外文翻譯冷凝器和蒸發(fā)器的熱力設計 制定和應用

Thermodynamicdesignofcondensersandevaporators:FormulationandapplicationsChristianJ.L.HermesabstractThispaperassessesthetherm-hydraulicdesignapproachintroducedinapreviouspublication(Hermes,2012)forcondensersandevaporatorsaimedatminimumentropygeneration.Analgebraicmodelwhichexpressesthedimensionlessrateofentropygenerationasafunctionofthenumberoftransferunits,the?uidproperties,thethermal-hydrauliccharacteristics,andtheoperatingconditionsisderived.Casestudiesarecarriedoutwithdifferentheatexchangercon?gurgitationsforsmall-capacityrefrigerationapplications.Thetheoreticalanalysisledtotheconclusionthatahigheffectivenessheatexchangerdoesnotnecessarilyprovidethebestthermal-hydraulicdesignforcondenserandevaporatorcoils,whentheratesofentropygenerationduetoheattransferand?uidfrictionareofthesameorderofmagnitude.Theanalysisalsoindicatedthatahighaspectratioheatexchangerproducesaloweramountofentropythanalowaspectratioone.Conceptionthermodynamiccondenseretdesse′evaporate:formulationetapplications.Keywords:floatinghead;heatexchanger;design;industry1.IntroductionCondensersandevaporatorsareheatexchangerswithfairlyuniformwalltemperatureemployedinawiderangeofHVACRproducts,spanningfromhouseholdtoindustrialapplications.Ingeneral,theyaredesignedaimingataccomplishingacertainheattransferdutyatthepenaltyofpumpingpower.Therearetwowell-establishedmethodsavailableforthethermalheatexchangerdesign,thelog-meantemperaturedifference(LMTD)andtheeffectiveness/numberoftransferunits(ε-NTU)approach(Kakac?andLiu,2002;ShahandSiliculose,2003).Thesecondhasbeenpreferredtotheformerforthesakeofcompactheatexchangerdesignastheeffectiveness(ε),de?nedastheratiobetweentheactualheattransferrateandthemaximumamountthatcanbetransferred,providesa1st-lawcriteriontoranktheheatexchanger.performance,whereasthenumberoftransferunits(NTU)comparesthethermalsizeoftheheatexchangerwithitscapacityofheatingorcoolingfluid.Furthermore,theε-NTUapproachavoidsthecumbersomeiterativesolutionrequiredbytheLMTDforoutlettemperaturecalculations.Nonetheless,neitherε-NTUorLMTDapproachesaresuitabletoaddresstheheattransfer/pumpingpowertrade-off,whichisthecruxforabalancedheatexchangerdesign.Forthispurpose,Bajan(1987)establishedtheso-calledthermodynamicdesignmethod,laterrenamedasentropygenerationminimizationmethod(Bajan,1996),whichbalancesthethermodynamicirreversibilitiesduetotheheattransferwitha?nitetemperaturedifferencetothoseassociatedwiththeviscous?uid?ow,thusprovidinga2nd-lawcriterionthathasbeenwidelyusedforthesakeofheatexchangerdesignandoptimization(SanandJan,2000;Leprousetal.,2005;AchaeanandWongwises,2008;Mishapetal.,2009;Kotciogluetal.,2010;Pussolietal.,2012;Hermesetal.,2012).However,themodelsadoptedinthosestudiesdonotprovideastraightforwardindicationofhowthedesignparameters(geometry,?uidproperties,workingconditions)affecttherateofentropygeneration.Theyalsorequirecomplexnumericalsolutions,beingthereforenotsuitableforback-of-the-envelopecalculationsintheindustrialenvironment.Inarecentpublication,Hermes(2012)advancedanexplicit,algebraicformulationwhichexpressesthedimensionlessrateofentropygenerationasafunctionofthenumberoftransferunits,the?uidproperties,thethermalhydrauliccharacteristics(jandfcurves),andtheoperating.conditions(heattransferduty,corevelocity,andcoilsurfacetemperature)forheatexchangerswithuniformwalltemperature.Anexpressionfortheoptimumheatexchangereffectiveness,basedontheworkingconditions,heatexchangergeometryand?uidproperties,wasalsopresented.ThepresentpaperisthereforeaimedatassessingtheformulationintroducedbyHermes(2012)fordesigningcondensersandevaporatorsforrefrigerationsystemsspanningfromhouse-holdapplication,whichamountsw10%oftheelectricalenergyconsumedworldwide(MaloandSilva,2010).2.MathematicalformulationIngeneral,condensersandevaporatorsforrefrigerationapplicationsaredesignedconsideringthecoil?oodedwithtwo-phaserefrigerant,andalsoawalltemperatureequaltotherefrigeranttemperature(BarbarossaandHermes,2008),insuchawayasthetemperaturepro?lesalongthestreamsarethoserepresentedinFig.1.Inaddition,theouter(e.g.,air,water,brine)sideheattransfercoef?cientandthephysicalpropertiesareassumedtobeconstant.Therefore,theheattransferrateifcalculatedfrom:（1）whereisthemass?owrate,Ti,ToandTsaretheinlet,outletandsurfacetemperatures,respectively,Q?hAs(TseTm)istheheattransferrate,Tmisthemean?owtemperatureovertheheattransferarea,As,andεistheheatexchangereffectiveness,calculatedfrom(KaysandLondon,1984):（2）whereNTU?hAs/mcpisthenumberoftransferunits.Thepressuredrop,ontheotherhand,canbecalculatedfrom(KaysandLondon,1984):（3）wherefisthefrictionfactor,ucisthevelocityintheminimum?owpassage,Ac,andthesubscripts“i”and“o”refertotheheatexchangerinletandoutletports,respectively.OneshouldnotethatEqs.(1)and(3)canbelinkedtoeachotherthroughthefollowingapproximationfortheGibbsrelation,（4）whereTmz(TitTo)/2,andtheentropyvariation,soesi,iscalculatedfromthe2nd-lawofThermodynamics,（5）wherethe?rsttermintheright-handsideaccountsforthereversibleentropytransportwithheat(_Q=Ts),whereas_Sgistheirreversibleentropygenerationduetoboththeheattransferwith?nitetemperaturedifferenceandtheviscousow.SubstitutingEqs.(1),(3)and(5)intoEq.(4),itfollowsthat:NS?