
Overview
The standard

model in
ANSYS FLUENT is based on the Wilcox

model [
379], which incorporates modifications for lowReynoldsnumber effects, compressibility, and shear flow spreading. The Wilcox model predicts free shear flow spreading rates that are in close agreement with measurements for far wakes, mixing layers, and plane, round, and radial jets, and is thus applicable to wallbounded flows and free shear flows. A variation of the standard

model called the SST

model is also available in
ANSYS FLUENT, and is described in Section
4.5.2.
The standard

model is an empirical model based on model transport equations for the turbulence kinetic energy (
) and the specific dissipation rate (
), which can also be thought of as the ratio of
to
[
379].
As the  model has been modified over the years, production terms have been added to both the and equations, which have improved the accuracy of the model for predicting free shear flows.
Transport Equations for the Standard

Model
The turbulence kinetic energy, , and the specific dissipation rate, , are obtained from the following transport equations:
and
In these equations, represents the generation of turbulence kinetic energy due to mean velocity gradients. represents the generation of . and represent the effective diffusivity of and , respectively. and represent the dissipation of and due to turbulence. All of the above terms are calculated as described below. and are userdefined source terms.
Modeling the Effective Diffusivity
The effective diffusivities for the  model are given by
(4.53)  
(4.54) 
where and are the turbulent Prandtl numbers for and , respectively. The turbulent viscosity, , is computed by combining and as follows:
(4.55) 
LowReynoldsNumber Correction
The coefficient damps the turbulent viscosity causing a lowReynoldsnumber correction. It is given by
where
Note that, in the highReynoldsnumber form of the  model, .
Modeling the Turbulence Production
Production of
The term represents the production of turbulence kinetic energy. From the exact equation for the transport of , this term may be defined as
To evaluate in a manner consistent with the Boussinesq hypothesis,
where is the modulus of the mean rateofstrain tensor, defined in the same way as for the  model (see Equation 4.422).
Production of
The production of is given by
(4.513) 
where
is given by Equation
4.511.
The coefficient is given by
where
= 2.95.
and Re
are given by Equations
4.56 and
4.57, respectively.
Note that, in the highReynoldsnumber form of the  model, .
Modeling the Turbulence Dissipation
Dissipation of
The dissipation of is given by
(4.515) 
where
where
(4.517) 
and
where Re is given by Equation 4.57.
Dissipation of
The dissipation of is given by
(4.523) 
where
The strain rate tensor, is defined in Equation 4.311. Also,
and are defined by Equations 4.519 and 4.528, respectively.
Compressibility Correction
The compressibility function, , is given by
where
Note that, in the highReynoldsnumber form of the  model, . In the incompressible form, .
Model Constants