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7.19.7 Modeling Porous Media Based on Physical Velocity

As stated in Section  7.19.1, by default FLUENT calculates the superficial velocity based on volumetric flow rate. The superficial velocity in the governing equations can be represented as

 {\vec v_{\rm superficial}} = \gamma {\vec v_{\rm physical}} (7.19-28)

where $\gamma$ is the porosity of the media defined as the ratio of the volume occupied by the fluid to the total volume.

The superficial velocity values within the porous region remain the same as those outside of the porous region. This limits the accuracy of the porous model where there should be an increase in velocity throughout the porous region. For more accurate simulations of porous media flows, it becomes necessary to solve for the true, or physical velocity throughout the flowfield, rather than the superficial velocity.

FLUENT allows the calculation on the physical velocity using the Porous Formulation region of the Solver panel. By default, the Superficial Velocity option is turned on.

Using the physical velocity formulation, and assuming a general scalar $\phi$, the governing equation in an isotropic porous media has the following form:

 \frac{\partial(\gamma\rho\phi)}{\partial t} + {\bf\nabla} \c... ...\bf\nabla} \cdot (\gamma\Gamma{\bf\nabla}\phi) + \gamma S_\phi (7.19-29)

Assuming isotropic porosity and single phase flow, the volume-averaged mass and momentum conservation equations are as follows:

 \frac{\partial(\gamma\rho)}{\partial t} + {\bf\nabla} \cdot (\gamma\rho{\vec v}) = 0 (7.19-30)

 \frac{\partial(\gamma\rho{\vec v})}{\partial t} + {\bf\nabla... ...\alpha} + \frac{C_2\rho}{2}\vert{{\vec v}}\vert\right){\vec v} (7.19-31)

The last term in Equation  7.19-31 represents the viscous and inertial drag forces imposed by the pore walls on the fluid.


Note that even when you solve for the physical velocity in Equation  7.19-31, the two resistance coefficients can still be derived using the superficial velocity as given in Section  7.19.6. FLUENT assumes that the inputs for these resistance coefficients are based upon well-established empirical correlations that are usually based on superficial velocity. Therefore, FLUENT automatically converts the inputs for the resistance coefficients into those that are compatible with the physical velocity formulation.


Note that the inlet mass flow is also calculated from the superficial velocity. Therefore, for the same mass flow rate at the inlet and the same resistance coefficients, for either the physical or superficial velocity formulation you should obtain the same pressure drop across the porous media zone.

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