### 4.1.12. The Detached Eddy Simulation Model (DES)

Note: The classical DES model family has been superseded by the newer model formulations of the SBES family (The Stress-Blended Eddy Simulation (SBES) Model).

In an attempt to improve the predictive capabilities of turbulence models in highly separated regions, Spalart [57] proposed a hybrid approach, which combines features of classical RANS formulations with elements of Large Eddy Simulations (LES) methods. The concept has been termed Detached Eddy Simulation (DES) and is based on the idea of covering the boundary layer by a RANS model and switching the model to a LES mode in detached regions. Ideally, DES would predict the separation line from the underlying RANS model, but capture the unsteady dynamics of the separated shear layer by resolution of the developing turbulent structures. Compared to classical LES methods, DES saves orders of magnitude of computing power for high Reynolds number flows. Though this is due to the moderate costs of the RANS model in the boundary layer region, DES still offers some of the advantages of an LES method in separated regions.

See Detached Eddy Simulation Theory in the CFX-Solver Theory Guide and the detailed CFX report [55] for theoretical model information.

Additional modeling advice can be found in Best Practices: Scale-Resolving Simulations in ANSYS CFD in the CFX Reference Guide.

#### 4.1.12.1. Using the Detached Eddy Simulation Model in CFX

##### 4.1.12.1.1. When to use DES

It is well known that RANS models does not accurately predict all flow details in massively separated flow regions. In addition, the RANS formulation does not provide any information on turbulent flow structures and spectral distribution, which might be of importance to predict flow-induced noise or vibrations. In these cases, DES can provide valuable details far exceeding RANS simulations. Typical examples of DES simulations are:

- Flow around non-aerodynamic obstacles (buildings, bridges, and so on)

- Flow around ground transport vehicles with massively separated regions (cars, trains, trucks)

- Flow around noise generating obstacles (such as car side mirrors)

- Massively separated flow around stalled wings

On the other hand, DES is a computer intensive method because large (detached) turbulent structures need to be resolved in space and time. While the grid resolution requirements are not significantly higher than RANS for simulations, the time resolution imposes high CPU demands. In CFX, steady-state solutions can typically be obtained within 100-200 iterations. A typical DES simulation requires several thousands timesteps using three coefficient loops each. DES is therefore at least one order of magnitude more computer intensive than RANS models. DES does not enable the use of symmetry conditions, because turbulent structures are usually not symmetric. Two-dimensional and axisymmetric simulations are not feasible, as turbulent structures are always three-dimensional. Hence, you should carefully weigh the need for additional information against the required resources.

#### 4.1.12.2. Setting up a DES Simulation

##### 4.1.12.2.1. Geometry for DES

The main issue with geometry is that 2D or axisymmetric simulations are not visible. In addition, in most cases, symmetry or periodicity conditions are not allowed. As an example, RANS simulations enable the use of a half model for a car simulation. As the turbulent structures are asymmetric, this is not possible in DES.

##### 4.1.12.2.2. Meshing Requirements for DES

There are many requirements in terms of grid generation, which depend on the selection of the specific formulation of the DES model (see report [55] or Turbulence and Wall Function Theory in the CFX-Solver Theory Guide). The grid resolution requirement in the attached boundary layers is the same as that of a regular RANS solution (10-15 nodes in the boundary layer). In the DES region, the grid has to be designed in all three space dimensions to enable a minimum resolution equivalent to the resolution of the largest turbulent structures. Because the largest grid spacing is used in the switch for the DES limiter, it is essential to have sufficient resolution in the spanwise direction (if it exists).

One of the main issues of DES models is the danger to produce grid-induced separation due to an activation of the DES limiter in the RANS region. For a detailed explanation, refer to [55]. The zonal formulation used in CFX helps to avoid the severity of this potential limitation.

Examples of DES grids are provided in [55]. For a cylinder in cross-flow, 50 nodes were used in the spanwise direction for an extension of 2 diameters. For the Ahmed car body, 70 nodes were used in the cross-flow direction.

##### 4.1.12.2.3. DES Timestep Considerations

Timestep selection is a sensitive issue, as it determines the quality of the resolution of the turbulent structures. In most cases, a typical shedding frequency can be estimated for the largest turbulent structures. An example is a cylinder in cross-flow. For a cylinder, the Strouhal number is of the order of:

| (4–11)

In the CFX simulation [55], the freestream velocity is U=46 m/s and the diameter is D=0.37 m. This results in a frequency f=24.8 1/s. A timestep of is sufficient to resolve the turbulent structures on the given grid.

##### 4.1.12.2.4. Boundary Conditions

In almost all cases, the same boundary conditions as in RANS simulation can be applied. Exceptions are symmetry or periodicity conditions, which may not be satisfied by the turbulent structures.

For a detailed discussion of inlet conditions, see [55]. In most cases, RANS inlet conditions can be applied, particularly for flows without profile distributions at the inlet, as mostly used in industrial flows.

