapor at i on regi on. Apl ace dependent descri pt i on of t he l ocal pr ocesses woul d requi r e knowl edgeof t he t wo phase f l ow, speci al l y of t he l ocal voi d f r act i on or of t he l ocalsl i p f act or . The compl ex char act er of t hese pr ocesses, especi al l y dur i ngnon st eady condi t i ons, pr event s a mor e det ai l ed t heor et i cal descr i pt i on oft he evapor at i on r egi on.Besi des, t he i nf l uence of t he pressur e drop and t he heat t r ansf er have t o becal cul at ed accor di ng t o cor r el at i ons whi ch ar e cor r ect ed f or t he evapor at orconf i gur at i on t o be descr i bed, i n bot h t he st eady and t he dynam ci mpl ement at i on. Thi s i s necessar y because t he cor r el at i ons i n l i t er at ur ear e based upon measur ement s on speci f i c, st r ai ght t ubes. Measur ement s wi l lbe necessar y, not onl y i n t he case t hat t he evapor at i on r egi on has beenmodel l ed as one l ump, but even wi t h a det ai l ed l ocal descr i pt i on.- The mass bal ance of t he r ef r i gerant i n t he super heat r egi on has beenr egar ded as quasi st at i c, because of t he smal l mass of t he vapour .The ener gy bal ance her e account s f or a di st r i but ed model and i s r epr esent edby t he steady st at e sol ut i on of t he par t i al di f f er ent i al equat i on whi chdescr i bes t hi s area f or t he st eady condi t i ons. A cor r ect i on f or t hedynam cal ef f ect s has been added t o t hi s sol ut i on, f or al l i nf l uenci ngpar amet er s, accor di ng t o t he anal yti cal dynam c sol ut i on f or t he case of t heevaporat i on t emper at ur e as i nput par amet er .- The expansi on devi ce model has been wor ked out f or t he usual t ype ofdevi ce i n combi nat i on wi t h a dr y evapor at or , t he t her most at i c expansi onval ve (TEV). The model l i ng of t hr ot t l e val ves of t hi s t ype r equi r es speci f i cempi r i cal dat a whi ch cannot be ext r act ed f r om cat al ogue pr esent at i ons ofcommer ci al l y avai l abl e val ves. Ther ef or e, ext ensi ve measur ement s of t hepr oper t i es of t he val ve body, t he t emperat ur e sensor bul b and t he t hr ot t l epr ocess wer e r equi r ed t o acqui r e dat a f or si mul at i on at di f f er ent oper at i ngranges. I t was f ound t hat t he dynam c behavi our of t he TEV, whi ch va3

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vi iconcent r at ed i n i t s f eel er bul b, coul d be r epr esent ed by a f i r st or dersystemThe model can be conver t ed t o make use of ot her sensor t ypes. I n t hi s st udyan " i deal " sensor , not based on vapour super heat , but on m xt ur e qual i t y( l i qui d/ t ot al mass f l ow r at i o) has been wor ked out . I t coul d be demonst r at edt hat such a devi ce does not r equi r e any pr e- adj ust ment as necessar y f or t heTEV. Such a devi ce i s not yet avai l abl e.- The compr essor coul d be descr i bed as quasi st at i c because of t he hi gherorder of speed of i t s pr ocesses compared wi t h t hose of t he ot her component sof t he r ef r i ger at i ng cyc l e.To m ni m ze t he i nf l uences f rom out si de dur i ng t he val i dat i on measur ement sof t he evapor at or , t he evapor at or was scr eened f r om t hem as much aspossi bl e. The i nf l uence of t he compr essor pr oper t i es on t he evapor at or wer eel i m nat ed by pl aci ng a r est r i c t i on wi t h superc r i t i cal f l ow i n t he suct i onl i ne of t he compr essor . The pr ocess condi t i ons af t er t hi s r est r i ct i on hadf or t hi s r eason no i nf l uence on t he amount of mass f l ow whi ch l ef t t heevaporator.- The condenser was dur i ng t he val i dat i on measur ement s f or t he evaporat orcont r ol l ed at a const ant pr essur e, t o screen of f t he evapor at or al so at i t sent r ance, whi l e t he subcool i ng was cont r ol l ed wi t h a separ at e heatexchanger . Theref or e t he condenser coul d be model l ed i n a si mpl e way,suppl yi ng t he TEV wi t h a r ef r i ger ant f l ow of const ant pr ocess condi t i ons.Lat er on wi t h t he model l i ng of t he condenser , t he condenser was spl i t upi nt o t wo regi ons, l i ke t he evapor at or .- The val i dat i on measur ement s wer e hel d wi t h a non- f r ost ed cool er, t oavoi d t he compl ex phenomena whi ch woul d r esul t f r om f r ost f or mat i on. Topr event t he f r ost i ng, t he ai r i n t he cool i ng room was dr i ed wi t h a secondcool er . i- The pr oper t i es of t he r ef r i ger ant ( R- 12) were, because of t he cal cul at i ont i me f or a dynam c si mul at i on, r epr esent ed on t he wor ki ng r ange by pol ynomswhi ch wer e based upon t abul at ed pr oper t i es i n l i t er at ur e ( [ A2] and [ V1 ] ) ,i nst ead of us i ng st andar d l i br ar i es.

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Vl l l

Concl usi ons and r ecommendat i onsThe devel oped model was abl e t o pr edi ct st abl e as wel l as i nst abl e operat i onof t he evaporat or/ expansi on val ve l oop accor di ng t o mechani sms whi ch agr eedwi t h t he val i dat i on measur ement s.The cor r el at i ons i n t he model f or t he t wo phase f l ow, phenomena ( heatt r ansf er , pr essur e dr op, voi d f r act i on) have been cor r ected f or t he speci f i cgeomet r y of t he t est evaporat ors and expansi on val ves accor di ng t o ownmeasur ement s. Thi s pr oved t o be necessar y i n or der t o obt ai n val ues accur at eenough f or t he pur pose of model l i ng. W t h t he cor r ect i ons f or t he t wo phasef l ow cor r el at i ons t he model i s abl e t o descr i be an evapor at or and TEVquant i t at i vel y rather accur at e. W t hout t hese cor r ect i ons onl y a qual i t at i vesi mul at i on i s possi bl e.The model can be usef ul t o st udy t he i nf l uences of di f f er ent cont r ol met hodsas has been done i n t hi s st udy. Al so i t can gi ve an under st andi ng of t hecompl ex pr ocesses and t he i mpor t ance of t he i nf l uenci ng par amet er s andpr ocess condi t i ons.W t h r espect t o t he pr ocesses and paramet ers i t was f ound t hat :- even a TEV whi ch sui t s wel l t o t he evapor at or di mensi ons, cannot wor kst abl e at l ow super heat condi t i ons when waves of unevapor at ed l i qui dr ef r i ger ant l eave the evapor at or , because of t he di st ur bi ng ef f ect of t hi sl i qui d on the measur ement of t he superheat t emper at ure.- t he r esul t i ng descr i pt i on of t he r egi on of heat l oads wher e st abi l i t yexi st s agr ees, accor di ng t o t hi s mechani sm wi t h t he M ni mum St abl eSuper heat l i nes as pr oposed by Huel l e al r eady i n 1967.- t he resul t s obt ai ned do not support t he of t en suggest ed r ul e " t he l ower

t he super heat , t he bet t er t he COP" . A superheat l ower t han t he one wherei nstabi l i t y s t ar t s wi l l normal l y not r esul t i n a bet t er COP of t her ef r i ger at i ng cycl e, somet i mes even i n a wor se one.- t he dom nat i ng i nf l uence of the l i qui d at t he out l et on t he st abi l i t y oft he evapor at or wi t h t he expansi on val ve makes t hat t hei r st eady s t at echar act er i st i cs have t o be descr i bed car ef ul l y. A good st eady model woul dbe abl e t o pr oduce t he necessar y i nf or mat i on on t hi s subj ect .- t he combi nat i on of a speci al TEV and evapor at or al one i s not usef ul . Agood choi ce of t he TEV and i t s set t i ng i s not possi bl e wi t hout i nf or mat i onabout t he pr ocess condi t i ons whi ch can be expect ed.- st abi l i t y cannot be guar ant eed by onl y i nf l uenci ng t he t i me const ant oft he f eel er bul b of t he TEV. W t h a sl ow bul b t he osci l l at i ons dur i ngi nst abi l i t y of t he mass f l ow t hr ough t he TEV wi l l be smal l er , but t hose oft he t emper at ur e at t he evapor at or out l et m ght i ncr ease.- a sl ower bul b, whi ch i s somet i mes even r ecommended i n t he l i t erat ur e f orthe case of s t abi l i t y, wi l l al so r esul t i n a l ower pr ot ect i on agai nstover f l ow of l i qui d ref r i ger ant out of t he evapor at or .- st abi l i t y and opt i mal set poi nt of t he expansi on val ve coul d be obt ai ned byusi ng anot her si gnal t han t he super heat f or t he cont r ol of t he val ve. Asi gnal based upon the pr esence of l i qui d ref r i ger ant at t he out l et coul dbe abl e t o guarant ee saf et y as wel l as a good COP.- a ver y l ow subcool i ng t emperat ur e can have under speci al condi t i ons anegat i ve ef f ect on t he st abi l i t y of t he syst em The super heat at whi chl i qui d st ar t s t o l eave t he evapor at or i ncr eases when a t oo l ow quant i t y off l ash gas r esul t s i n a l ow pr essur e dr op i n the di st r i but or pi pes. Thet hen r el at i vel y mor e i mpor t ant i nf l uence of t he gr avi t y makes t hedi st r i but i on of t he r ef r i ger ant uneven.

