FLOW-3D多孔介质模型-渗流模型

ExamplesofPorousMedia08December2022UserTrainingSpongeWireScreenStreambedSinterMetalFilterPaperTubeBundle第一页，共37页。PorouscomponentsRequire2computationalcellstoadequatelyresolveModelobjectascomponentifSignificantgradientsoccurthroughthicknessofmaterialMaterialisanisotropicPorousmaterialmaybeIsotropic(e.g.bedofuniformparticles)Anisotropic(e.g.tubebundles)PorousbafflesNothickness,resideoncellfacesBestformodelingscreensDragcanbelinearorquadraticModelassumesbaffleissaturated,nobubblepressureacrossTypesofPorousObjectsinFLOW-3D08December2022UserTraining第二页，共37页。

PorousMediaModelingTheory第三页，共37页。Listoftopics介绍达西定律（Darcylaw）介绍FLOW-3D®拖曳力模型(dragmodel)介绍饱和多孔介质模型(thesaturatedporousmediamodel)介绍拖曳力系数与渗透率的关系(dragcoefficientandpermeability)如何处理流体在多孔介质中的各向异性(anisotropy)特征介绍非饱和多孔介质模型(theunsaturatedporousmediamodel)第四页，共37页。达西定律（DarcyLaw）Q:unitsofvolumepertime(e.g.,m³/s)A:cross-sectionalarea(Pb−Pa):thepressuredropμ:dynamicviscosityΚ:thepermeabilityofthemedium(unitsofarea,e.g.m²)L:thelength第五页，共37页。Darcy’sLaw:Flowratethroughporousmediaisproportionaltopressuredropaccordingto:where

v=macroscopic(superficial)velocity(FLOW-3Dcomputesandreportsmicroscopicvelocity) K=intrinsicpermeability-maybeisotropicoranisotropic(directional)

m=dynamicviscosity P=fluidpressurePermeabilityPropertyoftheporousmaterialRepresentstheaverageresistancetoflowinacontrolvolumeDarcy’slawrepresentsviscouslossesthroughporesApplicablewhenporeReynoldsnumberRep~1,whereRep=ApplieswelltotightlypackedspheresandfibersDoesnotrepresentinertiallossesinlooselypackedbedsViscousDraginPorousMedia:Darcy’sLaw第六页，共37页。InertialdragbecomessignificantwhenRepexceeds10Darcy’sLawcanbeextendedtoincludeinertialeffectsQuadraticdrag:Forchheimer’sEquationInertialLosses:Forchheimer’sEquationviscoustransitionalinertialwherer=fluiddensity第七页，共37页。UnderstandingFLOW-3D®’s

DragModel由于流体在多孔介质中受到的很多阻力太小而无法求解，所以用一个均布的阻力系数来计算：K

表示拖曳力系数，也就是流体在多孔介质中的流动阻力。TotalaccelerationInertiaAcc.duetopress.gradientAccel.duetoviscosityAccel.duetogravityDrageffectsVf=Volumefraction(porosity)ofcomputationalcellAf=DiagonaltensorareafractionsofcellN-S张量方程第八页，共37页。Porousmaterialcharacterizedby:SolidstructurepermeatedbyinterconnectedcapillariesMayconsistoffibers,particles,openporesTwotypesofflowinsideporousmediaSaturatedAssumesmediaisalreadywetIfinterfacebetweenfluidandairexists,treatedassharpUnsaturatedDiffusefluid/airinterface-wickingHysteresis(filling/draining)effectsTwocontributionstofluiddraginporousmediaViscous(SkinDrag)Inertial(FormDrag)PorousMediaFlow第九页，共37页。Resolveallgeometry(FAVOR)ComputepressuresandvelocitiesdirectlyfromNavierStokesequationsUsefulforcharacterizingmaterialsComputationallyexpensiveApproachestoModelingPorousMaterialsDirectVolumeAveragedGeometryrepresentedasvolumefraction(porosity)opentoflowAssumeflowisuniformovercellRequiressomeknowledgeofmaterialPorosityPressuredropvsvelocity orParticle/fibersizeFocusofthispresentationisthevolumeaveragedapproach第十页，共37页。SaturatedFlowUnsaturatedFlowInterfacialEffects:CapillaryPressureGenerallyappliestoflowthroughporousregionsfilledwithwaterAir/waterinterfaceissharpCapillarypressurefunctionofporediameterAppliestoflowthroughporousregionswhichmaybewetordryAir/waterinterfaceisdiffuse(wicking)Capillarypressurefunctionofsaturationanddirection,i.e.fillingordraining第十一页，共37页。Porousmediasimulationsetupsteps:Decideflowtype:SaturatedorUnsaturatedDefineporousgeometryDragModel3choicesforsaturatedflow1choiceforunsaturatedflowCharacterizeMaterialPorosityFitdragcoefficientsexperimentaldatacomputefromfiber/particlesizeSettingUpAPorousMediaSimulationSaturatedUnsaturated第十二页，共37页。SaturatedporousmediaUsefulforsituationswherethereexistsawell-definedsaturationfrontwiththeporousmaterialModelassumesthatsaturatedregionsareseparatedfrom“dry”regionsbyathinsaturationfrontPressuredifferenceacrossthissaturationfrontisdictatedbyauser-definedcapillarypressure(Pcap)dafluidinaporesConcavecase(lowerpressureinliquid)isassumedtohave+vePcap第十三页，共37页。拖曳力与渗透率关系式OftenconfusionarisesbetweenDarcypermeability(κ)andthedragcoefficient(K).Therelationshipis:Thus,amaterialwith∞dragrepresents0permeability“Dragcoefficient”inFLOW-3Doutputis:

