A General Realizability Method for the Reynolds Stress for 2-Equation RANS Models
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
This report has described a general, robust method due to Chuck Cranfill for ensuring that the Boussinesq model for the turbulent variable density Reynolds stress tensor is always positive semi-definite (non-negative definite). The method uses a single constant or scale factor to keep the deviatoric part of the stress tensor well behaved, without changing the turbulent pressure part of the tensor. It should be kept in mind that this method does not address the accuracy or appropriateness of the Boussinesq approximation in the first place. That topic can be addressed by comparing components of the modeled tensor to the analagous stress correlations that come from high quality 3D DNS or experimental data. This report is really dealing with the fact that while the prevalent Boussinesq model for the stress tensor in the literature is symmetric, it does not guarantee (even for statistically 1D problems) that the 3 eigenvalues associated with the stress tensor will remain greater than or equal to zero as the turbulent flow evolves. When there are regions of the flow that contain strong compressions or rarefactions (or noisy velocity gradients), it is more likely for the tensor to suffer from realizability problems.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 1113388
- Report Number(s):
- LLNL-TR-414246
- Country of Publication:
- United States
- Language:
- English
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