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i xBoth t he evaporat or and t he TEV showed a st r ong non l i near behavi our . Fort he model l i ng a combi nat i on of t heor y and empi r i cs was necess ar y. Theprobl ems encount ered wi t h t he model l i ng wer e mai nl y due t o t he compl exi t y oft he t wo phase f l ow pr ocesses:- t he avai l abl e cor r el at i ons f or heat t r ansf er and pr essur e dr op i n t heevaporat i on r egi on are not capabl e t o be used f or t he ai m of model l i ng.Bei ng devel oped accor di ng t o measur ement s on st r ai ght pi pes t hei ri naccur acy of some 20% wi l l i ncrease f or t he case of mor e compl i cat edconf i gur at i ons.- t he sl i p f act or and consequent l y t he voi d f r act i on cannot be cal cul at ed i nt he case of shor t hor i zont al pi pes connect ed wi t h U- bends.- t he osci l l at i ons of t he t r ansi t i on poi nt or t he di st ance necessar y f orevapor at i on of l i qui d waves whi ch l ef t t he evapor at i on r egi on ar e t her esul t of compl ex f l ow phenomena i n t he t wo phase f l ow r egi on.- t r ansi ent pr ocess condi t i ons even i ncrease the compl exi t y of t he abovement i oned pr obl ems.- the thr ot t l i ng of the r ef r i ger ant i s i nf l uenced by t he f or mat i on of f l ashgas and by met ast abi l i t y.- t he i nf l uence of the posi t i on of the di str i but or on t he di st r i but i on oft he r ef r i ger ant al ong t he par al l el pi pes of t he evapor at or i s due t o t hei nhomogenei t y of t he t hr ot t l ed r ef r i ger ant .Al so t he t i me avai l abl e f or a dynam c si mul at i on has t o be r egarded. A modelt her ef or e shoul d be as si mpl e as possi bl e, wi t hout l osi ng accur acy.Remarkabl e i s t hat t he non abi l i t y of descri bi ng t he t wo phase f l owpr ocesses has i n a way a posi t i ve ef f ect on the cal cul at i on t i me, because anever i ncr easi ng preci si on of model l i ng by di vi di ng t he model i n smal l erl umps wi l l be wi t hout i nf l uence on the r el i abi l i t y of t he model .The repor t ed cor r ect i ons f or t he cor r el at i ons f or t he t wo phase f l owphenomena and t he heat t r ansf er coef f i ci ent s of t he wat er si de i n t he wat erchi l l er accor di ng t o measur ement s on t he t est st ands make f or each newconf i gurat i on t o be descr i bed new measur ement s necess ar y. For smal l changesof t he conf i gur at i on however t he, changed, model coul d st i l l be abl e t osuppl y good r esul t s.Fur t her i nvest i gat i on on the subj ect of model l i ng of t he r ef r i ger at i ng cycl eshoul d be:- a bet t er l ook at t he condenser . The model has t o be checked wi t hval i dat i on measurement s and pr obabl y changed or ext ended.- t he model l i ng of ot her ver si ons of t he component s of t he ref r i ger at i oncyc l e. For i nst ance a wet evapor at or or an ai r cool ed condenser .- t he i mpl ement at i on and val i dat i on of ser i es of conf i gur at i ons ofcomponent s, f or i nst ance dry evapor at or ai r cool er s, t o gai n i nf or mat i onabout t he necessar y f i t f act or s f or t he model as f unct i on of t heconf i gur at i on.- t he ext ensi on of t he ai r cool er model wi t h condensat i on or even f r ostf or mat i on on t he ai r s i de.- t he use of t he pr oduced col d shoul d be st udi ed. Based upon t he devel opedst eady st at e model of t he evapor at or t he dynam c behavi our of t he col dst or e r oom and t he pr oduct s st or ed i n i t can be model l ed f or i nst ance.

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Chapter 1I nt r oduct i on

1.1 Scope of t he I nvest i gat i onThe subj ect of t hi s st udy i s t he dynam c behavi our of a compr essi onref r i gera t i on c yc l e.A r ef r i ger at i ng c i r cui t i n i t s most s i mpl e f orm consi st s of a compr essor , acondenser , a t hr ot t l e devi ce and an evapor at or . Vapour r ef r i ger ant i scompr essed, cool ed, and condensed. Thi s l i qui d i s t hr ot t l ed, nor mal l y wi t ht he f or mat i on of f l ash gas. The t emper at ur e of t he ref r i ger ant decr eases duet o t he ener gy necessar y f or t hi s par t i al evapor at i on. At t hi s l owert emper at ur e t he r ef r i ger ant can r ecei ve ener gy f r om t he sur r oundi ngs, whi chwi l l be cool ed. Recei vi ng t hi s ener gy, t he r ef r i ger ant evapor at es and caneven be super heat ed bef ore i t i s compr essed agai n.Model s of a r ef r i gerat i on cycl e t hat can be i mpl ement ed on a comput er can beused t o si mul at e t he behavi our of such a cycl e. Opt i m zat i on t hen wi l l bepossi bl e because of t he amount of i nf l uenci ng par amet ers t hat can be t akeni nt o account and t he speed of t he cal cul at i on t hat can be r eal i zed.St eady st at e si mul at i on model s wer e al r eady common use as an assi st i ndesi gn and opt i m zat i on of i nst al l at i ons and component s . Dynam c model swhi ch can be used f or t he st udy of syst em or component behavi our dur i ngchanges of operat i ng condi t i ons have been devel oped t oo on several pl aces,but wer e not yet f ound abl e t o be used i n pr act i ce. Par t l y t hi s was due t o Jt he t r act abi l i t y of t he model s, and par t l y t o t he uncer t ai nt y about t her esul t s pr oduced by t hese model s.W t h t he i nt ent i on t o devel op a model t hat coul d real l y be used asi nst r ument , a pr oj ect was start ed at t he Del f t Uni ver si t y of Technol ogy,whi ch was made possi bl e by f i nanci al suppor t of t he " St i cht i ng Techni scheWet enschappen" . As par t of t hi s cooper at i on a "user s comm t t ee" f r omr epr esent at i ves of Dut ch i ndust r y had f ol l owed t he pr ogr ess and t he r esul t sof t he r esear ch, and suppl i ed usef ul suggest i ons r egar di ng t he scope of t hei nvest i gat i on and t he subj ect s t o be cover ed.

