Effects of Mach Number on Near-Wall Turbulence Structures in Supersonic Turbulent Boundary Layers

In order to examine the effects of high Mach number on turbulence structures in compressible turbulent boundary layers, we performed direct numerical simulation of a spatially evolving supersonic turbulent boundary layer. A hybrid numerical method coupling the 5th-order WENO scheme with a 5th-order upwind finite-difference scheme was used in order to compute turbulence accurately while capturing sharp gradients that might exist in high Mach number flows. The rescale-and-recycle method was used for the inflow boundary condition. The Mach numbers were varied from 2.5 to 7 while the Reynolds numbers based on the boundary-layer displacement, wall-shear velocity and the viscosity at the wall were kept about the same. In order to determine the relative importance of the true compressibility effect and the variable-property effect in high Mach number boundary layers, we also solved modified Navier-Stokes equations, in which the energy equation was modified to include a heat sink term (Coleman, Kim and Moser, J. Fluid Mech. 305). The effects of Mach number on turbulence statistics as well as an analysis of the near-wall turbulence structures will be presented.