When a nonzero gravity field and temperature gradient are present simultaneously, the - models in Ansys Fluent can account for the generation of due to buoyancy ( in  Equation 4–39, Equation 4–42, and Equation 4–53), and the corresponding contribution to the production of in Equation 4–40, Equation 4–43, and Equation 4–54.

The generation of turbulence due to buoyancy is given by

(4–64)

where 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 is 0.85. For non-premixed and partially premixed combustion models, is set equal to the PDF Schmidt number to ensure a Lewis number equal to unity. In the case of the RNG - model, = , where is given by Equation 4–47, but with . The coefficient of thermal expansion, , is defined as

(4–65)

For ideal gases, Equation 4–64 reduces to

(4–66)

It can be seen from the transport equations for (Equation 4–39, Equation 4–42, and Equation 4–53) that turbulence kinetic energy tends to be augmented () in unstable stratification. For stable stratification, buoyancy tends to suppress the turbulence (). In Ansys Fluent, the effects of buoyancy on the generation of are included by default when you have both a nonzero gravity field and a nonzero temperature (or density) gradient.

While the buoyancy effects on the generation of are relatively well understood, the effect on is less clear. In Ansys Fluent, by default, the buoyancy effects on are neglected simply by setting to zero in the transport equation for (Equation 4–40, Equation 4–43, or Equation 4–54).

However, you can include the buoyancy effects on in the Viscous Model Dialog Box. In this case, the value of given by Equation 4–66 is used in the transport equation for (Equation 4–40, Equation 4–43, or Equation 4–54).

The degree to which is affected by the buoyancy is determined by the constant . In Ansys Fluent, is not specified, but is instead calculated according to the following relation  [238]:

(4–67)

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.