Direct simulation of compressible turbulence in a shear flow

Abstract

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. Physical experiments have not been and perhaps cannot be performed for homogeneous shear flows at flow speeds which are sufficiently high to introduce compressible effects on the turbulence. However, direct numerical simulation (DNS) of this problem could provide meaningful data, especially since DNS for the incompressible problem ([1], [2]) has been successful in giving realistic flow fields akin to those obtained in physical experiments. The present simulations of the homogeneous shear problem augment and extend our previous results ([3], [4]) for compressible isotropic turbulence. The compressible Navier-Stokes equations are written in a frame of reference moving with the mean flow u. We use a Fourier collocation method for the spatial discretization of the governing equations. A third order, low storage Runge-Kutta scheme is used for advancing the solution in time. Up to 1283 points are used for the simulations. The simulated turbulent fields have Taylor microscale Reynolds numbers Re? up to 35 and turbulent Mach numbers Mt up to 0.6. The results are summarized below. We find that an increase in initial compressibility level, either due to increased turbulent Mach number or increased dilatational fraction of the velocity field decreases the growth of turbulent kinetic energy (and all its components) in the case of homogeneous shear flow. This is reminiscent of the reduction in turbulent velocity intensities observed in experiments on supersonic free shear