FLOW-3D多孔介质模型,渗流模型
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s Concave case (lower pressure iபைடு நூலகம் a
liquid) is assumed to have +ve Pcap
fluid in a pore
拖曳力与渗透率关系式
• Often confusion arises between Darcy permeability (κ) and the drag coefficient (K). The relationship is:
User Training 21 January 2015
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 unsaturated porous media model)
达西定律（Darcy Law）
Q : units of volume per time (e.g., m³ /s) A : cross-sectional area ( Pb − Pa ) : the pressure drop μ : dynamic viscosity Κ : the permeability of the medium (units of area, e.g. m² ) L : the length
Vf m
K
and
K
Vf m
• Thus, a material with ∞ drag represents 0 permeability • “Drag coefficient” in FLOW-3D output is:
1 DRG 1 Kt
This can vary between 0 (infinite drag) and 1 (zero drag) and is dimensionless
• Unsaturated Flow
• 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 draining
Focus of this presentation is the volume averaged approach
Interfacial Effects: Capillary Pressure
• Saturated Flow
• Generally applies to flow through porous regions filled with water • Air/water interface is sharp • Capillary pressure function of pore diameter
Accel. due Drag effects to gravity
Vf= Volume fraction (porosity) of computational cell Af= Diagonal tensor area fractions of cell
• K 表示拖曳力系数，也就是流体在多孔介质中的流动 阻力。
第四章、FLOW-3D 多孔介质模型
FLOW-3D® v9.4
Examples of Porous Media
Sponge
Streambed
Wire Screen
Paper
User Training
Sinter Metal Filter
Tube Bundle
21 January 2015
Types of Porous Objects in FLOW-3D
Approaches to Modeling Porous Materials
Direct
Volume Averaged
• •
• •
Resolve all geometry (FAVOR) Compute pressures and velocities directly from Navier Stokes equations Useful for characterizing materials Computationally expensive
•
• •
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
N-S张量方程
u 1 1 1 Af u u p A f u G Ku t V f V f
Total acceleration
Inertia Acc. due to press. gradient
Accel. due to viscosity
•
•
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 average resistance to flow in a control volume Darcy’s law represents viscous losses through pores uLpore m – 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
• Porous components – Require 2 computational cells to adequately resolve – Model object as component if • Significant gradients occur through thickness of 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
Saturated porous media
• Useful for situations where there exists a well-defined saturation front with the porous material – Model assumes that saturated regions are separated from “dry” regions by a thin saturation front – Pressure difference across this saturation front is dictated by a user-defined capillary pressure (Pcap) 4 cos Pcap d d
Porous Media Flow
• Porous material characterized by: – Solid 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 (filling/draining) effects • Two contributions to fluid drag in porous media – Viscous (Skin Drag) – Inertial (Form Drag)
• • 3 choices for saturated flow 1 choice for unsaturated flow
Saturated Unsaturated
4) Characterize Material
• • Porosity Fit drag coefficients
– – experimental data compute from fiber/particle size
Viscous Drag in Porous Media: Darcy’s Law
• Darcy’s Law: Flow rate through porous media is proportional to pressure drop according to:
where
P m v x K
P m u cK 1/ 2 u 2 x K
viscous transitional inertial
where = fluid density
Understanding FLOW-3D®’s Drag 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：
Inertial Losses: Forchheimer’s Equation
• Inertial drag becomes significant when Rep exceeds 10 • Darcy’s Law can be extended to include inertial effects • Quadratic drag: Forchheimer’s Equation
Setting Up A Porous Media Simulation
Porous media simulation setup steps:
1) Decide flow type: Saturated or Unsaturated 2) Define porous geometry
3) Drag Model
liquid) is assumed to have +ve Pcap
fluid in a pore
拖曳力与渗透率关系式
• Often confusion arises between Darcy permeability (κ) and the drag coefficient (K). The relationship is:
User Training 21 January 2015
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 unsaturated porous media model)
达西定律（Darcy Law）
Q : units of volume per time (e.g., m³ /s) A : cross-sectional area ( Pb − Pa ) : the pressure drop μ : dynamic viscosity Κ : the permeability of the medium (units of area, e.g. m² ) L : the length
Vf m
K
and
K
Vf m
• Thus, a material with ∞ drag represents 0 permeability • “Drag coefficient” in FLOW-3D output is:
1 DRG 1 Kt
This can vary between 0 (infinite drag) and 1 (zero drag) and is dimensionless
• Unsaturated Flow
• 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 draining
Focus of this presentation is the volume averaged approach
Interfacial Effects: Capillary Pressure
• Saturated Flow
• Generally applies to flow through porous regions filled with water • Air/water interface is sharp • Capillary pressure function of pore diameter
Accel. due Drag effects to gravity
Vf= Volume fraction (porosity) of computational cell Af= Diagonal tensor area fractions of cell
• K 表示拖曳力系数，也就是流体在多孔介质中的流动 阻力。
第四章、FLOW-3D 多孔介质模型
FLOW-3D® v9.4
Examples of Porous Media
Sponge
Streambed
Wire Screen
Paper
User Training
Sinter Metal Filter
Tube Bundle
21 January 2015
Types of Porous Objects in FLOW-3D
Approaches to Modeling Porous Materials
Direct
Volume Averaged
• •
• •
Resolve all geometry (FAVOR) Compute pressures and velocities directly from Navier Stokes equations Useful for characterizing materials Computationally expensive
•
• •
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
N-S张量方程
u 1 1 1 Af u u p A f u G Ku t V f V f
Total acceleration
Inertia Acc. due to press. gradient
Accel. due to viscosity
•
•
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 average resistance to flow in a control volume Darcy’s law represents viscous losses through pores uLpore m – 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
• Porous components – Require 2 computational cells to adequately resolve – Model object as component if • Significant gradients occur through thickness of 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
Saturated porous media
• Useful for situations where there exists a well-defined saturation front with the porous material – Model assumes that saturated regions are separated from “dry” regions by a thin saturation front – Pressure difference across this saturation front is dictated by a user-defined capillary pressure (Pcap) 4 cos Pcap d d
Porous Media Flow
• Porous material characterized by: – Solid 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 (filling/draining) effects • Two contributions to fluid drag in porous media – Viscous (Skin Drag) – Inertial (Form Drag)
• • 3 choices for saturated flow 1 choice for unsaturated flow
Saturated Unsaturated
4) Characterize Material
• • Porosity Fit drag coefficients
– – experimental data compute from fiber/particle size
Viscous Drag in Porous Media: Darcy’s Law
• Darcy’s Law: Flow rate through porous media is proportional to pressure drop according to:
where
P m v x K
P m u cK 1/ 2 u 2 x K
viscous transitional inertial
where = fluid density
Understanding FLOW-3D®’s Drag 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：
Inertial Losses: Forchheimer’s Equation
• Inertial drag becomes significant when Rep exceeds 10 • Darcy’s Law can be extended to include inertial effects • Quadratic drag: Forchheimer’s Equation
Setting Up A Porous Media Simulation
Porous media simulation setup steps:
1) Decide flow type: Saturated or Unsaturated 2) Define porous geometry
3) Drag Model