Numerical study of the effect of sidewalls on shock train behaviour

Abstract Strongly coupled sequences of shock waves, known as shock trains, are present in high-speed propulsion systems, where the presence of sidewalls substantially modifies the boundary layer thickness, skin friction and streamwise pressure distribution. In the present contribution, scale-resolved numerical simulations are performed on supersonic channel (infinite span) and square duct flows to evaluate the effect of sidewall confinement with and without shock trains. Comparable secondary flow vortices are observed in the duct case with and without the presence of the shock train. The absence of a separation region at the leading shock of the duct case results in lower flow deflection compared with the channel case, leading to a reduced shock strength. The principal effect of the sidewalls is to cause a shock train that is approximately twice as long and composed of a larger number of shocks. A modification of previous models, based on a momentum thickness-based blockage parameter, leads to an improved collapse of the channel and duct cases.