Detached Eddy Simulation (DES)

This section describes the theory behind the Detached Eddy Simulation (DES) model. Information is presented in the following sections:

4.11.1. Overview

4.11.2. DES with the Spalart-Allmaras Model 4.11.3. DES with the Realizable k-ε Model 4.11.4. DES with the BSL or SST k-ω Model 4.11.5. DES with the Transition SST Model

4.11.6. Improved Delayed Detached Eddy Simulation (IDDES)

For details about using the model in ANSYS Fluent, see Modeling Turbulence and Setting Up the Detached Eddy Simulation Model in the User’s Guide.

4.11.1. Overview

ANSYS Fluent offers five different models for the detached eddy simulation: the Spalart-Allmaras model, the realizable - model, the BSL - model, the SST - model, and the Transition SST model.

In the DES approach, the unsteady RANS models are employed in the boundary layer, while the LES treatment is applied to the separated regions. The LES region is normally associated with the core tur-bulent region where large unsteady turbulence scales play a dominant role. In this region, the DES models recover LES-like subgrid models. In the near-wall region, the respective RANS models are re-covered.

DES models have been specifically designed to address high Reynolds number wall bounded flows, where the cost of a near-wall resolving Large Eddy Simulation would be prohibitive. The difference with the LES model is that it relies only on the required RANS resolution in the boundary layers. The applic-ation of DES, however, may still require significant CPU resources and therefore, as a general guideline, it is recommended that the conventional turbulence models employing the Reynolds-averaged approach be used for most practical calculations.

The DES models, often referred to as the hybrid LES/RANS models, combine RANS modeling with LES for applications such as high-Re external aerodynamics simulations. In ANSYS Fluent, the DES model is based on the one-equation Spalart-Allmaras model, the realizable - model, the BSL - model, the

Detached Eddy Simulation (DES)

SST - model, and the Transition SST model. The computational costs, when using the DES models, is less than LES computational costs, but greater than RANS.

For information about the synthetic turbulence generation on inlets, refer to Inlet Boundary Conditions for the LES Model (p. 109).

4.11.2. DES with the Spalart-Allmaras Model

The standard Spalart-Allmaras model uses the distance to the closest wall as the definition for the length scale , which plays a major role in determining the level of production and destruction of turbulent viscosity (Equation 4.20 (p. 43),Equation 4.26 (p. 44), and Equation 4.29 (p. 44)). The DES model, as proposed by Shur et al. [422] (p. 782) replaces everywhere with a new length scale , defined as

(4.237) where is the grid spacing, which in the case of a rectilinear hexahedral cell is the maximum edge length (for other cell types and/or conditions, an extension of this concept is used). The empirical constant

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 , where is the size of the boundary layer,Equation 4.237 (p. 94) 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 , 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

[446] (p. 783) 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 is re-defined according to:

(4.238) where is given by:

(4.239) and

(4.240)

This formulation is the default settings.

4.11.3. DES with the Realizable k-ε Model

This DES model is similar to the Realizable - model discussed in Realizable k-ε Model (p. 50), with the exception of the dissipation term in the equation. In the DES model, the Realizable - RANS dissip-ation term is modified such that:

(4.241)

where

(4.242) Turbulence

(4.243) (4.244) where is a calibration constant used in the DES model and has a value of 0.61 and is the grid spacing, which in the case of a rectilinear hexahedral cell is the maximum edge length (for other cell types and/or conditions, an extension of this concept is used).

For the case where , you will obtain an expression for the dissipation of the formulation for the Realizable - model (Realizable k-ε Model (p. 50)): Similarly to the Spalart-Allmaras model, the delayed concept can be applied as well to the Realizable DES model to preserve the RANS mode throughout the boundary layer. The DES length in Equation 4.241 (p. 94) is redefined such that

(4.245)

Note

In Equation 4.245 (p. 95) is used as defined for the Spalart-Allmaras model in Equa-tion 4.239 (p. 94) with the excepEqua-tion that the value of the constant is changed from 8 to 20 and is replaced with ( ) in the calculation of in Equation 4.240 (p. 94).

4.11.4. DES with the BSL or SST k-ω Model

The dissipation term of the turbulent kinetic energy (see Modeling the Turbulence Dissipation (p. 59)) is modified for the DES turbulence model as described in Menter’s work [306] (p. 776) such that

(4.246) where is expressed as

(4.247)

where is a calibration constant used in the DES model and has a value of 0.61, and is the grid spacing, which in the case of a rectilinear hexahedral cell is the maximum edge length (for other cell types and/or conditions, an extension of this concept is used).

