文献翻译-板式换热器构型的最佳选择的筛选方法

外文翻译英文原文：ASCREENINGMETHODFORTHEOPTIMALSELECTIONOFPLATEHEATEXCHANGERCONFIGURATIONSJ.M.PintoandJ.A.W.GutDepartmentofChemicalEngineering,UniversityofSoPaulo,USPAbstract-Anoptimizationmethodfordeterminingthebestconfiguration(s)ofgasketedplateheatexchangersispresented.Theobjectiveistoselecttheconfiguration(s)withtheminimumheattransferareathatstillsatisfiesconstraintsonthenumberofchannels,thepressuredropofbothfluids,thechannelflowvelocitiesandtheexchangerthermaleffectiveness.Theconfigurationoftheexchangerisdefinedbysixparameters,whichareasfollows:thenumberofchannels,thenumbersofpassesoneachside,thefluidlocations,thefeedpositionsandthetypeofflowinthechannels.Theresultingconfigurationoptimizationproblemisformulatedastheminimizationoftheexchangerheattransferareaandascreeningprocedureisproposedforitssolution.Inthisprocedure,subsetsofconstraintsaresuccessivelyappliedtoeliminateinfeasibleandnonoptimalsolutions.Examplesshowthattheoptimizationmethodisabletosuccessfullydetermineasetofoptimalconfigurationswithaminimumnumberofexchangerevaluations.Approximately5%ofthepressuredropandchannelvelocitycalculationsand1%ofthethermalsimulationsarerequiredforthesolution.Keywords:plateheatexchanger,heatexchangerconfiguration,optimization,screeningmethod.INTRODUCTIONTheplateheatexchanger(PHE)consistsofapackofgasketedcorrugatedmetalplates,pressedtogetherinaframe.Thefluidsflowthroughaseriesofparallelflowchannelsandexchangeheatthroughthethincorrugatedmetalplates.Thegasketdesignandtheclosedportsoftheplatesdeterminethefluidflowarrangement,whichcanbeparallel,inseriesoroneofseveralpossiblecombinationsofthetwo.Theflowdistribution,numberofplates,typeofgasketsandfeedlocationscharacterizetheexchangerconfiguration.CONFIGURATIONCHARACTERIZATIONTocharacterizethePHEconfiguration,sixdistinctparametersareused:NC,PI,PII,f,YhandYf,whicharedescribedasfollows:NC:NumberofChannelsPIandPII:NumberofPassesonSidesIandIIf:FeedConnectionRelativeLocationYh:HotFluidLocationYf:TypeofFlowinChannels.Thisbinaryparameterdefinesthetypeofflowinsidethechannels,whichcanbestraightorcrosseddependingonthegaskettype(Fig.1).Thecrossedflowavoidstheformationofstagnationareas,butthestraightflowtypeiseasiertoassemble.Itisnotpossibletousebothtypestogether.IfYf=1,thentheflowiscrossedinallchannels.IfYf=0,theflowisstraightinallchannels.Thesixparameterscanrepresentanyregularconfigurationandanexampleofconfigurationsforanine-platePHEisshowninFig.(2).Foranygivennumberofchannels,NC,thefiveremainingparametershaveafinitesetofallowablevalues,whichlimitsthenumberofpossibleconfigurations,asshowninFig.(3).ThedispersepatternisduetothevariationinthenumberofintegerfactorsofNCIandNCII.Fortherangeofnumberofchannelsbetween2and500thereare284,976differentconfigurations.EquivalentConfigurationsForagivenvalueofnumberofchannelsandafixedtypeofflow,theexistenceofequivalentconfigurations(thathavethesamethermaleffectivenessandpressuredrops)ispossible.Identificationofequivalentconfigurationsisimportanttoavoidunnecessaryexchangerevaluations.Theequivalenceoftwoormoreconfigurationsoccursduetothepropertyofflowreversibility(Pignotti&Tamborenea,1988),tothepresenceofsinglepassortogeometricalsimilarity(theconfigurationcanbefreelyrotatedormirrored).AmethodologytodetectequivalentconfigurationsisshowninTab.(1).ForeachsetofNC,PI,PIIandYftherearegroupsofvaluesforparameterfthatresultinequivalentconfigurations.Inthecaseofeven-numberedNC,theremaybeequivalencybetweenYh=0andYh=1becausesidesIandIIhavethesamenumberofchannelsandthereforecanhavethesamenumbersofpasses.ConsiderforinstancetheexchangershowninFig.(2),whichisarrangedforf=1andYh=1;accordingtoTab.(1),changingthesidesofthefluids(Yh=1Yh=0)willyieldadifferentalthoughequivalentconfiguration.CONFIGURATIONOPTIMIZATIONTheconfigurationoptimizationproblemisformulatedastheminimizationofthenumberofchannels,NC,whichisequivalenttominimizingtheexchangerheattransferareaoritsfixedcost(Eq.1).Thereareconstraintsonthenumberofchannels(NC),fluidpressuredrops(DPhot,DPcold),channelflowvelocities(vhot,vcold)andexchangereffectiveness(E),asshowninConstraints(2a)to(2f).TheoptimizationmodelisalsosubjecttothePHEmodel,necessaryforcalculationoftheaforementionedvariables(Constraint3).subjecttoConstraint(2a)onthenumberofchannelsisrelatedtotheavailablenumberofplatesandexchangercapacity.Theminimumvaluesforfluidpressuredropavoidlargevariationsbetweentheaveragefluidpressuresthatcanbendtheplates.Lowerboundsonchannelflowvelocitiesavoidtheformationofpreferentialpathsorstagnationareasinsidethechannels.ThethermalandhydraulicmodelingofthePHE(Constraint3)wasdevelopedbyGutandPinto(2001).Therigorousthermalmodelaccountsforthevariationintheoverallheattransfercoefficientintheexchangerandconsistsofasystemofdifferentialandalgebraicnonlinearequations,whichcanbesolvedbynumericalmethods.Assumingtheheattransfercoefficientinvariable,therigorousmodelcanbereducedtotheso-calledsimplifiedthermalmodel,whichconsistsofasystemoflinearordinarydifferentialequationsandhasananalyticalsolution.Sincethereislittledifferencebetweenthemainsimulationresultsachievedbyrigorousandsimplifiedthermalmodels,thelatterwillbeusedfortheoptimization,keepingtheformerforfinalverificationoftheresults.TheScreeningMethodTheproposedoptimizationprocedureisbasedonthescreeningmethod,alsoemployedbyDaichendtandGrossmann(1994)forheatexchangernetworkoptimization.Inthisprocedure,constraintsaresuccessivelyusedtoremoveinfeasibleandnonoptimalsolutionsofaMINLPproblem,thusreducingitssizeandcomplexity.IntheoptimizationofaPHEconfiguration,theConstraintonthenumberofchannels(2a)definestheinitialset,IS,ofpossibleconfigurations,formedbycombinationsofthefiveremainingparameters.Anexhaustiveenumerationprocedurecouldbeusedtoobtaintheoptimalconfigurationswithinthisset;however,thisprocedurerequiresalargecomputationaleffortduetothelargenumberofthermalsimulationsneeded.Sinceitispossibletocalculate(DP,v)priortothethermalsimulationusingaveragevaluesforthefluidtemperatures,theconstraintsonpressuredropsandchannelvelocities