Porous Conditions

Porous conditions can be used to model a wide variety of applications, such as fluid flow through filters, packed beds, perforated plates, flow distributors, and tube banks. The porous medium is modeled as a momentum loss, the magnitude of which involves resistance coefficients.

The resistance coefficients control the momentum loss. In general, the loss consists of two parts, a linear term which models the resistance due to viscous losses, and a quadratic term which models the resistance due to inertial losses. The loss is expressed as:

Si=-(µ/α vi + ½ C2ρ|v|vi)

where

Si is the momentum source which accounts for the porous loss

C2 is the inertial resistance

α is the permeability

μ is the fluid viscosity

ρ is the fluid density

|v| is the velocity magnitude

vi is the velocity vector of the ith component in the medium

For low-Reynolds number flows, the viscous loss typically dominates, and the inertial resistance coefficient can often be set to 0. For turbulent flows, the inertial loss typically dominates, and the viscous resistance coefficient can often be set to 0.

The values you select for the viscous resistance coefficient and inertial resistance coefficient typically depend on the application and what data you know. For instance:
  • If you are modeling flow through a porous medium where Darcy’s law applies, set the viscous resistance coefficient to 1/α, where α is the permeability. (If the viscous resistance is large compared to other terms in the momentum equation, the governing equations will automatically recover Darcy’s law.)
  • If you are modeling flow in a packed bed, the Ergun equation is very similar to the momentum loss expression. The resistance coefficients can be derived from the Ergun equation parameters.
  • The inertial resistance coefficient can be interpreted as a loss coefficient per unit length. So, if you are modeling a device such as a perforated plate, filter, or tube bank with a known loss coefficient KL and thickness Δx, you can select C2=KL/Δx

  • If you have experimental tabulated data of pressure drop as a function of velocity for a porous medium of thickness Δx, you can derive the resistance coefficients:

    ΔP/Δx = -(µ/α v + ½ C2ρv2)

By default, the resistance coefficients are the same in all directions, isotropic. Alternatively, you can specify different coefficients in the streamwise and crossflow directions, bidirectional, or set a different value for each of the three directions, orthotropic. For the bidirectional and orthotropic options, the reference frame can be Cartesian or cylindrical, depending on the geometry selected using the Direction tool guide. See Specifying Bidirectional and Orthotropic Porous Media to specify the direction in other ways.

This section contains the following topics: