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-,1,NewInitiativesatFluentInc.,PhaseChangeinHeatExchangers,BrianBell,FluentInc.,UGM2001,-,2,Motivation,DemonstratetheuseofFluenttomodelphasechangeinheatexchangersProcessesofinterestCondensationEvaporationBoilingIllustratehowtomodelonesuchprocessthroughuseofadetailedexampleShell-and-tubecondenserProvidemotivationforuserstobegindevelopingmodelsoftheirowndevices,-,3,Outline,ProblemDescriptionShell-and-tubecondenserPurevaporcondensationNon-condensablegasesModelingApproachPorousmediumHeatandmasstransfermodelingModelImplementationUser-DefinedFunctionsandUser-DefinedMemoryResultsSteamcondenserwithnon-condensablegasesCommercialchillercondenser,-,4,DescriptionofProblem,Shell-and-tubecondenser,-,5,GoalsofCFDModeling,CondenserperformancecharacterizedbyheatandmasstransferrateCFDallowsevaluationoffactorsaffectingheatandmasstransferincondenserTubebundleconfigurationTubearrangementNumberofpassesLocationofinletportsBafflesPressuredropVelocityfieldNon-condensablesLocationandconfigurationofpurgesystemResultsallowidentificationofpotentialdesignimprovements,-,6,FilmCondensationProcess,DrivingpotentialforcondensationisthetemperaturedifferencebetweenvaporandcoolingwaterDrivingpotentialvariationcausedbyPressuredropRiseofcoolingwatertemperatureNon-condensables,-,7,CFDModelingTheory,PorousmediumapproachTubebundletreatedasporousmediumEnablescomputationallyefficientmodelingofentirecondenserComparisonwithdetailedmodelingapproachIn2-D,O(100)-O(1000)controlvolumespertubeversusmorethanonetubepercontrolvolumeHeatandmasstransfermodelsCondensationratecalculationCondensationratedeterminedfromlocalflowfieldandcoolingwatertemperatureLiquidfilmflowratetrackedinbundlefromtoptobottomCoolingwatertemperaturetrackedfrominlettooutlet,-,8,PorousMediumApproach,RepresentationoftubebundleasporousmediumPorosityisonlyrequiredparameterPorositydefinedasratiooffluidvolumetototalvolume,Example:staggeredtubebundlewithequilateraltriangularlayout,Porosity,b,expressedas:,-,9,TransportEquations,Generictransportequationforporousmediumapproach,DistributedresistancetakesformofsourcetermsthatmodeldetailsoftheflowthatarenotresolvedbythegridPorosityinconvectionanddiffusiontermsnotmodeledinFluentDistributedresistancetermsmostsignificantintubebundleregion,-,10,EvaluationofModelingApproach,AdvantagesComputationallyefficientDoesanalternate,tractableapproachexist?ApproachdemonstratedtogivemeaningfuldatabyseveralauthorsDisadvantagesLossofsomeflowdetailsduetoaveragingCanbeovercomebydetailedmodelingofsmallregionsofcondenser,-,11,HeatTransferProcess,Filmcondensationonhorizontaltube,CoolingWater,TubeWall,CondensateFilm,Liquid-vaporInterface,RefrigerantVapor,Latentheatreleasedatliquid-vaporinterfacetransferredtocoolingwater,-,12,HeatTransferModel,HeattransferismodeledbycouplingofthermalresistancenetworkwithCFDcode,Tcw,Tt,i,Tt,o,Ti,Rcw,Rtube,Rcond,CoolingWater,CFDcodeprovidesinterfacetemperature,TiCoolingwaterandtubethermalresistancesaregenerallywell-knownFilmheattransfercoefficientisrequiredforRcond,-,13,FilmHeatTransferCoefficient,CriticalcomponentofheattransfermodelObtainfromexperiment,OrobtainfromliteratureSteamcondensationonsmoothtubes,FigurecourtesyofKansasStateUniversity,ProfessorSteveEckles,andDuaneL.Randall,-,14,ModelingAssumptions,EffectofliquidonflowfieldisneglectedApproachcanalsobeimplementedinEulerian-EulerianmultiphaseframeworkSatisfactorymodelforliquidphaserepresentationnotcurrentlyavailablePublishedresultsofthistypeofmodeldonotappeartoshowsignificantadvantageVaporisassumedtobesaturatedNosuperheatingVaportemperaturedeterminedfrompressurefieldcalculatedbyCFDcode,-,15,ImplementationofModelwithUDFs,UDFsarerequiredfor:SourcetermsrequiredbyporousmediumapproachCondensationratePressuredropinporousregionRepresentationoftubebundlePorosityCondensatefilmflowrateaccountingCoolingwatertemperaturecalculationwithmultipletubepasses,-,16,CoolingwatertemperaturecalculationforeachsegmentEveryiteration,condensationrateissummedovereachsegmentInletcoolingwatertemperature=outlettemperaturefromprevioussegmentSegmentoutletcoolingwatertemperaturecalculatedbyenergybalance.Log-meantemperatureforeachsegmentcalculatedbasedonvaportemperatureandcoolingwaterinletandoutlettemperatures,TubeBundleRepresentation,BundleconsistsofNpassesandMsegmentsEachsegmentdefinedasuniquecellzone,Example:2PassbundleN=2,M=4,-,17,TubeBundleGridStructure,Structured,cartesiangridusedintubebundleEachcontrolvolumehasuniquei,j,kindex,GridstructurecreatedwithUDFsGridgenerator,solverdoNOTutilizestructureUsedtotrackcondensatefilmflowrate,-,18,SourceTerms,AlgorithmforsourcetermincontinuityequationObtainpressure,velocityandspeciesmassfraction(ifnecessary)fromcurrentsolutionvaluesObtainfilmReynoldsnumberandcoolingwatertemperaturefromUser-DefinedMemoryCalculateheatfluxbasedoncurrentvalueofsolutionvariablesTranslateheatfluxintovolumetricmasssourcetermUnder-relaxsourcetermSi+1=Si+a(SoSi)Requiredforsolutionstability.Alphatypically0.010.10Valueofsourcetermfrompreviousiteration,So,storedinUser-DefinedMemorySourceterminmomentumequationsCalculatedusingempiricalcorrelationswithtubebundleporosityandcurrentvelocity,-,19,Define_On_DemandFunctions,Define_On_DemandfunctionsexecutedonceperiterationUpdatecondensatefilmmassflowrateUpdatecoolingwatertemperatureAssumeuniformtemperatureforeachbundlesegmentNewvaluesstoredinUser-definedmemoryAutomaticDefine_On_DemandexecutionpossibleExample:,-,20,SolutionAlgorithm,InitializeSolution:Assignporosity,tubebundleorientation,Updatecoolingwatertemperatureandliquidcondensatemassflowrate,Calculatesourceterms,Solveflowequations,Yes,No,SolutionConverged?,Stop,-,21,Examples,Steamcondensationwithnon-condensablegases,McAllisterCondenserfrom:Bushetal.,1990,Proc.Int.Symp.OnCondensersandCondensation,-,22,McAllisterCondenserGeometry,BoundaryconditionsandmodelinputsShellDimensions1.02mX1.22mX0.78m,CoolingwaterflowdirectionInlettemperature:17.8CInletvelocity:1.19m/s,TubeBundleSinglepass,4segmentsOuterDiameter:.0254mInnerDiameter:.0242mPitch:.0349mPorosity:0.52,PurgeMassflowrate:.011kg/s,InletPressure:27670PaAirmassfraction:0.00122,-,23,CondenserGrid,15,000ControlVolumesSimplegeometryallowsstructuredgridthroughoutdomain,Gridprofileinx-zplane,-,24,Results,CondensationRate,InletmassflowrateCFD:2.124kg/sExp.:2.032kg/sError:4.5%,Coolingwatertemperaturecontours,Volumetriccondensationratecontours,-,25,McAllisterCondenserFlowField,VelocityMagnitudeMax:34.4m/sMin:0.02m/s,PressureMax:27,663PaMin:27,530Pa,AirMassFractionMax:.534Min:.00122,CondensationRate*Max:6.1kg/smMin:0.0kg/sm,*Minimumcondensationrateintubebundleis0.18kg/sm,-,26,EffectofAironCondensationRate,Volumetriccondensationratecontou
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