(Constraints2bto2e)canbeusedtoeliminateallinfeasibleelementsinsetIS.Therefore,areducedsetofconfigurations,RS,isgenerated.ItisimportanttonotethattoobtainsetRSitisnotnecessarytocalculate(DP,v)foralltheconfigurationsinISbecauseofthefollowing:A1)parameterfhasnoinfluenceover(DP,v),A2)(DP,v)isindependentforsidesIandII.Thus,foragivenNC,thecalculationsaremadeonlyonceforeachallowablenumberofpasses,A3)foragivenNC,DPisproportionaltothenumberofpasses;therefore,ifDPDPmaxisverified,anyconfigurationwithalargernumberofpassesalsoresultsinaninfeasiblesolution,A4)foraneven-numberedNC,sidesIandIIhavethesamenumberofchannelsandthereforethesameallowablenumbersofpasses.Inthiscase,(DP,v)willhavethesamevalueforYh=1andYh=0.OncesetRSisobtained,theeffectivenessConstraint(2f)isusedtoselecttheoptimalsetofconfigurations,OS.However,itisnotnecessarytothermallysimulateallelementsinRSbecauseofthefollowing:B1)thereareequivalentconfigurationswiththesameeffectiveness;thusonlyoneneedstobesimulated,B2)ifasearchisconductedinincreasingorderofNC,whentheoptimalsetisfound,allremainingconfigurationswithhighervaluesofNCcanbeneglected.SincetheinfluenceofparameterYfontheconvectivecoefficientsandfrictionfactorisusuallyunknown,thisparametermaybefixedpriortooptimization,thusreducingthenumberofpossibleconfigurationsby50%.Moreover,itisnotpossibletochangethetypeofflowinanexistingexchanger.Basedontheseprinciples,ascreeningalgorithmisdevelopedforthesolutionofthePHEconfigurationproblem.Thestepsofthescreeningalgorithmareasfollows.Forthisalgorithm,Yfmusthaveagivenvalue(Yf=0or1).IfthereisavailabledataontheinfluenceofYfontheheatexchangeandfrictioncorrelations,thisalgorithmcanbeusedonceforeachcaseandtheresultscompared.1.Therequireddataforplate(corrugationpattern,dimensions,areaenlargementfactorandthermalconductivity),hotandcoldfluids(flowrate,inlettemperature,foulingfactorandcorrelationsforfrictionfactor,convectiveheattransfercoefficientsandphysicalproperties)andconstraints(lowerandupperboundsforConstraints(2a)to(2f)areread.2.Initialization:RS=,NC(k)=NCmin,k=1.3.AllallowablenumbersofpassesforsidesIandII(PIi,PIIj)areobtainedforNCk.4.Verificationofconstraintsonpressuredropandchannelflowvelocities:4.1The(DP,v)pairiscalculatedforthecoldfluidlocatedonsideIforeachoneofthenumbersofpassesPIi(inincreasingorder).Iftheconstraintsof(DP,v)aresatisfied,thecold-fluid/sideI-passpairisselected.IfDPmaxisexceeded,thereisnoneedtoevaluatelargernumbersofpasses.ThisprocedureisappliedtothecoldfluidlocatedonsideIIforallthenumbersofpasses,PIIj,therebyselectingthecold-fluid/sideII-passpairs.4.2Thesameprocedureasthatinstep4.1isappliedtothehotfluid,obtainingthehot-fluid/sideI-passandhot-fluid/sideII-passpairs.5.Theselectedpairsofcold-fluid/sideI-passandhot-fluid/sideII-passarecombinedtogenerateallpossibleconfigurationswithYh=0.Eachcombinationresultsinfourconfigurationssincefhasfourvaluesequivalentto(DP,v).Thesameprocedureisappliedtotheselectedhot-fluid/sideI-passandcold-fluid/sideII-passpairs,yieldingconfigurationswithYh=1.AllgeneratedconfigurationsarestoredinRS.6.IfNC(k)=NCmax,thenproceedtostep7.Otherwise,NC(k+1)=NC(k)+1,k=k+1andreturntostep3.7.SetRSisnowcomplete.Itcontainsalltheconfigurationsthatsatisfytheconstraintsonpressuredropandchannelvelocityforbothsides.Nowtheoptimalset,OS,mustbeobtained.8.TheconfigurationsinRSwiththeminimumvalueofNCareselected.9.TheequivalentconfigurationsaredetectedandgroupedusingthemethodologyshowninTab.