Subgrid-scale modeling of shock-turbulence interaction for large-eddy simulations

The study of the interaction of a shock passing through a turbulent velocity field has been the focus of considerable attention for several decades. Being a fundamental fluid mechanics problem, a wide range of fields and applications can benefit from an improved understanding of it, such as aeronautics (supersonic and hypersonic flight), astrophysics (supernovae explosions), and energy generation (inertial confinement fusion). Theoretical studies based on the mode decomposition of turbulence in supersonic flows (Kovásznay 1953) were first developed in Ribner's linear analysis (Ribner 1953, 1954) and revisited by Lee et al. (1992). Lele (1992) combined rapid distortion theory (RDT) with gas dynamics to formulate the jump relations across a shock in a turbulent mean flow, whereas Jacquin et al. (1993) used RDT and Helmholtz's decomposition of the fluctuating field to obtain two regimes (solenoidal-acoustic and " pressure-released ") thus limiting the amplification of turbulent kinetic energy that occurs when the fluid is processed by the shock. Rapid distortion theory incorporates more restrictive assumptions than does the broader linear interaction analysis, resulting in its more limited scope and agreement with experiments. By using recently developed analytical techniques, Wouchuk et al. (2009) constructed an exact analytical model of the shock-turbulence interaction obtaining closed-form expressions for several quantities of interest. Experiments have been carried out in shock tubes and wind tunnels with different means of generating turbulence. Hesselink & Sturtevant (1988) considered the propagation of weak shocks in a random medium and explained the wave front distortion they encountered in terms of medium inhomogeneities that focus/defocus the front. Keller & Merzkirch (1990) used a shock tube with grid-generated turbulence and a shock wave reflecting at the end wall; they saw amplification of turbulence occurring at larger scales, but not at the small scale structures. Barre et al. (1996) studied, with hot-wire and laser Doppler velocimetry techniques, the interaction in a wind-tunnel of a normal shock and quasi-homogeneous isotropic turbulence generated using a multinozzle in a Mach 3 flow. They found close agreement with Ribner's linear theory for the amplification of velocity fluctuations, and some discrepancy with earlier experiments for the turbulent energy amplification present at low wave numbers. In an experiment by Agui et al. (2005), an incident shock generated an induced flow behind it that passed later through a grid to obtain a nearly homogeneous and isotropic flow field, that was then processed by the reflected shock. Intense-vorticity structures were suggested as …