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The flow of high-speed air in ducts may result in the occurrence of multiple shock-wave/boundary-layer interactions. Understanding the consequences of such interactions, which may include distortion of the velocity field, enhanced turbulence production, and flow separation, is of great importance in understanding the operating limits and performance of a number of systems, for example, the high-speed intake of an air-breathing missile. In this paper, the results of a computational study of multiple shock-wave/boundary-layer interactions occurring within a high-speed intake are presented. All of the results were obtained using the in-house computational fluid dynamics solver of Glasgow University, HMB3. First simulations of a Mach    $$M=1.61$$  M = 1.61 multiple shock-wave/boundary-layer interaction in a rectangular duct were performed. The    $$M=1.61$$  M = 1.61 case, for which experimental data is available, was used to establish a robust numerical approach, particularly with respect to initial and boundary conditions. A number of turbulence modelling strategies were also investigated. The results suggest that Reynolds-stress-based turbulence models are better suited than linear eddy-viscosity models. This is attributed to better handling of complex strain, in particular modelling of the corner separation. The corner separations affect the separation at the centre of the domain which in turn alters the structure of the initial shock and the subsequent interaction. Having established a robust numerical approach, the results of a parametric study investigating the effect of Mach number, Reynolds number, and confinement on the baseline solution are then presented. Performance metrics are defined to help characterize the effect of the interactions. The results suggest that reduced flow confinement is beneficial for higher-pressure recovery.

Parametric study of multiple shock-wave/turbulent-boundary-layer interactions with a Reynolds stress model