Detached Shock Past a Blunt Body

Abstract

In R-2, a symmetric blunt body W-b is fixed by smoothing out the tip of a symmetric wedge W(0 )with the half-wedge angle theta(w )is an element of (0, pi/2). We first show that if a horizontal supersonic flow of uniform state moves toward W(0 )with a Mach number M-infinity >1 being sufficiently large depending on theta(w), then the half-wedge angle theta(w) is less than the detachment angle so that there exist two shock solutions, a weak shock solution and a strong shock solution, with the shocks being straight and attached to the vertex of the wedge W-0. Such shock solutions are given by a shock polar analysis, and they satisfy entropy conditions. The main goal of this work is to construct a detached shock solution of the steady Euler system for inviscid compressible irrotational flow in R-2 \ W-b. Especially, we seek a shock solution with the far-field state given as the strong shock solution obtained from the shock polar analysis. Furthermore, we prove that the detached shock forms a convex curve around the blunt body W-b if the Mach number of the incoming supersonic flow is sufficiently large, and if the boundary of W(b )is convex.