Condenser l " ^ ^ ^ ^ ^" ^ ^ ^ ^ " " * I c o mp r e s s o r

figu re 1.1 Compressionrefrigerat ion cycle cons i s t ing of- a compressor,- a condenser,- a thermostatic expansion valve,- an evaporator.TEV EvaporatorIF

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21. 2 Li t er at ur eI n the f i el d of r ef r i ger at i on engi neer i ng t he use of mat hemat i cal model s hasnot yet f ound t he wi de appl i cat i on whi ch can be obser ved i n some ot herf i el ds of t echnol ogy, such as el ectr i cal and cont r ol engi neer i ng, andengi neer i ng mechani cs. However , i n t he l ast t wo decades al so i n t he f i el d ofr ef r i ger at i on t he l i t er at ur e r el at i ng t o mat hemat i cal model s and comput ersi mul at i on i s growi ng st eadi l y. I n a l i t er at ur e sur vey made i n 1983 CT1]concer ni ng r ef r i ger at i on machi nery and heat pumps, a number of 61 ar t i cl esr el at i ng t o model l i ng and si mul at i on was made f or t he decade 1971- 1981; f ort he t wo year s f ol l owi ng, 1882- 1983, 160 ar t i cl es wer e count ed. Onl y a smal lnumber of t he publ i cat i ons coul d be cl assi f i ed as r el at ed t o dynam c model s,r espect i vel y 7 f or t he decade and 13 f or t he t wo f ol l owi ng year s. Ther emai ni ng publ i cat i ons wer e r el at ed ei t her t o st eady st at e si mul at i on ofcompl et e syst ems or component s and t o speci f i c model s f or t he si mul at i on oft he cycl e i n r eci pr ocat i ng compr essor s.The l i t er at ur e on dynam cal model l i ng, as f ar as r el evant f or t hi s t hesi s,wi l l be r evi ewed bel ow. Some of t he mat er i al pr esent i n t he l i t er at ur e coul dbe used i n t hi s i nvest i gat i on, but none of t he model s was consi der ed t o beof such a nat ur e t hat i t coul d be used as a rel i abl e basi s f or t he modelenvi si oned i n t hi s st udy: a dry evapor at or i nt er act i ng wi t h an expansi ondevi ce. Ther ef ore i n t hi s t hesi s model s have been newl y devel oped st ar t i ngf r om the basi c physi c equat i ons.I n the f ol l owi ng sur vey s peci al l y t he evapor at or combi ned wi t h at her most at i c expansi on val ve ( TEV) wi l l be envi si oned, because her e mostpr obl ems concer ni ng t he dynam cs are l ocat ed.A l i t er at ur e st udy has t o make cl ear whi ch met hods of model l i ng coul d beused, and whi ch pr obl ems and possi bi l i t i es can be expect ed.Chi and Di di on [ C5] descr i bed t he t r ansi ent behavi our of an ai r t o ai r heatpump, where t he component s ar e descr i bed i n l umped f orm Bot h evaporat or andcondenser can consi st of a ser i es of el ement s. The TEV i s model l ed as havi nga l i near r el at i onshi p bet ween t he val ve openi ng and t he super heat pr essur e.The ti me st ep f or t he cal cul at i on pr ocess was 0. 005 seconds. The model wasr epor t ed t o be i n accor dance wi t h t est r esul t s i n the l abor at or y.J ames [ J 1] ment i ons t he l ack of i nf or mat i on of f l ow r egi mes i n evapor at or sbut good r esul t s coul d be obt ai ned by met hods used bef ore i n st eamgenerators. The evapor at or can be di vi ded i n sect i ons. Usi ng t hr ee sect i onsf or t he r ef r i ger ant and t hr ee f or t he medi um t o be cool ed, al so repr esent i ngt he ther mal i ner t i a of t he met al , gave reasonabl e r esul t s f or a l i qui dchi l l er but not f or an ai r cool er . The TEV can be appr oxi mat ed i f noi nt er est i n t he st abi l i t y of t he evapor at or - expansi on val ve cont r ol l oopexi s t s . The mass f l ow t hr ough t he val ve t hen can be descr i bed as a l i nearf unct i on of t he super heat wi t h a f i r st or der dynam cal r esponse, i n case t hesi t uat i on does not change much f r om t he wor ki ng poi nt .Dhar and Soedel [ D2] publ i shed one of t he f i r st model s f or t he t r ansi entbehavi our of r ef r i ger at i on syst ems. The pr esent at i on i s mor e good l ooki ngt han maki ng t he model cl ear. The evapor at or consi st s of t wo ref r i ger antl umps wi t h heat t r ansf er bet ween t he sat ur at ed and t he superheat edr ef r i ger ant . The model needs s ome empi r i cal obt ai ned dat a, as heat t r ansf ercoef f i ci ent s and l i qui d f l ow out of t he evapor at or i n case of suddenpr essur e dr op. The TEV i s ext ensi ve model l ed f or t he case t hat vapour f l owst hr ough i t , but poor f or t he case of l i qui d. The f l ow t hr ough ar ea i scal cul at ed as f unct i on of t he t her mobul b t emper at ur e.

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3Har gr eaves and J ames [ H1] model l ed a chi l l ed wat er pl ant wi t h at her modynam cal model . A t r ansf er f unct i on model woul d depend on goodmeasur ed dat a f or i t s accur acy, whi l e because of t he non l i near i t y of t hesyst em any gi ven t r ansf er f unct i on woul d onl y be val i d on a smal l oper at i ng

r ange. The use of var i abl e t i me const ant s i n the model coul d onl y be donesaf e when a f ul l under st andi ng of t he non l i near i t i es exi st s.The evapor at or i s l i ke t he one report ed by J ames, but because t he dynam csof t he evaporat or are much f ast er t han t hose of t he r emai ni ng syst em t wozones f or t he r ef r i ger ant and one f or t he chi l l ed wat er wer e suf f i c i ent . Thet wo l umps do not di st i ngui sh bet ween t he evapor at i on and t he superheatr egi on. The heat t r ansf er t o the r ef r i ger ant i s a f i t t ed f or mul a based uponexper i ment al dat a obt ai ned f r om t he evapor at ors manuf act ur er s. The TEV has amass f l ow based upon i t s known capaci t y, usi ng a square r oot equat i on. Thet i me dependency of t he TEV i s model l ed wi t h a f i r st or der syst em wi t h a t i meconst ant of 5 seconds. The dynam cs of t he wat er chi l l i ng syst em wer e wel laccor di ng t o measur ed t est s, but mor e ext ensi ve t est s on t he dynam cs af t erl oad changes wer e st i l l t o be hel d.Naj or k et al [ N2] si mul at ed a r ef r i ger at i on cycl e on an anal og comput er ,usi ng f or each component a ser i es of boxes. The non l i near st at i ccharact eri st i cs and t he worki ng poi nt dependent t i me const ant s wer e der i vedf r om ext ensi ve measur ement s. The i nt er dependence of t he out put val ues andt he cl osed ci r cui t made appr opr i at e exper i ment al mani pul at i on necessar y. Thedependence of t he evaporat or on an i ncr ease i n t he mass f l ow had beenst udi ed bef or e wi t h a separ at e model , f or const ant pr essur e condi t i on. Adead t i me of 2 seconds was measur ed, but not used i n t he model . Ext r a t est smade cl ear t hat t he hum di t y f r om t he ai r on t he evapor at or act ed as anaddi t i onal heat accumul at or , and t hat a hi gher concent r at i on of oi l i n t heevapor at or di d not have a measur abl e i nf l uence on t he dynam c behavi our . TheTEV i s model l ed r at her ext ensi ve, wi t h di f f er ent i nf l uences of pr ocesscondi t i ons, based upon measur ement s.Naj or k [ N3] i nvest i gat ed al so t he possi bi l i t i es t o i mpr ove t he st abi l i t y oft he dynam c behavi our of an evapor at or wi t h a t her most at i c expansi on val vewi t h a bl ock model on t he anal og comput er .De Br ui j n, van der J agt and Machi el sen [ B7] t oo i mpl ement ed t he model of .t he r ef r i ger at i ng cycl e on an anal og comput er . I n or der t o see how t hel i near i zat i on of t he t her modynam cal r el at i ons around t hei r wor ki ng poi ntaf f ect ed t he gener al pr oper t i es of t he or i gi nal model , a back up model wasi mpl ement ed on a di gi t al comput er . When car ef ul l y appl i ed, t hesi mpl i f i cat i ons di d not seem t o have much i nf l uence.The evapor at or i s model l ed as one evapor at i on and t hr ee super heat s ect i ons.The TEV i s model l ed accor di ng t o capaci t i es f r om t he cat al ogue, wi t h adynam cal r esponse of t he bul b based on t he bul b wal l and f i l l i ng.Yasuda, Machi el sen and Touber [ Y2] used an evaporat or model wi t h t wo zonesf or t he r ef r i ger ant , a t wo phase and a super heat zone, maki ng use of avar i abl e boundary. The met al of t he evapor at or wal l can be di vi ded i nt osmal l subdi vi si ons. The TEV was st at i cal l y model l ed accor di ng t o capaci t ydat a f r om t he cat al ogue, t he dynam c behavi our of t he bul b was r epr esent edwi t h t wo non l i near di f f er ent i al equat i ons. The model was r epor t ed t o be i ngood agr eement wi t h val i dat i on r esul t s, st at i cal l y as wel l as dynam cal l y.Hoekst r a [ I H1] compared a l umped model of t he same dr y evapor at or f or aquasi st at i c and a, one l umped, dynam c model l ed s uper heat r egi on. Whi l e t hesi mul at i on r esul t s wer e more or l ess t he same, t he cal cul at i on t i me wasr educed wi t h a f actor 20 by usi ng t he quasi st at i c cal cul at i on. A f actor 10because of t he smal l er t i me const ant s i n t he dynam c equat i ons descr i bi ng

