Concave Bump for Impinging-Shock Control in Supersonic Flows

In the present study, a novel concave bump for impinging-shock control in two-dimensional supersonic flows is investigated. An analytical method for preliminary bump design based on a generalized shape of a shock-canceling bump has been developed and verified numerically. An extensive proof-of-concept study was performed at a freestream Mach number ranging from 2.5 to 5.0 for shock-generator angles varying from 6 to 12 degrees. It could be demonstrated that a concave bump designed for a given flow-deflection angle is capable of significantly reducing the size of the separation bubble as well as the total pressure losses throughout the Mach number range investigated. The achievable gains depend on the Mach number, the flow-deflection angle, and the relative impingement position of the incident shock front on the bump. The highest values of separation-length reduction (up to 100%), momentum thickness reduction (up to 31%), and pressure recovery factor increase (up to 33%) were obtained at the optimum shock impingement position for the largest deflection angle studied. The concave bump is less effective, and in some cases even disadvantageous, when the incident shock wave does not optimally strike the bump crest.