### 2.6.2. Delayed and Shielded DES-SST Model Formulation

Note: The DDES and SDES models are not available in CFX.

The main practical problem with the DES formulation (both for the Spalart Allmaras and the standard SST-DES model) is that there is no mechanism for preventing the limiter from becoming active in the attached portion of the boundary layer. This will happen in regions where the is less than the boundary layer thickness. In this case, the flow can separate as a result of the mesh spacing (mesh-induced separation), which is undesirable. The DES formulations reduce the impact of the DES term inside the boundary layer. This is achieved by function , which protects the boundary layer. For , the original SST model is recovered; for , the original DES model is utilized.

| (2–195)

There are several historic formulations for the function . Originally, the and blending functions of the SST model were used [56]. Later, a specifically tuned function termed was added [226].

| (2–196)

Where is the wall distance, is the von Karman constant, and .

is superseded by the Shielded DES function (SDES). The function offers essentially asymptotic shielding under mesh refinement and is recommended (and also set as the default). This function is unpublished and proprietary to ANSYS.

In addition, the SDES model features an alternative definition of the mesh length scale:

| (2–197)

where is the volume of the cell and is its maximum edge length. Finally, for SDES, the model coefficient is reduced to . Both of these changes result in much reduced eddy viscosity levels in detached shear layers and quicker “transition” from RANS to LES.

Figure 2.2: Eddy viscosity profiles for DDES and SDES models under mesh refinement shows the effect of improved shielding on boundary layer flows. The parameter is the local ratio of grid spacing, , to boundary layer thickness, . The grid spacing is for the DDES model and for the SDES model. Note, in the figure, that the range of is much wider for SDES. Nevertheless, the SDES model is able to preserve the RANS model eddy viscosity whereas the DDES model deteriorates for values of .

Figure 2.2: Eddy viscosity profiles for DDES and SDES models under mesh refinement

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