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Density corrections for turbulence models. (English) Zbl 0986.76027

Summary: The paper deals with the improvement of predictions of high-Mach-number boundary layers. Two-equation models have been shown to poorly predict the logarithmic region of the boundary layer in the presence of large density gradients. This induces significant errors in the prediction of the skin friction coefficient. Thus we suggest a correction of diffusion terms in two-equation models to account for density variations and to retrieve the logarithmic law. The analysis yields the result that new quantities involved in transport are combinations of the product \(\rho k\) and the length scale \(\ell\). Then we derrive standard forms of transport equations, with extra terms linked to density variations. Tests cases on flat plate boundary layers, over a wide range of Mach numbers, Reynolds numbers and wall to adiabatic temperature ratios as well as flat plate experiments confirm the present analysis.

MSC:

76F40 Turbulent boundary layers
76F50 Compressibility effects in turbulence
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