(1).10.Thesimplifiedthermalmodel(theoverallheattransfercoefficientisconstant)isusedtosimulateoneoftheconfigurationsineachgroup,obtainingthecorrespondingthermaleffectiveness.11.Ifoneormoregroupsofequivalentconfigurationssatisfytheeffectivenessconstraint,theyarestoredinsetOSandthereisnoneedtosimulateotherelementsofRS.Otherwise,proceedtothenextvalueofNCinsetRSandreturntostep9.12.TherigorousthermalmodelisusedtosimulatethenonequivalentelementsinOStoverifytheeffectivenessresults.Incaseofdiscrepancy(|EsimplifiedErigorous|/Erigorouse),therigorousmodelshouldbeusedintheprevioussimulationsafterstep8.Otherwise,theoptimalsolutionisachieved.OPTIMIZATIONRESULTSItwasverifiedthatthenumberofchannelsperpasshasastrongeffectonthepressuredrop,andconsequently,about98%oftheelementsinISareeliminatedinthefirstpartofthescreening(steps1through8).Comparedtoanexhaustiveenumerationprocedure,thescreeningmethoddemandsapproximately5%oftherequiredevaluationsof(DP,v).Further,toobtainsetOSonlyafewelementsarethermallysimulated(approximately1%oftheelementsinISor20%oftheelementsinRS).Asanexampletoshowtheefficiencyofthescreeningmethod,considertheselectionofaconfigurationforaprocess-water(26.0kg/s,67C)/cooling-water(62.5kg/s,22C)PHEwith1.4mchevronplateswithcrossedchannelflow(Yf=1).TheconstraintboundsareshowninConstraints(4a)to(4f).Inthisproblem,IShas26,240elementsandonly1.8%ofthe(DP,v)calculationsand0.06%ofthesimulationswerenecessaryforthesolutionoftheproblembythescreeningmethod.ThecomparativeperformanceofthescreeningandenumerationmethodsisshowninFig.(4).ThesetRSobtainedcontains84configurations,rangingfromNC=43toNC=144,withpassarrangementsof1/2,2/3and2/4forhotfluid/coldfluid.Theproblemsolutionconsistsoftwopairsofequivalentconfigurations,allwith120channels,twopassesforthehotfluidandthreepassesforthecoldfluid,asshowninTab.(2).TherequiredCPUtimeinaDEC-Unixworkstationforthesimulationsofthesimplifiedmodelwasunder1min,and5minwerenecessarytovalidatetheresultsusingtherigorousmodel(thedeviationsinEwereunder1%).CONCLUSIONSTheconfigurationofagasketedplateheatexchanger(PHE)wasrepresentedbyasetofsixdistinctparametersandamethodologytodetectequivalentconfigurationswaspresented.TheproblemofoptimizingthePHEconfigurationwasformulatedastheminimizationoftheheattransferarea,subjecttoconstraintsonthenumberofchannels,thepressuredropandchannelflowvelocitiesforhotandcoldfluidsandtheexchangerthermaleffectivenessaswellasthePHEsimulationmodel.SinceitisnotpossibletoderiveamathematicalmodelofthePHEthatisexplicitlyafunctionoftheconfigurationparameters,amixed-integernonlinearprogramming(MINLP)