Analytic Solution for Hypersonic Flow Past a Slender Elliptic Cone Using Second-Order Perturbation Approximations

Abstract

An approximate analytical solution is obtained for hypersonic flow past a slender elliptic cone using second-order perturbation techniques in spherical coordinate systems. The analysis is based on perturbations of hypersonic flow past a circular cone aligned with the free stream, the perturbations stemming from the small cross-section eccentricity. By means of hypersonic approximations for the basic cone problem, closed-form second-order approximate solutions for the perturbation equations are obtained within the framework of hypersonic small-disturbance theory. Results for the shock shape, shock-layer structure, and surface pressure are presented for all ranges of Mach number s, together with comparisons with experimental data. Also a complete vortical layer analysis is presented to prove the suitability of the surface boundary conditions.