ANALYTICAL SOLUTIONS FOR HYPERSONIC FLOW PAST SLENDER POWER-LAW BODIES AT SMALL-ANGLE OF ATTACK

Hypersonic flows around axisymmetrical power-law slender bodies are calculated for high, but finite, Mach numbers and for low angles of attack. This is done by a small perturbation expansion of self-similar solutions using the equivalence principle. The solutions depend only on the exponent n of the power law defining the body and on the specific heat ratio gamma of the gas, which is assumed to be perfect and inviscid. These solutions, the shock equation, the pressure coefficient on the body, and the aerodynamic coefficients are obtained in universal analytical form and depend on numerical coefficients determined once and for all for each pair (eta,gamma). The effects of the angle of attack for nonconical noses is an innovation presented here: we observe that the effect of gamma on the shift of the shock and on the normal force and pitching coefficients depends, both in its sense and its intensity, on the shape of the nose cone. Finally, the stream functions are found to generalize Hayes' and Probstein's entropy correction principle to these three-dimensional flows. The results tabulated in this paper are intended to be used as test cases for inviscid numerical simulation and comparisons with specific experiments.