gammaSST transition and turbulence model

A three-equation transition and turbulence model for OpenFOAM proposed by Menter, Smirnov, et al..

The model is based on the intermittency transport equation with empirical correlations for the transition onset and the intermittency production terms. The main difference with the original four-equation $\gamma-Re_\theta$ model is the equation for $Re_\theta$ is avoided.

The model reads as follows:

$$\begin{align*}\frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho U_j k)}{\partial x_j} &= \gamma P_k + P_k^{lim} - \tilde{D}_k + \frac{\partial}{\partial x_j} \left[ \left( \mu + \mu_t\sigma_k \right) \frac{\partial k}{\partial x_j} \right], \\\ \frac{\partial (\rho \omega)}{\partial t} + \frac{\partial (\rho U_j \omega)}{\partial x_j} &= \alpha\frac{P_k}{\nu_t} - D_\omega + Cd_\omega + \frac{\partial}{\partial x_j} \left[ \left( \mu + \mu_t\sigma_\omega \right) \frac{\partial \omega}{\partial x_j} \right], \\\ \frac{\partial (\rho \gamma)}{\partial t} + \frac{\partial (\rho U_j \gamma)}{\partial x_j} &= P_\gamma - E_\gamma + \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_\gamma} \right) \frac{\partial \gamma}{\partial x_j} \right]. \end{align*}$$

For details on the model, please refer to the original publication by Menter, Smirnov, et al..

Boundary conditions for intermittency $\gamma$ are zero normal flux (i.e. zeroGradient) at the wall and $\gamma=1$ at the inlet.

Differences to original model

• The intermittency $\gamma$ is implmented as gammaInt (in order to be compatible with the kOmegaSSTLM model).
• The model contains optional for cross flow transition term C1 CFX Theory Guide (disabled by default), the term can be enabled by setting crossFlow on; in the gamaSSTCoeffs.

Installation

1. Download the source code from the repository using git:

   git clone git://github.com/furstj/gammaSST.git

2. Enter the directory where the source code has been extracted, and compile it by typing:

   ./Allwmake

3. Add the following line to the controlDict of your case:

   libs ( "libIncompressibleGammaSSTModel.so" ) ;

   or

   libs ( "libCompressibleGammaSSTModel.so" ) ;

4. Add the following lines to the turbulenceProperties dictionary of your case:

   RAS
   {
       RASModel        gammaSST;
       turbulence      on;
       printCoeffs     on;
   }
   

Test cases

There are several test cases in the testCases directory including:

• ERCOFTAC T3A case of zero pressure gradient flat plate flows with inlet turbulence intensity Tu=3%
• ERCOFTAC T3A- case of zero pressure gradient flat plate flows with inlet turbulence intensity Tu=0.9%
• ERCOFTAC T3B case of zero pressure gradient flat plate flows with inlet turbulence intensity Tu=6%

Author

The model has been developed by Jiří Fürst, e-mail: jiri.furst@gmail.com.

References

1. MENTER, Florian R., SMIRNOV, Pavel E., LIU, Tao and AVANCHA, Ravikanth, 2015. A one-equation local correlation-based transition model. Flow, Turbulence and Combustion. 5 December 2015. Vol. 95, no. 4, p. 583–619. doi:10.1007/s10494-015-9622-4.
2. Ansys CFX Theory Guide