How to Create a Porous Media?

Objective

Porous media is a medium filled with solid particles, which lets fluid to pass through. The arrangement of the flow path can be regular or irregular.

Consolidated medium: Solid-body has internal pores. Fluid passes through the pores.

Unconsolidated medium: A pile of solid particles is packed inside a bed. Fluid flows around the particles.

Using porous media simplification reduces CAD and mesh complexity, and saves computational time and expenses.

How to use Porous Media Future

You can check this project as an example.

Under Advanced Concepts, choose one of the porous media.

Assign the Darcy and Forchheimer resistance coefficients with respect to local coordinates.

Assign Unit vector 1 and Unit vector 2 with respect to global coordinates.

Choose the porous media region:

• If you created the region in a CAD model and defined it as a zone, then pick the volume
• If not, then create a cartesian box, using geometry primitives and select the box

While the sponge-like structures permit the flow evenly in every direction (isotropic), perforated plates transmit the flow in a particular direction (anisotropic). To simulate an isotropic structure, d_x, d_y, d_z and f_x, f_y, f_z should be the same.

If you would like to learn how to predict Darcy and Forchheimer Coefficients using experimental data, check the this page

How to Predict Darcy and Forchheimer Coefficients using Empirical Equations

Darcy–Forchheimer equation is an empirical equation, which relates the pressure loss, due to friction along with a porous medium, with respect to the velocity of the flow inside the medium.

\[\Delta P = \mu \cdot d \cdot L \cdot u + \frac{\rho }{2} \cdot f \cdot L \cdot u^{2}\]

Friction is occurred by a combination of shear forces and the pressure forces. While the shear forces are represented by a linear equation, pressure forces are represented by a quadratic equation. Therefore d (Darcy) is a linear resistance coefficient and f (Forchheimer) is a quadratic resistance coefficient.

Porosity:

\[\phi = \frac{Open\: area\: of\: the\: perforated\: plate\: [m^2]}{Total\: area\: of\: the\: perforated\: plate\: [m^2]}\]

For circular holes, hydraulic diameter is the diameter of the hole. For non-circular conduit, the following equation can be used to calculate hydraulic diameter:

\[d_{h} = \frac{4 \cdot Open\: Area\cdot [m^2] }{Wet\: perimeter\: [m]}\]

or

\[d_{h} = \frac{4 \cdot Open\: Volume\cdot [m^3] }{Wet\: surface\: area\: [m^2]}\]

If the medium is composed of uniform spherical particles, mean particle diameter (spherical particles) can be found as follows:

\[\mathbf{d_{m}} = \frac{3 \cdot \left ( 1-\phi \right ) \cdot d_{h}}{2 \cdot \phi }\]

Darcy and Forchheimer coefficients can be calculated as follows:

\[d = 150 \cdot \frac{(1-\phi )^{2}}{\left ( \phi^{3} \cdot d_{m}^{2} \right )}\]

\[f = 3.5 \cdot \frac{\left ( 1-\phi \right )}{\left ( \phi^{3} \cdot d_{m} \right )}\]