外文翻译冷凝器和蒸发器的热力设计 制定和应用

Thermodynamicdesignofcondensersandevaporators:FormulationandapplicationsChristianJ.L.HermesabstractThispaperassessesthetherm-hydraulicdesignapproachintroducedinapreviouspublication(Hermes,2012)forcondensersandevaporatorsaimedatminimumentropygeneration.Analgebraicmodelwhichexpressesthedimensionlessrateofentropygenerationasafunctionofthenumberoftransferunits,thefluidproperties,thethermal-hydrauliccharacteristics,andtheoperatingconditionsisderived.Casestudiesarecarriedoutwithdifferentheatexchangerconfigurgitationsforsmall-capacityrefrigerationapplications.Thetheoreticalanalysisledtotheconclusionthatahigheffectivenessheatexchangerdoesnotnecessarilyprovidethebestthermal-hydraulicdesignforcondenserandevaporatorcoils,whentheratesofentropygenerationduetoheattransferandfluidfrictionareofthesameorderofmagnitude.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),definedastheratiobetweentheactualheattransferrateandthemaximumamountthatcanbetransferred,providesa1st-lawcriteriontoranktheheatexchanger.performance,whereasthenumberoftransferunits(NTU)comparesthethermalsizeoftheheatexchangerwithitscapacityofheatingorcoolingfluid.Furthermore,theε-NTUapproachavoidsthecumbersomeiterativesolutionrequiredbytheLMTDforoutlettemperaturecalculations.Nonetheless,neitherε-NTUorLMTDapproachesaresuitabletoaddresstheheattransfer/pumpingpowertrade-off,whichisthecruxforabalancedheatexchangerdesign.Forthispurpose,Bajan(1987)establishedtheso-calledthermodynamicdesignmethod,laterrenamedasentropygenerationminimizationmethod(Bajan,1996),whichbalancesthethermodynamicirreversibilitiesduetotheheattransferwithafinitetemperaturedifferencetothoseassociatedwiththeviscousfluidflow,thusprovidinga2nd-lawcriterionthathasbeenwidelyusedforthesakeofheatexchangerdesignandoptimization(SanandJan,2000;Leprousetal.,2005;AchaeanandWongwises,2008;Mishapetal.,2009;Kotciogluetal.,2010;Pussolietal.,2012;Hermesetal.,2012).However,themodelsadoptedinthosestudiesdonotprovideastraightforwardindicationofhowthedesignparameters(geometry,fluidproperties,workingconditions)affecttherateofentropygeneration.Theyalsorequirecomplexnumericalsolutions,beingthereforenotsuitableforback-of-the-envelopecalculationsintheindustrialenvironment.Inarecentpublication,Hermes(2012)advancedanexplicit,algebraicformulationwhichexpressesthedimensionlessrateofentropygenerationasafunctionofthenumberoftransferunits,thefluidproperties,thethermalhydrauliccharacteristics(jandfcurves),andtheoperating.conditions(heattransferduty,corevelocity,andcoilsurfacetemperature)forheatexchangerswithuniformwalltemperature.Anexpressionfortheoptimumheatexchangereffectiveness,basedontheworkingconditions,heatexchangergeometryandfluidproperties,wasalsopresented.ThepresentpaperisthereforeaimedatassessingtheformulationintroducedbyHermes(2012)fordesigningcondensersandevaporatorsforrefrigerationsystemsspanningfromhouse-holdapplication,whichamountsw10%oftheelectricalenergyconsumedworldwide(MaloandSilva,2010).2.MathematicalformulationIngeneral,condensersandevaporatorsforrefrigerationapplicationsaredesignedconsideringthecoilfloodedwithtwo-phaserefrigerant,andalsoawalltemperatureequaltotherefrigeranttemperature(BarbarossaandHermes,2008),insuchawayasthetemperatureprofilesalongthestreamsarethoserepresentedinFig.1.Inaddition,theouter(e.g.,air,water,brine)sideheattransfercoefficientandthephysicalpropertiesareassumedtobeconstant.Therefore,theheattransferrateifcalculatedfrom:（1）whereisthemassflowrate,Ti,ToandTsaretheinlet,outletandsurfacetemperatures,respectively,Q¼hAs(TseTm)istheheattransferrate,Tmisthemeanflowtemperatureovertheheattransferarea,As,andεistheheatexchangereffectiveness,calculatedfrom(KaysandLondon,1984):（2）whereNTU¼hAs/mcpisthenumberoftransferunits.Thepressuredrop,ontheotherhand,canbecalculatedfrom(KaysandLondon,1984):（3）wherefisthefrictionfactor,ucisthevelocityintheminimumflowpassage,Ac,andthesubscripts“i”and“o”refertotheheatexchangerinletandoutletports,respectively.OneshouldnotethatEqs.(1)and(3)canbelinkedtoeachotherthroughthefollowingapproximationfortheGibbsrelation,（4）whereTmz(TiþTo)/2,andtheentropyvariation,soesi,iscalculatedfromthe2nd-lawofThermodynamics,（5）wherethefirsttermintheright-handsideaccountsforthereversibleentropytransportwithheat(_Q=Ts),whereas_Sgistheirreversibleentropygenerationduetoboththeheattransferwithfinitetemperaturedifferenceandtheviscousow.SubstitutingEqs.(1),(3)and(5)intoEq.(4),itfollowsthat:NS¼（6）whereNSisthedimensionlessrateofentropygeneration.TheerrorsassociatedtotheapproximationusedinEq.(4)aremarginal:notingthatDTm<20Kinmostsmall-capacityrefrigerationapplications,itfollowsthatthedifferencebetweentheexactandapproximatedmeantemperatureneverexceeds1K,whichinturnaffectsthedimensionlessentropygenerationbylessthan1%.NownotingthatbothcondensersandevaporatorsaredesignedtoprovideaheattransferdutysubjectedtoflowrateandfaceareaconstraintsEq.(6)canbere-writtenasfollows(Hermes,2012):（7）AndQ¼(ToeTi)/TsadimensionlesstemperaturedifferencewithbothToandTiknownfromtheapplication.Oneshouldnotethatthefirstandsecondtermsoftheright-handsideofEq.(7)standforthedimensionlessentropygenerationratesassociatedwiththeheattransferwithfinitetemperaturedifferenceandtheviscousflow,respectively.TheoptimumheatexchangerdesignNTUoptthatminimizestherateofentropygenerationisobtainedfrom(Hermes,2012):（8）dropeffects,whichruletheentropygenerationforthelowaspectratiodesigns,areattenuatedforlowNTUvalueswheretheentropygenerationduetofinitetemperaturedifferenceisDominant.4.CasestudiesForthesakeofheatexchangerdesign,Eq.(8)hastobesolvedconcurrentlywithε¼(ToeTi)/(TseTi)asthecoilsurfacetemperature,Ts,mustbefreetovarythusensuringthatQ(andso_Qand_m)isconstrained.However,thesolutionisimplicit.forTs,thusrequiringaniterativecalculationprocedure:aguessedTsvalueisneededtocalculatetheeffectivenessandNTU¼eln(1eε),whichisusedinEq.(8)withj¼j(Re)andf¼f(Re)curves,andalsowiththedimensionlesscorevelocitytocomeoutwithQ,whichinturnisusedtorecalculateTsuntilconvergenceisachieved.Firstlyconsideranair-suppliedtube-fincondenserforsmall-capacityrefrigerationappliancesrunningunderthefollowingworkingconditions:_Q¼1kW,_V¼1000m3h1Ti¼300K(Waltrichetal.,2011;Hermesetal.,2012).Letsassumetwoheatexchangerconfigurations:(i)circulartubeswithflatfins(i.e.,KaysandLondon’ssurface8.0-3/8T),whosethermal-hydrauliccharacteristicsarej¼0.16$Re,tubesandfins(KaysandLondon’ssurfaceCF-8.72),whosethermal-hydrauliccharacteristicsarej¼0.22$Re0.4f¼0.20$Re0.2,s¼0.524andDh¼3.93mm.AlsonotethatPrz0.7forair.Fig.4comparestheperformancecharacteristics(jandfcurves)ofsurfaces8.0-3/8TandCF-8.72asfunctionsofRe¼rucDh/m.Fig.5comparesthedimensionlessentropygenerationObservedforbothsurfacesasafunctionofNTU.Acurveofε¼ε(NTU),whichthesameforbothsurfaces,isalsoplottedtobeusedasareference.Itcanbeclearlyseenthatthe(ε,NTU)designwhichminimizestherateofentropygenerationis(0.61,0.95)forsurface8.0-3/8Tand(0.57,0.81)forsurfaceCF-8.72.Itcanalsobenotedthatthecircular-finsurface3/8TforthesameReynoldsnumber(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,smallerlengthintheflowdirection)producesasignificantlyloweramountofentropyincomparisontoalowaspectratiodesign(lowerfacearea,largerlength).ItcanbeadditionallyobservedthattheNScurvesconvergeforlowNTUvalues.Thisissoasthepressuredropeffects,whichruletheentropygenerationforthelowaspectratiodesigns,areattenuatedforlowNTUvalueswheretheentropygenerationduetofinitetemperaturedifferenceisDominant.Nowconsideranair-suppliedevaporatorforhouseholdrefrigerationappliances,comprisedof10tuberowsintheflowdirectionand2rowsinthetransversaldirection,whoseperformancecharacteristicsareasfollowsfz5.8isthefinningfactor,Lz0.2mistheheatexchangerFig.7showstherateofentropygenerationasafunctionofNTUfortheno-frostevaporator.Itcanbeclearlyseenthatthelength,Dtz8mmisthetubeO.D.,Afz0.02misthefacearea,andsz0.72.Theworkingconditionsare:Tiz260K.Inthefollowinganalysis,themasstransferandtherelatedfrostaccretionphenomenahavenotbeentakenintoaccount.minimumentropygenerationtakesplaceforNTUw6.5andε/1,thusindicatingthat,inthistypeofevaporator,thepressuredropeffectsarenegligibleincomparisonwiththeheattransferwithfinitetemperaturedifference.Nonetheless,thesefiguresmaychangedramaticallyinpresenceoffrost,whichincreasesnotonlythepressuredropbutalsothethermalconductionresistance.alsonotedthattheminimumdimensionlessentropygenerationratenotonlyincreasesassdecreases,butalsothattheoptimamovetowardstheleft,IndicatingthatthepressuredropeffectsbecomedominantforlowerNTUvaluesassdecreases.ItcanalsobenotedthatthecurvesfordifferentsconvergeforlowNTUvaluesasmainlyaffectsthepressuredropratherthanthetemperaturedifference,beingtheformerattenuatedforlowNTUvalues.Inadditiontotheoptimafoundforthenumberoftransferunitsand,consequently,fortheheatexchangereffectiveness,twootherimportantdesignparameters,theflowpath,4L/Dh,andtheheatexchangersurfaceareadensity,b¼As/AfL,doalsohaveoptimumvalues(seeFig.9)sincebotharestronglydependentonNtu:4L/Dh¼NTU/St(seeFig.9a)andb¼4s/Dh(seeFig.9b)whereSt¼j/Pr2/3istheStantonnumber.Inbothcases,theoptimumflowpathandheatexchangersurfaceareadensityarecalculatedasfollows:（9）（10）Fig.9illustratesEqs.(9)and(10).UnlikeFig.8,thecurvesinFig.9adonotconvergeforlowNTUvaluesaslowersvaluesimplyonhighercorevelocitieswhichenhancetheheattransferprocess(higherjorSt)evenincaseoflowNTU.InFig.9b,itcanbenotedthatthecurvescrosseachotherincaseoflowNTUvalues,whichisduetotheinflu-enceofsonb.SummaryandconclusionsThisstudyassessedananalyticalformulationthatconflatestwodifferentheatexchangerdesignmethodologies,theKaysandLondon’s(1984)ε-NTUapproachandtheBejan’s(1996)methodofentropygenerationminimization.Expressionsforoptimumheatexchangereffectiveness,numberoftransferunits,flowpathandheatexchangersurfaceareadensityarealsodevised.Itwasshownthattheredoesexistaparticularε-NTUdesignforcondensersandevaporatorsthatminimizesthedimensionlessrateofentropygeneration.Tothisobser-vationfollowstheconclusionthatahigheffectivenessheatexchangerhasnotnecessarilythebestthermal-hydraulicdesign,astheeffectivenessdoesnotaccountforthepumpingpowereffect.Casestudiesconsideringatube-fincondenserforlightcommercialrefrigerationapplicationsandanevaporatorforfrost-freerefrigeratorswerealsocarriedout.Incaseofthecondensercoil,wheretheentropyproductionduetoviscousfluidflowisofthesameorderofthatduetofinitetemperaturedifference,theanalyticalformulationofHermes(2012)showedtobesuitableforthermodynamicoptimizations.Theanalysisalsoindicatedthataheatexchangerdesignwithahighaspectratioispreferabletoalowaspectratiooneastheformerproducesadramaticallyloweramountofentropy.Inaddition,itwasfoundthatincaseofa“no-frost”evaporatorworkingunderdrycoilconditions,thepressuredropeffectonthedimensionlessentropyproductionisnegligibleincomparisontothefinitetemperaturedifference,thusindi-catingthatEq.