Direct-Numerical and Large-Eddy Simulations of Hypersonic Turbulent Couette Flow at Mach 6, 7 and 8

Abstract

Direct numerical simulations of hypersonic Couette flows are performed with the top wall Mach number of 6, 7 and 8. The main objective is to investigate exact subfilter scale (SFS) stresses, which are modeled in large-eddy simulations (LES), in wall-bounded turbulent flows at hypersonic conditions. The friction Reynolds number ranges from 621 to 713 and it increases with increase in Mach number, whereas the semi-local friction Reynolds number ranges from 213 to 277 and it decreases with increase in Mach number. An investigation of mean profiles shows that mean temperature and density largely vary in the wall-normal direction, however Trettel \& Larsson transformation works well for the mean streamwise velocity profiles. In addition, there are good agreements of semi-local scaled velocity fluctuation correlations between the different Mach number cases. These results regarding mean flow fields indicate that compressible effects are not substantial in the present conditions. On the other hand, an analysis of the SFS stress profile reveals that the SFS stress has a negative peak, which is not reported in incompressible channel flows. The ratio of SFS stress values between the maximum peak and the negative peak becomes lower with increase in Mach number. This result implies that the negative peak of the SFS stress can be attributed to compressible effects. The contrasting results between mean flow fields and SFS stress imply that LES needs to account for compressible effects even at conditions where compressible effects on mean flow fields are not significant.