Approximation for hypersonic flow past an inclined cone.

An approximate analytical solution is obtained for hypersonic flow past an inclined circular cone. The governing equations are simplified by means of the constant-density approximation, and the ensuing quadrature solution is evaluated in closed form by approximations based on hypersonic small disturbance theory. This solution corresponds to the outer solution in a matched asymptotic expansion scheme and describes the region outside the thin vortical layer that lies adjacent to the surface of the cone. The results are in good agreement with tabulated numerical solutions and are also valid for values of the hypersonic similarity parameter that lie outside the range of the tabulated results. The present approximation is also applicable to much broader flow regimes than previous analytical descriptions, such as that of the Newtonian approximation. The results of this analysis are useful whenever analytical expressions are desired and can be coupled with one of the existing inner solutions for the vortical layer to form a composite uniformly-valid approximation to first order in angle of attack, valid for a wide range of hypersonic similarity parameters.