Shock curvature and gradients at the tip of pointed axisymmetric bodies in non-equilibrium flow

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Abstract
The shock curvature and flow variable gradients at the tip of a pointed body caused by non-equilibrium effects are considered. Co-ordinates introduced by Chester (1956) are used since they offer a convenient way of treating the boundary conditions. The desired functions are obtained by solving numerically a system of linear ordinary differential equations. These equations have a singularity; the nature of the singularity is found analytically, and its numerical treatment is discussed. The specific non-equilibrium effect considered is vibrational relaxation in a pure diatomic gas. Representative results are given for flow of N2over a cone for a comprehensive range of Mach number and cone angle. There is a point analogous to the Crocco point. The exact results are compared with predictions from (i) a hypersonic, small disturbance theory; (ii) the application of an integral method; (iii) characteristic calculations. In an appendix, a comparative discussion is given of results for frozen flow over ogival bodies.