This is an OpenFOAM Implementation of the SST-CND model described in this article. The SST-CND model is based on Menter's Shear-stress-transport model with a correction term for separated flow (especially separated shear layer) derived by machine learning method. The correction term has a closed analytical form, which is derived by symbolic regression method. This characteristic ensures the model to be interpretable and computationally economic. The SST-CND model is tested on various 2D and 3D cases and shows good generalizability.

The implementation is tested on OpenFOAM-v2312, OpenFOAM-v2306 and works fine.

Chenyu Wu, Tsinghua University (wcy22@mails.tsinghua.edu.cn)

Yufei Zhang, Tsinghua University (zhangyufei@tsinghua.edu.cn)

Below are some comparisons between the SST-CND model and the SST model in various 2D and 3D cases. More detailed comparisons can be found in this article. Note that Cf's mean square error in the separation zone is compared in the Hump case and the CBFS case. The error of the SST model is scaled to 100%. The NLR7301 high lift device is computed by CFL3D.

Besides the separated flows, the SST-CND model only deviates 1% from the Cf prediction of the baseline SST model in the zero-pressure-gradient flat plate, demonstrating its ability to protect attached boundary layer from being negatively impacted by the correction. This is done by applying a technique called Conditioned field inversion (FI-CND) in the data assimilation process. For more information about this method can be found in this article.

First, you should have OpenFOAM-v2312 installed on your system. Then you can follow the steps below to compile the model.

• Clone the repository to anywhere you want on your system (you can also just download the zip file from GitHub if you wish):

  git@github.com:chairmanmao256/SSTCND-OpenFOAM.git
  

• From the root of the repository, run the following commands:

  ./Allwmake.sh
  

• If you want to use the model for your simulation:

  • add the following line to the system/controlDict file (just pick one of them depending on your case):

    // For incompressible flows
    lib(libCNDIncompressibleTurbulenceModels)
    
    // For compressible flows
    lib(libCNDCompressibleTurbulenceModels)
    

  • specify the turbulence model in constant/turbulenceProperties

    RASModel kOmegaSSTCND
    

Two tutorial cases are included in the cases directory. They are the NASA hump (cases/NASA-hump) and the zero gradient flat plate (cases/ZPG-flatPlate). To run the tutorial cases, just type the following command in each case:

./Allrun.sh

Depending on your system, you might have to do some chmod stuffs before running the script to make or .sh files in the tutorial cases executable:

chmod 755 *.sh

The Allrun.sh script runs both the baseline SST model and the SST-CND model for the given case and compare their results.

After running the script, if you have gnuplot correctly installed on your system (sudo apt-get install gnuplot), you can reproduce the following images. The Cf distribution in the NASA hump case shows that the SST-CND model is able to predict a separation zone closer to the experiment. On the other hand, the Cf distribution in the ZPG flat plate case shows that the SST-CND model does not negatively impact the baseline SST model's performance in zero-pressure-gradient boundary layer.

If you find the SST-CND model interesting and helpful to your work, please cite the paper:

@misc{wu2024development,
      title={Development of a Generalizable Data-driven Turbulence Model: Conditioned Field Inversion and Symbolic Regression}, 
      author={Chenyu Wu and Yufei Zhang},
      year={2024},
      eprint={2402.16355},
      archivePrefix={arXiv},
      primaryClass={physics.flu-dyn}
}