After the SDES model switches to LES mode, the additional source term is activated and reduces the eddy viscosity to a level comparable to a conventional LES model. The level of the achieved eddy viscosity can be estimated by imposing equilibrium on the source terms of the underlying RANS model (in this case, the SST model). This means that the convection and diffusion terms in both the - and -equations are neglected, and the source and sink terms are equated. The result is:

(4–294)

where is the strain rate, and and are the constants of the source and sink terms in the -equation, respectively. represents the constants and used in the different models, and represents the definition of the grid spacing used in the different models. The formulation is obviously equivalent to the classical Smagorinsky model (see Subgrid-Scale Models). The combination of (/)^3/4 is equivalent to the constant in the Smagorinsky model. Using the outer constants from the SST model that are relevant for the LES region (=0.44, =0.083, =0.61) produces an equivalent =0.175 for the DES / DDES models. This is close to the value of =0.18, which is recommended for the Smagorinsky model for Decaying Isotropic Turbulence (DIT) simulations. This is not surprising, as the LES portion of DES / DDES was calibrated for DIT. However, it is known that the Smagorinsky model requires different calibration constants for DIT and shear turbulence. The value for shear flows is closer to =0.11. Since shear flows are much more relevant for engineering simulations than DIT, it was decided to use a value of =0.4 in the SDES model, which results in the desired value for the equivalent constant.

The definition of the LES length scale is = in the DES / DDES models. This definition is problematic, as it can result in overly high levels of eddy viscosity in separating shear layers, where the mesh aspect ratio is typically high (for example, separating flow from a backward facing step, where the spanwise grid spacing is much larger than the grid spacing in the other two directions). This can lead to a slow 'transition' from RANS to LES mode. In order to avoid this issue, the SDES model uses the following formulation for the LES length scale:

(4–295)

The first part is the classical length scale based on the volume of the cell, and the second part ensures a viable limit for very high aspect ratios. This formulation is smaller by a factor of five for high aspect ratio meshes compared to the DES definition.

It is important to note that both the constant / and the mesh definitions enter the equivalent Smagorinsky model quadratically. For highly stretched meshes, as is typical for separating shear layers, the combined effect of a lower constant and a smaller grid spacing definition results in a reduction by a factor 60 in the eddy viscosity level for SDES compared to DES / DDES.

It should also be noted that both modifications could equally be applied to the DES / DDES model formulations. However, such changes would severely reduce the shielding properties of the DES / DDES formulation, which are based on the combination of . Lowering these values alone or in combination would impair the shielding properties of these models.