On a singular point in the Newtonian theory of hypersonic flow

Abstract

An examination of the Newtonian inviscid theory of hypersonic flow past a sphere is made in the neighbourhood of the singular point which occurs at θ = 60°. A uniformly valid theory is developed in this neighbourhood which exhibits the limiting detached ‘free-layer’ behaviour postulated by Hayes and Lighthill in the limit as γ → 1. A complete solution is obtained which gives details of streamline and shock wave shape, pressure distribution, etc. for γ − 1 small.Reasons are given why the empirical ‘modified’ Newtonian theory of Lees proves to be a good approximation to experimentally determined pressure distributions.A novel check to the theory is provided by a simple power-law relation between the pressure on the sphere surface and the distance of the shock wave away from sphere at the same point.