CFD-modelling-and-validation-of-wall-condensation-

NuclearEngineeringandDesign279(2014)137–146ContentslistsavailableatScienceDirectNuclearEngineeringandDesignjournalhomepage:∗,T.Franka,A.D.BurnsbaANSYSGermanyGmbH,Staudenfeldweg12,Otterfing83624,GermanybANSYSUKLtd,97MiltonPark,Abingdon,OxfordshireOX144RY,UKhighlights•AwallcondensationmodelwasimplementedandvalidatedinANSYSCFX.•Condensationrateisassumedtobecontrolledbytheconcentrationboundarylayer.•Validationwasdoneusingtwolaboratoryscaleexperiments.•CFDcalculationsshowgoodagreementwithexperimentaldata.articleinfoArticlehistory:Received5March2014Accepted17March2014abstractTheaimofthispaperistopresentandvalidateamathematicalmodelimplementedinANSYSCFDforthesimulationofwallcondensationinthepresenceofnon-condensablesubstances.Themodelemploysamasssinkatisothermalwallsorconjugateheattransfer(CHT)domaininterfaceswherecondensationtakesplace.ThemodelwasvalidatedusingthedatareportedbyAmbrosinietal.(2008)andKuhnetal.(1997).©2014ElsevierB.V.Allrightsreserved.1.IntroductionDuringapostulatedlossofcoolantaccident(LOCA)largeamountsofsteamarereleasedintothenuclearcontainmentbuild-ing.CondensationonthecontainmentwallsisforeseenasoneofseveralpassivemechanismstokeeppressurebelowthedesignthresholdingenerationIIIandIII+reactors(delaRosaetal.,2009).InsuchaLOCAscenario,itisexpectedthatthewallcondensationprocessishinderedbythepresenceofnon-condensablegases(e.g.airoriginallypresentinnuclearcontainment),sincetheyaccumu-lateattheliquid–gasinterfacecreatingadiffusionbarrierforthewatervapour.Inordertoefficientlymodelthewallcondensationinthepresenceofnon-condensablegasesusingCFD,severalbound-aryconditionformulationshavebeenproposedinthepastforlaminar(e.g.KarkoszkaandAnglart,2008)andturbulentflows(e.g.Ambrosinietal.,2005;Houkemaetal.,2008;Kelm,2010).Thispaperdescribesthemathematicalformulationofthewall∗Correspondingauthor.Tel.:[phone].E-mailaddress:[e-mail](G.Zschaeck).condensationmodelforturbulentflowsimplementedinANSYSCFXanditsvalidationagainsttwodifferentlaboratoryscalecases.2.MathematicalmodelThepresentmodelemploysamasssinktoamulti-componentgaseousfluid,whichisamixtureofcondensableandnon-condensablecomponents.Thismasssinkisdefinedatwallboundariesandconjugateheattransfer(CHT)interfacestosim-ulatetheremovalofcondensablecomponentsonsurfaceswhicharesufficientlycoldtopermitcondensationontoathinliquidfilmonthewall.ForCHTinterfaces,anenergysourcetermisaddedtoaccountforthelatentheatduetocondensation.Thefollowingmainassumptionsapplytotheproposedwallcondensationmodel(seeFig.1):•Thefluidconsistsofamulti-componentgaseousmixturewithonecondensableandatleastonenon-condensablecomponent•Thecondensationrateiscontrolledbytheconcentrationbound-arylayer•Thepartialpressureofthecondensablecomponentatthewallisequaltoitssaturationpressureevaluatedattheinterfacetemperature©2014ElsevierB.V.Allrightsreserved.138G.Zschaecketal./NuclearEngineeringandDesign279(2014)137–146Fig.1.WallcondensationofcomponentBinthepresenceofnon-condensablegasA:leftcondensationprocess,rightsimplifiedmodel.AdaptedfromKelm(2010).•Thedetailsoftheliquidfilmarenotmodelled(thesimulationissinglephase)andthemassofgaseousphasewhichislostbycondensationisremovedfromthesystem,i.e.re-evaporationandcondensateaccumulation/transportisnottakenintoaccount•Wallfunctionsarenotinfluencedbywallsuction•AtaCHTinterface,thelatentheatreleasedbycondensationisassumedtobeabsorbedbythesolidmaterialattheinterfaceInaturbulentboundarylayer,themassfluxesMAwandMBwofanon-condensablecomponent(A)andacondensablecomponent(B)ofabinarygaseousmixturearegivenby:MAw=MMix·YAw−k··(YAp−YAw)(1)MBw=MMix·YBw−k··(YBp−YBw)(2)whereYisthemassfraction,thedensityandkistheturbulentmasstransfercoefficient,whichisafunctionofy+andthemolecularSchmidtnumber,asinKader(1981).Here,wsubscriptsrefertowallquantities;psubscriptsrefertonearwallmeshpoints.TheequationsaboveareaspecialformofFick’sfirstlaw(Birdetal.,1960).SincecomponentAdoesnotcondense,MBw=MMix.Hence,sub-stitutingintoEq.(2)andrearranginggives:MBw=−k(y+,Sc)··YBp−YBw1−YBw(3)ThevalueofYBpisobtainedfromthesolutionofatransportequationforthecondensablesubstance.ThevalueofYBwiscalcu-latedfromthecondensablecomponent’smolarfractionXBw,whichisdeterminedbyassumingthatthevapourisinthermalequilib-riumwiththeliquidfilmattheinterface,andhenceitspartialpressureisequaltoitssaturationpressureattheinterfacetem-perature.Inreality,thevapourattheedgeoftheboundarylayermaybeasupersaturatedwetvapour,ormist.Onlythedrypartofthevapourwillformtheconcentrationgradientwhichdrivesthecondensationmassflux.Hence,onlythemolarfractionofdryvapourisusedtodeterminethemassflux.Fortheenergyequation,twoconditionsareallowedforthecon-densationmodel:anisothermalwallorafluid–solidinterface.Incaseofanisothermalwallboundary,thewallisassumedtoconsti-tuteaninfinitereservoironwhichtheeffectofthecondensationheatsourceisnegligible;henceitismaintainedatitsconst