Detached Eddy Simulation (DES)

Detached Eddy Simulation (DES) is a hybrid modeling approach that combines features of Reynolds-Averaged (RANS) simulation in some parts of the flow and Large Eddy Simulation (LES) in others.

The unsteady RANS equations are applicable to transient situations where the unsteadiness is either imposed, such as by a time-varying boundary condition, or is inherent, such as the vortex shedding in a massively separated flow. In the latter case, transient simulations often yield better results than attempting use a steady-state approach. However, successful unsteady RANS simulations require that the time scales of the turbulence be disparate from the mean-flow unsteadiness. Furthermore, the limitations of the turbulence model may preclude good unsteady results.

DES turbulence models are set up so that boundary layers and irrotational flow regions are solved using a base RANS closure model. However, the turbulence model is intrinsically modified so that, if the grid is fine enough, it will emulate a basic LES subgrid scale model in detached flow regions. In this way, one gets the best of both worlds: a RANS simulation in the boundary layers and an LES in the unsteady separated regions. For more background on DES, see [362].

Simcenter STAR-CCM+ provides the DES modeling approach for three different RANS models:

Spalart-Allmaras DES
Elliptic Blending K-Epsilon DES
SST K-Omega DES

The following DES variants are implemented:

Delayed Detached Eddy Simulation (DDES)
Improved Delayed Detached Eddy Simulation (IDDES)

The DDES model incorporates a delay factor that enhances the ability of the model to distinguish between LES and RANS regions on meshes where spatial refinement could give rise to ambiguous behavior.

For IDDES, the subgrid length-scale includes a dependence on the wall distance. This approach allows RANS to be used in a much thinner near-wall region, in which the wall distance is much smaller than the boundary-layer thickness. IDDES was introduced in order to provide some WMLES (Wall-modelled LES) capabilities to the DES formulation.

While DES holds great promise for certain types of simulations, it must be cautioned that this technology is not the answer to all turbulence modeling problems. The creation of suitable grids is something of an art, and an unsteady simulation is required, with statistics gathered to obtain a mean field as in a LES.

Flow Simulation Methodology

The momentum equations for the RANS averaged velocity $\bar{v}$ and the LES filtered velocity $\tilde{v}$ are defined as:

Figure 1. EQUATION_DISPLAY

\frac{\partial}{\partial t} (ρ \bar{v}) + \nabla\cdot (ρ \bar{v} \otimes \bar{v}) = - \nabla\cdot \bar{p} I + \nabla\cdot (\bar{T} + T_{RANS}) + f_{b}

(1402)

Figure 2. EQUATION_DISPLAY

\frac{\partial}{\partial t} (ρ \tilde{v}) + \nabla\cdot (ρ \tilde{v} \otimes \tilde{v}) = - \nabla\cdot \tilde{p} I + \nabla\cdot (\tilde{T} + T_{SGS}) + f_{b}

(1403)

For a RANS model, the Reynolds-stress tensor $T_{RANS}$ is a function of a time-and length-scale

Figure 3. EQUATION_DISPLAY

T_{RANS} = f (\nabla \cdot \bar{v}, k, ε)

(1404)

and for LES,

Figure 4. EQUATION_DISPLAY

T_{SGS} = f (\nabla \cdot \tilde{v}, Δ)

(1405)

In Eqn. (1405), the most crucial role is played by the filter width, or length-scale, which is used not only for the definition of the subgrid-scale eddy viscosity, but is also used in many models for the definition of the transition region.

The similarities of Eqn. (1402) and Eqn. (1403) suggest that a unified approach can be used to solve for a quantity $\hat{u_{i}}$ , that is dependant on the local definition:

Figure 5. EQUATION_DISPLAY

\frac{\partial}{\partial t} (ρ \hat{v}) + \nabla\cdot (ρ \hat{v} \otimes \hat{v}) = - \nabla\cdot \hat{p} I + \nabla\cdot (\hat{T} + T_{model}) + f_{b}

(1406)

where the modeled stress tensor $T_{model}$ is defined as:

Figure 6. EQUATION_DISPLAY

T_{model} = f_{Δ} (\frac{Δ}{l_{k}}) T_{RANS}

(1407)

where:

$Δ$ is the local measure of the grid size.
$l_{k}$ is the turbulent length-scale.
$f_{Δ}$ is a damping function that depends on the DES variant (DDES or IDDES) .