The standard Reynolds stress model in Ansys CFX is based on the 
-equation.
The CFX-Solver solves the following equations for the transport of the
Reynolds stresses:
 | (2–89) |
where 
is the pressure-strain correlation, and 
, the exact production term, is given by:
 | (2–90) |
The production due to buoyancy is
 | (2–91) |
where the second term represents the buoyancy contribution from
the pressure-strain term (Launder [196]), and 
is
given by
 | (2–92) |
If the Boussinesq buoyancy model is used, then 
is modeled
as
 | (2–93) |
where 
is the thermal expansion coefficient. Otherwise
the term is modeled as (full buoyancy model based on density differences)
 | (2–94) |
As the turbulence dissipation appears in the individual stress
equations, an equation for 
is still required. This now has
the form:
 | (2–95) |
In these equations, the anisotropic diffusion coefficients of the original models have been replaced by an isotropic formulation, which increases the robustness of the Reynolds stress model.
The Reynolds stress model is also available with anisotropic diffusion coefficients. In this case, the CFX-Solver solves the following equations for the transport of the Reynolds stresses:
 | (2–96) |
where 
is the pressure-strain correlation, and 
, the exact production term, is given by Equation 2–90.
In this case the production due to buoyancy is for the Boussinesq approximation modeled as:
 | (2–97) |
Otherwise the term is modeled as (full buoyancy model based on density differences):
 | (2–98) |
The equation for 
is:
 | (2–99) |
The model constants are listed below for each model.
One of the most important terms in Reynolds stress models is
the pressure-strain correlation, 
. It acts to drive turbulence towards an isotropic
state by redistributing the Reynolds stresses.
The pressure strain term can be split into two parts:
 | (2–100) |
where 
is
the ‘slow’ term, also known as the return-to-isotropy
term, and 
is
called the ‘rapid’ term.
There are three varieties of the standard Reynolds stress models
based on the 
-equation available. These are
known as LRR-IP, LRR-QI and SSG. The LRR-IP and LRR-QI models were
developed by Launder, Reece and Rodi [4]. In both models, the pressure-strain
correlation is linear. "IP" stands for Isotropization
of Production and is the simplest of the 3 models. The two terms read:
 | (2–101) |
 | (2–102) |
The values of the two coefficients are 
and 
. 
is given
by 
.
"QI" stands for Quasi-Isotropic and differs from the IP model in the formulation of the rapid term:
 | (2–103) |
where 
is given by:
 | (2–104) |
The SSG model was developed by Speziale, Sarkar and Gatski [5] and uses a quadratic relation for the pressure-strain correlation.
In order to compare the pressure-strain correlations for the
three models, a general form can be derived based on the anisotropy
tensor 
and the mean strain rate tensor and vorticity
tensor, 
and 
respectively.
The general form reads:
 | (2–105) |
 | (2–106) |
where
 | (2–107) |
 | (2–108) |
 | (2–109) |
This general form can be used to model linear and quadratic correlations by using appropriate values for the constants. The constants are listed in the table below for each model.
|
Model |
|
|
|
|
|
|
|---|---|---|---|---|---|---|
|
LRR-IP |
0.1152 |
1.10 |
0.22 |
0.18 |
1.45 |
1.9 |
|
LRR-QI |
0.1152 |
1.10 |
0.22 |
0.18 |
1.45 |
1.9 |
|
SSG |
0.1 |
1.36 |
0.22 |
0.18 |
1.45 |
1.83 |
|
Model |
|
|
|
|
|
|
|
|---|---|---|---|---|---|---|---|
|
LRR-IP |
1.8 |
0.0 |
0.0 |
0.8 |
0.0 |
0.6 |
0.6 |
|
LRR-QI |
1.8 |
0.0 |
0.0 |
0.8 |
0.0 |
0.873 |
0.655 |
|
SSG |
1.7 |
-1.05 |
0.9 |
0.8 |
0.65 |
0.625 |
0.2 |
Selection of the appropriate model is carried out on the Fluid Models panel of the Domains form in CFX-Pre. The following options correspond to the types of models listed above:
Reynolds Stress Model - LRR-IP
SSG Reynolds Stress Model - SSG
QI Reynolds Stress Model - LRR-IQ
The coefficients of the pressure strain term can be specified
in CFX-Pre in the general form for the LRR-QI and SSG models. The
LRR-IP model has been added for completeness in the table above. In CFX-Pre the
pressure strain coefficients of the LRR-IP are asked in the form as
given in Equation 2–101 and Equation 2–102. For the Boussinesq
buoyancy model the default value of 
is 0.9 for LRR-IP and
LRR-QI and 2/3 for SSG. In the full buoyancy model based on density
differences the default value of 
is 1.0 for all models.