FLOW-3D多孔介质模型-渗流模型

第四章、FLOW-3D多孔介质模型FLOW-3D®v9.4ExamplesofPorousMedia18March2020UserTrainingSpongeWireScreenStreambedSinterMetalFilterPaperTubeBundle•Porouscomponents–Require2computationalcellstoadequatelyresolve–Modelobjectascomponentif•Significantgradientsoccurthroughthicknessofmaterial•Materialisanisotropic–Porousmaterialmaybe•Isotropic(e.g.bedofuniformparticles)•Anisotropic(e.g.tubebundles)•Porousbaffles–Nothickness,resideoncellfaces–Bestformodelingscreens–Dragcanbelinearorquadratic–Modelassumesbaffleissaturated,nobubblepressureacrossTypesofPorousObjectsinFLOW-3D18March2020UserTrainingPorousMediaModelingTheoryListoftopics•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)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•Darcy’sLaw:Flowratethroughporousmediaisproportionaltopressuredropaccordingto:wherev=macroscopic(superficial)velocity(FLOW-3Dcomputesandreportsmicroscopicvelocity)K=intrinsicpermeability-maybeisotropicoranisotropic(directional)m=dynamicviscosityP=fluidpressure•Permeability–Propertyoftheporousmaterial–Representstheaverageresistancetoflowinacontrolvolume•Darcy’slawrepresentsviscouslossesthroughpores–ApplicablewhenporeReynoldsnumberRep~1,whereRep=–Applieswelltotightlypackedspheresandfibers–DoesnotrepresentinertiallossesinlooselypackedbedsViscousDraginPorousMedia:Darcy’sLawvKxPmmporeLu•InertialdragbecomessignificantwhenRepexceeds10•Darcy’sLawcanbeextendedtoincludeinertialeffects•Quadraticdrag:Forchheimer’sEquationInertialLosses:Forchheimer’sEquation22/1ucKuKxPmviscoustransitionalinertialwhere=fluiddensityUnderstandingFLOW-3D®’sDragModel•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。uGuAuuAuffKVpVtff111TotalaccelerationInertiaAcc.duetopress.gradientAccel.duetoviscosityAccel.duetogravityDrageffectsVf=Volumefraction(porosity)ofcomputationalcellAf=DiagonaltensorareafractionsofcellN-S张量方程•Porousmaterialcharacterizedby:–Solidstructurepermeatedbyinterconnectedcapillaries–Mayconsistoffibers,particles,openpores•Twotypesofflowinsideporousmedia–Saturated•Assumesmediaisalreadywet•Ifinterfacebetweenfluidandairexists,treatedassharp–Unsaturated•Diffusefluid/airinterface-wicking•Hysteresis(filling/draining)effects•Twocontributionstofluiddraginporousmedia–Viscous(SkinDrag)–Inertial(FormDrag)PorousMediaFlow•Resolveallgeometry(FAVOR)•ComputepressuresandvelocitiesdirectlyfromNavierStokesequations•Usefulforcharacterizingmaterials•ComputationallyexpensiveApproachestoModelingPorousMaterialsDirectVolumeAveraged•Geometryrepresentedasvolumefraction(porosity)opentoflow•Assumeflowisuniformovercell•RequiressomeknowledgeofmaterialPorosityPressuredropvsvelocityorParticle/fibersizeFocusofthispresentationisthevolumeaveragedapproach•SaturatedFlow•UnsaturatedFlowInterfacialEffects:CapillaryPressure•Generallyappliestoflowthroughporousregionsfilledwithwater•Air/waterinterfaceissharp•Capillarypressurefunctionofporediameter•Appliestoflowthroughporousregionswhichmaybewetordry•Air/waterinterfaceisdiffuse(wicking)•Capillarypressurefunctionofsaturationanddirection,i.e.fillingordrainingPorousmediasimulationsetupsteps:1)Decideflowtype:SaturatedorUnsaturated2)Defineporousgeometry3)DragModel•3choicesforsaturatedflow•1choiceforunsaturatedflow4)CharacterizeMaterial•Porosity•Fitdragcoefficients–experimentaldata–computefromfiber/particlesizeSettingUpAPorousMediaSimulationSaturatedUnsaturatedSaturatedporousmedia•Usefulforsituationswherethereexistsawell-definedsaturationfrontwiththeporousmaterial–Modelassumesthatsaturatedregionsareseparatedfrom“dry”regionsbyathinsaturationfront–Pressuredifferenceacrossthissaturationfrontisdictatedbyauser-definedcapillarypressure(Pcap)dPcapcos4dafluidinaporesConcavecase(lowerpressureinliquid)isassumedtohave+vePcap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)andisdimensionlessKVfmandmfVKtKDRG11拖曳力系数（Thedragcoefficient）bdrgfVadrgKbdrgFadrgKdbdrgVVadrgVVKffffRe11mbdrgSadrgKSbdrgPexpCMNeSFFFadrgK1orSettingupaproblemwithsaturatedporousmedia•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ModelinganisotropicmaterialswithFLOW-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Settinganisotropicmaterialsexample•Supposewehaveasheet-likematerialwhere:•Thentheporosityinthex,ydirectionsshouldbesetto0.6(thetrueporosity)•Theporosityin