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A porous medium is a solid with voids distributed more or less uniformly throughout the bulk of the body.

The basic characteristic of this medium is *porosity.* The *bulk porosity* Π of a material is defined as the ratio of void volume V_{v} to body volume V_{0}, Π = V_{v}/V_{0}. Since the remaining portion V_{s} of the total volume of the material is in the form of a solid “skeleton”, then

For example, the porosity of porous materials with the skeleton formed by spherical particles with diameter d_{p} can be found from the relation

where N_{p} is the number of particles per unit volume. These spheres can be arranged in various ways (Figures 1a and b). The cubic arrangement of spheres of the same diameter is characterized by a porosity of 0.476, while at a denser, rhombic, packing the porosity reduces to 0.259 (theoretically, this is the minimum porosity of packing of uniform spheres without deformation of the solid). The real porosity generally is estimated using its relation to density ρ_{Σ} = ρ_{0}(1−Π) or Π = 1(ρ_{Σ}/ρ_{0}), where ρ_{Σ} and ρ_{0} are the densities of the medium and of the solid material forming its skeleton, respectively.

*Permeability* (or gas permeability) is the property which gives a measure of the gas flow through a porous medium exposed to a pressure difference. The superficial velocity V of fluid flow depends on permeability and pressure gradient in accordance with a modified *Darcy equation*

Here, superficial velocity v is defined as the volumetric flow rate of the fluid per unit cross section of the medium. The coefficent α allows for friction losses that are characterized by the fluid viscosity η and the structure of a porous matrix. The coefficient of inertia β takes into account the losses associated with expansion, constriction, and bends in the pore channels; these losses are approximately proportional to ρV^{2}.

The modified Darcy equation is universal and describes isothermal liquid and gas flow in any porous solids without allowance for capillary forces. The influence of capillary forces (an increase in viscosity) is observed in water at the pore sizes d_{p} < 1 μm. As a consequence, the ratio of water to gas flow rates for identical pressure difference may be either proportional to the ratio of their viscosities at high d_{p} or decrease by nearly a factor of 20 for porous channels of small diameter.

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In this tutorial you will learn to simulate a porous medium in 2D using ANSYS Fluent. First, we will build a geometry and then we will generate the mesh using a structured mesh in Ansys Meshing.

## Ansys Fluent Tutorial | Modeling Species Transport and Gaseous Combustion

In this tutorial, you will learn how to simulate Species transport and gaseous combustion using Ansys Fluent. You can do this tutorial with Ansys student version. Please visit our website www.cfd.ninja for more information.

## Ansys Fluent | Flow Through Porous Media

In this tutorial, you will learn how to simulate a porous media using Ansys Fluent. In the first part, you can create the geometry and the mesh and the second part Ansys Fluent setup.

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