| Although the standard k-e model with variable mean density is capable of predicting supersonic boundary layer flows, it is not able to reproduce the decrease in growth rate and peak Reynolds stress observed in high speed mixing layers. When current models for compressibility effects due to the pressure dilatation and dilatational dissipation are included, mixing layer predictions are improved but boundary layer calculations are adversely affected. A new model for the pressure dilatation and dilatational dissipation is proposed which depends on the transport of the density variance. A transport equation for the density variance and an algebraic expression for the averaged mass fluctuating velocities are developed to close the set of equations. The new model is applied to several basic compressible flows including isotropic decay of turbulence, adiabatic boundary layers, mixing layers with matched total temperature, and axisymmetric jets. A comparison of calculations with DNS and experimental data shows reasonable agreement for both free shear layers and wall-bounded flows. Also, compressibility effects in the dissipation equation are found to be small for low to moderate turbulent Mach numbers. |
