LES of canonical shock-turbulence interaction

The interaction between shock waves and turbulence is present in a large variety of high-speed flows with relevance in scientific and engineering applications. The use of largeeddy simulations (LES) to predict such flows requires subgrid-scale (SGS) models capable of accurately representing the physics behind this interaction at the unresolved scales. The canonical shock-turbulence interaction problem, consisting of isotropic turbulence passing through a nominally normal shock, isolates the fundamentals of this mutual interaction and can be considered a good benchmark case to test the performance of SGS models. The problem of shock-turbulence interaction has been studied theoretically (Ribner 1953; Lee et al. 1992; Lele 1992; Jacquin et al. 1993; Wouchuk et al. 2009), experimentally (Hesselink & Sturtevant 1988; Keller & Merzkirch 1990; Barre et al. 1996; Agui et al. 2005) and numerically, both through direct numerical simulations (DNS) (Lee et al. 1993, 1997; Hannappel & Friedrich 1995; Mahesh et al. 1997; Larsson & Lele 2009) and LES (Lee 1992; Ducros et al. 1999). LES of the canonical case are nonetheless scarce in the literature, compared, for example, with LES of the shock-boundary layer interaction. The aim of the present work is to compare the performance of several SGS models for LES of the canonical shock-turbulence interaction problem, focusing on the region immediately downstream of the shock, which poses most of the modeling challenges (BermejoMoreno 2009). DNS results obtained following Larsson & Lele (2009) will be used for comparison. Section 2 describes the mathematical formulation, geometric configuration and numerical method used in this study. The SGS models implemented for comparison are introduced in Section 3. We propose in Section 4 a conditional application of the SGS model that avoids adding SGS dissipation to flow regions where excessive numerical dissipation is expected. LES results are presented in Section 5 for different flow conditions and compared with filtered DNS data, also evaluating the influence of the grid resolution, numerical scheme and conditional SGS application. Conclusions and future plans are presented in Section 6.