Estimation Of Shock Stand-Off Distance Using The Curved Shock Theory And Its Validation Via Numerical Modelling

Curved shocks that are locally oriented normal to the direction of the pre-shock flow vector appear on bluff and blunt bodies in supersonic flow and at the center lines of axisymmetric air intakes. There have been numerous studies to analytically approximate the shock stand-off distance associated with these curved normal shock waves; however, in view of the absence of satisfactory results across the entire range of freestream Mach numbers, further efforts are warranted. In this study, the Curved Shock Theory (CST) is used to derive analytical expressions for the pressure gradient right behind convex normal shocks in uniform upstream flow. This pressure gradient can be converted to gradients of other variables using the conservations laws and the isentropic relations. Using these gradients at the curved normal shock and an additional assumption on their variation between the shock and the blunt body it is possible to develop relations for the ratio of the shock stand-off distance to the radius of curvature of the shock surface as a function of freestream Mach number and the specific heat ratio. CST predictions are compared with experimental data from the literature and the CFD results obtained in the present study for freestream Mach numbers ranging from 1.2 to 8.