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1t he r egi on and a f act or 2 because t he di f f er ent i al equat i ons t hen coul d bewr i t t en i n expl i c i t f or m wi t h no need f or a spec i al sol ut i on met hod.The evaporat or model i s based on t her modynam c pr i nci pl es, wi t h empi r i calcor r el at i ons f or pr essur e dr op and heat t r ansf er coef f i c i ent i n t he t wophase f l ow r egi on, based on measur ement s on t he t est st and. The model of t heTEV i s t he same as Yasuda used. Val i dat i on measur ement s made cl ear t hat mor er esear ch on t he subj ect was necessar y.Bont e and van Vel dhoven [ B3] , [ I B1] model l ed t he dynam c behavi our of t heevapor at or af t er a st ep change i n t he compr essor capaci t y, usi ng t r ansf erf unct i ons. The st eady condi t i ons, i n bet ween t he dynam cs ar e descr i bed, ar ecal cul at ed wi t h a separat e physi cal model . The model of t he TEV as pr esent edi s not ver y surveyabl e because i t i s al r eady r earr anged f or t he met hod ofsequent i al subst i t ut i on used t o sol ve t he st eady st at e equat i ons. Ent hal pydi f f er ences have been used i nst ead of pr essur e and t emper at ur e di f f er encesbecause of avai l abl e subr out i nes.

Zor z i ni , Panozzo and For nasi er i [ Z1] made an exper i ment al det erm nat i on oft he t r ansf er f unct i ons f or an evaporat or of a vapour compr essi onr ef r i ger at i on ci r cui t . Found was t hat t he measured super heat had a dead t i meof 3 seconds af t er an i ncrease i n t he r ef r i ger ant f l ow t o t he evapor at or ,possi bl e due t o a t r anspor t at i on l ag dur i ng whi ch var i at i ons i n mass i nsi det he evaporat or t ake pl ace.J osi assen [ J 6] devel oped an evaporat or as wel l as a condenser model basedupon a one l umped model wi t h l i qui d and vapour i n equi l i br i um condi t i ons.Bot h super heat i ng and subcool i ng ar e not del t wi t h. The expansi on val ve i smodel l ed ext ensi ve f or t he case t hat vapour l eaves t he condenser , whi l e f orl i qui d onl y a squar e root equat i on i s used t o descr i be t he mass f l ow oft hrot t l ed r ef r i ger ant .A si mpl e ext ensi on of model s out of l i t er at ur e wi t h t he necessar y number ofpar t i al der i vat i ves wi t h r egar d to t i me f or t he dynam c descr i pt i on of t wophase f l ow pr ocesses i n an evapor at or i s r eport ed. Based on t he si ze of t hemodel s and t he amount of cal cul at i on t i me i nvol ved, such ext ensi ons wer e nott hought t o be usef ul .However i t i s r at her quest i onabl e i f such der i vat i ves of cor r el at i onsdevel oped f or st eady condi t i ons are usef ul i n t r ansi ent condi t i ons. J ustusi ng quasi st at i c equat i ons t hen woul d at l east not gi ve t he i mpr essi on ofan abi l i t y to t hreat t r ans i ent s i t uat i ons cor r ec t l y.MacAr t hur s model [ M1] of t he t r ansi ent heat pump behavi our i s a pur et heor et i cal , heur i s t i c , i nvest i gat i on, wi t hout exper i ment al val i dat i on. I thas been assumed t hat knowl edge of t he moment um bal ance i s not necess ar y.The evaporat or i s di vi ded i n zones. The f l ow t hr ough t he expansi on val ve wasdescr i bed by a squar e r oot equat i on, but t hi s model wi l l be ext ended andwi l l i ncr ease more compl ex f l ow phenomena as choked, soni c, f l ow condi t i ons.Kr ug [ K1] used a bl ock model of t he evaporat or t o st udy t he behavi our oft he TEV. The t r ansf er f unct i ons even i ncl uded a dead t i me f or t he evaporat orr esponse, dependi ng on t he evapor at i on t emper at ure.Cl el and [ C6] si mul at ed an i ndust r i al r ef r i ger at i on pl ant under var i abl el oad condi t i ons usi ng a model l i ke J ames and Mars hal l [ J 2] , however wi t hdi sr egar di ng t he i nf l uence of t he suct i on pi pe. Lat er on, af t er bei ngupdat ed especi al l y f or t he f r eezi ng pr oduct par t , t he model has beenval i dat ed [ C73.St ol ar ski , Szarynger and Zak [ S7] pr opose t he use of a si mpl i f i ed model ofa househol d compr essi on r ef r i ger at or , t o use f or r epeat ed opt i m zat i on. Acompl i cat ed mat hemat i cal model i s devel oped, t aki ng i nt o account as muchi nf l uenc i ng par amet er s as poss i bl e. L i near i t i es , i nt er val s of var i at i on andoccur r ence of ext r emes are f ound by cal cul at i ons wi t h t he compl ex model .

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5W t h appr oxi mat i on of t hese resul t s t he si mpl i f i ed model i s set up, and usedf or i t er at i ve cal cul at i ons on t he ar ea checked al r eady bef or e wi t h t hecompl ex model .Bul l ock, W obl ewski and Gr of f [ B8] devel oped a dynam c si mul at i on model f orr esi dent i al ai r - t o- wat er heat pump syst ems. The heat pump i t sel f i s rathersi mpl e, wher e t he heat i ng capaci t y and t he power i nput are expr essed asf unct i ons of t he out door ai r t emper at ur e and t he heat i ng syst em wat ert emper at ur e. Per i odi c def r ost i ng of t he out door coi l i s al so i nc l uded, anddynam c ef f ect s are model l ed by t i me const ant s. The heat pump i s par t of abi gger syst emSt oecker [ S3] st udi ed t he st abi l i t y of t he evapor at or - expansi on val vecont r ol l oop wi t h a bl ock di agr am cont ai ni ng t hr ee t i me dependent el ement s.The syst em has been envi si oned wi t h and wi t hout t r anspor t at i on l ag i n t heevapor at or dynam cs. The assumed t i me l ags were 1 or 2 seconds, but t oget herwi t h Shar on and Mumma [ S4] , St oecker made mor e measur ement s on t hi s s ubj ect .The t r anspor t at i on l ag i n t he r eact i on of t he super heat t emper at ur e t hen,af t er a st ep decr ease or i ncrease of t he mass f l ow t o t he evaporat or, wasf ound i n t he or der of 8 seconds. The model i s r epor t ed t o be r at hersi mpl i f i ed and i s posed mor e as exampl e t han as f i nal met hod.Domanski and Di di on [ D5] made a st eady model of an ai r - t o- ai r heat pumpwi t h a capi l l ar y t ube. They used a f i r st pr i nc i pl e, or t her modynam cal ,model i nst ead of one based on a sequence of r egr essi on anal yses, because oft he advant ages i n under st andi ng t he i mpact of l ocal phenomena on the over al lsyst em Besi des, i f desi gned cor r ect l y, t he amount of i nput dat a i s f ar l essand easi er t o obt ai n. The model has been val i dat ed.Beckey [ B1] model l ed a vapour compressi on heat pump. The evaporat or andcondenser are r epr esent ed i n the same mat hemat i cal f ashi on, bei ng br oken upi nt o cont r ol vol umes wi t h conservat i on of mass and ener gy t o expr ess t her el at i onshi p bet ween t he bul k par amet er val ues f or each vol ume. The f or t hi smet hod necessary assumpt i on about t he r ef r i ger ant vel oci t i es was ahomogenei t y of t he f l ow i n each cont r ol vol ume. Each vol ume has onet emper at ur e, t he condenser bei ng di vi ded i nt o f our , t he evapor at or i nt ot hr ee vol umes. Pur e empi r i cal cor r el at i ons f or t he heat t r ansf er have beenused. Some s i mul at i ons coul d be compar ed wi t h measur ement s , showi ng a goodagr eement f or t he condenser and t he evaporat or pressure and t he compressormass f l ow. The pressur e dr op i s negl ect ed except f or t he t hr ot t l e pr ocess.The mass f l ow t hr ough t he expansi on val ve, model l ed as a f i xed val ve wi t ht he mass f l ow as a squar e r oot f unct i on of t he pr essur e di f f er ence, was notmeas ur ed.Raj endr an and Pat e [ R1] model l ed a vapour compr essi on r ef r i gerat i on syst emf or t he s i mul at i on of t he star t up t r ansi ent s . The r ef r i ger ant i n eachcomponent i s descr i bed as a l umped syst em wi t h a si ngl e node t o repr esenteach phase regi on. Heat t r ansf er cor r el at i ons f r om l i t er at ur e are used, andpr essur e drops ar e negl ect ed except f or t he t hr ot t l e pr ocess. The TEV i sdescr i bed wel l f or t he case of vapour l eavi ng t he condenser, but f or l i qui dor l i qui d wi t h vapour a si mpl e cor r el at i on i n used, negl ect i ng any possi bl ei nf l uence of met ast abi l i t y. The val ve openi ng i s l i near wi t h t he super heat ,and t he dynam cs of t he bul b ar e r epr esent ed by a f i r st or der syst em Noval i dat i on measur ement s have been made.Tr ee and Wei ss [ T2] pr oposed a si mpl e t wo t i me const ant model f or t hedynam c behavi our of r esi dent i al heat pumps. The bl ack box has as out put t het emper at ure change of t he i ndoor c o i l . The t wo t i me const ant s are br ought i nr el at i on t o t he mass of t he coi l and t he t i me r equi r ed t o tr anspor tr ef r i ger ant t o or f r om t he evapor at or . At st ar t up when a part of t he

