FLOW-3D多孔介质模型-渗流模型

1、第四章、FLOW-3D 多孔介质模型,FLOW-3D v9.4,Examples of Porous Media,July 19, 2020,User Training,Sponge,Wire Screen,Streambed,Sinter Metal Filter,Paper,Tube Bundle,Porous components Require 2 computational cells to adequately resolve Model object as component if Significant gradients occur through thickness of

2、material Material is anisotropic Porous material may be Isotropic (e.g. bed of uniform particles) Anisotropic (e.g. tube bundles) Porous baffles No thickness, reside on cell faces Best for modeling screens Drag can be linear or quadratic Model assumes baffle is saturated, no bubble pressure across,T

3、ypes of Porous Objects in FLOW-3D,July 19, 2020,User Training,Porous Media Modeling Theory,List 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 un

4、saturated porous media model),达西定律（Darcy Law）,Q : units of volume 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 length,Darcys Law: Flow rate through porous media is proportional to pr

5、essure drop according to: where v = macroscopic (superficial) velocity (FLOW-3D computes and reports microscopic velocity) K = intrinsic permeability - may be isotropic or anisotropic (directional) m = dynamic viscosity P = fluid pressure Permeability Property of the porous material Represents the a

6、verage resistance to flow in a control volume Darcys law represents viscous losses through pores Applicable when pore Reynolds number Rep 1, where Rep = Applies well to tightly packed spheres and fibers Does not represent inertial losses in loosely packed beds,Viscous Drag in Porous Media: Darcys La

7、w,Inertial drag becomes significant when Rep exceeds 10 Darcys Law can be extended to include inertial effects Quadratic drag: Forchheimers Equation,Inertial Losses: Forchheimers Equation,viscous,transitional,inertial,where r = fluid density,Understanding 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，

8、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 acceleration,Inertia,Acc. due to press. gradient,Accel. due to viscosity,Accel. due to gravity,Drag effects,Vf= Volume fraction (porosity) of computational cell,Af= Diagonal tensor area fractions of cell,N-S张量方程,Porous material characterized by: Sol

9、id structure permeated by interconnected capillaries May consist of fibers, particles, open pores Two types of flow inside porous media Saturated Assumes media is already wet If interface between fluid and air exists, treated as sharp Unsaturated Diffuse fluid/air interface - wicking Hysteresis (fil

10、ling/draining) effects Two contributions to fluid drag in porous media Viscous (Skin Drag) Inertial (Form Drag),Porous Media Flow,Resolve all geometry (FAVOR) Compute pressures and velocities directly from Navier Stokes equations Useful for characterizing materials Computationally expensive,Approach

11、es to Modeling Porous Materials,Direct,Volume Averaged,Geometry represented as volume fraction (porosity) open to flow Assume flow is uniform over cell Requires some knowledge of material Porosity Pressure drop vs velocity or Particle/fiber size,Focus of this presentation is the volume averaged appr

12、oach,Saturated Flow Unsaturated Flow,Interfacial Effects: Capillary Pressure,Generally applies to flow through porous regions 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

13、 is diffuse (wicking) Capillary pressure function of saturation and direction, i.e. filling or draining,Porous media simulation setup steps: Decide flow type: Saturated or Unsaturated Define porous geometry Drag Model 3 choices for saturated flow 1 choice for unsaturated flow Characterize Material P

14、orosity Fit drag coefficients experimental data compute from fiber/particle size,Setting Up A Porous Media Simulation,Saturated,Unsaturated,Saturated porous media,Useful for situations where there exists a well-defined saturation front with the porous material Model assumes that saturated regions ar

15、e separated from “dry” regions by a thin saturation front Pressure difference across this saturation front is dictated by a user-defined capillary pressure (Pcap),Concave 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 t

16、he drag coefficient (K). The relationship is: Thus, a material with drag represents 0 permeability “Drag coefficient” in FLOW-3D output is: This can vary between 0 (infinite drag) and 1 (zero drag) and is dimensionless,and,拖曳力系数（The drag coefficient）,or,Setting up a problem with saturatedporous medi

17、a,激活 Porous media 多孔介质物理模型 创建 porous component (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（ 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

18、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 ) 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,Setting anisotropic materialsexample,Suppose we have a sheet-like material where: Then the porosity in the x, y directions should be set to 0.6 (the true porosity) T

19、he 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=210-6cm2,z=1.510-6cm2,Porosity=0.6,Sample: multilayer porous material,Drop is absorbed into three layer porous material Saturated model used,Permeabi

20、lity ratio for middle layer: z/ r=0.71,0s,0.1s,0.2s,1s,Unsaturated porous media model,With this option, model simulates saturation gradients and varies capillary pressure throughout Regions with lower saturation predicted to have greater (i.e. more negative) capillary pressure Model (w/o customizati

21、on) presumes wetting medium to model fluid Hysteresis in capillary pressure predicted Drag is function of saturation (fraction of pore space occupied by fluid),or,Capillary pressure model forunsaturated porous media,Sample curves at left show both filling and draining curves Pcap will follow appropr

22、iate curve during continuous filling or draining When region of porous material switches between filling and draining, Pcap will follow scanning curve until it reaches main curve,Defining composites of differentmaterials,As with the saturated porous media models, composites are defined first by crea

23、ting components Specifications for capillary pressure curves are made in input file pcap namelist must first be created within input file located between the scalar and bcdata namelists,Setting up the input file forunsaturated porous media modeling,Create pcap namelist provide global values for fcmn, fcmx, fpcmx, pcmx, pexp These will apply to all components by default Add component-specific values if desired in obs namelist provide values for ofcmn, ofcmx, ofp