Superdetonative flow of gaseous propellant mixtures over sphere-cone bodies

This research is motivated by determining the upper "speed limit" of a Superdetonative Ram Accelerator (SDRA). To this end, heat release and detonation double-wave models, proposed by Pratt and by Korobeinikov respectively, have been used to investigate the general characteristics of a sphere-cone projectile immersed in a uniform supersonic flow of a combustible gas mixture, well in excess of the Chapman-Jouguet speed. Sphere-cone projectiles are examined, as a spherical nose of some radius is required at the upper limit of SDRA operation to withstand the thermal load. For engineering analysis and design, general engineering correlations for predicting shock wave shapes for flows with and without heat addition are presented. Approximate equations are derived which locate the bifurcation of a detached reacting shock wave into a detonation and deflagration wave. Due to the blunt nose, there exists a cylindrical pencil of propellant gases which will necessarily be consumed on the projectile forebody prior to being ingested into the annulus, thereby reducing the amount of the propellant available to provide thrust. The "doomed propellant fraction" (DPF) may be estimated as a multiple of the ratio of the tube-to-nose radius, by specifying the approach Mach number, mass specific heat release, and cone half-angle. Hence, the upper "speed limit" is determined by the condition where the DPF approaches unity. Guidelines enabling prediction of SDRA size and performance limitations due to projectile forebody processes have been developed.; In order to verify the approximate equations used to locate the bifurcation point, an approximate inverse technique is developed for calculating supersonic flow of gaseous propellant mixtures associated with the formation of detonation and deflagration fronts over sphere-cone bodies. The accuracy of the exothermic inverse technique is assessed by comparing computed shock standoff distance, the position of the deflagration front, and the body shape to Lehr's ballistic-range experimental shadowgraph. Results indicate excellent agreement on the nose region, but show a growing diverging discrepancy beginning at the shoulder. The strong dependency of the solution technique on the shock radius of curvature is established.