ANSYS FLUENT 12.0 Theory Guide - 4.9.5 Effects of Buoyancy on Turbulence

4.9.5 Effects of Buoyancy on Turbulence

The production terms due to buoyancy are modeled as

$G_{ij} = (\overline{J_{i}U_{j}} + \overline{J_{j}U_{i}}) = - \beta(g_{i}\overline{u_{j}\theta} + g_{j}\overline{U_{i}\theta})$

(4.9-24)

$\overline{U_{i}\theta} = \frac{\mu_{t}}{\rm Pr_{t}}(\frac{\partial T}{\partial X_{i}})$

(4.9-25)

where Pr 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 4.4-24, the following expression is obtained for $G_{ij}$ for ideal gases:

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

(4.9-26)

Note that the buoyancy effects are not included if low-Re omega based RSM model is used.

Previous: 4.9.4 Modeling the Pressure-Strain
Up: 4.9 Reynolds Stress Model
Next: 4.9.6 Modeling the Turbulence