Two-equation turbulence models allow the determination of both, a turbulent length and time scale by solving two separate transport equations. The standard - model in Ansys Fluent falls within this class of models and has become the workhorse of practical engineering flow calculations in the time since it was proposed by Launder and Spalding  [342]. Robustness, economy, and reasonable accuracy for a wide range of turbulent flows explain its popularity in industrial flow and heat transfer simulations. It is a semi-empirical model, and the derivation of the model equations relies on phenomenological considerations and empiricism.

The standard - model  [342] is a model based on model transport equations for the turbulence kinetic energy () and its dissipation rate (). The model transport equation for is derived from the exact equation, while the model transport equation for was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart.

In the derivation of the - model, the assumption is that the flow is fully turbulent, and the effects of molecular viscosity are negligible. The standard - model is therefore valid only for fully turbulent flows.

As the strengths and weaknesses of the standard - model have become known, modifications have been introduced to improve its performance. Two of these variants are available in Ansys Fluent: the RNG - model  [721] and the realizable - model  [591].

The turbulence kinetic energy, , and its rate of dissipation, , are obtained from the following transport equations:

(4–39)

and

(4–40)

In these equations, represents the generation of turbulence kinetic energy due to the mean velocity gradients, calculated as described in Modeling Turbulent Production in the k-ε Models. is the generation of turbulence kinetic energy due to buoyancy, calculated as described in Effects of Buoyancy on Turbulence in the k-ε Models. represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, calculated as described in Effects of Compressibility on Turbulence in the k-ε Models. , , and are constants. and are the turbulent Prandtl numbers for and , respectively. and are user-defined source terms.

The turbulent (or eddy) viscosity, , is computed by combining and as follows:

(4–41)

where is a constant.

The model constants and have the following default values  [342]:

These default values have been determined from experiments for fundamental turbulent flows including frequently encountered shear flows like boundary layers, mixing layers and jets as well as for decaying isotropic grid turbulence. They have been found to work fairly well for a wide range of wall-bounded and free shear flows.

Although the default values of the model constants are the standard ones most widely accepted, you can change them (if needed) in the Viscous Model Dialog Box.