Pressure distribution induced by the interaction between the shock wave and the turbulent boundary layer around a compression corner

Abstract

The pressure distribution induced in the interaction between the shock wave and the unseparated supersonic turbulent boundary layer at a compression corner is considered, with the Mach number of the undisturbed external flow lower than five. The method of asymptotic expansions is used, with solutions valid in the double limits as Reynolds number tends to infinity and the corner angle is much smaller than unity. The undisturbed boundary layer is characterized by the law of the wall in the wall layer and the law of the wake in the velocity defect layer for the compressible flow. It is shown that the induced pressure distribution can be calculated only in the velocity defect layer without considering the wall layer and is independent of the closure condition. In the case of a supersonic turbulent boundary layer with no separation, the sonic line is so close to the wall that the upstream influence is very small. The analysis of the pressure consists of two parts; the outer solution of the defect layer which covers most interaction region except the small region around the shock root and the inner solution of the defect layer which explains the upstream influence near the shock root.