Density corrections for turbulence models

Abstract

The present paper deals with the improvement of the predictions of high Mach number boundary layers. Two-equation models have been shown to poorly predict the logarithmic region of the boundary layer in presence of large density gradients. This induces significant errors in the skin friction coefficient prediction. A correction of the diffusion terms in two-equation models is suggested to account for the density variations and to retrieve the logarithmic law. The analysis yields the result that new quantities involved in transport are combinations of the product ρk and the length scale ℓ. Standard forms of transport equations, with extra terms linked to density variations can be derived. 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 have confirmed the present analysis. © 2000 Éditions scientifiques et médicales Elsevier SAS.