##### 4.1.12.2.5. DES Initialization

It is recommended that you start the DES simulation from a converged RANS solution. For comparison purposes, it is useful to use the same RANS model as in the DES formulation (in CFX this means the SST model). The RANS solution supplies to the DES formulation important elliptic information on the pressure field, which might take a long time to build up in an unsteady simulation.

##### 4.1.12.2.6. Monitoring a DES Simulation

Due to high computing costs, it is essential to monitor a DES run to ensure that it approaches an appropriate solution. It is recommended that you check the blending function for DES model during the simulation (every 50-100 timesteps). In regions where the function is zero, the LES model is used, and the region where its value is one, the RANS model is activated. Figure 4.7: Blending Function for DES Model for Flow Around Cube. shows a typical example for the flow around a cube. The blue region behind the cube is governed by the LES part, and the red region by the RANS model. This is desirable for this case as only the structures behind the obstacle are of interest.

Figure 4.7: Blending Function for DES Model for Flow Around Cube.

A second variable to monitor is the invariant:

| (4–12)

where S is the absolute value of the strain rate (S = Shear Strain Rate in CFD-Post) and is the absolute value of the vorticity. Note that the vorticity has to be activated in order to be available in CFD-Post. The following lines are to be added to the solver CCL:

    LIBRARY:
       VARIABLE: vorticity
          Output to Postprocessor = Yes
       END
    END

In CFD-Post, you have to define a user variable based on the following expression:

    LIBRARY:
       CEL:
          EXPRESSIONS:
             Invariant = Vorticity^2 - Shear Strain Rate^2
          END
       END
    END
    USER SCALAR VARIABLE:VelGradInvariant
       Boundary Values = Conservative
       Expression = Invariant
       Recipe = Expression
    END

Figure 4.8: Strain Rate Invariant for Flow Around Cube

The above figure shows a typical picture of a successful DES simulation. In case that only single scale (or no) vortex shedding is observed, it might be necessary to consider the following options:

- Reduce timestep

- Refine grid

- Use FSST=F1 or even FSST=0 (see report [55] or Turbulence and Wall Function Theory in the CFX-Solver Theory Guide).

After the turbulent structures are visually established, the averaging process within CFX can be started. Variables of interest are vorticity, eddy viscosity, pressure, velocity and k and . This is achieved by the following steps (for example, start averaging at timestep 2087):

    FLOW:
       OUTPUT CONTROL:
          TRANSIENT STATISTICS: mean1
             Output Variables List = Vorticity, Eddy Viscosity, \
             Pressure, Velocity, \
             Turbulence Eddy Frequency, \
             Turbulence Kinetic Energy
             Option = Arithmetic Average
             Start Iteration List = 2087,2087,2087,2087,2087,2087
          END
       END
    END

#### 4.1.12.3. Limitations/Concerns of Using the DES Model

One of the requirements for DES is that the flow must develop a strong instability once the LES mode is activated. Otherwise the RANS model is reduced, but the unsteady structures do not develop quickly enough to keep the overall turbulent kinetic energy (resolved + modeled) consistent. Such a situation occurs inside boundary layers or channel/pipe flows, if the grid is refined below a critical level. Once this level is reached, the RANS model is reduced, but in most cases no instability develops quickly enough to compensate for the lowered stresses. In severe cases, this can result in grid-induced separation, as shown by Menter et al. [133]. For industrial applications this is a practical concern, as standard DES models have a RANS grid limit of , where is the maximal local cell length and is the boundary layer thickness. This limit can easily be reached in industrial CFD simulations. In order to reduce this problem, Menter [133] proposed shielding functions that protect the RANS boundary layer from grid impact.

A second requirement for DES is that the grid spacing in the LES region must immediately be of LES-quality, as otherwise the turbulence model will produce a mix of RANS and LES components ([135], [137]). A good example is the flow over a backward-facing step. Assume that the grid is of LES-quality behind the step in the main flow plane (x,y) and that the "spanwise" resolution defines the DES limiter, . In the case that is larger than an upper critical limit , the model will operate in RANS mode and produce a steady-state solution. In the case that is lower than a lower critical limit , the model will operate in LES mode and develop a flow instability past the step with the correct balance of the stresses. However, if , the model is undefined, and the solution will be neither RANS nor LES. The most likely scenario is that starting from , refinement will impact the underlying RANS model, without enabling an unsteady solution to develop. As a result, the separation zone will grow much larger than in the experiments. From a certain point of refinement, unsteady structures will develop, but instead of starting at the step, they will start further downstream, where the DES limiter has a stronger influence. Again, this results in an overly large separation bubble. With further grid refinement, the unsteadiness will move further upstream and eventually the entire separation zone will be computed in LES mode, when is reached. The situation for is shown in Figure 4.9: Unsteady flow from DES over backward facing step using insufficient spanwise grid resolution where the backward facing step of Jovic and Driver [138] was computed with the SST-DES model with a grid with only 21 cells in spanwise (2xH - H-step height) direction. The turbulent structures appear much too late and time-averaged flow reattachment takes place at Lreattach~15H.

Figure 4.9: Unsteady flow from DES over backward facing step using insufficient spanwise grid resolution

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