ExamplesofPorousMedia08December2022UserTrainingSpongeWireScreenStreambedSinterMetalFilterPaperTubeBundle第一頁，共37頁。PorouscomponentsRequire2computationalcellstoadequatelyresolveModelobjectascomponentifSignificantgradientsoccurthroughthicknessofmaterialMaterialisanisotropicPorousmaterialmaybeIsotropic(e.g.bedofuniformparticles)Anisotropic(e.g.tubebundles)PorousbafflesNothickness,resideoncellfacesBestformodelingscreensDragcanbelinearorquadraticModelassumesbaffleissaturated,nobubblepressureacrossTypesofPorousObjectsinFLOW-3D08December2022UserTraining第二頁，共37頁。

PorousMediaModelingTheory第三頁，共37頁。Listoftopics介紹達(dá)西定律（Darcylaw）介紹FLOW-3D?拖曳力模型(dragmodel)介紹飽和多孔介質(zhì)模型(thesaturatedporousmediamodel)介紹拖曳力系數(shù)與滲透率的關(guān)系(dragcoefficientandpermeability)如何處理流體在多孔介質(zhì)中的各向異性(anisotropy)特征介紹非飽和多孔介質(zhì)模型(theunsaturatedporousmediamodel)第四頁，共37頁。達(dá)西定律（DarcyLaw）Q:unitsofvolumepertime(e.g.,m3/s)A:cross-sectionalarea(Pb?Pa):thepressuredropμ:dynamicviscosityΚ:thepermeabilityofthemedium(unitsofarea,e.g.m2)L:thelength第五頁，共37頁。Darcy’sLaw:Flowratethroughporousmediaisproportionaltopressuredropaccordingto:where

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

m=dynamicviscosity P=fluidpressurePermeabilityPropertyoftheporousmaterialRepresentstheaverageresistancetoflowinacontrolvolumeDarcy’slawrepresentsviscouslossesthroughporesApplicablewhenporeReynoldsnumberRep~1,whereRep=ApplieswelltotightlypackedspheresandfibersDoesnotrepresentinertiallossesinlooselypackedbedsViscousDraginPorousMedia:Darcy’sLaw第六頁，共37頁。InertialdragbecomessignificantwhenRepexceeds10Darcy’sLawcanbeextendedtoincludeinertialeffectsQuadraticdrag:Forchheimer’sEquationInertialLosses:Forchheimer’sEquationviscoustransitionalinertialwherer=fluiddensity第七頁，共37頁。UnderstandingFLOW-3D?’s

DragModel由于流體在多孔介質(zhì)中受到的很多阻力太小而無法求解，所以用一個(gè)均布的阻力系數(shù)來計(jì)算：K

表示拖曳力系數(shù)，也就是流體在多孔介質(zhì)中的流動(dòng)阻力。TotalaccelerationInertiaAcc.duetopress.gradientAccel.duetoviscosityAccel.duetogravityDrageffectsVf=Volumefraction(porosity)ofcomputationalcellAf=DiagonaltensorareafractionsofcellN-S張量方程第八頁，共37頁。Porousmaterialcharacterizedby:SolidstructurepermeatedbyinterconnectedcapillariesMayconsistoffibers,particles,openporesTwotypesofflowinsideporousmediaSaturatedAssumesmediaisalreadywetIfinterfacebetweenfluidandairexists,treatedassharpUnsaturatedDiffusefluid/airinterface-wickingHysteresis(filling/draining)effectsTwocontributionstofluiddraginporousmediaViscous(SkinDrag)Inertial(FormDrag)PorousMediaFlow第九頁，共37頁。Resolveallgeometry(FAVOR)ComputepressuresandvelocitiesdirectlyfromNavierStokesequationsUsefulforcharacterizingmaterialsComputationallyexpensiveApproachestoModelingPorousMaterialsDirectVolumeAveragedGeometryrepresentedasvolumefraction(porosity)opentoflowAssumeflowisuniformovercellRequiressomeknowledgeofmaterialPorosityPressuredropvsvelocity orParticle/fibersizeFocusofthispresentationisthevolumeaveragedapproach第十頁，共37頁。SaturatedFlowUnsaturatedFlowInterfacialEffects:CapillaryPressureGenerallyappliestoflowthroughporousregionsfilledwithwaterAir/waterinterfaceissharpCapillarypressurefunctionofporediameterAppliestoflowthroughporousregionswhichmaybewetordryAir/waterinterfaceisdiffuse(wicking)Capillarypressurefunctionofsaturationanddirection,i.e.fillingordraining第十一頁，共37頁。Porousmediasimulationsetupsteps:Decideflowtype:SaturatedorUnsaturatedDefineporousgeometryDragModel3choicesforsaturatedflow1choiceforunsaturatedflowCharacterizeMaterialPorosityFitdragcoefficientsexperimentaldatacomputefromfiber/particlesizeSettingUpAPorousMediaSimulationSaturatedUnsaturated第十二頁，共37頁。SaturatedporousmediaUsefulforsituationswherethereexistsawell-definedsaturationfrontwiththeporousmaterialModelassumesthatsaturatedregionsareseparatedfrom“dry”regionsbyathinsaturationfrontPressuredifferenceacrossthissaturationfrontisdictatedbyauser-definedcapillarypressure(Pcap)dafluidinaporesConcavecase(lowerpressureinliquid)isassumedtohave+vePcap第十三頁，共37頁。拖曳力與滲透率關(guān)系式OftenconfusionarisesbetweenDarcypermeability(κ)andthedragcoefficient(K).Therelationshipis:Thus,amaterialwith∞dragrepresents0permeability“Dragcoefficient”inFLOW-3Doutputis:

Thiscanvarybetween0(infinitedrag)and1(zerodrag) andisdimensionlessand第十四頁，共37頁。拖曳力系數(shù)（Thedragcoefficient）or第十五頁，共37頁。Settingupaproblemwithsaturated

porousmedia激活Porousmedia多孔介質(zhì)物理模型創(chuàng)建porouscomponent(s)多孔材料每一個(gè)component可以由多個(gè)sub-components或STL文件來創(chuàng)建更復(fù)雜的形狀在每一個(gè)component需指定孔隙率（porosity），毛細(xì)管壓力（capillarypressure）及拖曳系數(shù)（dragcoefficients）每一個(gè)component可以設(shè)定不同屬性第十六頁，共37頁。Modelinganisotropicmaterials

withFLOW-3D?滲透率（Permeability）是具有各向異性的，也就意味著流體的滲透率在每個(gè)流動(dòng)方向都不同。在

FLOW-3D?軟件中，用戶可以指定各方向的孔隙率（porosity），其可控制各方向的面積比例值（theareafraction-Af)若設(shè)定一個(gè)方向的數(shù)值比其它兩個(gè)方向小，那么在該方向流動(dòng)時(shí)開口面積會(huì)變小總的孔隙率設(shè)定為三個(gè)方向中最大值第十七頁，共37頁。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第十八頁，共37頁。Sample:multilayerporousmaterialDropisabsorbedintothreelayerporousmaterialSaturatedmodelusedPorosityPcapadrgbdrgTop&bottomlayers50%6×1033.5×1071×105Middlelayer35%9×1035×1071×105Permeabilityratioformiddlelayer:κz/κr=0.710s0.1s0.2s1s第十九頁，共37頁。第二十頁，共37頁。UnsaturatedporousmediamodelWiththisoption,modelsimulatessaturationgradientsandvariescapillarypressurethroughoutRegionswithlowersaturationpredictedtohavegreater(i.e.morenegative)capillarypressureModel(w/ocustomization)presumeswettingmediumtomodelfluidHysteresisincapillarypressurepredictedDragisfunctionofsaturation(fractionofporespaceoccupiedbyfluid)or第二十一頁，共37頁。Capillarypressuremodelfor

unsaturatedporousmediaSamplecurvesatleftshowbothfillinganddrainingcurvesPcapwillfollowappropriatecurveduringcontinuousfillingordrainingWhenregionofporousmaterialswitchesbetweenfillinganddraining,PcapwillfollowscanningcurveuntilitreachesmaincurveDrainingcurveFillingcurveSamplescanningcurves第二十二頁，共37頁。Definingcompositesofdifferent

materialsAswiththesaturatedporousmediamodels,compositesaredefinedfirstbycreatingcomponentsSpecificationsforcapillarypressurecurvesaremadeininputfilepcapnamelistmustfirstbecreatedwithininputfilelocatedbetweenthescalarandbcdatanamelists第二十三頁，共37頁。Settinguptheinputfilefor

unsaturatedporousmediamodelingCreatepcapnamelistprovideglobalvaluesforfcmn,fcmx,fpcmx,pcmx,pexpThesewillapplytoallcomponentsbydefaultAddcomponent-specificvaluesifdesiredinobsnamelistprovidevaluesforofcmn,ofcmx,ofpcmx,opcmx,opexpApplyonlytospecificcomponentAlso,idfitoriodfitparameterscontroldragfunction1–powerlawfunction2–exponentfunction第二十四頁，共37頁。實(shí)例:多個(gè)孔隙率材料的仿真Component1Component4Component5Component3Component2ComponentpcmxfpcmxPexp11×1060.150.922.5×1050.20.535×105