（6）whereNSisthedimensionlessrateofentropygeneration.TheerrorsassociatedtotheapproximationusedinEq.(4)aremarginal:notingthatDTm<20Kinmostsmall-capacityrefrigerationapplications,itfollowsthatthedifferencebetweentheexactandapproximatedmeantemperatureneverexceeds1K,whichinturnaffectsthedimensionlessentropygenerationbylessthan1%.Nownotingthatbothcondensersandevaporatorsaredesignedtoprovideaheattransferdutysubjectedto?owrateandfaceareaconstraintsEq.(6)canbere-writtenasfollows(Hermes,2012):（7）AndQ?(ToeTi)/TsadimensionlesstemperaturedifferencewithbothToandTiknownfromtheapplication.Oneshouldnotethatthe?rstandsecondtermsoftheright-handsideofEq.(7)standforthedimensionlessentropygenerationratesassociatedwiththeheattransferwith?nitetemperaturedifferenceandtheviscous?ow,respectively.TheoptimumheatexchangerdesignNTUoptthatminimizestherateofentropygenerationisobtainedfrom(Hermes,2012):（8）dropeffects,whichruletheentropygenerationforthelowaspectratiodesigns,areattenuatedforlowNTUvalueswheretheentropygenerationdueto?nitetemperaturedifferenceisDominant.4.CasestudiesForthesakeofheatexchangerdesign,Eq.(8)hastobesolvedconcurrentlywithε?(ToeTi)/(TseTi)asthecoilsurfacetemperature,Ts,mustbefreetovarythusensuringthatQ(andso_Qand_m)isconstrained.However,thesolutionisimplicit.forTs,thusrequiringaniterativecalculationprocedure:aguessedTsvalueisneededtocalculatetheeffectivenessandNTU?eln(1eε),whichisusedinEq.(8)withj?j(Re)andf?f(Re)curves,andalsowiththedimensionlesscorevelocitytocomeoutwithQ,whichinturnisusedtorecalculateTsuntilconvergenceisachieved.Firstlyconsideranair-suppliedtube-?ncondenserforsmall-capacityrefrigerationappliancesrunningunderthefollowingworkingconditions:_Q?1kW,_V?1000m3h1Ti?300K(Waltrichetal.,2011;Hermesetal.,2012).Letsassumetwoheatexchangercon?gurations:(i)circulartubeswith?at?ns(i.e.,KaysandLondon’ssurface8.0-3/8T),whosethermal-hydrauliccharacteristicsarej?0.16$Re,tubesand?ns(KaysandLondon’ssurfaceCF-8.72),whosethermal-hydrauliccharacteristicsarej?0.22$Re0.4f?0.20$Re0.2,s?0.524andDh?3.93mm.AlsonotethatPrz0.7forair.Fig.4comparestheperformancecharacteristics(jandfcurves)ofsurfaces8.0-3/8TandCF-8.72asfunctionsofRe?rucDh/m.Fig.5comparesthedimensionlessentropygenerationObservedforbothsurfacesasafunctionofNTU.Acurveofε?