ANSYS FLUENT 12.0 Theory Guide - 16.4.3 Momentum Equation

16.4.3 Momentum Equation

The momentum equation for the mixture can be obtained by summing the individual momentum equations for all phases. It can be expressed as

$\frac{\partial}{\partial t} (\rho_m {\vec v}_m) + \nabla \cdo... ...t(\nabla {\vec v}_m + \nabla {\vec v}_m^{\rm T}\right)\right] +$

$\rho_m {\vec g} + {\vec F} + \nabla \cdot \left(\sum_{k=1}^... ...ha_k \rho_k {\vec v}_{{\rm dr},k} {\vec v}_{{\rm dr},k}\right)$

(16.4-4)

where is the number of phases, $\vec F$ is a body force, and $\mu_m$ is the viscosity of the mixture:

$\mu_m = \sum_{k=1}^{n} {\alpha_k \mu_k }$

(16.4-5)

$\vec{v}_{{\rm dr},k}$ is the drift velocity for secondary phase :

$\vec{v}_{{\rm dr},k} = \vec{v}_k - \vec{v}_m$

(16.4-6)

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