Porous Zones

A porous-dominant simulation is one in which the porous drag forces are far greater than the forces of advection and diffusion in the analysis, so the pressure drop at the outlets is mainly due to the porous drag. When you define a porous-dominant simulation, the analysis does not describe the nature of the flow within the porous media itself; only the gross effect of the porous media on the overall simulation downstream and upstream from the porous media is considered.

The app models porous media as a source term in the momentum equation. The source term is given as:

S_{i} = - \sum_{j = 1}^{3} (α_{i j} μ ν_{j} + β_{i j} \frac{1}{2} ρ | ν | ν_{j}),

where $S_{i}$ is the source term for the $i^{t h}$ momentum equation, $| ν |$ is the magnitude of the velocity, and $α_{i j}$ and $β_{i j}$ are the viscous and inertial resistance tensor, respectively.

You can specify $S_{i}$ by choosing an orientation and specifying the diagonal terms of the two tensors $α_{i j}$ and $β_{i j}$ .

The pressure drop that occurs from adding a porous zone is estimated as:

\frac{Δ P}{Δ x_{i}} \approx \sum_{j = 1}^{3} (α_{i j} μ ν_{j} + β_{i j} \frac{1}{2} ρ | ν | ν_{j}) .

If you are solving for energy, the solid and fluid material of the porous media contribute their corresponding fraction of total energy to the total energy equation. This fraction is characterized by specifying porosity, $ϵ$ . Thus, porosity plays a role only in the energy equation.

The effective thermal conductivity tensor can be defined as:

Κ_{e f f} = ϵ Κ_{f} + (1 - ϵ) Κ_{s},

where $Κ_{f}$ is the fluid thermal conductivity, and $Κ_{s}$ is the solid thermal conductivity.

The effect of porous zone on the transient total energy term is given by the following formula:

\frac{\partial}{\partial t} (ϵ ρ_{f} E_{f} + (1 - ϵ) ρ_{s} E_{s}),

where $ρ_{f}$ and $ρ_{s}$ are the fluid and solid density, respectively; and $E_{f}$ and $E_{s}$ are the fluid and solid total energy, respectively.