Modelling of compressibility effects in mixing layers

Abstract

The ability of Reynolds-averaged Navier–Stokes (RANS) turbulence models to predict self-similar mixing layers is investigated. Low-speed flows are first considered. The influence of the velocity ratio is well captured. But standard models predict a wrong sensitivity of the mixing layer to density differences. A general correction previously derived from the balance in the logarithmic region of the boundary layer, stating that the variables to be dealt with must be combinations of the turbulent kinetic energy per unit mass and the length scale, hardly improves the prediction. A correction accounting for baroclinic effect is derived but its present form is not satisfactory. High-speed flows are then investigated. Analysis of the self-similar equations shows that no information about the speed of sound and hence about compressibility effects is available for the standard model. A revised form of the sonic eddy concept, which yields a smaller length scale than Kim's proposal, is shown to improve predictions. This length scale reduction allows one to reproduce the spreading rate evolution, whatever the turbulence model. A model form, suitable for Navier–Stokes codes, is proposed. Difficulties to validate models from experimental data, due to unknown boundary conditions such as external turbulence levels, are pointed out.

This paper was chosen from Selected Proceedings of the Third International Symposium on Turbulence and Shear Flow Phenomena (Sendai, Japan, 24–27 June 2003).