The shear-stress transport (SST) - model was developed by Menter [ 224] to effectively blend the robust and accurate formulation of the - model in the near-wall region with the free-stream independence of the - model in the far field. To achieve this, the - model is converted into a - formulation. The SST - model is similar to the standard - model, but includes the following refinements:
These features make the SST - model more accurate and reliable for a wider class of flows (e.g., adverse pressure gradient flows, airfoils, transonic shock waves) than the standard - model. Other modifications include the addition of a cross-diffusion term in the equation and a blending function to ensure that the model equations behave appropriately in both the near-wall and far-field zones.
Transport Equations for the SST - Model
The SST - model has a similar form to the standard - model:
In these equations, represents the generation of turbulence kinetic energy due to mean velocity gradients, calculated as described in Section 4.5.1. represents the generation of , calculated as described in Section 4.5.1. and represent the effective diffusivity of and , respectively, which are calculated as described below. and represent the dissipation of and due to turbulence, calculated as described in Section 4.5.1. represents the cross-diffusion term, calculated as described below. and are user-defined source terms.
Modeling the Effective Diffusivity
The effective diffusivities for the SST - model are given by
where and are the turbulent Prandtl numbers for and , respectively. The turbulent viscosity, , is computed as follows:
where is the strain rate magnitude and
is defined in Equation 4.5-6. The blending functions, and , are given by
where is the distance to the next surface and is the positive portion of the cross-diffusion term (see Equation 4.5-52).
Modeling the Turbulence Production
The term represents the production of turbulence kinetic energy, and is defined as:
where is defined in the same manner as in the standard - model. See Section 4.5.1 for details.
The term represents the production of and is given by
Note that this formulation differs from the standard - model. The difference between the two models also exists in the way the term is evaluated. In the standard - model, is defined as a constant (0.52). For the SST - model, is given by
where is 0.41.
Modeling the Turbulence Dissipation
The term represents the dissipation of turbulence kinetic energy, and is defined in a similar manner as in the standard - model (see Section 4.5.1). The difference is in the way the term is evaluated. In the standard - model, is defined as a piecewise function. For the SST - model, is a constant equal to 1. Thus,
The term represents the dissipation of , and is defined in a similar manner as in the standard - model (see Section 4.5.1). The difference is in the way the terms and are evaluated. In the standard - model, is defined as a constant (0.072) and is defined in Equation 4.5-24. For the SST - model, is a constant equal to 1. Thus,
Instead of having a constant value, is given by
and is obtained from Equation 4.5-39.
The SST - model is based on both the standard - model and the standard - model. To blend these two models together, the standard - model has been transformed into equations based on and , which leads to the introduction of a cross-diffusion term ( in Equation 4.5-33). is defined as
For details about the various - models, see Section 4.4.
All additional model constants ( , , , , , , , , and M ) have the same values as for the standard - model (see Section 4.5.1).