DNS studies of turbulence in compressible mixing layers

The direct numerical simulation (DNS) of two-dimensional compressible turbulent mixing layers is reported in this paper. The numerical approach is based on a proven high-order finite difference method and results are presented for convective Mach numbers M_c =0.5, 0.8 and 1.0. All scales of flow are resolved with a 256² grid, although results are also obtained for 64², 96² and 128² grids for the purpose of determining the effective accuracy and grid-independence of our calculations. Results are reported for the growth rate of the vorticity thickness, the vortex roll-up in the flow field and the distribution of density. Furthermore, each term in the evolution equations for the Reynolds stress tensor has been computed for the purpose of examining the intensity of turbulence at the various Mach numbers. The effect of Mach number is reported for the 'shear' components of the anisotropy tensor, the dissipation tensor, pressure-strain, and the triple correlation tensor. For the Reynolds stress tensor the three components (R₁₁, R₁₂, R₂₂) are compared for M_c =0.8. To our knowledge, these results on mixing layers are new but are quite invaluable in guiding modeling efforts intended for generating engineering design data.