ε(NTU),whichthesameforbothsurfaces,isalsoplottedtobeusedasareference.Itcanbeclearlyseenthatthe(ε,NTU)designwhichminimizestherateofentropygenerationis(0.61,0.95)forsurface8.0-3/8Tand(0.57,0.81)forsurfaceCF-8.72.Itcanalsobenotedthatthecircular-?nsurface3/8TforthesameReynoldsnumber(seeFig.4).ForlowNTUvalues,wheretheentropygenerationisruledbyNS,DT,bothsurfacesshowedsimilarNSvaluesastheirj-curvesareclose(seeFig.4).Fig.6comparesthreedifferentcondenserdesignsconsid-eringsurface8.0-3/8Tandfaceareasvaryingfrom0.025to0.1m2runningunderthesameworkingconditions.Theheatexchangerlengthwasalsovariedinordertoaccommodatetheheattransfersurfaceareafordifferentfaceareas.Foravertical,constantNTUline(i.e.sameheattransferarea),itcanbeclearlyobservedthataheatexchangerdesignwithhighaspectratio(higherfacearea,smallerlengthinthe?owdirection)producesasigni?cantlyloweramountofentropyincomparisontoalowaspectratiodesign(lowerfacearea,largerlength).ItcanbeadditionallyobservedthattheNScurvesconvergeforlowNTUvalues.Thisissoasthepressuredropeffects,whichruletheentropygenerationforthelowaspectratiodesigns,areattenuatedforlowNTUvalueswheretheentropygenerationdueto?nitetemperaturedifferenceisDominant.Nowconsideranair-suppliedevaporatorforhouseholdrefrigerationappliances,comprisedof10tuberowsinthe?owdirectionand2rowsinthetransversaldirection,whoseperformancecharacteristicsareasfollowsfz5.8isthe?nningfactor,Lz0.2mistheheatexchangerFig.7showstherateofentropygenerationasafunctionofNTUfortheno-frostevaporator.Itcanbeclearlyseenthatthelength,Dtz8mmisthetubeO.D.,Afz0.02misthefacearea,andsz0.72.Theworkingconditionsare:Tiz260K.Inthefollowinganalysis,themasstransferandtherelatedfrostaccretionphenomenahavenotbeentakenintoaccount.minimumentropygenerationtakesplaceforNTUw6.5andε/1,thusindicatingthat,inthistypeofevaporator,thepressuredropeffectsarenegligibleincomparisonwiththeheattransferwith?nitetemperaturedifference.Nonetheless,these?guresmaychangedramaticallyinpresenceoffrost,whichincreasesnotonlythepressuredropbutalsothethermalconductionresistance.alsonotedthattheminimumdimensionlessentropygenerationratenotonlyincreasesassdecreases,butalsothattheoptimamovetowardstheleft,IndicatingthatthepressuredropeffectsbecomedominantforlowerNTUvaluesassdecreases.ItcanalsobenotedthatthecurvesfordifferentsconvergeforlowNTUvaluesasmainlyaffectsthepressuredropratherthanthetemperaturedifference,beingtheformerattenuatedforlowNTUvalues.Inadditiontotheoptimafoundforthenumberoftransferunitsand,consequently,fortheheatexchangereffectiveness,twootherimportantdesignparameters,the?owpath,4L/Dh,andtheheatexchangersurfaceareadensity,b?As/AfL,doalsohaveoptimumvalues(seeFig.9)sincebotharestronglydependentonNtu:4L/Dh?NTU/St(seeFig.9a)andb?4s/Dh(seeFig.9b)whereSt?j/Pr2/3istheStantonnumber.Inbothcases,theoptimum?owpathandheatexchangersurfaceareadensityarecalculatedasfollows:（9）（10）Fig.9illustratesEqs.