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## 7.2 Turbulence models

The momentumTransport dictionary is read by any solver that includes turbulence modelling. Within that ﬁle is the simulationType keyword that controls the type of turbulence modelling to be used, either:

- laminar
- uses no turbulence models;
- RAS
- uses Reynolds-averaged simulation (RAS) modelling;
- LES
- uses large-eddy simulation (LES) modelling.

### 7.2.1 Reynolds-averaged simulation (RAS) modelling

If RAS is selected, the choice of RAS modelling is speciﬁed in a RAS sub-dictionary which requires the following entries.

- model: name of RAS turbulence model.
- turbulence: switch to turn the solving of turbulence modelling on/oﬀ.
- printCoeffs: switch to print model coeﬀs to terminal at simulation start up.
- <model>Coeffs: dictionary of coeﬃcients for the respective model, to override the default coeﬃcients.

Turbulence models can be listed by running a solver with the -listMomentumTransportModels option, e.g.

simpleFoam -listMomentumTransportModels

The RAS models used in the tutorials can be listed using foamSearch with the following command. The lists of available models are given in the following sections.

foamSearch $FOAM_TUTORIALS momentumTransport RAS/model

foamInfo buoyantKEpsilon

#### 7.2.1.1 Incompressible RAS turbulence models

For incompressible ﬂows, the RAS model can be chosen from the list below.

- LRR
- Launder, Reece and Rodi Reynolds-stress turbulence model for incompressible ﬂows.
- LamBremhorstKE
- Lam and Bremhorst low-Reynolds number k-epsilon turbulence model for incompressible ﬂows.
- LaunderSharmaKE
- Launder and Sharma low-Reynolds k-epsilon turbulence model for incompressible ﬂows.
- LienCubicKE
- Lien cubic non-linear low-Reynolds k-epsilon turbulence models for incompressible ﬂows.
- LienLeschziner
- Lien and Leschziner low-Reynolds number k-epsilon turbulence model for incompressible ﬂows.
- RNGkEpsilon
- Renormalization group k-epsilon turbulence model for incompressible ﬂows.
- SSG
- Speziale, Sarkar and Gatski Reynolds-stress turbulence model for incompressible ﬂows.
- ShihQuadraticKE
- Shih’s quadratic algebraic Reynolds stress k-epsilon turbulence model for incompressible ﬂows
- SpalartAllmaras
- Spalart-Allmaras one-eqn mixing-length model for incompressible external ﬂows.
- kEpsilon
- Standard k-epsilon turbulence model for incompressible ﬂows.
- kOmega
- Standard high Reynolds-number k-omega turbulence model for incompressible ﬂows.
- kOmega2006
- Standard (2006) high Reynolds-number k-omega turbulence model for incompressible ﬂows.
- kOmegaSST
- Implementation of the k-omega-SST turbulence model for incompressible ﬂows.
- kOmegaSSTLM
- Langtry-Menter 4-equation transitional SST model based on the k-omega-SST RAS model.
- kOmegaSSTSAS
- Scale-adaptive URAS model based on the k-omega-SST RAS model.
- kkLOmega
- Low Reynolds-number k-kl-omega turbulence model for incompressible ﬂows.
- qZeta
- Gibson and Dafa’Alla’s q-zeta two-equation low-Re turbulence model for incompressible ﬂows
- realizableKE
- Realizable k-epsilon turbulence model for incompressible ﬂows.
- v2f
- Lien and Kalitzin’s v2-f turbulence model for incompressible ﬂows, with a limit imposed on the turbulent viscosity given by Davidson et al.

#### 7.2.1.2 Compressible RAS turbulence models

For compressible ﬂows, the RAS model can be chosen from the list below.

- LRR
- Launder, Reece and Rodi Reynolds-stress turbulence model for compressible ﬂows.
- LaunderSharmaKE
- Launder and Sharma low-Reynolds k-epsilon turbulence model for compressible and combusting ﬂows including rapid distortion theory (RDT) based compression term.
- RNGkEpsilon
- Renormalization group k-epsilon turbulence model for compressible ﬂows.
- SSG
- Speziale, Sarkar and Gatski Reynolds-stress turbulence model for compressible ﬂows.
- SpalartAllmaras
- Spalart-Allmaras one-eqn mixing-length model for compressible external ﬂows.
- buoyantKEpsilon
- Additional buoyancy generation/dissipation term applied to the k and epsilon equations of the standard k-epsilon model.
- kEpsilon
- Standard k-epsilon turbulence model for compressible ﬂows including rapid distortion theory (RDT) based compression term.
- kOmega
- Standard high Reynolds-number k-omega turbulence model for compressible ﬂows.
- kOmega2006
- Standard (2006) high Reynolds-number k-omega turbulence model for compressible ﬂows.
- kOmegaSST
- Implementation of the k-omega-SST turbulence model for compressible ﬂows.
- kOmegaSSTLM
- Langtry-Menter 4-equation transitional SST model based on the k-omega-SST RAS model.
- kOmegaSSTSAS
- Scale-adaptive URAS model based on the k-omega-SST RAS model.
- realizableKE
- Realizable k-epsilon turbulence model for compressible ﬂows.
- v2f
- Lien and Kalitzin’s v2-f turbulence model for compressible ﬂows, with a limit imposed on the turbulent viscosity given by Davidson et al.

