A study of compressibility effects in the high-speed turbulent shear layer using direct simulation

Abstract

Direct simulations of the turbulent shear layer are performed for subsonic to supersonic Mach numbers. Fully developed turbulence is achieved with profiles of mean velocity and turbulence intensities that agree well with laboratory experiments. The thickness growth rate of the shear layer exhibits a large reduction with increasing values of the convective Mach number, M_c. In agreement with previous investigations, it is found that the normalized pressure–strain term decreases with increasing M_c, which leads to inhibited energy transfer from the streamwise to cross-stream fluctuations, to the reduced turbulence production observed in DNS, and, finally, to reduced turbulence levels as well as reduced growth rate of the shear layer. An analysis, based on the wave equation for pressure, with supporting DNS is performed with the result that the pressure–strain term decreases monotonically with increasing Mach number. The gradient Mach number, which is the ratio of the acoustic time scale to the flow distortion time scale, is shown explicitly by the analysis to be the key quantity that determines the reduction of the pressure–strain term in compressible shear flows. The physical explanation is that the finite speed of sound in compressible flow introduces a finite time delay in the transmission of pressure signals from one point to an adjacent point and the resultant increase in decorrelation leads to a reduction in the pressure–strain correlation.

The dependence of turbulence intensities on the convective Mach number is investigated. It is found that all components decrease with increasing M_c and so does the shear stress.

DNS is also used to study the effect of different free-stream densities parameterized by the density ratio, s = ρ₂/ρ₁, in the high-speed case. It is found that changes in the temporal growth rate of the vorticity thickness are smaller than the changes observed in momentum thickness growth rate. The momentum thickness growth rate decreases substantially with increasing departure from the reference case, s = 1. The peak value of the shear stress, uv, shows only small changes as a function of s. The dividing streamline of the shear layer is observed to move into the low-density stream. An analysis is performed to explain this shift and the consequent reduction in momentum thickness growth rate.