Some aspects of hypersonic flow over power law bodies

Abstract

This study concerns the hypersonic flow over blunt bodies in two specific cases. The first is the case when the Mach number is infinite and the ratio of the specific heats approaches one. This is sometimes referred to as the 'Newtonian limit'. The second is the case of infinite Mach number and very large streamwise distance from the blunt nose with a strong shock wave, or the 'blast wave limit'. In both cases attention is restricted to power law bodies. Experiments are described of such flows at M∞ = 7.55 in air. The Newtonian flow over bodies of the shape y ∝ x^m at zero incidence is shown to be divisible into three regions: the attached layer at small x, the free layer and the blast wave region. As m increases from zero, the free-layer region reduces in extent until it disappears at m = 1/(2+j) (j = 1 and 0 for axisymmetric and plane flow respectively). A difficulty arises in a transition solution of the type given by Freeman (1962b) connecting the free layer with the blast wave result. At m > 2/(3+j) the attached layer merges smoothly into the Lees-Kubota solution which replaces the blast-wave result in this range. In the blast wave limit, solutions were obtained for flow over axisymmetric power law shapes in the range [fraction one-half]γ < m < ½. Second-order results taking account of the body shape are given. These solutions are compared with experimental results obtained in air at a free stream Mach number of 7.55 and stagnation temperature of 630 °K, as well as with numerical solutions at Mach number of 100. The numerical method is tested by comparing solutions corresponding to the experimental conditions with experiment.

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