Calculations for steady propagation of a generic ram accelerator configuration

This study describes a methodology and gives analysis to determine the steady propagation speed of a projectile fired into a gaseous mixture of fuel and oxidizer. So that numerical results can be analytically verified in limiting cases, a simple model and geometry are used: the steady supersonic flow of an in viscid, calorically perfect, ideal, reacting gas with high activation energy over an unconfined symmetric double wedge is considered. Typical predicted flow fie Ids consist of a lead inert oblique shock followed by a thick induction zone, thin reaction zone, rarefaction, and trailing oblique shock. The reaction strengthens the lead shock to the extent that the far-field wave angle is that of a Chapman-Jouguet (CJ) oblique detonation. Propagation speeds are found that give rise to shocks of such strength as to induce the reaction zone to be in a region that 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 quasistatic perturbations, whereas the solution at the lower Mach number is unstable. The steady solutions are superdetonative in that the projectile velocities that give rise to force balances are greater than the CJ velocity for a detonation wave aligned normal to the direction of projectile motion. This methodology can be applied to analyze devices that have more complex geometries, such as the ram accelerator or oblique detonation wave engine.