approachcouldnotbeused.Ascreeningprocedurewasthenproposedtosolvetheoptimizationproblem.Inthisprocedure,subsetsoftheconstraintsweresuccessivelyusedtoeliminateinfeasibleandnonoptimalelementsfromthesetdefinedbytheboundsonthenumberofchannels.Analgorithmwasdevelopedtoperformthescreeningwithminimumcomputationaleffort.Examplesshowthatthisalgorithmcansuccessfullyselectagroupofoptimalconfigurations(ratherthanasinglesolution)foragivenapplicationusingaveryreducednumberofthermalsimulations.中文翻译：板式换热器构型的最佳选择的筛选方法J.M.Pinto和J.A.W.GutUSP圣保罗大学化学工程系摘要：一种确定垫片式板式换热器的最佳配置的优化方法。目标是选择仍然满足约束条件的信道数目的最小传热面积的配置，两种流体的压力降，该通道的流速和换热器的热效率。热交换器的结构由6个参数，如下定义的信道数目，通行证的每一侧的流体的位置，进给位置和不同的流中的信道的数目。生成的配置优化问题转化为尽量减少换热面积，并提出了其解决方案的筛选程序。在此过程中，依次施加约束的子集，以消除不可行的和非最佳的解决方案。实施例表明，该优化方法能够成功地确定一组最优的配置与最小数量的热交换器评估。约5的压力降和信道的速度计算和1的热模拟所需的解决方案。关键词：板式热交换器，热交换器的配置，优化，筛选方法。简介板式换热器（PHE）由一包垫圈的金属波纹板，在一个框架中压合在一起。通过一系列的平行流动通道进行热交换，通过薄金属波纹板构成的流体。板的垫圈设计和关闭的端口确定的流体流动装置，它可以是平行的，串联或几种可能的组合的两个。流板，分布，数量型垫片和进料位置交换配置的特点。构型表征为了表征的PHE配置，六个不同的参数用于NC，PI，PII，F，YH，YF，描述如下：NC：通道数PI和PII：两侧的传球数I和IIF：进给连接的相对位置YH：热流体地点YF：通道中的流量类型。这个二进制参数定义了不同的内部流动通道，它可以是直链或划线根据对垫片的类型（图1）。交叉流可避免形成的停滞区，但直路的流类型是更容易组装。一起使用这两种类型，这是不可能的。如果Yf的=1，则流程的所有通道中的交叉。如果Yf的=0时，流程是直链的所有通道中。6个参数可以表示任何常规配置和九板的板式换热器的配置的一个例子示于图。（2）。对于任何给定的信道数，NC，五个其它参数允许值的有限集合，这限制了可能的配置数，在图所示。（3）。分散模式是由于NCI和NCII数量的整数因子的变化。如果在2和500之间的信道数的范围内，有284976个不同的组态。图3：通道数可能出现的常规组态的函数等效配置对于一个给定的信道和一个固定的不同的流数的值，等效的构型（即具有相同的热效率和压力下降）的存在是可能的。相当于配置的识别是很重要的，以避免不必要的热交换器评价。两个或两个以上的配置等价的发生是由于流量可逆性的财产（PignottiTamborenea，1988），单通的存在或几何相似（构型可以自由旋转或镜像）。一种方法来检测同等构型标签。（1）。对于每一组的NC，PI，PII和Yf各组的值，结果在相当于构型参数f。在偶数NC的情况下，有可能是YH=0和YH=1之间的适合的，因为I和II两侧具有相同的信道数，因此可以有相同的遍数。考虑例如图中所示的热交换器。（2），它被设置为f=1，YH=1;为制表。（1），改变流体的两侧（YH=1（R）YH=0）将产生不同虽然等效的构型。构型优化配制成的信道的数目，NC，这相当于最小化的换热面积或者其固定费用（式1）的最小化的构型的最优化问题。通道（NC），流体压力的的下降（DPhotDPcold），通道的流速（vhot，vcold）和换热效率（E）的数量上有限制，如图以约束（2A）（2F）。优化模型也受到PHE模型，计算上述变量（约束3）所必需的。得到（2a）中的信道数目的约束有关的可利用的数字板和交换容量。流体压力降的最低值，避免了大的变化，可以弯曲板之间的平均流体压力。下界通道的流速避免的优先路径或通道内的停滞区的形成。筛选方法建议优化程序是基于的筛选方法，Daichendt之外，格罗斯曼（1994）也采用换热网络优化。在此过程中，依次使用约束除去不可行的和非最佳的MINLP问题的解决方案，从而降低了它的大小和复杂性。在板式换热器的构型的最优化，约束的数量的信道（2a）中定义的初始设置，IS，可能的构型，形成的5个其它参数组合。穷举程序，可以被用来获得该组合内的最佳构型，但是，此过程需要一个大的计算工作量，由于需要大量的热模拟。因为它是可以计算（DP，v）的前热模拟使用的流体温度的平均值，压力下降，信道速度（2b中的约束到2e）上的约束可以被用来消除所有不可行元素在套IS。因此，一组简化的构型，RS，生成的。重要的是要注意，要获得设置的RS（DP，v）的计算中的所有构型为由于下述原因，这是没有必要的：A1）参数f有没有影响（DP，V），A2）（DP，v）的独立的I和II两侧。因此，对于一个给定的NC，是由计算只有一次，每个允许的遍数，A3）对于一个给定NC，DP是遍数成比例，因此，如果DPDPMAX验证，也通过与更大数量的任何构型的查询结果在一个不可行的解决方案，A4）的偶数NC，侧面I和II具有相同数量的信道，因此，相同的允许的遍数。在这种情况下，（DP，v）的YH=1和YH=0具有相同的值。一旦设置RS获得的有效性约束（2f）的用于选择最佳的一组构型，操作系统。然而，这是没有必要的热模拟RS因为下列因素中的所有元素：B1）是等价的配置具有相同的有效性，因此只有一个需要被模拟B2），如果搜索进行数值越高，数控数控递增的顺序，找到最优集时，所有剩余的构型可以忽略不计。由于参数Yf的对流系数和摩擦系数的影响通常是未知的，是固定的，这个参数可能在优化之前，从而减少了50，可能的构型。此外，它是不可能改变现有的热交换器中的流动不同的。基于这些原则，筛选算法开发的解决方案，的PHE构型问题。筛选算法的步骤如下所示。对于此算法，Yf的必须有一个给定的值（Yf的=0或1）。Yf的热交换和摩擦的相关性的影响，如果有可用的数据，这种算法可以使用一次，每一种情况下的结果进行了比较。1。所需的数据，板（波纹图案，尺寸，面积的扩大系数和热导率），热流体和冷流体（流量，进口温度，污垢系数和摩擦系数的相关性，对流传热系数和物理性质），和约束（低级和上界约束（2A）到（2F）被读取。2。初始化：RS=AE，NC（K）=NCmin，K=1。3。所有允许的遍数，得到了双