The turbulent length scale is the parameter that defines this RANS model:

(4.248)

The DES-BSL / SST model also offers the option to “protect” the boundary layer from the limiter (delayed option). This is achieved with the help of the zonal formulation of the BSL / SST model. is modified according to

(4.249) Detached Eddy Simulation (DES)

with , where and are the blending functions of the BSL / SST model. Alternatively, the DDES shielding function or the IDDES function can be selected [157] (p. 767),[446] (p. 783). The default setting is to use DDES.

Note

In the DDES and IDDES implementations, is used as defined for the Spalart-Allmaras model in Equation 4.239 (p. 94) with the exception that the value of the constant is changed from 8 to 20.

The default setting is to use DDES. The blending function is given by:

(4.250) where =20, =3, and

(4.251)

Here is the magnitude of the strain rate tensor, is the magnitude of vorticity tensor, is the wall distance, and =0.41.

4.11.5. DES with the Transition SST Model

The Transition SST model can be combined with the DES approach. The dissipation term of the transport equation for the turbulence kinetic energy will be modified in the same way as for the SST - turbulence model (see Equation 4.246 (p. 95)). All shielding functions outlined in DES with the BSL or SST

k-ω Model (p. 95) are also available for DES with the Transition SST model.

4.11.6. Improved Delayed Detached Eddy Simulation (IDDES) 4.11.6.1. Overview of IDDES

The Improved Delayed Detached Eddy Simulation (IDDES) model ([421] (p. 782),[157] (p. 767)) is a hybrid RANS-LES model (consisting of a combination of various new and existing techniques) that provides a more flexible and convenient scale-resolving simulation (SRS) model for high Reynolds number flows.

Since the model formulation is relatively complex and the application of the model is non-trivial, it is recommended that you consult the original publications of Shur et al.[421] (p. 782) and Gritskevich et al.[157] (p. 767).

The IDDES model has the following goals in addition to the formulation of the standard DES model:

• Provide shielding against Grid Induced Separation (GIS), similar to the DDES model ([446] (p. 783)).

• Allow the model to run in Wall-Modeled LES (WMLES) mode in case unsteady inlet conditions are provided to simulate wall boundary layers in unsteady mode. The IDDES model is designed to allow the LES simulation of wall boundary layers at much higher Reynolds numbers than standard LES models.

As an alternative to unsteady inlet conditions, unsteadiness could also be triggered by an obstacle (such as a backward facing step, or a rib inside or upstream of the boundary layer).

The IDDES model implemented in ANSYS Fluent is based on the BSL / SST model ([303] (p. 775)) with the application of IDDES modifications as given in [157] (p. 767). Similar to DES, the k-equation of the Turbulence

BSL / SST model is modified to include information on the local grid spacing. In case the grid resolution is sufficiently fine, the model will switch to LES mode. However, the goal is to cover stable boundary layers (meaning no unsteady inlet conditions and no upstream obstacles generating unsteadiness) in RANS mode. In order to avoid affecting the BSL / SST model under such conditions, the IDDES function provides shielding similar to the DDES model, meaning it attempts to keep the boundary layer in steady RANS mode even under grid refinement.

If you want to resolve the wall boundary layer in WMLES mode, unsteady inlet conditions need to be provided (see Vortex Method (p. 110) or Spectral Synthesizer (p. 111)). The model can also be run with the Embedded LES (ELES) option (see Embedded Large Eddy Simulation (ELES) (p. 112)) and the IDDES option (see Detached Eddy Simulation (DES) in the User's Guide) in ANSYS Fluent.

4.11.6.2. IDDES Model Formulation

The IDDES-BSL / SST model is based on modifying the sink term in the k-equation of the BSL / SST model. (The -equation remains unmodified.)

(4.252)

(4.253)

where .

In Equation 4.253 (p. 97), is based on the RANS turbulent length scale and the LES grid length scales. Note that the sub-grid length scale differs from the DES formulation. In the IDDES formulation, a more general formulation for is used that combines local grid scales and the wall distance . The complete formulation is relatively complex and has been implemented as published by [157] (p. 767), except for the value of ; while this variable is defined as the maximum edge length in the case of a rectilinear hexahedral cell in ANSYS Fluent, for other cell types and/or conditions an extension of this concept is used.