Compressibility effects and turbulent kinetic energy exchange in temporal mixing layers

Abstract

The kinetic energy exchange between the mean and fluctuating fields is analyzed using large-eddy simulation of a temporally developing compressible mixing layer. A solution database is generated by varying the convective Mach number over the interval of with an initial Reynolds number of Re = 100. Both mean and turbulent kinetic energy equations are considered, and the effect of compressibility on the production, pressure dilatation, and dissipation terms are considered. It is shown that the production term linearly decreases with the increase of within the interval of , which in turn leads to a linear reduction of the mixing layer growth rate. The pressure dilatation term in the mean kinetic energy equation is on average positive and transfers internal energy into mean kinetic energy by dilatation, whereas its counterpart in the turbulent kinetic energy equation is on average negative, and transfers turbulent kinetic energy into internal energy by compression. Although the turbulent viscous dissipation term is reduced by increasing the convective Mach number, it remains the primary kinetic energy dissipation mechanism at all convective Mach numbers. At the subgrid-scale level, it is found that the magnitude of the dynamic Smagorinsky model coefficient, Cs, monotonically decreases with the increase of and results in the reduction of all turbulent stress tensor components. Furthermore, increasing the convective Mach number results in a monotonic reduction of subgrid-scale dissipation of the turbulent kinetic energy, whereas the subgrid-scale dissipation of the mean kinetic energy stays almost unaffected. The sum of subgrid-scale pressure dilatation and pressure transport terms, which is modelled with a gradient transport model, is also suppressed by the increase of compressibility and the convective Mach number.