Analysis for Steady Propagation of a Generic Ram Accelerator / Oblique Detonation Wave Engine Configuration

This study describes a methodology and gives analyses to determine the steady propagation speed of a projectile fired into a gaseous mixture of fuel and oxidizer. For tractability, the steady supersonic flow of an inviscid calorically perfect ideal reacting gas with high activation energy over a symmetric double wedge, unconfined by a cowl, is considered. Propagation speeds are found which give rise to shocks of such strength which induce a reaction zone to be in a region which allows the combustion-induced thrust to balance the wave drag. For a fixed heat release greater than a critical value, two steady propagation speeds are predicted. The solution at the higher Mach number is stable to quasi-static perturbations while the solution at the lower Mach number is unstable. This methodology can be applied to analyze devices which have more complex geometries such as the ram accelerator or oblique detonation wave engine. This paper gives both a simple proof of concept analysis based on Rankine-Hugoniot jump conditions and a detailed numerical analysis of the governing partial differential equations. The simple analysis and numerical analysis are shown to be in qualitative agreement.