Mach reflection in steady supersonic flow considering wedge boundary-layer correction

Abstract Mach reflection in steady supersonic flow is an important phenomenon having received extensive studies, among which simplified theoretical models to predict the size of Mach stem and other flow structure are of particular interest. Past efforts for such models were based on inviscid assumption while in real cases the flow is viscous. Here in this paper we consider the influence of wedge boundary layer on the Mach stem height. This is done by including a simplified boundary layer model into a recently published inviscid model. In this viscous model, the wedge angle and the trailing edge height, which control the Mach stem height, are replaced by their equivalent ones accounting for the displacement effect of the wedge boundary layer, with the boundary layer assumed to be laminar or fully turbulent. This viscous model is shown to compare well with numerical results by computational fluid dynamics and gives a Mach stem height as function of the Reynolds number and Mach number. It is shown that due to the viscous effect, the Mach stem height is increased, through increasing the effective wedge angle.