4.4.3. Shear-Stress Transport (SST) k-ω Model

4.4.3.1. Overview

The SST - model includes all the refinements of the BSL - model, and in addition accounts for the transport of the turbulence shear stress in the definition of the turbulent viscosity.

These features make the SST - model (Menter [428]) more accurate and reliable for a wider class of flows (for example, adverse pressure gradient flows, airfoils, transonic shock waves) than the standard and the BSL - models.

4.4.3.2. Modeling the Turbulent Viscosity

The BSL model described previously combines the advantages of the Wilcox and the - model, but still fails to properly predict the onset and amount of flow separation from smooth surfaces. The main reason is that both models do not account for the transport of the turbulent shear stress. This results in an overprediction of the eddy-viscosity. The proper transport behavior can be obtained by a limiter to the formulation of the eddy-viscosity:

(4–118)

where is the strain rate magnitude and is defined in Equation 4–75. is given by

(4–119)

(4–120)

where is the distance to the next surface.

4.4.3.3. Model Constants

All additional model constants (, , , , , , , , and ) have the same values as for the standard - model (see Model Constants).

4.4.3.4. Treatment of the SST Model for Icing Simulations

An alternative SST roughness model has been implemented based on the Colebrook correlation by Aupoix [32]. As in the Spalart-Allmaras model, the concept of wall turbulent viscosity has been adopted, and it is estimated by modelling the wall values of k and ω.

Note that this modelling approach automatically disables the -insensitive wall treatment which is outlined in y+-Insensitive Near-Wall Treatment for ω-based Turbulence Models at the respective wall.

Specifically, Aupoix proposed the following formulations to compute the non-dimensional wall values, , [32]:

(4–121)

(4–122)

where , a standard constant in the SST k-ω model. and are defined as:

(4–123)

(4–124)

Therefore, all the wall values of k and ω are known:

(4–125)

(4–126)