Wall modeled large-eddy simulation of shock wave/turbulent boundary layer interaction with separation

The objective of this work is to assess the ability of large-eddy simulations employing an equilibrium wall model to reproduce the flow features present in strong interactions between an oblique shock wave and the turbulent boundary layers of an internal (duct) flow leading to mean flow separation. Such interactions (denoted STBLI) are pertinent, among other applications, to supersonic flight propulsion and have been extensively studied experimentally (Green 1970; Dolling 2001; Dupont et al. 2005, 2006; Piponniau et al. 2009; Souverein et al. 2010; Helmer et al. 2012; Campo et al. 2012) and numerically (see, for example, Wu & Martin 2008; Edwards 2008; Priebe et al. 2009; Touber & Sandham 2009a,b; Hadjadj et al. 2010; Pirozzoli et al. 2010; Pirozzoli & Bernardini 2011; Priebe & Martin 2012; Morgan et al. 2013). Existing numerical simulations, however, are often performed at reduced Reynolds numbers and on simplified geometries that forgo the three-dimensionality of practical configurations. The study presented in this brief is part of a larger enterprise (see Bermejo-Moreno et al. 2014) whose novelty is in the use of a wall model in a large-eddy simulation setting (thus allowing matching of the experimental Reynolds numbers) and the inclusion of three-dimensional effects (by considering the duct sidewalls ignored in the majority of previous simulations). We consider the experiments of an oblique shock wave impinging on a turbulent boundary layer at a Mach number of approximately 2.3 performed by Dupont et al. (2005, 2006), Piponniau et al. (2009), Piponniau (2009) and Souverein et al. (2010). These experiments were done for several shock intensities in the continuously operated supersonic wind tunnel at the Institut Universitaire des Systèmes Thermiques Industriels (IUSTI). The shock intensity is set by varying the deflection angle of a sharp-edge plate (shock generator) attached to the top wall of the wind tunnel. The shock generator spans the tunnel crosssection and is located in the free-stream. The strongest interaction case, corresponding to the largest deflection angle (9.5◦) of the incident shock tested experimentally, will be considered in our simulations, as it resulted in the strongest mean flow reversal observed experimentally. These experiments have been used in previous computational studies for validation purposes, mainly focusing on a lower (8◦) deflection angle with milder separation. Most of these prior computational studies considered spanwise periodicity and a lower Reynolds number than in the experiments, to reduce the computational cost of the DNS or wall-resolved LES (see, for example, Garnier et al. 2002; Touber & Sandham 2009a; Pirozzoli & Bernardini 2011; Morgan et al. 2013). However, Garnier (2009) performed Stimulated Detached Eddy Simulation (SDES) for the 9.5◦ shock deflection angle case, including the top and sidewalls of the wind tunnel in the computational domain.