Three-dimensional interaction of a shock with lateral low-density gas channel of round, elliptic or rectangular cross-section is numerically studied using Euler’s equations. The structure of formed shock wave precursor is described in detail. Internal shear layer instabilities in three-dimensional flow are shown to develop faster than in axisymmetric case. Moderate amplification of high-pressure jet cumulation effect is noted for elliptic and rectangular channel cases. Dependence of precursor growth rate on cross-section shape is studied. It is found that stretching of cross-section shape significantly increases the duration of linear precursor growth phase.

On the basis of the Euler equations, the interaction of a shock wave in a combustible gas with an elliptical bubble of an inert gas of increased density is numerically simulated within a plane two-dimensional formulation. The finite-volume Godunov-type method of the second order of approximation is applied. Gas combustion is modeled using the Korobeinikov-Levin two-stage kinetics. Various values of the Mach number of the incident wave and the elongation of the inert bubble are considered, and the refraction and focusing of the incident shock are described. Qualitatively different regimes of gas detonation initiation have been found, including direct initiation by a strong wave, ignition upon reflection of an average-intensity wave from the gas interface, and upon focusing of secondary shock waves at lower shock Mach numbers. The dependence of the ignition mode on the shock intensity and the shape of the bubble is determined.

Two-dimensional interaction of a shock in air with elliptic area (two-dimensional gas bubble) filled with propane-oxygen mixture with addition of heavy gas is numerically studied using Euler’s equations. Propane combustion is modeled with one-stage Arrhenius kinetics. Three different ignition regimes are found: direct detonation initiation by sufficiently strong shock, detonation near the triple point formed during weaker shock refraction and detonation at the focusing point of even weaker shock. The latter regime is observed only for significantly elongated bubbles. Detonation initiation regime dependence on shock Mach number and bubble diameter ratio is determined. It is shown that due to bubble elongation, critical Mach number may be significantly lowered in comparison with direct initiation.

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