Criticality for stabilized oblique detonation waves around spherical bodies in acetylene/oxygen/krypton mixtures

We have experimentally studied self-sustained oblique detonation waves around projectiles as part of a fundamental investigation of the application of an oblique detonation wave engine and a high-efficiency detonation wave combustor as a power generator. In previous papers we used optical observation to clarify the fluid-dynamic structure of self-sustained oblique detonations stabilized around cone-nosed projectiles. In this study we investigated the criticality for detonation waves. The first expression of the criticality was a mean-curvature coefficient, a rate between a detonation cell width and a mean-curvature radius in which the normal velocity component was the Chapman-Jouguet (C-J) velocity, of 5.03. The mean-curvature coefficient was constant and did not depend on the type of fuel mixture (H₂/O₂/Ar or C₂H₂/O₂/Ar), initial mixture pressure, projectile diameter, projectile velocity, or diluent mole fraction. We obtained a more accurate mean-curvature coefficient for stabilized oblique detonation around symmetric spherical bodies in highly krypton-diluted acetylene/oxygen mixtures that have extremely low C-J velocities. The mean-curvature coefficient of 7.8 was determined to be the most important value for stabilizing the self-sustained oblique detonation waves around multidimensional bodies. Based on experimental results obtained athigh- and low-projectile-velocity ranges, it may be concluded that a lower-velocity projectile can stabilize a self-sustained oblique detonation wave more effectively than can a higher-velocity one. In the high-projectile-velocity region, the experimental critical condition is inconsistent with Lee's detonation initiation theory. We propose a semiempirical criticality equation for the stabilization, which was the secondary expression of the criticality and identical with present and past experimental results.