12.5.2 Shear-Stress Transport (SST) - Model

Overview

The shear-stress transport (SST) - model was developed by Menter [ 237] 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:

• The standard - model and the transformed - model are both multiplied by a blending function and both models are added together. The blending function is designed to be one in the near-wall region, which activates the standard - model, and zero away from the surface, which activates the transformed - model.

• The SST model incorporates a damped cross-diffusion derivative term in the equation.

• The definition of the turbulent viscosity is modified to account for the transport of the turbulent shear stress.

• The modeling constants are different.
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:

 (12.5-32)

and
 (12.5-33)

In these equations, represents the generation of turbulence kinetic energy due to mean velocity gradients, calculated as described in Section  12.5.1. represents the generation of , calculated as described in Section  12.5.1. 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  12.5.1. 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

 (12.5-34) (12.5-35)

where and are the turbulent Prandtl numbers for and , respectively. The turbulent viscosity, , is computed as follows:
 (12.5-36)

where is the strain rate magnitude and
 (12.5-37) (12.5-38)

is defined in Equation  12.5-6. The blending functions, and , are given by
 (12.5-39) (12.5-40) (12.5-41)

 (12.5-42) (12.5-43)

where is the distance to the next surface and is the positive portion of the cross-diffusion term (see Equation  12.5-52).

Modeling the Turbulence Production

Production of

The term represents the production of turbulence kinetic energy, and is defined as:

 (12.5-44)

where is defined in the same manner as in the standard - model. See Section  12.5.1 for details.

Production of

The term represents the production of and is given by

 (12.5-45)

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
 (12.5-46)

where
 (12.5-47) (12.5-48)

where is 0.41.

Modeling the Turbulence Dissipation

Dissipation of

The term represents the dissipation of turbulence kinetic energy, and is defined in a similar manner as in the standard - model (see Section  12.5.1). 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,

 (12.5-49)

Dissipation of

The term represents the dissipation of , and is defined in a similar manner as in the standard - model (see Section  12.5.1). 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  12.5-24. For the SST - model, is a constant equal to 1. Thus,

 (12.5-50)

Instead of a having a constant value, is given by
 (12.5-51)

and is obtained from Equation  12.5-39.

Cross-Diffusion Modification

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  12.5-33). is defined as

 (12.5-52)

For details about the various - models, see Section  12.4.

Model Constants

All additional model constants ( , , , , , , , , and M ) have the same values as for the standard - model (see Section  12.5.1).

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