Mach stem evolution and shock wave propagation mechanism in double-charge synchronous underwater explosions

The Mach stem evolution and shock wave propagation mechanisms in double-charge underwater explosions are investigated in this study. A numerical model for simulating underwater multi-point explosions is developed by the arbitrary Lagrangian–Eulerian method and validated against Shanes' experimental results. Based on this model, the influences of charge spacing on the spatiotemporal characteristics of shock waves and the evolution of the Mach stem in double-charge simultaneous underwater explosions are numerically investigated. The attenuation mechanism of pressure along the Mach stem front is theoretically analyzed. In addition, the cavitation cutoff characteristics induced by shock–bubble interactions are discussed. The results indicate that the combined theoretical model, which incorporates Mach reflection, von Neumann reflection, and diffraction mechanisms, can effectively reproduce the overall evolution of the triple-point trajectory in the double-charge underwater explosion. The error between the theoretical triple-point trajectory initialized with the critical incidence angle and the numerical simulation results ranges from −37.67% to −50.26%. However, after incorporating the reflection–diffraction transition point extracted from the numerical simulations into the theoretical model, the maximum errors are significantly reduced to −10.86% and −28.25%, respectively. The peak pressure on the symmetry plane of the double-charge configuration is primarily governed by the linear superposition of the shock fronts generated by the individual charges, with relative errors near the origin being −3.38% and −13.13% when nonlinear effects are neglected. Nevertheless, once the radial distance exceeds the critical threshold for Mach reflection formation, the predictions from the linear superposition model converge across different charge spacings, failing to capture the additional propagation loss introduced by the formation of the Mach stem, leading to potential errors of 12.96%–20.43%. Theoretical analysis further confirms that the attenuation behavior of the peak pressure along the Mach stem propagation direction lies between that of nonlinear cylindrical wave and nonlinear spherical wave, and is significantly higher than that predicted by nonlinear tube wave based on the triple-point trajectory. The rarefaction wave reflected from the bubble interface does not overtake the Mach stem front. In the smaller charge spacing case, the breaking front induced by cavitation collapse blocks the propagation of the head of the rarefaction wave, making the shock decay time in the double-charge explosion comparable to that of a single-charge explosion. When the charge spacing exceeds 6.073, within r/a0,d < 60, its influence is mainly confined to the shock profile corresponding to approximately 1.8–6 decay time constants.