Modelling the Compressibility Effect with Second-Moment Closure

Abstract

Compressibility is well known to suppress turbulence, the cause of the compressibility effects remains, however, unclear. Previous studies carried out in the early 1990s conjectured that the main compressible effects were associated with the dilatations of velocity fluctuation. Later, it was shown that the main compressibility effect came from the reduced pressure-strain term due to reduced pressure fluctuations. Although better understanding of the compressible turbulence had generally been achieved with the increased DNS and experimental efforts, there are still some discrepancies among these recent findings. In the present work the effect of compressibility on shear flows are characterized in three categories corresponding to three regions of turbulent Mach numbers M _t : the low-M _t , the transition-M _t ; and the high-M _t ; regions. It is observed in these three regions that the effect of compressibility on the growth rate of the turbulent mixing layer is rather different. A simplified approach to model the reduced pressure-strain effect may not necessarily reduce the mixing-layer growth rate, rather, an increase in the growth rate may occur. The present work develops a new second-moment model for the compressible turbulence through the introduction of some blending functions of M _t to account for the compressibility effects on the flow. The model has successfully applied to the compressible mixing layers.