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6r ef r i ger ant i s supposed t o l eave t he evapor at or as l i qui d, t he react i on oft he model had t o be qui cker t han under normal condi t i ons.The const ant s ar e obt ai ned by r egr essi on f i t of exper i ment al dat a. I n somecases t he r esul t coul d be bet t er by usi ng a t i me del ay and/ or. a t hi r d t i meconstant.Thi s met hod i s advi sed f or cont r ol pur poses, when a si mul at i on model coul dand al so shoul d wor k f ast er t han t hose nor mal l y pr esent ed i n l i t er at ur e.W t h respect t o t hi s t he model of Chen [ CM] i s t aken as exampl e. However ,wi t h a cal cul at i on t i me of 12 hour s on a CDC 6500 comput er f or 6 m nut essi mul at i on t i me, Chen' s model of a heat exchanger wi t h al l pr oper t i eschangi ng w t h bot h t i me and pl ace, i s not a r epr esent at i on of t he model spr esent ed i n l i t er at ur e. Never t hel ess t he i dea of t he two t i me const antappr oach can be ver y usef ul .Wedeki nd, Bhat t and Beck [ WM] used a mean voi d f r act i on model t o pr edi ctvar i ous t r ansi ent phenomena associ at ed wi t h t wo- phase evaporat i ng andcondensi ng f l ows. Good r esul t s ar e r epor t ed i n pr edi ct i ng t he mot i on of t hemean val ue of t he t r ansi t i on poi nt , or t he end poi nt of t he evapor at i onr egi on, and i n t he mass f l ow of t he superheat ed vapour af t er a st ep changeof t he mass f l ow t o an evaporat or up to 20 % . The model i t sel f has t headvant ages of si mpl i ci t y. The voi d f r act i on used i s a mean val ue f or t he t wophase f l ow r egi on, and i s t i me i nvar i ant . W t hout l ooki ng t o spec i f i cl ocal i zed phenomena, t he model does not cont ai n empi r i cal const ant s as such,and handl es t he t wo phase f l ow r egi on as a l umped paramet er syst em Fr omphysi cal per spect i ve t he t i me i nvar i ance i s expl ai ned wi t h a qui ckr edi st r i but i on of t he l i qui d and t he vapour wi t hi n t he t wo phase r egi on. Thecur r ent r at e of under st andi ng on t he redi st r i but i on mechani sm i s r at heri ncompl et e, but such a qui ck r eact i on shoul d be due t o t he hi gh vapourvel oci t y i nst ead of due t o the l i qui d. The r esul t s are repor t ed t o agr eewel l wi t h val i dat i on measur ement s.However , t hese measur ement s show a di st i nct dead t i me of a t hree seconds(al so not ed i n [ S4] , f i gure 11 and 12) , i n cont r ar y w t h the resul t s of t hemodel . Thi s dead t i me i s not envi si oned by t he aut hor s i n t hei r compari son.Anot her di sadvant age i s t hat t he model i s onl y val i d f or const antevapor at i on t emper at ur e si t uat i ons, and needs i nput ed val ues of f or i nst ancet he heat t ransf er coef f i c i ent .1. 3 Concl us i ons f rom t he l i t er at ur eThe sur vey of l i t er at ur e made cl ear t hat sever al poss i bi l i t i es exi s t t omodel a r ef r i ger at i on cycl e, or component s f r om t hi s cycl e.- A f i r st pr i nci pl e model or t her modynam cal model i s based on t hef undament al l aws and t he necessar y ( sem ) empi r i cal cor r el at i ons f or f ori nst ance heat t r ansf er coef f i ci ent s and pr essur e dr op. Such a model canbecome r at her ext ensi ve, whi l e the accur acy i s l i m t ed by t he cor r el at i onsused.- A r egr essi on anal yses model i s based on measur ement s of a speci al t estst and on a speci al wor ki ng r ange. W t h such model s f or t he component s, t her esul t i ng cycl e can be si mul at ed, compari ng di f f er ent component s or speci als i t uat i ons f or t he pr ocess condi t i ons. The resul t s can be as accur at e as t het hermodynam cal model s, but t hen mor e i nput data ar e needed f or t he samewor ki ng r ange.- For dynam cal si t uat i ons t he t hermodynam cal model s cont ai n t hedi f f er ent i al equat i ons of t he par t s of t he model t hat ar e of i nt er est f or

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7t he t ot al behavi our . Par t s t hat ar e r el at i vel y qui ck can t hen be r egar ded asquasi st at i c , t hus avoi di ng st i f f ness pr obl ems. Si mpl i f i cat i ons m ght benecessar y t o avoi d par t i al di f f er ent i al or even i mpl i c i t wr i t t endi f f er ent i al equat i ons, t o avoi d l ong cal cul at i on t i mes.- The bl ack box met hod i n dynam cal si t uat i ons makes use of t r ansf erf unct i ons, whose const ant s al so have t o be obt ai ned f r om r egr essi on ofr esul t s of measur ement or , i n t he si mpl e case, of anal yt i cal st udy.Thi s met hod shoul d onl y be used i f t he pr ocesses are f ul l y under st ood. I fnot, t he r esul t s shoul d be checked af t er war ds exper i ment al l y.The t her modynam c met hod coul d be r ecommended when t he wor ki ng of t hecomponent s ar e not yet f ul l y under st ood, as a desi gn anal ysi s t ool . Al so i nt he case of bi gger wor ki ng r anges, whi ch woul d r equi r e each t i me newmeasur ement s and new r egr essi ons i n the case of t he r egr essi on met hod i t canbe bet t er used. Fi nal l y t he r esul t s of changes i n a component can beexpect ed t o be bet t er pr edi ct ed, even when the cor r el at i ons used had beenadj ust ed f or t he or i gi nal conf i gur at i on.A model coul d al so been bui l t up as a m x of model s accordi ng t o t he abovedescr i bed met hods, i n or der t o make opt i mal use of t hei r possi bi l i t i es. Fori nst ance i f t he wor ki ng of a ( gr oup of ) component ( s) i s r at her compl i cat edbut has an al most negl ect abl e or si mpl e i nf l uence on t he ot her component s.Al so i f t he pr oper t i es of one speci al component ar e i nvest i gat ed, t hen t heot her component s of t he cycl e can of t en be descr i bed i n a mor e si mpl e way.Thi s s t udy on t he subj ect of opt i m zat i on of t he dynam c behavi our ofcompr essi on ref r i ger at i on cycl es, had t o deal wi t h whet her st eady condi t i onscan be r eached and how t hey wi l l be r eached.Ther ef or e t he subj ect of st abi l i t y of t he evapor at or - TEV cont r ol l oop had t obe exam ned. Because t he pr obl ems concer ni ng t hi s s ubj ect were not ver ycl ear , a t her modynam cal model was t o be pref er r ed above a bl ack box w t hr egr essi on obt ai ned pr oper t i es.Thi s opens al so t he possi bi l i t y t o use t he model f or desi gn pur poses, whenf or i nst ance t he i nf l uence of di amet er s or f i n di st ances, accor di ng t o t hecor r el at i ons used i n t he model , i s to be st udi ed.The i nt er est i n the cont r ol of t he evapor at or makes al so t hat a model wi t h avar i abl e boundar y coul d be used bet t er t han one di vi ded i nt o f i xed part swi t h one r ef r i ger ant t emper at ur e per par t , because of t he bet t er cal cul at i onof t he t emper at ur e of t he super heat ed vapour .None of t he t her modynam cal model s pr esent ed i n l i t erat ur e was r eport ed t opr ovi de a f ul l y under st andi ng of t he dynam c behavi our of a dr y evapor at orwi t h a TEV. Thi s t oget her wi t h t he i nsi ght obt ai ned wi t h pr evi ous model sdevel oped i n t he Laborat or y of Ref r i ger at i on and I ndoor Cl i mat e Cont r ol( [ B 7 ] , [ Y2 ] ) , made cl ear t hat a new model shoul d be devel oped, abl e t o beext ended i f necessar y accor di ng t o val i dat i on measur ement s.W t h r espect t o the cor r el at i ons t o be used, i t has t o be exam ned i f t heycan di r ect l y be used l i ke pr esent ed i n l i t er at ur e or t hat each conf i gur at i oni n pr act i ce needs i t s own adj ust ment s. I f so, t he desi gn pur pose of t hemodel f or a si ngl e component of t he r ef r i ger at i ng cycl e coul d be t he subj ectof di scuss i on.

