When a nonzero gravity field and temperature gradient are present
simultaneously, the

models in
FLUENT account for the generation of
due to buoyancy (
in Equations
12.41,
12.44,
and
12.415), and the corresponding contribution to the
production of
in Equations
12.42,
12.45, and
12.416.
The generation of turbulence due to buoyancy is given by
(12.423)
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
12.49, but with
.
The coefficient of thermal expansion,
, is defined as
It can be seen from the transport equations for
(Equations
12.41,
12.44, and
12.415)
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 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
FLUENT, by default,
the buoyancy effects on
are neglected simply by setting
to zero
in the transport equation for
(Equation
12.42,
12.45,
or
12.416).
However, you can include the buoyancy effects on
in
the
Viscous Model panel. In this case, the value of
given by Equation
12.425 is used in the transport equation for
(Equation
12.42,
12.45, or
12.416).
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]:
(12.426)
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.