### 12.1.2. Detached Eddy Simulation (DES)

Detached Eddy Simulation (DES) was introduced by Spalart and co-workers (Spalart et al., 1997 [30], 2000 [31], Travin et al., 2000 [34], Strelets, 2001 [33]), to eliminate the main limitation of LES models by proposing a hybrid formulation that switches between RANS and LES based on the grid resolution provided. By this formulation, the wall boundary layers are entirely covered by the RANS model and the free shear flows away from walls are typically computed in LES mode. The formulation is mathematically relatively simple and can be built on top of any RANS turbulence model. DES has attained significant attention in the turbulence community as it was the first SRS model that allowed the inclusion of SRS capabilities into common engineering flow simulations.

Within DES models, the switch between RANS and LES is based on a criterion like the following:

| (12–4)

where is the maximum edge length of the local computational cell. The actual formulation for a two-equation model (for example, the -equation of the model) is:

| (12–5)

| (12–6)

As the grid is refined below the limit the DES-limiter is activated and switches the model from RANS to LES mode. For wall boundary layers, this translates into the requirement that the RANS formulation is preserved as long as the following condition holds: , where is the boundary layer thickness. The intention of the model is to run in RANS mode for attached flow regions, and to switch to LES mode in detached regions away from walls. This switch suggests that the original DES formulation, as well as its later versions, require a grid and time step resolution to be of LES quality once they switch to the grid spacing as the defining length scale. Once the limiter is activated, the models lose their RANS calibration and all relevant turbulence information must be resolved. For this reason, for example in free shear flows, the DES approach offers no computational savings over a standard LES model. However, it allows you to avoid the high computing costs of covering the wall boundary layers in LES mode.

It is also important to note that the DES limiter can already be activated by grid refinement inside attached boundary layers. This is undesirable as it affects the RANS model by reducing the eddy viscosity; this can lead to Grid-Induced Separation (GIS), as discussed by Menter and Kuntz, 2002 [19], where the boundary layers can separate at arbitrary locations depending on the grid spacing. In order to avoid this limitation, the DES concept has been extended to Delayed-DES (DDES) by Spalart et al., 2006 [32], following the proposal of Menter and Kuntz, 2002 [19] of “shielding” the boundary layer from the DES limiter. The DDES extension was also applied to the DES-SA formulation resulting in the DDES-SA model, as well as to the SST model giving the DDES-SST model.

For two-equation models, the dissipation term in the -equation is thereby re-formulated as follows:

| (12–7)

| (12–8)

The function is designed in such a way as to give inside the wall boundary layer and away from the wall. The definition of this function is intricate as it involves a balance between proper shielding and not suppressing the formation of resolved turbulence as the flow separates from the wall. As the function blends over to the LES formulation near the boundary layer edge, no perfect shielding can be achieved. The limit for DDES is typically in the range of and therefore allows for meshes where is a factor of five smaller than for DES, without negative effects on the RANS-covered boundary layer. However, even this limit is frequently reached and GIS can appear even with DDES.

There are a number of DDES models available in ANSYS CFD. They follow the same principal idea with respect to switching between RANS and LES mode. The models differ therefore mostly by their RANS capabilities and should be selected accordingly.

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