# Sig Turbulence/Library Added Incompressible RAS Models/zetaF0

## Contents

## 1 zetaF0 incompressible RAS model

The original version of this model was developed by Hanjalic and Popovac (A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD, Int. J. Heat Fluid Flow, 25, 1047–1051. 2004 [1]), while the current version implemented here has been presented at the 7th OpenFOAM Workshop (OpenFOAM Implementation of an Incompressible Eddy Viscosity Turbulence Model with Zero Wall Boundary Condition Elliptic Relaxation Function. 25-28 June 2012, Darmstadt, Germany [2]).

### 1.1 Implementation

As for the OpenFOAM implementation of the zetaF0 model itself, it is analogous to that of realizableKE model: both are based on the k-eps definition of the turbulent viscosity, including the "correction function" to account for the near-wall effects. The difference in the implementation, however, is the definition of the "correction function": in the case of the realizable k-eps model this is the damping function rCmu

**realizableKE:**

// Correction function tmp<volScalarField> realizableKE::rCmu (gradU, S2, magS) { volScalarField As volScalarField Us return 1.0/(A0_ + As*Us*k_/(epsilon_ + epsilonSmall_)); } // Re-calculate viscosity nut_ = rCmu(gradU, S2, magS)*sqr(k_)/epsilon_;

whereas in the case of the zeta-f0 model takes form of the normalized wall-normal velocity fluctuation component . Furthermore, the realizabililty constraints are introduced through an appropriate time scale definition.

**zetaF0:**

// Time scale scalarField TimeScale=max(min(k_/(epsilon_ + epsilonSmall_), CT_/(sqrt(6*2*magSqr(dev(symm(fvc::grad(U_)))))*Cmu_*zeta_+TinvMin_)), Ctau_*sqrt(nu()/(epsilon_ + epsilonSmall_))); // Re-calculate viscosity nut_ = Cmu_*k_*zeta_*TimeScale_;

### 1.2 Usage

Modify the RASModel in constant/RASproperties to:

RASModel zetaF0;

and add the coefficients to the same file (optional):

zetaF0Coeffs { Cmu 0.22; sigmaK 1.0; sigmaEps 1.3; sigmaZeta 1.2; Ceps10 1.4; Ceps11 0.012; Ceps2 1.9; Cf1 1.4; Cf2 0.65; Ceta 85.0; CL 0.36; Ctau 6.0; CT 0.6; }

Make sure that the addedIncormpressibleRASModels library is linked to by adding at the end of the system/controlDict file:

libs ("libaddedIncompressibleRASModels.so");

### 1.3 Current limitations

- It's not really a limitation, but rather a reminder: this model has been developed for wall-bounded flows.

### 1.4 Tutorial

In the zetaF0 directory there is a pitzDaily tutorial

Run:

cd $WM_PROJECT_USER_DIR/src/turbulenceModels/incompressible/RAS/zetaF0/pitzDaily blockMesh simpleFoam

## 2 Others

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