4.10.1 Spalart-Allmaras Based DES Model

The standard Spalart-Allmaras model uses the distance to the closest wall as the definition for the length scale $d$, which plays a major role in determining the level of production and destruction of turbulent viscosity (Equations  4.3-6, 4.3-12, and 4.3-15). The DES model, as proposed by Shur et al. [ 314] replaces $d$ everywhere with a new length scale $\widetilde{d}$, defined as

where the grid spacing, $\Delta$, is based on the largest grid space in the $x$, $y$, or $z$ directions forming the computational cell. The empirical constant $C_{\rm des}$ has a value of 0.65.

For a typical RANS grid with a high aspect ratio in the boundary layer, and where the wall-parallel grid spacing usually exceeds $\delta$, where $\delta$ is the size of the boundary layer, Equation  4.10-1 will ensure that the DES model is in the RANS mode for the entire boundary layer. However, in case of an ambiguous grid definition, where $\Delta << \delta$, the DES limiter can activate the LES mode inside the boundary layer, where the grid is not fine enough to sustain resolved turbulence. Therefore, a new formulation  [ 332] of DES is available in ANSYS FLUENT to preserve the RANS mode throughout the boundary layer. This is known as the delayed option or DDES for delayed DES.

The DES length scale $\widetilde{d}$ is re-defined according to:

where $f_d$ is given by:

This formulation is the default settings.