Analytical prediction of the transition from Mach to regular reflection over cylindrical concave wedges

Abstract

Two formulas, based on analytical considerations, which are capable of predicting the wedge angle of transition from Mach to regular reflection over cylindrical concave wedges, are developed. They are derived using Hornung, Oertel & Sandeman's (1979) conclusion that a Mach reflection can exist only if the corner-generated signals can catch up with the incident shock wave. The good agreement between the present models and the experimental results confirm Hornung et al.'s (1979) concept. The predictions of these models are in better agreement with experimental results than the predictions of Itoh, Okazaki & Itaya's (1981) model. The present models are very simple to use and apply but, like Itoh et al.'s (1981) model, they also lack the ability to account for the dependence of the transition angle on the radius of curvature of the cylindrical wedge.