Reynolds and Mach number effects in compressible turbulent channel flow

Abstract

The effect of Reynolds and Mach number variation in compressible isothermal channel flow is investigated through a series of direct numerical simulations (DNS), at bulk Mach number Mb=1.5,3 and bulk Reynolds number up to Reb=34000, which is sufficient to sense sizeable high-Reynolds-number effects not reached before in this type of flow. Dedicated incompressible DNS are also performed at precisely matching Reynolds number, to directly gauge the performance of compressibility transformations for the mean velocity profiles and Reynolds stresses. As in previous studies, we find inaccuracy of the classical van Driest transformation to remove effects of variable density and viscosity, especially at low Reynolds number. On the other hand, almost perfect matching of incompressible mean velocity and Reynolds stress distributions is recovered throughout the wall layer by using a recently introduced transformation (Trettel and Larsson, 2014,2016), the only remaining effect of compressibility being the increase of the streamwise turbulence intensity peak with the Mach number. Temperature/velocity relations are scrutinized, with the main finding that a recent relation by Zhang et al. (2014), which explicitly accounts for finite wall heat flux, is more accurate than the classical Walz relation. The size of the typical turbulent eddies is studied through spanwise spectral densities of the velocity field, which support validity of a scaling based on the local mean shear and the local friction velocity, with the main conclusion that the actual size of the eddies does not vary with the Mach number, at a fixed outer wall distance.