The locus of the inflection point of a diffracting cylindrical shock segment

Abstract

A discussion on the diffraction of convex cylindrical shock wave segments is presented. Cylindrical shock waves are considered diffracting around several convex sharp corners with different wall angles ( $$27.5^{\circ }, 45^{\circ }$$ ). It is shown that the behaviour of cylindrical shocks is qualitatively similar to that of plane shocks but quantitatively different. These differences can be attributed to the cylindrical shock’s non-constant Mach number and its varying orientation along its profile. The analysis follows the concept of a first disturbance on the shock front and its locus in the laboratory’s frame of reference. Using the concept of disturbances propagating on the shock front introduced by Whitham, a method for determining the locus of the first disturbance is presented. A comparison is made between the loci calculated using this method and those obtained from CFD simulations. Finally, an analytical method for determining the locus of the inflection point is also introduced. The results from the methods presented show good correspondence with calculations from CFD.