Direct numerical simulation of compressible turbulence in a counter-flow channel configuration

Counter-flow configurations, whereby two streams of fluid are brought together from opposite directions, are highly efficient mixers due to the high turbulence intensities that can be maintained. In this paper, a simplified version of the problem is introduced that is amenable to direct numerical simulation. The resulting turbulent flow problem is confined between two walls, with one non-zero mean velocity component varying in the space direction normal to the wall, corresponding to a simple shear flow. Compared to conventional channel flows, the mean flow is inflectional and the maximum turbulence intensity relative to the maximum mean velocity is nearly an order of magnitude higher. The numerical requirements and turbulence properties of this configuration are first determined. The Reynolds shear stress is required to vary linearly by the imposed forcing, with a peak at the channel centreline. A similar behaviour is observed for the streamwise Reynolds stress, the budget of which shows an approximately uniform distribution of dissipation, with large contributions from production, pressure-strain and turbulent diffusion. A viscous sublayer is obtained near the walls and with increasing Reynolds number small-scale streaks in the streamwise momentum are observed, superimposed on the large-scale structures that buffet this region. When the peak local mean Mach number reaches 0.55, turbulent Mach numbers of 0.6 are obtained, indicating that this flow configuration can be useful to study compressibility effects on turbulence.