Initiation of detonation in interaction of a shock wave with combustible gas bubble of various densities

Interaction of a shock wave in a gas with a combustible gas bubble of an elevated density is numerically simulated based on the Euler equations. Three qualitatively different regimes of detonation initiation are described: direct initiation of detonation in the frontal part of the bubble at sufficiently high Mach numbers of the incident wave and detonation initiation in the rear part of the bubble due to wave refraction and focusing of secondary shock waves at lower Mach numbers. It is shown that the detonation initiation regime depends to a large extent both on the shock wave intensity and on the density of the mixture in the bubble. Based on a series of computations, a diagram of initiation regimes is composed. It is demonstrated that the effect of shock wave focusing ensures successful initiation of detonation with a much lower intensity of the incident wave as compared to direct initiation.