ANSYS FLUENT 12.0 Theory Guide - 16.4.2 Continuity Equation

16.4.2 Continuity Equation

The continuity equation for the mixture is

$\frac{\partial}{\partial t} (\rho_m) + \nabla \cdot (\rho_m {\vec v}_m) = 0$

(16.4-1)

where $\vec v_m$ is the mass-averaged velocity:

$\vec{v}_m = \frac{ \sum_{k=1}^{n} { \alpha_k \rho_k \vec{v}_k }}{\rho_m}$

(16.4-2)

and $\rho_m$ is the mixture density:

$\rho_m = \sum_{k=1}^{n} {\alpha_k \rho_k }$

(16.4-3)

$\alpha_k$ is the volume fraction of phase .

Previous: 16.4.1 Overview and Limitations
Up: 16.4 Mixture Model Theory
Next: 16.4.3 Momentum Equation