## 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**and

_{z}**f**,

_{x}**f**,

_{y}**f**should be the same.

_{z}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:

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

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