Effect of the numerical discretization scheme in Shock-Driven turbulent mixing simulations

Abstract

We evaluate the effects of distinct numerical strategies in simulations of shock-driven turbulent mixing. An air-SF6-air gas curtain subjected to Mach 1.2 shock-waves is computed with Implicit Large-Eddy Simulation based on three numerical schemes: directional-split with Harten-Lax-van Leer (HLL) solver; directional-unsplit using HLL-Contact (HLLC) solver; and directional-unsplit with HLLC solver and a Low Mach number Correction (LMC). The results illustrate the importance of the numerical strategy to the accuracy of the predictions. Whereas both split and unsplit schemes result in a similar spatial development of the initial shock-driven instability, only the unsplit schemes can predict the turbulent mixing transition after reshock observed by the laboratory experiments. Such feature increases the mixing rate of the two fluids, this being particularly pronounced when the LMC is active due to i) the reduced flow Mach number, and ii) the larger effective Reynolds number. Since the selected mixing problem is driven by the deposition of vorticity at the fluids’ interface, the resultant flow physics is analyzed by investigating the contribution of distinct inviscid mechanisms to the production of vorticity: baroclinicity, stretching, and dilatation. As expected, it is observed that the production of vorticity is initially dominated by the baroclinicity mechanism. Yet, the relevance of the remainder mechanisms is enhanced after the reshock and may even surpass the baroclinicity term.