COMSOL微孔流动

SolvedwithCOMSOLMultiphysics4.3b©2013COMSOL1|PORE-SCALEFLOWPore-ScaleFlowIntroductionThismodelusesCreepingFlow(StokesFlow)tosolvetheflowintheintersticesofaporousmedium.Themodelcomesfrompore-scaleflowexperimentsconductedbyArturoKeller,MariaAuset,andSanyaSirivithayapakornoftheUniversityofCalifornia,SantaBarbara.Toproducethemodelgeometrytheyusedelectronmicroscopeimages.Thistypeofnon-conventionalpore-scalemodelingwithCOMSOLMultiphysicsshedsnewlightonthemovementoflargeparticulatesandcolloidsmovingthroughvariable-poregeometriesinthesubsurface.SeveraloftheseresearchershavepublishedresultsfromtheirCOMSOLMultiphysicsmodelinginthepublicationWaterResourcesResearch(Ref.1andRef.2).Keller,Auset,andSirivithayapakorndesignedtheirlabexperimentsonthebasisofscanningelectronmicroscope(SEM)imagesofthinlyslicedrocksections(Figure1).Theyetchedthegeometricpatternsfromtheimagesontoasolidwithanelaborateprocesssimilartotheetchingofsiliconwafers.TheythentransferredtheseimagestoDXFfiles,whichtheyfinallyimportedintoCOMSOLMultiphysics.Figure1:Scanningelectronmicroscopeimageoftherepeatpatterninthesiliconwafer.Thescaleatbottomindicatesthatporethroatandbodydimensionsareontheorderof1μm–100μm(Ref.1).SolvedwithCOMSOLMultiphysics4.3b2|PORE-SCALEFLOW©2013COMSOLItistypicaltorepresentfluidflowinthesubsurfaceasacontinuumprocessusingaverageor“continuous”propertiesforthebulkratherthandetailingtheshapeandorientationofeachsolidparticlewithinaporousmedium.Insertingthebulkpropertiesintoanequation,suchasDarcy’slaworBrinkmanequations,givesanaverageflowrateforthetotalvolume.Whilebulkapproximationstypicallyproduceexcellentestimatessufficientforconsideringflowoverlargeareas,theymightmissthebetween-grainnuancesthataclose-upStokesflowanalysiswouldgive.Thisexerciseisdividedintwomodels:ThefirstmodeltakesoneoftheSEMimagesofKeller,Auset,andSirivithayapakornandsolvesfortheflowvelocityandpressuredropintheporethroatsusingtheCreepingFlowinterface.ThegeometryisimportedasDXFfileandonlytheporespaceismeshed,butnotthesolidregions.Thesecondmodelisdevotedtothemodelingofthewholeslice,byimportingtheSEMimageandderivingporousmediumproperties,suchasporosityandpermeabilityforfurtheruseintheBrinkmanEquationsinterface.ModelDefinitionTheentiremodelcovers640μmby320μm.Watermovesfromrighttoleftacrossthegeometry.Theflowintheporesdoesnotpenetratethesolidgrains.Theinletandoutletfluidpressuresareknown.Assumenoflowatthetopandbottomboundaries.Theprimaryzoneofinterestistherectangularregionwithanupperleftcornerat(0,0)μmandlowerrightcoordinatesat(581.6,−265.0)μm.InletOutletSymmetrySymmetryFigure2:A640μmby320μmgeometryandboundaryconditions.Sincethechannelsareatmost0.1mminwidthandthemaximumvelocityislowerthan10-4m/s,themaximumReynoldsnumberislessthan0.01.SinceReynoldsSolvedwithCOMSOLMultiphysics4.3b©2013COMSOL3|PORE-SCALEFLOWnumberisfarlessthanone,themodelusestheCreepingFlow(StokesFlow)interface,insteadoftheLaminarFlow(Navier-Stokes)interface.Thefluidisconsideredisothermalandwithconstantdensity.Owingtotheproblem’ssmallscale,themodeldoesnotconsidergravity.TheCreepingFlowinterfacesolvesStokesequationsinthechannels.Theincompressibleassumptiontogetherwiththestationaryconditionreadshere,pisthepressure,uisthevelocityfield,andμisthedynamicviscosityofthefluid.Atthemodel’sphysicalboundaries,theinletpressureandtheoutletpressureareknown.Velocitiesarezeroatthegrainboundaries,whichimpliesano-slipcondition.Theflowissymmetricaboutthetopandbottomboundaries.Table1summarizestheboundaryconditions.BOUNDARYTYPEBOUNDARYCONDITIONVALUEInletPressure,noviscousstressp=p0OutletPressure,noviscousstressp=0GrainwallsWallnoslipSymmetrysidesSymmetry-Herep0isaspecifiedpressuredrop.Table2collectstherelevantmodeldata.QUANTITYVALUEDESCRIPTIONρ01000kg/m3Fluiddensityμ00.001kg/(m·s)Fluiddynamicviscosityp00.715PaPressuredropResultsandDiscussionFigure3showstheCOMSOLMultiphysicssolutionpredictedwiththecreepingflowanalysisforthefluidvelocityfieldintheporespacesofamicro-scaleporousslice.Thevelocitymagnitudeishigherinthenarrowestporesthanattheinlet,tendingtodecreaseinstretcheswherethechannels’cross-sectionalareaincreases.TABLE1:BOUNDARYCONDITIONSTABLE2:MODELDATA0∇–p∇μ∇u∇uT+()⋅+=∇u⋅0=SolvedwithCOMSOLMultiphysics4.3b4|PORE-SCALEFLOW©2013COMSOLFigure3:SurfaceandarrowplotsofthevelocityfieldcalculatedbytheCreepingFlowinterface.ModelDefinitionThesecondmodeltakesacompletelydifferentapproachthanthefirstmodel.Here,thescanningelectronmicroscopeimageisimportedandphysicalpropertiesarederivedfromthecolorscale.Asopposedtoconsumercameras,SEMimagesaregrayscale,butinthisexample,thecolorcodeisbinary,seeFigure4.Insteadofsolvingforthecreepingflowinthechannels,theincompressible,stationaryBrinkmanequations,withtheStokes-Brinkmanassumptionisusedhere,pisthepressure,uisDarcy’svelocityfield,μisthedynamicviscosityofthefluid,εpistheporosity,andκisthepermeabilityofthemedium.0∇–p∇μεp-----∇u∇uT+()μκ---u–⋅+=∇u⋅0=SolvedwithCOMSOLMultiphysics4.3b©2013COMSOL5|PORE-SCALEFLOWInordertodefinephysicalpropertiesfromtheimagecolorcode,thefollowingrelationshasbeenimplementedfortheporosi