Approximate solutions for oblique detonations in the hypersonic limit

This article describes analytic solutions for hypersonic flow of a premixed reactive ideal gas over a wedge. This flow is characterized by a shock followed by a spatially resolved reaction zone. Explicit solutions are given for the irrotational flow field behind a straight shock attached to a curved wedge and for the rotational flow field behind a curved shock attached to a straight wedge. Continuous solution trajectories exist which connect the state just past the shock to the equilibrium end states found from a Rankine-Hugoniot theory for changes across oblique discontinuities with energy release. The analytic results are made possible by the hypersonic approximation, which implies that a fluid particle's kinetic energy is much larger than its thermal and chemical energy. The leading order solution is an inert oblique shock. The effects of heat release are corrected for at the next order. These results can be used to verify numerical results and are necessary for more advanced analytic studies. In addition, the theory has application to devices such as the oblique detonation wave engine, the ram accelerator, hypersonic airframes, or re-entry vehicles.