Non-equilibrium inviscid flows behind a spherical-segment shock wave are investigated with the method of series truncation. This semi-analytical technique developed at Stanford is based on a systematic co-ordinate-perturbation scheme. The flow variables are expanded in series in powers of the longitudinal curvilinear co-ordinate leading away from the stagnation point. The problem is thus reduced to one of numerical integration of ordinary differential equations for functions of the normal co-ordinate. Unlike the similar situation of the Blasius series in boundary-layer theory, the present scheme–having to deal with elliptic equations–must resort to series truncation. As a consequence, a truncation error is introduced. The present paper shows a simple way of reducing this error.The simplified air chemistry adopted is based on non-equilibrium dissociation and recombination of oxygen diluted in inert nitrogen. A wide spectrum of non-equilibrium régimes is investigated for a fixed set of flight conditions. In particular, near-frozen flows are followed to the vicinity of the stagnation point through a region of large temperature and concentration gradients located near the body. This equilibrium-drive region, arising from the singular nature of the frozen limit, is studied in some detail.

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A reacting flow free of molecular transport exhibits noteworthy behaviour in the neighbourhood of a blunt, symmetrical stagnation point. A local analytical study using the Lighthill-Freeman gas model reveals the basic structure of such a flow. Chemical activity is found to affect some, but not all, of the local characteristics of the flow. Unaffected are the pressure and velocity fields near the stagnation point, where the pressure varies quadratically and the velocity varies linearly as in an inert flow. In addition, the stagnation point is found to be in chemical equilibrium for all non-zero reaction rates. On the other hand the density, temperature, and concentration fields are affected by the non-equilibrium reactions. The extent of this effect can be predicted on the basis of a reaction parameter that measures the rate of reaction in terms of the velocity gradient at the stagnation point. A rapidly reacting flow (with reaction parameter greater than unity) approaches the stagnation point with vanishing gradients of density and temperature, whereas a slowly reacting flow approaches with infinite gradients. The flow field is represented mathematically by functions that are regular along the body but non-analytic in the normal direction. Numerical computations support the validity of the local closed-form solution, and provide information on the local effects of the chemical history of the flow.

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