## 12.4.5 Effects of Buoyancy on Turbulence in the - Models

When a non-zero gravity field and temperature gradient are present simultaneously, the - models in FLUENT account for the generation of due to buoyancy ( in Equations  12.4-1, 12.4-4, and 12.4-15), and the corresponding contribution to the production of in Equations  12.4-2, 12.4-5, and 12.4-16.

The generation of turbulence due to buoyancy is given by

 (12.4-23)

where Pr is the turbulent Prandtl number for energy and is the component of the gravitational vector in the th direction. For the standard and realizable - models, the default value of Pr is 0.85. In the case of the RNG - model, Pr = , where is given by Equation  12.4-9, but with . The coefficient of thermal expansion, , is defined as
 (12.4-24)

For ideal gases, Equation  12.4-23 reduces to
 (12.4-25)

It can be seen from the transport equations for (Equations  12.4-1, 12.4-4, and 12.4-15) that turbulence kinetic energy tends to be augmented ( ) in unstable stratification. For stable stratification, buoyancy tends to suppress the turbulence ( ). In FLUENT, the effects of buoyancy on the generation of are always included when you have both a non-zero gravity field and a non-zero temperature (or density) gradient.

While the buoyancy effects on the generation of are relatively well understood, the effect on is less clear. In FLUENT, by default, the buoyancy effects on are neglected simply by setting to zero in the transport equation for (Equation  12.4-2, 12.4-5, or 12.4-16).

However, you can include the buoyancy effects on in the Viscous Model panel. In this case, the value of given by Equation  12.4-25 is used in the transport equation for (Equation  12.4-2, 12.4-5, or 12.4-16).

The degree to which is affected by the buoyancy is determined by the constant . In FLUENT, is not specified, but is instead calculated according to the following relation [ 140]:
 (12.4-26)

where is the component of the flow velocity parallel to the gravitational vector and is the component of the flow velocity perpendicular to the gravitational vector. In this way, will become 1 for buoyant shear layers for which the main flow direction is aligned with the direction of gravity. For buoyant shear layers that are perpendicular to the gravitational vector, will become zero.

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