A Blunt-Nosed Thin Body in Hypersonic Flow

Abstract

An inverse problem is posed to simulate the influence of the nose bluntness on the hypersonic inviscid steady flow field around a slender two-dimensional section. In this formulation a bow shock is given in advance whereas the body contour comes at the end of analysis being identified with a particular streamline. An equation for the shock shape involves two terms in the form of different powers of the distance measured along the direction of oncoming stream. The leading term derives from a classical similar solution for the strong viscous/inviscid interaction regime; a correction to it models bluntness effects at large distances downstream. Matched asymptotic expansions are used to solve the problem within the hypersonic small- disturbance theory. In the outer region bounded by the shock, two sets of ordinary differential equations control the pressure, density, and velocity distributions. The second-order approximation admits of an explicit integral obtainable from a consideration of the finite drag exerted on the blunted nose of a section. The use of the momentum conservation law allows us to predict the power of the exponent of the correction term entering the shock equation. The asymptotic behavior of both first- and second-order approximations is established and employed for providing conditions for a solution in the inner region occupied by a high-entropy layer. Governing equations here are solved, explicitly determining a dependence of the body shape on the correction in the shock representation. A thorough analysis of the Newtonian approach reveals certain limitations inherent in this sim- plified treatment of steady hypersonic flows.