models.ssf.convection_porous_medium.pdf

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1、SolvedwithCOMSOLMultiphysics4.3bFreeConvectioninPorousMediaIntroductionThisexampledescribessubsurfaceflowinporousmediadrivenbydensityvariationsthatresultfromtemperaturechanges.ThemodelcomesfromHossainandWilson(Ref.1)whouseaspecializedin-housecodetosolvethisfree-convectio

2、nproblem.ThisCOMSOLMultiphysicsexamplereproducestheirworkusingtheBrinkmanEquationsinterfaceandtheHeatTransferinPorousMediainterface.Theresultsofthismodelmatchthoseofthepublishedstudy.ModelDefinitionThefollowingfiguregivesthemodelgeometry.Waterinaporousmediumlayercanmovew

3、ithinthelayerbutnotexitfromit.Temperaturesvaryfromhightolowalongtheouteredges.Initiallythewaterisstagnant,buttemperaturegradientsalterthefluiddensitytothedegreethatbuoyantflowoccurs.Theproblemstatementspecifiesthattheflowissteadystate.Figure1:Domaingeometryandboundarycon

4、ditionsfortheheatbalanceinthefree-convectionproblem.ThisahighertemperaturethanTc,whilesisavariablethatrepresentstherelativelengthofaboundarysegmentandgoesfrom0to1alongthesegment.©2013COMSOL1

5、FREECONVECTIONINPOROUSMEDIASolvedwithCOMSOLMultiphysics4.3bYoumodelthisfree-conv

6、ectionproblembyintroducingaBoussinesqbuoyancytermtotheBrinkman’smomentumequation,andthenlinkingtheresultingfluidvelocitiestotheHeatTransferinPorousMediainterface.TheBoussinesqbuoyancytermthatappearsontheright-hand-sideofthemomentumequationaccountsfortheliftingforceduetot

7、hermalexpansionμμT---u+∇p–∇⋅---()∇u+()∇u=ρgβ()TT–(1)κεc∇⋅u=0.Intheseexpressions,TrepresentstemperaturewhileTcisareferencetemperature,gdenotesthegravityacceleration,ρgivesthefluiddensityatthereferencetemperature,εistheporosity,andβisthefluid’scoefficientofvolumetrictherma

8、lexpansion.TheheatbalancecomesfromtheheattransferequationρCu⋅∇∇T–⋅()k∇T=0(2)Leqwherekeqdenotestheeffectivethermalconductivityofthefluid-solidmixture,andCListhefluid’sheatcapacityatconstantpressure.TheboundaryconditionsfortheBrinkmanequationsareallno-slipconditions.Usingo

9、nlyvelocityboundariesgivesnoinformationonthepressurewithinthedomain,whichmeansthatthemodelproducesestim