Scale effect of spherical projectiles for stabilization of oblique detonation waves

Oblique detonation waves (ODWs) were stabilized by launching a spherical projectile with 1.2–1.4 times the Chapman–Jouguet (C–J) velocity into detonable mixtures at rest. We used smaller projectiles (3.18 mm diameter) than those (4.76 mm diameter) in our previous studies and investigated the effect of the projectile scale on the stabilization of ODWs. We carried out high time resolution schlieren visualization using a high-speed camera. The detonable mixtures used were stoichiometric oxygen mixtures with acetylene, ethylene or hydrogen. They were diluted with argon with a 50 % volumetric fraction, and a dilute mixture containing 75 % argon was also tested for the acetylene/oxygen mixture. Here, we discuss the detonation stability in terms of the curvature effect arising from the three-dimensional nature of a stabilized ODW around a projectile. The curvature effect attenuated the detonation wave to below its C–J velocity in the vicinity of the projectile before the wave velocity asymptotically reached the C–J velocity in the far field. Our previous study showed that the propagation limit of the curvature effect is responsible for the stabilizing criticality of detonation waves. By obtaining detailed distributions of the wave propagation velocity and radius of curvature at the stabilizing criticality, we showed that the radius of curvature at the local minimum point of the wave propagation velocity represents the critical radius of curvature required for curved self-sustained detonation. In this study, we focused on this critical mode of the stabilized ODW for a small projectile (3.18 mm diameter). Distributions of the wave velocity and radius of curvature were obtained in the critical mode of the stabilized ODW. We compare these distributions with those for a larger projectile (4.76 mm diameter) and discuss the stabilizing criticality. For the small projectile, the observed combustion regimes had qualitatively the same trend for the initial pressure of the mixture as that observed for the large projectile. However, the initial pressure for each combustion regime was quantitatively different for the different projectile scales. The small projectile required a higher initial pressure to stabilize the ODW than the large projectile. For the critical mode of the stabilized ODW, the wave velocity distribution had a local minimum value (0.8–0.9 times the C–J velocity) due to the curvature effect. The radius of curvature at this characteristic point was about five times the projectile radius, regardless of the mixture composition. The radius of curvature normalized by the cell size was about 8–10 and 15 for mixtures diluted with 50  and 75 % argon, respectively, regardless of the projectile diameter. These results mean that the projectile radius (diameter) proportionally affects the geometrical scale of the wave around the projectile, and the fraction of the gas used for dilution affects the cell size required to sustain a curved detonation wave. The stabilizing criticality, expressed as the dimensionless projectile diameter (projectile diameter normalized by cell size), was about 3.5 and 5.5 for mixtures diluted with 50 and 75 % argon, respectively. These criticalities agreed with those of the large projectile of the previous study. This indicates that the dimensionless projectile diameter is a unique parameter for the stabilizing criticality regardless of the projectile diameter.