Effect of compressibility on strong shock and turbulence interactions

Abstract

The interactions between turbulent flows and shock waves are important in many natural processes as well as scientific and engineering applications. One of the fundamental building blocks in these complex processes and applications is the canonical problem of isotropic turbulence and a normal shock. Unfortunately, even this fundamental problem is not well understood. Recent direct numerical simulation (DNS) results of perfect gas flow showed some new trends in turbulent statistics as mean Mach number is increased. In this paper, we first conduct extensive DNS studies on canonical strong shock and turbulence interaction problem of perfect gas flow with mean Mach numbers ranging from 2 to 30, with the emphasis on investigating the effect of compressibility. The results show that maximum values of variance of streamwise vorticity fluctuations first increase and then decrease as shock strength is increased. The peak of streamwise vorticity fluctuations is observed for shock and turbulence interactions with Mach 2.8 shock. For stronger than Mach 2.8 shocks, there is a decrease in streamwise vorticity fluctuations. The amplification of Reynolds stress R11 decreases as mean Mach number is increased till 8.8, which is consistent with findings of linear interaction analysis. This trend, however, reverses as shock strength is increased beyond Mach 8.8. For stronger than Mach 8.8 shocks, Reynolds stress R11 is amplified as mean Mach number keeps increasing. Since gas temperature increases dramatically after strong shocks, we are also working on DNS of non- equilibrium flow, where non-equilibrium flow effects including internal energy excitations, translation-vibration energy relaxation, and chemical reactions among different species are considered based on the 5-species air chemistry and recently thermal property models. The code and corresponding thermo-chemical models have been tested on two cases of non-equilibrium flow over cylinders.