Detonation of a Combustible Gas Mixture upon the Interaction of a Shock Wave with an Ellipsoidal Inert Gas Bubble

The interaction of a shock wave in a combustible gas mixture with an ellipsoidal region of an inert gas of increased density is numerically simulated using the Euler equations in the two-dimensional plane and axisymmetric formulations. Four qualitatively different regimes of indirect initiation of detonation have been found: upon reflection of a wave from the gas interface, upon focusing of secondary transverse shock waves on the axis/plane of symmetry, upon amplification of a transverse wave converging to the axis of symmetry, and upon secondary focusing of waves in front of the bubble. It is shown that the mode of detonation initiation depends significantly on both the intensity of the shock wave and the shape of the bubble. Based on a series of simulations, the dependence of the threshold Mach numbers of the incident wave on the shape of the bubble is determined. In the plane flow, a moderate elongation of the bubble leads to a significant decrease in the threshold Mach number. In an axisymmetric flow, the lower threshold Mach number is less sensitive to the shape of the bubble, and the most effective detonation initiation is carried out using a spherical bubble. The effect of shock wave focusing makes it possible to achieve successful initiation of detonation at a fundamentally lower intensity of the incident wave compared to direct initiation.