A numerical study of compressible turbulent boundary layers

TLDR: In this paper, the effect of Mach number on turbulence statistics and near-wall turbulence structures was analyzed by means of direct numerical simulation of the Navier-Stokes equations, and it was shown that supersonic/hypersonic boundary layers at zero pressure gradient exhibit close similarities to incompressible boundary layers.

Abstract: Compressible turbulent boundary layers with free-stream Mach number ranging from 2.5 up to 20 are analyzed by means of direct numerical simulation of the Navier–Stokes equations. The fluid is assumed to be an ideal gas with constant specific heats. The simulation generates its inflow condition using the rescaling-recycling method. The main objective is to study the effect of Mach number on turbulence statistics and near-wall turbulence structures. The present study shows that supersonic/hypersonic boundary layers at zero pressure gradient exhibit close similarities to incompressible boundary layers and that the main turbulence statistics can be correctly described as variable-density extensions of incompressible results. The study also shows that the spanwise streak’s spacing of 100 wall units in the inner region y + 15 still holds for the considered high Mach numbers. The probability density function of the velocity dilatation shows significant variations as the Mach number is increased, but it can also be normalized by accounting for the variable-density effect. The compressible boundary layer also shows an additional similarity to the incompressible boundary layer in the sense that without the linear coupling term, near-wall turbulence cannot be sustained. © 2011 American Institute of Physics. doi:10.1063/1.3541841