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8

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Chapt er 2Mode l l i ng t he evapor at or

2. 1 Evapor at or mode l l i ngW t h the i n t ent i on t o make a mode l o f a dr y expans i on evapor at or capab l e o fs i mu l a t i n g t he dy nam c b eh av i our , i t was t hought t o be wi se t o s t a r t wi t hmode l l i n g a s i mpl e e vapo r a t o r wi t h good p oss i b i l i t i e s of me asu r i ng andcont r o l l i n g t he p r oce ss cond i t i ons . On t he o t her h an d, t h e mode l obt a i ne dshoul d be capabl e of bei ng ext ended t o t he model of a mor e c ompl i cat ede v a p o r a t o r .These wi shes l ead t o a s i ngl e pass l i qu i d cool e r as t he evapor at or t o bemode l l e d. The l abo r a t o r y set - u p compr i se d a bl ock of t en h or i z ont a l t ub esc o nne ct ed i n s e r i es by u- bends i n a v er t i c al s e r p ent i ne c onf i gur a t i o n. Eac hs t r a i gh t pa r t o f e v apo r a t o r pi pe was sur r ounded by an annul a r l i qui dc h an ne l , wi t h s e pa r a t e and c ont r ol l abl e l i qui d f e ed. W t hout p ar a l l el pi pes ,pr obl e ms wi t h u ne ve n d i s t r i bu t i on o f t he r e f r i g er ant and wi t h a secondt hr o t t l i ng i n t he di s t r i but o r c o ul d be a vo i ded. By us i ng a n oi l s epar at o ra f t er t he c o mpr e s s o r , t he oi l c o nt ent s i n t he r e f r i ge r a n t wa s l e s s t h an 0. 5%and coul d be negl ect ed i n t he mass and ener gy bal ances .T o i s o l a t e t he e va po r a t o r f r o m i nf l uenc es f r om o t he r c o mpo ne nt s , a wa t e rcool ed condenser was chosen equi pped wi t h P I D pr ess ur e cont r o l l e r and ase pa r a t e cont r o l of t he su bcool i ng t e mp er a t u r e . A l so a t h r o t t l e v a l v e waspl aced at t he out l e t o f t he e vapo r a t o r i n t he su c t i on p i p e: as l ong aschoked f l ow was r eal i zed t he compr essor woul d have no i n f l uence on t heevapor at or per f o r mance .I t was r e qui r e d t ha t t he mode l coul d pr edi c t i n s t abl e behavi our of t hee va po r a t o r l i qui d f eed c o nt r o l l o op , e. g. h unt i ng. Bec a us e t h er e wa sunc e r t a i nt y about t he i mpo r t a nc e o f s ever al f a c t o r s i nf l uenc i ng t hes t a bi l i t y , a s ma ny f a c t o r s a s pr ac t i c abl e we r e t a k en i nt o a c c oun t .On t he o t he r h and , f or a mode l t o b e used i n p r ac t i ce , t he cal cu l a t i on t i meshoul d be kept t o a m n i mum Ther e f or e a r a t her s i mp l e mode l concept wasc h os e n, l ea di ng t o o nl y a s ma l l number of d i f f e r e nt i a l e qu at i o ns , s e ef i g ur e 2. 1 .

figure 2.1 Block diagram of theevaporator, with maas and energyflows. It contains three regions:saturated liquid, saturated vapourand superheated vapour. In themodel equations the saturatedregions will be taken together.

The model i s a l umped one. W t h t he sat urat ed l i qui d and vapour t akent o ge t h er , i t c o ns i s t s o f t wo v ol ume s , v i z . an e va po r a t i o n s e c t i o n and asu pe r h e at i n g se c t i on, wi t h a v ar i abl e bounda r y b e t we en t h emI n ear l i e r r esear ch [ Y1 ] , a mu l t i - l umped mode l was a l r eady abandoned becauseof t he l ack of knowl edge about t he p r i nc i p l es gover n i ng t he t wo phase f l ow.Vo i d f r ac t i on ( t he r e l a t i v e par t of t he v ol ume of t h e v apour i n t he t o t a lt wo phas e f l ow) , hea t t r ans f e r and p r e ssu r e dr op a r e i nf l ue nce d by t he f l ow

M u jta.hn

i A i

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10pat t er n. I n steady s i t uat i ons the voi d f ract i on has no di r ect i nf l uence, ont he cont r ar y wi t h t he heat t r ansf er and pr essur e dr op. The exact i nf l uencesare di f f i cul t t o pr edi ct i n t he case of shor t hor i zont al pi pes connected t oeach ot her wi t h U- bends. I n non st eady si t uat i ons t hi s pr obl em i s evenbi gger because of t he t hen st i l l mor e compl i cat ed t wo phase f l ow pat t er n.Al so t he voi d f r act i on t hen i s of dom nat i ng i nf l uence on t he dynam cbehavi our .W t hout suf f i c i ent knowl edge of val ues of voi d f r act i on or s l i p f act or , adet ai l ed model l i ng woul d onl y cost a l ot of cal cul at i on t i me, wi t houti mpr ovi ng t he capabi l i t i es of t he model . I ndeed, s i mpl i f i cat i on of such amodel i nt o one consi st i ng of t wo homogeneous cont r ol vol umes of r ef r i ger antwas f ound not t o have real l y i nf l uence on the qual i t y of t he si mul at i onr esul t s whi l e t he pr of i t on saved cal cul at i on t i me was wor t hwhi l e [ Y1] .Ther ef ore t he basi c model was kept si mpl e as much as poss i bl e. Lat er on t hemodel was ext ended i f necessar y, dependi ng on t he resul t s of val i dat i onmeasur ement s.2. 2 Model equat i onsA homogeneous cont r ol vol ume r equi r es t hermodynam c equi l i br i um l i qui d canonl y exi st i n t he pr esence of sat ur at ed and not of super heat ed vapour .Negl ect i ng t he possi bi l i t y of a subcool ed r egi on, t he evapor at or can bespl i t up i nt o t hr ee par t s :- a sat urated l i qui d regi on,- a sat ur at ed vapour r egi on, and- a super heat ed vapour r egi on.The mass bal ances f or t he ref r i ger ant i n these t hr ee par t s ar e ( f i gur e 2. 1) :

( 1)( 2)( 3)

The ener gy bal ances ar e:d/ dt ( M Ul ) =m . ( h l i +0. 5 cj +g Zj) + Qwl - Ql v -

~ m i v ( V 0 ' 5 c L + g Zm ) " A l o ( h l o + 0 - 5 c l V g Z o ) d / d t (M u ) = m . ( h . + 0 . 5 c 2 . + g z j + Q + Q, +v v vi v i v i i wv lv

