Numerical study of stress-transport turbulence models: Implementation and validation issues

The primary goal of this work is to implement, validate and compare in shear-free and simple wall-bounded turbulent flows the performance of five stress-transport turbulence models that have recently appeared in the open literature. A secondary goal of this work is to analyze and study the effort and difficulties encountered by programmers when implementing turbulence models developed by other researchers. The need for standardized procedures and for the development of efficient numerical techniques is advocated as a means to reduce the model-variance and code dependency of turbulent models. The second-order models chosen for this study are the Launder–Shima, the Jakirlic–Hanjalic, the elliptic-blending model of Manceau, the Turbulent Potential Model proposed by Perot and an unidentified model. For comparison reasons, Wilcox k–ωk–ω eddy-viscosity model was included in the study. The validation and the study of the performance of the models were performed through the comparison of the numerical solutions with experimental data and analytical solutions. The five benchmark flowfields considered in this study encompass the shear-free and wall-bounded regimes and are the flat plate without pressure gradient, the flow over a plate with a moderately adverse pressure gradient, and the self-similar flows of the mixing layer, the plane jet and the axi-symmetric jet. The tested stress-transport models produced results in general agreement with the experiments. However, no clear advantage of the stress-transport model over Wilcox k–ωk–ω model was noticed in these simple flowfields. The Launder–Shima model could not predict accurately the skin friction on a flat plate but it performed well in all the other cases. Although the test cases used were simple, a major difficulty encountered in this effort is the unreliability of the open literature as a resource for turbulence model implementation. A general lack of consistency was observed between model versions published in different journals or at different times. The detrimental effect that such a lack of structure and consistency has on the CFD community is discussed.