Thiscanvarybetween0(infinitedrag)and1(zerodrag) andisdimensionlessand第十四页，共37页。拖曳力系数（Thedragcoefficient）or第十五页，共37页。Settingupaproblemwithsaturated

porousmedia激活Porousmedia多孔介质物理模型创建porouscomponent(s)多孔材料每一个component可以由多个sub-components或STL文件来创建更复杂的形状在每一个component需指定孔隙率（porosity），毛细管压力（capillarypressure）及拖曳系数（dragcoefficients）每一个component可以设定不同属性第十六页，共37页。Modelinganisotropicmaterials

withFLOW-3D®渗透率（Permeability）是具有各向异性的，也就意味着流体的渗透率在每个流动方向都不同。在

FLOW-3D®软件中，用户可以指定各方向的孔隙率（porosity），其可控制各方向的面积比例值（theareafraction-Af)若设定一个方向的数值比其它两个方向小，那么在该方向流动时开口面积会变小总的孔隙率设定为三个方向中最大值第十七页，共37页。Settinganisotropicmaterials

exampleSupposewehaveasheet-likematerialwhere:Thentheporosityinthex,ydirectionsshouldbesetto0.6(thetrueporosity)Theporosityinthez-directionissetto0.45(0.6×1.5/2)Thedragcoefficientissetaccordingtothehigherpermeability(3000s-1inthiscase)κx,κy=2×10-6cm2κz=1.5×10-6cm2Porosity=0.6第十八页，共37页。Sample:multilayerporousmaterialDropisabsorbedintothreelayerporousmaterialSaturatedmodelusedPorosityPcapadrgbdrgTop&bottomlayers50%6×1033.5×1071×105Middlelayer35%9×1035×1071×105Permeabilityratioformiddlelayer:κz/κr=0.710s0.1s0.2s1s第十九页，共37页。第二十页，共37页。UnsaturatedporousmediamodelWiththisoption,modelsimulatessaturationgradientsandvariescapillarypressurethroughoutRegionswithlowersaturationpredictedtohavegreater(i.e.morenegative)capillarypressureModel(w/ocustomization)presumeswettingmediumtomodelfluidHysteresisincapillarypressurepredictedDragisfunctionofsaturation(fractionofporespaceoccupiedbyfluid)or第二十一页，共37页。Capillarypressuremodelfor

unsaturatedporousmediaSamplecurvesatleftshowbothfillinganddrainingcurvesPcapwillfollowappropriatecurveduringcontinuousfillingordrainingWhenregionofporousmaterialswitchesbetweenfillinganddraining,PcapwillfollowscanningcurveuntilitreachesmaincurveDrainingcurveFillingcurveSamplescanningcurves第二十二页，共37页。Definingcompositesofdifferent

materialsAswiththesaturatedporousmediamodels,compositesaredefinedfirstbycreatingcomponentsSpecificationsforcapillarypressurecurvesaremadeininputfilepcapnamelistmustfirstbecreatedwithininputfilelocatedbetweenthescalarandbcdatanamelists第二十三页，共37页。Settinguptheinputfilefor

unsaturatedporousmediamodelingCreatepcapnamelistprovideglobalvaluesforfcmn,fcmx,fpcmx,pcmx,pexpThesewillapplytoallcomponentsbydefaultAddcomponent-specificvaluesifdesiredinobsnamelistprovidevaluesforofcmn,ofcmx,ofpcmx,opcmx,opexpApplyonlytospecificcomponentAlso,idfitoriodfitparameterscontroldragfunction1–powerlawfunction2–exponentfunction第二十四页，共37页。实例:多个孔隙率材料的仿真Component1Component4Component5Component3Component2ComponentpcmxfpcmxPexp11×1060.150.922.5×1050.20.535×105