Asymptotic solution to the problem of hypersonic flow over bodies in the neighborhood of the separation point of a thin shock layer

Abstract

A study is made of the problem of hypersonic flow of an inviscid perfect gas over a convex body with continuously varying curvature. The solution is sought in the framework of the asymptotic theory of a strongly compressed gas [1–4] in the limit M∞ → ∞ when the specific heat ratio γ tends to 1. Under these assumptions, the disturbed flow is situated in a thin shock layer between the body and the shock wave. At the point where the pressure found by the Newton-Buseman formula vanishes there is separation of the flow and formation of a free layer next to the shock wave [1–4]. The singularity of the asymptotic expansions with respect to the parameter ɛ1 = (γ −1)/(γ + 1) associated with separation of the strongly compressed layer has been investigated previously by various methods [3–9]. Local solutions to the problem valid in the neighborhood of the singularity have been obtained for some simple bodies [3–7]. Other solutions [7, 9] eliminate the singularity but do not give the transition solution entirely. In the present paper, an asymptotic solution describing the transition from the attached to the free layer is constructed for a fairly large class of flows.