+ ft. (h +0.5 c 2 +g z ) - m (h +0.5 c 2 + g z ) (5)lv v lv m vg vo vo od/ dt (M u ) = m (h +0. 5 c 2 +g z ) + Q - m (h +0. 5 c 2 +g z ) ( 6)g g vg vo vo B o wg go go go 6 oThese 6 equat i ons cont ai n 8 unknown var i abl es :M , M , M , u, , u , u , A, , and m1' v' g 1 v' g' l v' vgThe necessi t y t hat t he evapor at or i s f i l l ed compl et el y wi t h r ef r i ger antgi ves an ext r a equat i on:

d/ dtd/ dtd/ dt

(V = * l i - m l v "( V = Av i + V(M ) = m - mg vg go

mnl omvg

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11M v + M v + M v = V ( 7)1 1 v v g g evapAnother equat i on i s the descr i pt i on of the voi d f r act i on, whi ch shoul df ol l ow f r om t he momentum bal ance of t he t wo phase f l ow i n t he evapor at i on

r egi on: M v = (M v +M. v. ) a p ( 8)V V V V 1 1 VfThe set of 8 equat i ons w t h 8 unknown var i abl es coul d be r esol ved, howevers i mpl i f i cat i on i s possi bl e. When both the l i q u i d and the vapour aresaturated, the evapor at i on r egi on i s i n equi l i br i um and the t emper at ures ofl i q u i d and vapour her e ar e the same:T = T = T ( 9)v i e

The syst em wi l l now be wr i t t en as a set of 6 expl i c i t di f f er ent i al equat i onsf or t he var i abl es: M , M , M , A. , T and T . Thi s i s desi r ed becausesol vi ng t he set of equat i ons t hen wi l l need l ess cal cul at i on ti me dur i ng t hesi mul at i on t han when they woul d have been i mpl i ci t l y wr i t t en.Subst i t ut i on of ( 1) , ( 2) , ( M) and ( 9) i n ( 5) gi ves:d/ dt ( Te) = [ Qwl +Qwv- C V u) m v + { ( h n - Ul > +0. 5< + g z ^ m ^

+ " \ r uv ) +0' 5 cv i + g z i } Ki' { ( h l o- Ul >+0- 5 C L + g Zo} f t l o"- {(h - u ) +0.5 c2+ g z } m 1 / [Md/dT (u, ) +M d/dT (u ) ] (10)g v g o vgJ L 1 1 v v J

or :d/dt (Te) = [ Q w l + Qwy- ( h y - h l ) m l v+ p l V ; L d/dt (Mx) + P v v y d/dt

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12The maj or pr obl ems wi t h t he cal cul at i on of t he heat f l ow ar e t he coef f i ci entof t he heat t r ansf er f or t he boi l i ng t wo phase f l ow and t he l engt h of t heevapor at i on regi on whi ch i s r el at ed to t he mass of t h r ef r i ger ant M by t heval ue of t he mean voi d f r act i on. The heat t r ansf er can var y 20% wi t h val uesobt ai ned wi t h avai l abl e cor r el at i ons, whi l e the voi d f r act i on cannot bedescri bed at al l dur i ng non st eady condi t i ons. Usi ng t he quasi st at i c val ueof t he voi d f r act i on wi l l gi ve at l east a 10? devi at i on f rom t he r eal val ue.Er r or s i n t he cal cul at ed heat f l ow bet ween t he r ef r i ger ant and t he wal l wi l lbe of a hi gher or der t han t he maxi mum possi bl e i nf l uence of t he wor k f ordecreasi ng or i ncreasi ng t he evapor at i on vol umes. Al so t hese wi l l be ofhi gher or der t han t he i nf l uences of t he pr essur e dr op, t he vel oci t i es andt he di f f er ences i n hei ght . Ther ef or e t hese i nf l uences coul d be negl ect ed i nt he modelThe denom nator of equat i on ( 10) can be made easi er t o handl e al so bychangi ng t he t er ms du/ dT t o dh/ dT. The val ues of t he ent hal py h ar e bet t eravai l abl e as a f unct i on of t he t emper at ur e t han t hose of t he ener gy u. Thei nf l uence of t hi s change i s negl ect abl e ( i n t he or der of one percent):

d/ dT ( u) = d/ dT ( h) - d/ dT (p v) ( 14)The r ewr i t t en ener gy bal ance of t he evaporat i on r egi on ( 10) now can ber epl aced by equat i on ( 15) :d /d t (Te) = [ Qe- ( hv- h1) f t ] / [ M1d/ dT( h1) +Myd/ dT( hy) ] ( 1 5 )Wher e h. i s the ent hal py of t he r ef r i ger ant bef or e t he t hr ot t l e devi ce.Fi gur e 2. 2 shows a di agr am of t he r ewr i t t en and si mpl i f i ed model .

T* f ig ur e 2.2 Block d iagram of therewr i t t en se t o f eq u at i on s o f t h eevaporator model as Implemented inthe computer program. A subc oole dl i q u i d reg i on i s n ot h an d l edseparate. Only the unknownparameters from the equat ions usedare marked.

r? M Tv eE 7 Z f

M. T j *- 1 e '*=-$

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132. 4 Ext endi ng t he model2. 4. 1 The dynam c behavi our of t he evaporat i on r egi onI n st eady condi t i ons t he l engt h of t he evapor at i on r egi on and theevapor at i on t emper at ur e have such val ues t hat t he heat f l ow t o t he l i qui d i sequal t o t he amount necessary f or compl et e evapor at i on.I n dynam c condi t i ons, af t er f or i nst ance an i ncrease of t he mass f l ow ofr ef r i ger ant , t o t he evapor at or , t he evapor at i on t emper at ur e wi l l i ncreasebecause of t wo ef f ect s ( see f i gur e 2. 3, case a) :

i

figure 2. 3 Measured change of theevaporator pressure after astepward change of the opening ofthe expansion valve. In case (a)the opening increased, in case (b ) I 1 1 r it decreased.0 \0 60 SOi [c.lFi r st l y, l ess l i qui d wi l l evapor at e because of t he ext r a vapour t hat ent er st he evapor at or , whi l e t he amount of vapour t hat l eaves st ays t he same.Consequent l y t he pr essur e and the t emper at ur e wi l l r i se accor di ng t oequat i on ( 15) .Secondl y, t he amount of ext r a l i qui d ent er i ng, i n' combi nat i on wi t h t he l owerquant i t y bei ng evaporat ed, causes an i ncrease of t he l i qui d mas s .Accor di ngl y, t he l engt h of t he evapor at i on r egi on wi l l i ncr ease, and so t heamount of heat t r ansf er r ed t o thi s l i qui d. Bot h pr essur e and t emper at ur e, i nequi l i br i um t hen wi l l i ncrease a second t i me.The, mai n, ef f ect of t he second mechani sm wi l l be del ayed by t he di st ancewhi ch t he ext r a amount of l i qui d r ef r i ger ant has t o tr avel bef or e i t r eachest he end of t he evapor at i on r egi on and i ncreases t he l engt h of t hi s r egi on.The voi d f r act i on wi l l be di f f er ent f rom t he quasi st eady val ue, dur i ng t het i me t hat t hi s ext r a mass f l ow i s t r avel l i ng t hr ough t he evapor at i on r egi on.Cor r el at i ons t o descr i be the voi d f r act i on dur i ng tr ansi ent si t uat i ons arenot avai l abl e, and usi ng a st eady st at e cor r el at i on woul d gi ve ani nst ant aneous change of t he l engt h of t he evaporat i on r egi on af t er a changeof f or i nst ance t he i ncom ng l i qui d mass f l ow. Thi s woul d gi ve an i mmedi at eand t oo qui ck r eact i on of t he evapor at i on t emper at ur e, compared wi t h t hemeasur ement s. To avoi d t hi s , a new way t o obt ai n t he l engt h of t heevaporat i on r egi on dur i ng non st eady si t uat i ons had t o be devel oped.Not e t hat such a del ay wi l l not appear i n t he case of a r ot at i onal syst em asr epor t ed by Macken [ M2] . I n such an evaporat or t he l i qui d annul us and t hevapour cor e can be envi si oned as l umped s yst ems. The t r ansi ent r esponse ofsuch a l umped evaporat or appear ed t o be qui cker t han t hat of a di st r i but edone, wher e each por t i on of t he two phase f l ow i n t he pi pe has t o communi cat ewi t h t he next . Thi s i nt r oduces an ext r a pr ocess and a sl ower r esponse.The del ay of al l i nf l uenci ng par amet er s on t he l engt h of t he evapor at i onr egi on wi l l be di f f er ent f or each par amet er . The f ol l owi ng assumpt i ons havebeen made:( a) The l i qui d f l ow t o t he evapor at i on regi on has t o t r avel t he whol e l engt hof t he r egi on bef or e i t i nf l uences t he l engt h of t hi s regi on.

