Understanding Porous Flow Blockage resistance methods

To calculate the porous blockage a resistance force is added to the source term of the momentum equations. Five methods exist to calculate the resistance force:

• Inertial resistance is selected by setting Head Loss and Permeability method and selecting Inertial Resistance check box.

• Darcy resistance is selected by setting Head Loss and Permeability method and selecting Permeability check box.

• Resistance due to pressure drop is selected by setting Pressure Drop per Length method.

• Resistance due to packed bed of spheres is selected by setting Packed Bed of Spheres method.

• Resistance due to fibrous porous media is selected by setting Fibrous Porous Media method.

Inertial resistance

The resistance force per unit volume,F, in the direction of the flow isF=-1/2 hloss ρ V2 where hloss is the specified head loss per length (in units of one over the length), ρ is the fluid density and V is the fluid velocity magnitude.

This method is available for both Porous Blockage — Isotropic and Porous Blockage — Orthotropic. It can be used in addition to Darcy resistance.

In the case of Porous Blockage — Orthotropic, the head loss per length is different for the three orthogonal directions, thus the resistance force has three components, one for each direction. The fluid velocity magnitude is multiplied by the velocity component of that principal coordinate direction. For complete blockage (infinite head loss) in one or two directions, you must use a real value to represent infinity. Use a value equal to 1000 times the next highest value you have entered for another direction.

Darcy resistance

The resistance force in this case is F = -μ / k * V where μ is the dynamic viscosity of the fluid, k is the specified permeability and V is the fluid velocity magnitude. Permeability is a measure of the ability of a material to transmit fluids. It is a property of the porous material and not of the fluid. Its dimension is length squared.

This method is available for both Porous Blockage — Isotropic and Porous Blockage — Orthotropic. It can be used in addition to Inertial resistance.

For the Porous Blockage — Orthotropic material, the specified permeability has three different values for the three principal directions, thus the resistance force has three components, one for each direction. The fluid velocity magnitude is multiplied by the velocity component of the principal coordinate direction.

Resistance due to pressure drop

The resistance force,F, is calculated asF = -ΔP / L whereΔP is the specified pressure drop and L is the specified blockage length. You define the pressure force as a function of the fluid velocity magnitude through a table.

This method is only available for Porous Blockage — Isotropic.

Resistance due to packed bed of spheres

If you select Packed Bed of Spheres from the Specify Method list, the software uses a packed bed of spheres as the material for the flow blockage. The pressure drop in this case is calculated using the Ergun equation.

where ΔP is the pressure drop, L is the blockage length, D is the specified diameter of the sphere, ρ and μ are respectively the density and the dynamic viscosity of the fluid, and Vs is the superficial velocity (the volumetric flow rate of the fluid, Q, over the cross-sectional area of the bed,A). The specified void fraction (also called porosity) of the bed, ε, is the ratio of the void volume to the total volume of the packed bed.

This method is only available for Porous Blockage — Isotropic.

Resistance due to fibrous porous media

The fibrous porous media are composed of very long particles randomly oriented in all three directions. The constituent fibers of the porous media are long enough that aspect ratio is not a parameter. Thus the fiber size is given by a single cross dimension, the diameter. The pressure drop is modeled using the Darcy's Law: Q / A = k / μ * ΔP / L where Q is the volumetric flow rate of the fluid, A, is the cross-sectional area of the porous media, k is the permeability, μ is the dynamic viscosity of the fluid, ΔP is the pressure drop and L is the blockage length. The permeability, k, is a function of the specified diameter of the fiber, D, and the specified void fraction, ε. The void fraction or porosity is the ratio of the void volume to the total volume of the fibrous porous media.

This method is only available for Porous Blockage — Isotropic.

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