(9)and(10).UnlikeFig.8,thecurvesinFig.9adonotconvergeforlowNTUvaluesaslowersvaluesimplyonhighercorevelocitieswhichenhancetheheattransferprocess(higherjorSt)evenincaseoflowNTU.InFig.9b,itcanbenotedthatthecurvescrosseachotherincaseoflowNTUvalues,whichisduetothein?u-enceofsonb.SummaryandconclusionsThisstudyassessedananalyticalformulationthatcon?atestwodifferentheatexchangerdesignmethodologies,theKaysandLondon’s(1984)ε-NTUapproachandtheBejan’s(1996)methodofentropygenerationminimization.Expressionsforoptimumheatexchangereffectiveness,numberoftransferunits,?owpathandheatexchangersurfaceareadensityarealsodevised.Itwasshownthattheredoesexistaparticularε-NTUdesignforcondensersandevaporatorsthatminimizesthedimensionlessrateofentropygeneration.Tothisobser-vationfollowstheconclusionthatahigheffectivenessheatexchangerhasnotnecessarilythebestthermal-hydraulicdesign,astheeffectivenessdoesnotaccountforthepumpingpowereffect.Casestudiesconsideringatube-?ncondenserforlightcommercialrefrigerationapplicationsandanevaporatorforfrost-freerefrigeratorswerealsocarriedout.Incaseofthecondensercoil,wheretheentropyproductionduetoviscous?uid?owisofthesameorderofthatdueto?nitetemperaturedifference,theanalyticalformulationofHermes(2012)showedtobesuitableforthermodynamicoptimizations.Theanalysisalsoindicatedthataheatexchangerdesignwithahighaspectratioispreferabletoalowaspectratiooneastheformerproducesadramaticallyloweramountofentropy.Inaddition,itwasfoundthatincaseofa“no-frost”evaporatorworkingunderdrycoilconditions,thepressuredropeffectonthedimensionlessentropyproductionisnegligibleincomparisontothe?nitetemperaturedifference,thusindi-catingthatEq.(8)shouldbeusedwithgreatcaretoavoidaneconomicallyunfeasible(highNTU)design.Ononehand,sincethecoiltemperatureistreatedasa?oatingparameterduringtheoptimizationexercise,thedesignforheattransferenhancementleadstoloweraveragetemperaturedifferencesand,therefore,tolowercondensingtemperatureandhigherevaporatingtemperature.Ontheotherhand,theoptimizationforpressuredropreductionyieldsahighermass?owrateforthesamepumpingpower,thusimprovingtheheattransfercoef?cientwhichalsotendstoreducethecondensertemperatureorincreasetheevaporatingtemperature.SincetherefrigerationsystemCOPobeystheTevap/(TcondeTevap)scale,itcanbestatedthattheheatexchangerdesignthatpresentsthebestlocal(componentlevel)performanceintermsofminimumentropygenerationalsoleadstothebestglobal(system-level)performance.冷凝器和蒸發(fā)器的熱力設計:制定和應用摘要這份評估旨在用以前出版物中的最小熵產(chǎn)生法介紹的蒸發(fā)器及冷凝器中熱液的設計方法。其中表示無量綱率的熵產(chǎn)生作為函數(shù)的轉(zhuǎn)讓單位、液體屬性、熱-水力特性和運行條件數(shù)的代數(shù)模型產(chǎn)生而來。與不同換熱器配置為小容量制冷的應用進行了個體案例研究。