(8)shouldbeusedwithgreatcaretoavoidaneconomicallyunfeasible(highNTU)design.Ononehand,sincethecoiltemperatureistreatedasafloatingparameterduringtheoptimizationexercise,thedesignforheattransferenhancementleadstoloweraveragetemperaturedifferencesand,therefore,tolowercondensingtemperatureandhigherevaporatingtemperature.Ontheotherhand,theoptimizationforpressuredropreductionyieldsahighermassflowrateforthesamepumpingpower,thusimprovingtheheattransfercoefficientwhichalsotendstoreducethecondensertemperatureorincreasetheevaporatingtemperature.SincetherefrigerationsystemCOPobeystheTevap/(TcondeTevap)scale,itcanbestatedthattheheatexchangerdesignthatpresentsthebestlocal(componentlevel)performanceintermsofminimumentropygenerationalsoleadstothebestglobal(system-level)performance.冷凝器和蒸发器的热力设计:制定和应用摘要这份评估旨在用以前出版物中的最小熵产生法介绍的蒸发器及冷凝器中热液的设计方法。其中表示无量纲率的熵产生作为函数的转让单位、液体属性、热-水力特性和运行条件数的代数模型产生而来。与不同换热器配置为小容量制冷的应用进行了个体案例研究。理论分析得出的结论为高效率换热器并不一定提供冷凝器和蒸发器的线圈，最佳的热工水力设计时的热转移和液体摩擦的熵产生率的数量级相同。分析报告也表明高纵横比换热器产生熵比低的纵横比一个较低的数额。关键字：冷凝器；蒸发器；概念；优化介绍冷凝器和蒸发器是具有相当均匀壁温的换热器，是被用于范围较大的的暖通空调的研发产品，是跨越从家庭到工业的应用。一般情况下，它们设计旨在以很大的功率完成一种特定的热转换任务。如今有两种有效的方法可用于热换热器设计、温度平均对数比和效能/传质单元数的办法，第二个一直是首选，前者主要用于板式换热器的设计，为了紧凑式换热器设计的有效性，定义为实际的热传递率之间的比率，可以传输的最大金额。提供了一个第一定律标准等级的热交换器的性能，而数量的传输单位比较热的大小与它的容量换热器的加热或冷却液,此外,ε-NTU方法避免了繁琐的解决方案所需的温度平均对数比对于出口温度的计算.尽管如此,无论是ε-NTU或温度平均对数比方法都不适合解决传热/泵功率交换,这是一个平衡的换热器设计的关键。为此，Bejan（1987）建立了叫做的热力学设计方法，后改名为熵产生最小化方法，平衡的热力学不可逆性，由于传热的粘性流体流相关联的那些具有有限的温度差，从而提供了已被广泛应用为换热器设计与优化。从而提供了一种第二法的标准，已被广泛用于热交换器的设计和优化的缘故，然而，在这些研究中所采用的模型并没有提供一个简单的标志的设计参数是如何影响的熵产生率。在最近的一份出版物中，爱马仕（2012年）提出一个明确的，代数的配方，它表示的无量纲熵产率的函数的传质单元数流体性质水力特性（j和f曲线），和热交换器的运行条件具有均匀壁温。并根据工作条件给出了一个表达式的优化换热器效率和换热器几何和流体性质,因此，本论文旨在评估制定出台爱马仕（2012年）设计的冷凝器和蒸发器的制冷系统，涵盖从家庭到轻型商用应用程序，这相当于全球10％的电能消耗。数学模型板式换热器数值分析法用到了对流结构和U型结构中。四个APVSR3标准的板形成三个流动通道。两侧的通道有向下流的热流体，然而中间通道有向上流动的冷流体。换热器的中间通道的V型区域被分为五个轴向部分，这样流体从一个轴向部分进入下一个部分。进口和出口处是在板的左下角和右上角。可是相对中间通道而言，两侧通道进口和出口处是与之相反的。应该指出的，在换热器的不同区域，三角形分布器的存在会使热交换部位每一单元长度都是有区别的。然而这种区别在本文并不值得推崇，因为这些节点是在主要的V型部位，这样轴向分段被假设是均等的。板的几何体和流程在(Haseler高庆宇,1992年)中用于局部温度测量实验。这使两种数据的对比更加有意义。数学模型基于以下假设条件可通过能量平衡方程建立：轴向流传导在流动通道和板上表现不显著;换热器的尾部板是绝缘的;稳态条件;热流体均匀分布在两侧边通道;忽略热损失;没有相变（沸腾和冷凝）;除了粘度，其他物理性质不变;一维流动;通过子通道的温度变化忽略不计。假设在每条通道的垂直方向，一维流动的流体会保持一个平均速度运动。假设均匀分布的流体在冷热流体通道的流速是恒定的。基于以上的假设，图1控制体的能量方程是：（1）采用稳态假定条件，方程（1）可简化为：(2)对称的几何形状和流动使控制体（如图1）从两侧的通道均等的吸收能量，并且th在侧边通道与之相同，由于这个原因，方程（2）可变为：(3)无论是左手边的通道还是右手边的通道，一个相似的控制体只从一边的通道来吸收能量。其中一边通道的控制体的能量平衡方程是：将方程（3）和（4）组成方程组，通过方程组来控制换热器相邻通道流体的温度分布。对U很大变化的解析解，除了如(Mehrabian,2003)等一些特殊情况下，会变得非常复杂并且不切合实际。(4)数值分析数值分析法中使换热器分成一些轴向的部分。一个典型的轴向部分都有一个表面积。对于这个增加的表面积，冷热流体的温度分别是和，我们可以假设总传热系数可以作为这些温度的函数而表示出来。这样：等式2可以应用在轴截面上，表示为：(5)等式（3）和（4）也可以运用在换热器相邻通道的两个轴截面上，可写为：(6)(7)上述方程的解的获得是当空间导数存在偏差时。以viscosities(Yaws,2003)为依据的温度数据表被编入计算机程序中，并且这个程序可以表示出每个轴截面上，流体流动时的温度下的黏度。线性插值的操作就开始进行，此时温度数值与表值不一致。像密度、热导率等一些其他的流体性质与温度无关。每种流体的这些特性的数值以平均流体温度来指定，并且作为输入数据。冷热流体的入口温度作为数值分析的边界条件。板式换热器通道中的流体无量纲传热系数可看成是与热传递相关的一种类型(Raoetal.,2002)：(8)ShahandFocke(1988)进行了实验研究板式换热器热传递和压降特性。他们注意到，常数C取决于换热板的类型和换热器的几何形状，而常数n取决于流体的流态。Edwardsetal.(1974)研究证明得出，在雷诺数大约小于10时，实验数据是以标绘的，而不是APVJuniorParaflow板落在表明典型传热关系的坡度线1/3处的Re值：在雷诺数较高时（Re大于10），坡度约为，这样会得