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12.7.5 Effects of Buoyancy on Turbulence

The production terms due to buoyancy are modeled as

 G_{ij} = \beta \frac{\mu_t}{{\rm Pr}_t} \left( g_i \frac{\p... ...partial x_j} + g_j \frac{\partial T}{\partial x_i} \right) (12.7-26)

where Pr $_t$ is the turbulent Prandtl number for energy, with a default value of 0.85.

Using the definition of the coefficient of thermal expansion, $\beta$, given by Equation  12.4-24, the following expression is obtained for $G_{ij}$ for ideal gases:
 G_{ij} = - \frac{\mu_t}{\rho {\rm Pr}_t} \left( g_i \frac{\... ...rtial x_j} + g_j \frac{\partial \rho}{\partial x_i} \right) (12.7-27)


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