理論分析得出的結(jié)論為高效率換熱器并不一定提供冷凝器和蒸發(fā)器的線圈，最佳的熱工水力設計時的熱轉(zhuǎn)移和液體摩擦的熵產(chǎn)生率的數(shù)量級相同。分析報告也表明高縱橫比換熱器產(chǎn)生熵比低的縱橫比一個較低的數(shù)額。關鍵字：冷凝器；蒸發(fā)器；概念；優(yōu)化介紹冷凝器和蒸發(fā)器是具有相當均勻壁溫的換熱器，是被用于范圍較大的的暖通空調(diào)的研發(fā)產(chǎn)品，是跨越從家庭到工業(yè)的應用。一般情況下，它們設計旨在以很大的功率完成一種特定的熱轉(zhuǎn)換任務。如今有兩種有效的方法可用于熱換熱器設計、溫度平均對數(shù)比和效能/傳質(zhì)單元數(shù)的辦法，第二個一直是首選，前者主要用于板式換熱器的設計，為了緊湊式換熱器設計的有效性，定義為實際的熱傳遞率之間的比率，可以傳輸?shù)淖畲蠼痤~。提供了一個第一定律標準等級的熱交換器的性能，而數(shù)量的傳輸單位比較熱的大小與它的容量換熱器的加熱或冷卻液,此外,ε-NTU方法避免了繁瑣的解決方案所需的溫度平均對數(shù)比對于出口溫度的計算.盡管如此,無論是ε-NTU或溫度平均對數(shù)比方法都不適合解決傳熱/泵功率交換,這是一個平衡的換熱器設計的關鍵。為此，Bejan（1987）建立了叫做的熱力學設計方法，后改名為熵產(chǎn)生最小化方法，平衡的熱力學不可逆性，由于傳熱的粘性流體流相關聯(lián)的那些具有有限的溫度差，從而提供了已被廣泛應用為換熱器設計與優(yōu)化。從而提供了一種第二法的標準，已被廣泛用于熱交換器的設計和優(yōu)化的緣故，然而，在這些研究中所采用的模型并沒有提供一個簡單的標志的設計參數(shù)是如何影響的熵產(chǎn)生率。在最近的一份出版物中，愛馬仕（2012年）提出一個明確的，代數(shù)的配方，它表示的無量綱熵產(chǎn)率的函數(shù)的傳質(zhì)單元數(shù)流體性質(zhì)水力特性（j和f曲線），和熱交換器的運行條件具有均勻壁溫。并根據(jù)工作條件給出了一個表達式的優(yōu)化換熱器效率和換熱器幾何和流體性質(zhì),因此，本論文旨在評估制定出臺愛馬仕（2012年）設計的冷凝器和蒸發(fā)器的制冷系統(tǒng)，涵蓋從家庭到輕型商用應用程序，這相當于全球10％的電能消耗。數(shù)學模型板式換熱器數(shù)值分析法用到了對流結(jié)構(gòu)和U型結(jié)構(gòu)中。四個APVSR3標準的板形成三個流動通道。兩側(cè)的通道有向下流的熱流體，然而中間通道有向上流動的冷流體。換熱器的中間通道的V型區(qū)域被分為五個軸向部分，這樣流體從一個軸向部分進入下一個部分。進口和出口處是在板的左下角和右上角?？墒窍鄬χ虚g通道而言，兩側(cè)通道進口和出口處是與之相反的。應該指出的，在換熱器的不同區(qū)域，三角形分布器的存在會使熱交換部位每一單元長度都是有區(qū)別的。然而這種區(qū)別在本文并不值得推崇，因為這些節(jié)點是在主要的V型部位，這樣軸向分段被假設是均等的。板的幾何體和流程在(Haseler高慶宇,1992年)中用于局部溫度測量實驗。這使兩種數(shù)據(jù)的對比更加有意義。數(shù)學模型基于以下假設條件可通過能量平衡方程建立：軸向流傳導在流動通道和板上表現(xiàn)不顯著;換熱器的尾部板是絕緣的;穩(wěn)態(tài)條件;熱流體均勻分布在兩側(cè)邊通道;忽略熱損失;沒有相變（沸騰和冷凝）;除了粘度，其他物理性質(zhì)不變;一維流動;通過子通道的溫度變化忽略不計。假設在每條通道的垂直方向，一維流動的流體會保持一個平均速度運動。假設均勻分布的流體在冷熱流體通道的流速是恒定的。基于以上的假設，圖1控制體的能量方程是：（1）采用穩(wěn)態(tài)假定條件，方程（1）可簡化為：(2)對稱的幾何形狀和流動使控制體（如圖1）從兩側(cè)的通道均等的吸收能量，并且th在側(cè)邊通道與之相同，由于這個原因，方程（2）可變?yōu)椋?3)無論是左手邊的通道還是右手邊的通道，一個相似的控制體只從一邊的通道來吸收能量。其中一邊通道的控制體的能量平衡方程是：將方程（3）和（4）組成方程組，通過方程組來控制換熱器相鄰通道流體的溫度分布。對U很大變化的解析解，除了如(Mehrabian,2003)等一些特殊情況下，會變得非常復雜并且不切合實際。(4)數(shù)值分析數(shù)值分析法中使換熱器分成一些軸向的部分。一個典型的軸向部分都有一個表面積。對于這個增加的表面積，冷熱流體的溫度分別是和，我們可以假設總傳熱系數(shù)可以作為這些溫度的函數(shù)而表示出來。這樣：等式2可以應用在軸截面上，表示為：(5)等式（3）和（4）也可以運用在換熱器相鄰通道的兩個軸截面上，可寫為：(6)(7)上述方程的解的獲得是當空間導數(shù)存在偏差時。以viscosities(Yaws,2003)為依據(jù)的溫度數(shù)據(jù)表被編入計算機程序中，并且這個程序可以表示出每個軸截面上，流體流動時的溫度下的黏度。線性插值的操作就開始進行，此時溫度數(shù)值與表值不一致。像密度、熱導率等一些其他的流體性質(zhì)與溫度無關。每種流體的這些特性的數(shù)值以平均流體溫度來指定，并且作為輸入數(shù)據(jù)。冷熱流體的入口溫度作為數(shù)值分析的邊界條件。板式換熱器通道中的流體無量綱傳熱系數(shù)可看成是與熱傳遞相關的一種類型(Raoetal.,2002)：(8)ShahandFocke(1988)進行了實驗研究板式換熱器熱傳遞和壓降特性。他們注意到，常數(shù)C取決于換熱板的類型和換熱器的幾何形狀，而常數(shù)n取決于流體的流態(tài)。Edwardsetal.(1974)研究證明得出，在雷諾數(shù)大約小于10時，實驗數(shù)據(jù)是以標繪的，而不是APVJuniorParaflow板落在表明典型傳熱關系的坡度線1/3處的Re值：在雷諾數(shù)較高時（Re大于10），坡度約為，這樣會得