### 7.2.2 Large eddy simulation (LES) modelling

If LES is selected, the choice of LES modelling is speciﬁed in a LES sub-dictionary which requires the following entries.

- model: name of LES turbulence model.
- delta: name of delta model.
- <model>Coeffs: dictionary of coeﬃcients for the respective model, to override the default coeﬃcients.
- <delta>Coeffs: dictionary of coeﬃcients for the delta model.

The LES models used in the tutorials can be listed using foamSearch with the following command. The lists of available models are given in the following sections.

foamSearch $FOAM_TUTORIALS momentumTransport LES/model

#### 7.2.2.1 Incompressible LES turbulence models

For incompressible ﬂows, the LES model can be chosen from the list below.

- DeardorﬀDiﬀStress
- Diﬀerential SGS Stress Equation Model for incompressible ﬂows
- Smagorinsky
- The Smagorinsky SGS model.
- SpalartAllmarasDDES
- SpalartAllmaras DDES turbulence model for incompressible ﬂows
- SpalartAllmarasDES
- SpalartAllmarasDES DES turbulence model for incompressible ﬂows
- SpalartAllmarasIDDES
- SpalartAllmaras IDDES turbulence model for incompressible ﬂows
- WALE
- The Wall-adapting local eddy-viscosity (WALE) SGS model.
- dynamicKEqn
- Dynamic one equation eddy-viscosity model
- dynamicLagrangian
- Dynamic SGS model with Lagrangian averaging
- kEqn
- One equation eddy-viscosity model
- kOmegaSSTDES
- Implementation of the k-omega-SST-DES turbulence model for incompressible ﬂows.

#### 7.2.2.2 Compressible LES turbulence models

For compressible ﬂows, the LES model can be chosen from the list below.

- DeardorﬀDiﬀStress
- Diﬀerential SGS Stress Equation Model for compressible ﬂows
- Smagorinsky
- The Smagorinsky SGS model.
- SpalartAllmarasDDES
- SpalartAllmaras DDES turbulence model for compressible ﬂows
- SpalartAllmarasDES
- SpalartAllmarasDES DES turbulence model for compressible ﬂows
- SpalartAllmarasIDDES
- SpalartAllmaras IDDES turbulence model for compressible ﬂows
- WALE
- The Wall-adapting local eddy-viscosity (WALE) SGS model.
- dynamicKEqn
- Dynamic one equation eddy-viscosity model
- dynamicLagrangian
- Dynamic SGS model with Lagrangian averaging
- kEqn
- One equation eddy-viscosity model
- kOmegaSSTDES
- Implementation of the k-omega-SST-DES turbulence model for compressible ﬂows.

### 7.2.3 Model coeﬃcients

The coeﬃcients for the RAS turbulence models are given default values in their respective source code. If the user wishes to override these default values, then they can do so by adding a sub-dictionary entry to the RAS sub-dictionary ﬁle, whose keyword name is that of the model with Coeffs appended, e.g. kEpsilonCoeffs for the kEpsilon model. If the printCoeffs switch is on in the RAS sub-dictionary, an example of the relevant …Coeffs dictionary is printed to standard output when the model is created at the beginning of a run. The user can simply copy this into the RAS sub-dictionary ﬁle and edit the entries as required.

### 7.2.4 Wall functions

A range of wall function models is available in OpenFOAM that are applied as boundary conditions on individual patches. This enables diﬀerent wall function models to be applied to diﬀerent wall regions. The choice of wall function model is speciﬁed through the turbulent viscosity ﬁeld in the 0/nut ﬁle. For example, a 0/nut ﬁle:

17dimensions [0 2 -1 0 0 0 0];

18

19internalField uniform 0;

20

21boundaryField

22{

23 movingWall

24 {

25 type nutkWallFunction;

26 value uniform 0;

27 }

28 fixedWalls

29 {

30 type nutkWallFunction;

31 value uniform 0;

32 }

33 frontAndBack

34 {

35 type empty;

36 }

37}

38

39

40// ************************************************************************* //

There are a number of wall function models available in the release, e.g. nutWallFunction, nutRoughWallFunction, nutUSpaldingWallFunction, nutkWallFunction and nutkAtmWallFunction. The user can get the full list of wall function models using foamInfo:

foamInfo wallFunction

Having selected the particular wall functions on various patches in the nut/mut ﬁle, the user should select epsilonWallFunction on corresponding patches in the epsilon ﬁeld and kqRwallFunction on corresponding patches in the turbulent ﬁelds k, q and R.