FLOW-3D多孔介質(zhì)模型,滲流模型

第四章、FLOW-3D

多孔介質(zhì)模型

FLOW-3D?v9.4ExamplesofPorousMedia5/14/2024UserTrainingSpongeWireScreenStreambedSinterMetalFilterPaperTubeBundlePorouscomponentsRequire2computationalcellstoadequatelyresolveModelobjectascomponentifSignificantgradientsoccurthroughthicknessofmaterialMaterialisanisotropicPorousmaterialmaybeIsotropic(e.g.bedofuniformparticles)Anisotropic(e.g.tubebundles)PorousbafflesNothickness,resideoncellfacesBestformodelingscreensDragcanbelinearorquadraticModelassumesbaffleissaturated,nobubblepressureacrossTypesofPorousObjectsinFLOW-3D5/14/2024UserTraining

PorousMediaModelingTheoryListoftopics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)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:thelengthDarcy’sLaw:Flowratethroughporousmediaisproportionaltopressuredropaccordingto:where

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

m=dynamicviscosity P=fluidpressurePermeabilityPropertyoftheporousmaterialRepresentstheaverageresistancetoflowinacontrolvolumeDarcy’slawrepresentsviscouslossesthroughporesApplicablewhenporeReynoldsnumberRep~1,whereRep=ApplieswelltotightlypackedspheresandfibersDoesnotrepresentinertiallossesinlooselypackedbedsViscousDraginPorousMedia:Darcy’sLawInertialdragbecomessignificantwhenRepexceeds10Darcy’sLawcanbeextendedtoincludeinertialeffectsQuadraticdrag:Forchheimer’sEquationInertialLosses:Forchheimer’sEquationviscoustransitionalinertialwherer=fluiddensityUnderstandingFLOW-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Porousmaterialcharacterizedby:SolidstructurepermeatedbyinterconnectedcapillariesMayconsistoffibers,particles,openporesTwotypesofflowinsideporousmediaSaturatedAssumesmediaisalreadywetIfinterfacebetweenfluidandairexists,treatedassharpUnsaturatedDiffusefluid/airinterface-wickingHysteresis(filling/draining)effectsTwocontributionstofluiddraginporousmediaViscous(SkinDrag)Inertial(FormDrag)PorousMediaFlowResolveallgeometry(FAVOR)ComputepressuresandvelocitiesdirectlyfromNavierStokesequationsUsefulforcharacterizingmaterialsComputationallyexpensiveApproachestoModelingPorousMaterialsDirectVolumeAveragedGeometryrepresentedasvolumefraction(porosity)opentoflowAssumeflowisuniformovercellRequiressomeknowledgeofmaterialPorosityPressuredropvsvelocity orParticle/fibersizeFocusofthispresentationisthevolumeaveragedapproachSaturatedFlowUnsaturatedFlowInterfacialEffects:CapillaryPressureGenerallyappliestoflowthroughporousregionsfilledwithwaterAir/waterinterfaceissharpCapillarypressurefunctionofporediameterAppliestoflowthroughporousregionswhichmaybewetordryAir/waterinterfaceisdiffuse(wicking)Capillarypressurefunctionofsaturationanddirection,i.e.fillingordrainingPorousmediasimulationsetupsteps:Decideflowtype:SaturatedorUnsaturatedDefineporousgeometryDragModel3choicesforsaturatedflow1choiceforunsaturatedflowCharacterizeMaterialPorosityFitdragcoefficientsexperimentaldatacomputefromfiber/particlesizeSettingUpAPorousMediaSimulationSaturatedUnsaturatedSaturatedporousmediaUsefulforsituationswherethereexistsawell-definedsaturationfrontwiththeporousmaterialModelassumesthatsaturatedregionsareseparatedfrom“dry”regionsbyathinsaturationfrontPressuredifferenceacrossthissaturationfrontisdictatedbyauser-definedcapillarypressure(Pcap)dafluidinaporesConcavecase(lowerpressureinliquid)isassumedtohave+ve

Pcap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拖曳力系數(shù)（Thedragcoefficient）orSettingupaproblemwithsaturated

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=0.6Sample:multilayerporousmaterialDropisabsorbedintothreelayerporousmaterialSaturatedmodelusedPorosityPcapadrgbdrgTop&bottomlayers50%6×1033.5×1071×105Middlelayer35%9×1035×1071×105Permeabilityratioformiddlelayer:κz/κr=0.710s0.1s0.2s1sUnsaturatedporousmediamodelWiththisoption,modelsimulatessaturationgradientsandvariescapillarypressurethroughoutRegionswithlowersaturationpredictedtohavegreater(i.e.morenegative)capillarypressureModel(w/ocustomization)presumeswettingmediumtomodelfluidHysteresisincapillarypressurepredictedDragisfunctionofsaturation(fractionofporespaceoccupiedbyfluid)orCapillarypressuremodelfor

unsaturatedporousmediaSamplecurvesatleftshowbothfillinganddrainingcurvesPcapwillfollowappropriatecurveduringcontinuousfillingordrainingWhenregionofporousmaterialswitchesbetweenfillinganddraining,PcapwillfollowscanningcurveuntilitreachesmaincurveDrainingcurveFillingcurveSamplescanningcurvesDefiningcompositesofdifferent

materialsAswiththesaturatedporousmediamodels,compositesaredefinedfirstbycreatingcomponentsSpecificationsforcapillarypressurecurvesaremadeininputfilepcap

namelistmustfirstbecreatedwithininputfilelocatedbetweenthescalarandbcdata

namelistsSettinguptheinputfilefor

unsaturatedporousmediamodelingCreatepcap

namelistprovideglobalvaluesforfcmn,fcmx,fpcmx,pcmx,pexpThesewillapplytoallcomponentsbydefaultAddcomponent-specificvaluesifdesiredinobs

namelistprovidevaluesforofcmn,ofcmx,ofpcmx,opcmx,opexpApplyonlytospecificcomponentAlso,idfitoriodfitparameterscontroldragfunction1–powerlawfunction2–exponentfunction實(shí)例:多個(gè)孔隙率材料的仿真Component1Component4C