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1U( b) The vapour f l ow ent er i ng t he evapor at or has a di r ect i nf l uence on t hel engt h of t he evaporat i on r egi on ( see par agr aph 2. 4. 2) .( c) The evapor at i ng r ef r i ger ant evaporat es al ong t he whol e l engt h of t heevapor at i on r egi on. So t he i ncr ease/ decr ease of t h l i qui d mass

r esul t i ng f r om t hi s changed vapour f l ow, i s spr ead al ong t he whol eevaporat i on r egi on. Dependi ng on t he di st ance t o t he out l et , each par tof t he evapor at ed f l ow has t o be del ayed wi t h a di f f er ent t i me;( d) Li qui d mass f l ow, as descr i bed i n par agr aph 2. 4. 3, l eavi ng t heevapor at or has no di r ect i nf l uence on the l engt h of t he evapor at i onr egi on. I t woul d resul t i n, non des i r ed, ext r a osci l l at i ons of t heendpoi nt of t hi s regi on. I t s t i l l has an, i ndi rect , i nf l uence by thel i qui d mass and t he voi d f r act i on.( e) The f or ce that br i ngs t he t wo phase f l ow pat t er n af t er a di st ur bance i naccor dance agai n wi t h t he quasi st at i c val ue of t he voi d f r act i on i st hought t o wor k al ong t he whol e l engt h of t he evapor at i on r egi on.These assumpt i ons were used i n order t o obt ai n a usef ul cor r el at i on f or t hecal cul at i on of t he l engt h of t he evapor at i on r egi on dur i ng non st eadycondi t i ons. The met hod i s based on the di f f er ent i at i on t o t he t i me of t hel engt h of t he evapor at i on regi on

1 = M / {p A ( 1- a) } ( 16)e 1 ed/ dt (1 ) - 1/ {p A ( 1- a) } d/ dt ( M. ) + 1 / ( 1- a) d/ dt ( a) - 1 / p d/ dt ( p) ( 17)e e I e eThe f i r st t erm on t he r i ght si de of t he equal s i gn i n equat i on ( 17)descr i bes t he i nf l uence of t he der i vat i ve of t he l i qui d mass; > t he second oft he voi d f r act i on and t he thi r d of t he densi t y of t he l i qui d. The change oft hi s densi t y per t i me st ep however can be negl ect ed. The der i vat i ve of t hemass can be cal cul at ed, wi t h t he mass f l ows t o and f r om t he evapor at i onr egi on. The der i vat i ve of t he voi d f r act i on, on t he cont r ar y, cannot becal cul at ed. No cor r el at i ons are avai l abl e at al l f or t hi s t ermThe i nf l uence of a non homogeneous voi d f r act i on i n dynam c condi t i ons hast her ef or e been descr i bed by usi ng a der i vat i ve of t he mass of l i qui d basedon del ayed mass f l ows i nst ead of t he r eal mass f l ows i n t he f i r st t.ermoft he equat i on. The used i nf l uences of t he mass f l ows i nt o and out of t heevapor at i on r egi on, see equat i on ( 1) , on t he l engt h of t hi s r egi on ar e:1 - Onl y t he l i qui d component of t he i ncom ng mass f l ow has an i nf l uence ont he l engt h and i s del ayed wi t h a t r anspor t at i on l ag and a f i r st or der

system ( a , b ) .2 - The out goi ng vapour f l ow i s del ayed wi t h a f i r st or der syst em( c) .3 - l i qui d mass f l ow l eavi ng t he evapor at i on r egi on has no di r ect i nf l uenceon the l engt h of t hi s r egi on ( d) .The val ues of t he del ay t i mes and of t he t i me const ant s of t he f i r st or dersyst ems have been t aken proport i onal wi t h t he l engt h of t he evapor at i onr egi on ( see next paragraph).Now, f r om t he t hr ee t er ms i n equat i on ( 17) , onl y t he f i r st r emai ned. Howevera second, ext r a t er m i s necessar y, t o descri be a mechani sm t hat pushes t hevoi d f r act i on back t o i t s quasi st at i c val ue af t er a di st ur bance. W t houtt hi s cor r ecti on t he st eady st at e voi d f r act i on af t er t r ansi ent behavi ourwoul d be i nf l uenced by t hese t r ansi ent s i nst ead of onl y by t he new st eadycondi t i ons. The shape of t hi s extr a t er m i s based on t he second t er m i nequat i on ( 17) and on assumpt i on ( e) . The l engt h of t he evapor at i on^

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15wher e t he subscr i pt d st ands f or del ayed, a i s t he mean quasi st at i c voi df r act i on, and a i s t he act ual mean voi d f r act i on:

a = 1 - M / (1 p A ) ( 16' )1 e eThe del ayed val ues of t he voi d f r act i ons ar e used t o avoi d a spoi l i ng of t hedel ay of t he i nf l uence of t he mass f l ows, because a change of a mass f l owwi l l di r ect l y change the voi d f r act i on.The const ant s i n t he above descr i bed mechani sm were der i ved f r om exper i ment son t he evapor at or t est st and. St ar t i ng f rom st eady si t uat i ons wi t h a handcont r ol l ed expansi on val ve, t he val ve openi ng was changed s t ep wi se. Ther esul t i ng dynam cs, see f i gur e 2. 3, wer e recor ded and compar ed wi t h r esul t sf r om t he si mul at i on model . By syst emat i c changi ng t he const ant s of t hedel ayi ng mechani sm unt i l agr eement was r eal i zed, t he best combi nat i on f ort he ser i es of measur ement s was f ound [ I W3LThe i ncom ng mass f l ow m i s modi f i ed by a del ay of 3 s and a f i r st or derr esponse of 6 s i nt o f t , t he out com ng mass f l ow f t by a f i r st orderr esponse of 1 s i nt o t . . . The const ant f act or t f f or the voi d f r ac t i onhad a val ue of 25 s.The obt ai ned const ant s were used i n t he si mul at i on model of t he evapor at or .The above descr i bed bl ack box appr oach t o modi f y t he homogeneous basi cmodel f or t he ef f ect of t r anspor t at i on t i mes i s a coar se one, but i t i sf easi bl e and cont r i but es t o t he accur acy of t he model .

2. 4. 2 Tr anspor t at i on t i mes i n t he evapor at i on r egi onThe t r anspor t at i on t i mes of t he l i qui d and t he vapour r ef r i ger ant t hr ought he evaporat i on r egi on coul d be cal cul at ed when t he sl i p f act or bet ween t het wo vel oci t i es woul d be known. Based on the t he cor r el at i ons of Chawl a [ C2]and [ C3] , t he f ol l owi ng st udy can be made:W t h t he vel oci t y of t he vapour : c = t / A( x/ p + ( 1- x) / ( e p. . )) ( 19)t he vel oc i t y of t he l i qui d: cn= A/ A (e x/ p +( 1- x) / p, ) ( 20)1 e v 1t he sl i p f act or : . , _e - c v / C ; L = ( 1 - x ) / x 9 .1 (R e F r ) ^ / D ( p v / p 1 ) U - y ( n v / n 1 ) ^ (21)t h e R ey no lds num ber: Re., = A/A (1 -x ) d / n , (22)

2 2 2 2and t he Fr oude number : Fr = f t ( 1- x ) / ( A p g d) ( 23)t he t i me necessar y f or t r ansport at i on t hr ough t he evapor at i on r egi on can becal cul at ed, what has been done f or const ant heat t r ansf er t owar ds t here f r i ger ant :A t y - Jjf 1 / c v d l (24) At 1= Jjf 1 / ^ d l (25)

dl = (h - h ) rh / (q A) dx ( 26)I n f i gur e 2. 4. 1 t he cal cul at ed t r anspor t at i on t i mes are depi ct ed as f uncti onof t he l engt h of t he evapor at i on r egi on, when t hi s l engt h has been di vi dedi n hundr ed par t s, each of const ant condi t i ons. The t i mes show a pr oport i onal

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16

15

At5.

t(s )

m = 0.01 k g/s m = 0.02 k g/sx .= 0 .110L (m) 15

f igure 2 .1 .1 Influence of thelength of the evaporat ion region onthe t ransportat ion t imes of thevapour and the l iquid refr igerantthrough the evaporat ion region.Calculat ion based upon the s l ipcorrelat ion of Chawla.

f igure 2 .1 . 2 Influence of thetotal mass f low of refr igerant onthe t ranspor t a t ion t imes o f thevapour and the l iquid refr igerantthrough the evaporat ion region.Calculat ion based upon the s l ipcorrelat ion of Chawla.

25

20

lb|

10

5-

t \

v

\ \

[1

x - 0 7' = 0 . 1 '= 0.2 11 = 8.1 me 1.005 .01 .02m ( k g / s )

i ncr ease wi t h t he l engt h. Fi gur e 2. 4. 2 shows t hat al so t he mass f l ow ofr ef r i ger ant coul d