FLOW3D多孔介质模型渗流模型

1、FLOW3D多孔介质模型渗流模型Examples of Porous Media8/22/2022User TrainingSpongeWire ScreenStreambedSinter Metal FilterPaperTube BundlePorous componentsRequire 2 computational cells to adequately resolveModel object as component ifSignificant gradients occur through thickness of materialMaterial is anisotropicP

2、orous material may beIsotropic (e.g. bed of uniform particles)Anisotropic (e.g. tube bundles)Porous baffles No thickness, reside on cell facesBest for modeling screensDrag can be linear or quadraticModel assumes baffle is saturated, no bubble pressure acrossTypes of Porous Objects in FLOW-3D8/22/202

3、2User Training Porous Media ModelingTheoryList of topics 介绍达西定律Darcy law介绍 FLOW-3D拖曳力模型(drag model)介绍饱和多孔介质模型 (the saturated porous media model)介绍拖曳力系数与渗透率的关系 (drag coefficient and permeability)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 (the unsaturated porous media model)达西定律Darcy LawQ : units of v

4、olume per time (e.g., m/s)A : cross-sectional area( Pb Pa ) : the pressure drop : dynamic viscosity : the permeability of the medium (units of area, e.g. m) L : the lengthDarcys Law: Flow rate through porous media is proportional to pressure drop according to:where v = macroscopic (superficial) velo

5、city (FLOW-3D computes and reports microscopic velocity)K = intrinsic permeability - may be isotropic or anisotropic (directional)m = dynamic viscosityP = fluid pressurePermeabilityProperty of the porous materialRepresents the average resistance to flow in a control volumeDarcys law represents visco

6、us losses through poresApplicable when pore Reynolds number Rep 1, where Rep = Applies well to tightly packed spheres and fibersDoes not represent inertial losses in loosely packed bedsViscous Drag in Porous Media: Darcys LawInertial drag becomes significant when Rep exceeds 10Darcys Law can be exte

7、nded to include inertial effectsQuadratic drag: Forchheimers EquationInertial Losses: Forchheimers Equation viscoustransitionalinertialwhere r = fluid densityUnderstanding FLOW-3DsDrag Model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。Total accelerationInertiaAcc. due to press

8、. gradient Accel. due to viscosityAccel. due to gravityDrag effectsVf= Volume fraction (porosity) of computational cellAf= Diagonal tensor area fractions of cellN-S张量方程Porous material characterized by:Solid structure permeated by interconnected capillariesMay consist of fibers, particles, open pores

9、Two types of flow inside porous mediaSaturatedAssumes media is already wet If interface between fluid and air exists, treated as sharpUnsaturatedDiffuse fluid/air interface - wickingHysteresis (filling/draining) effectsTwo contributions to fluid drag in porous mediaViscous (Skin Drag)Inertial (Form

10、Drag)Porous Media FlowResolve all geometry (FAVOR)Compute pressures and velocities directly from Navier Stokes equationsUseful for characterizing materialsComputationally expensiveApproaches to Modeling Porous MaterialsDirectVolume AveragedGeometry represented as volume fraction (porosity) open to f

11、lowAssume flow is uniform over cellRequires some knowledge of materialPorosityPressure drop vs velocityorParticle/fiber sizeFocus of this presentation is the volume averaged approach Saturated FlowUnsaturated FlowInterfacial Effects: Capillary Pressure Generally applies to flow through porous region

12、s filled with water Air/water interface is sharp Capillary pressure function of pore diameter Applies to flow through porous regions which may be wet or dry Air/water interface is diffuse (wicking) Capillary pressure function of saturation and direction, i.e. filling or drainingPorous media simulati

13、on setup steps:Decide flow type: Saturated or Unsaturated Define porous geometryDrag Model3 choices for saturated flow1 choice for unsaturated flowCharacterize MaterialPorosityFit drag coefficientsexperimental datacompute from fiber/particle sizeSetting Up A Porous Media SimulationSaturatedUnsaturat

14、edSaturated porous mediaUseful for situations where there exists a well-defined saturation front with the porous materialModel assumes that saturated regions are separated from “dry regions by a thin saturation frontPressure difference across this saturation front is dictated by a user-defined capil

15、lary pressure (Pcap)dafluid in a poresConcave case (lower pressure in liquid) is assumed to have +ve Pcap拖曳力与渗透率关系式Often confusion arises between Darcy permeability () and the drag coefficient (K). The relationship is:Thus, a material with drag represents 0 permeability“Drag coefficient in FLOW-3D o

16、utput is: This can vary between 0 (infinite drag) and 1 (zero drag) and is dimensionlessand拖曳力系数The drag coefficientorSetting up a problem with saturatedporous media激活 Porous media 多孔介质物理模型创立 porous component (s) 多孔材料每一个 component 可以由多个sub-components 或 STL 文件 来创立更复杂的形状在每一个component需指定孔隙率porosity，毛细管

17、压力 capillary pressure及拖曳系数 drag coefficients 每一个 component 可以设定不同属性Modeling anisotropic materialswith FLOW-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the area fraction- Af )假设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Setting anisotropic m

18、aterialsexampleSuppose we have a sheet-like material where:Then the porosity in the x, y directions should be set to 0.6 (the true porosity)The porosity in the z-direction is set to 0.45 (0.61.5/2)The drag coefficient is set according to the higher permeability (3000 s-1 in this case)x, y=210-6cm2z=

19、1.510-6cm2Sample: multilayer porous materialDrop is absorbed into three layer porous materialSaturated model usedPorosityPcapadrgbdrgTop & bottom layers50%61033.51071105Middle layer35%910351071105Permeability ratio for middle layer: z/ r0s1sUnsaturated porous media modelWith this option, model simul

20、ates saturation gradients and varies capillary pressure throughoutRegions with lower saturation predicted to have greater (i.e. more negative) capillary pressureModel (w/o customization) presumes wetting medium to model fluidHysteresis in capillary pressure predictedDrag is function of saturation (f

21、raction of pore space occupied by fluid)orCapillary pressure model forunsaturated porous mediaSample curves at left show both filling and draining curvesPcap will follow appropriate curve during continuous filling or drainingWhen region of porous material switches between filling and draining, Pcap

22、will follow scanning curve until it reaches main curve Draining curveFilling curveSample scanning curvesDefining composites of differentmaterialsAs with the saturated porous media models, composites are defined first by creating componentsSpecifications for capillary pressure curves are made in inpu

23、t filepcap namelist must first be created within input filelocated between the scalar and bcdata namelistsSetting up the input unsaturated porous media modelingCreate pcap namelistprovide global values for fcmn, fcmx, fpcmx, pcmx, pexpThese will apply to all components by defaultAdd component-specific values if desired in obs namelistprovide values for ofcmn, ofcmx, ofpcmx, opcmx, opexpApply only to specific componentAlso, idfit or i