Wave-front restructuring in gas–solid detonations: From double-front formation to wave merging

Particle-laden detonations can exhibit double-front detonation (DFD), quasi-double-front detonation (quasi-DFD), and wave merging; however, the mechanism governing their transition and, in particular, the timescale of wave merging remain unclear. Using one-dimensional simulations and weakly nonlinear asymptotic analysis of hydrogen–aluminum detonations, we show that DFD, quasi-DFD, and wave merging are transiently connected stages of a common post-shock restructuring process. To extract the dominant physics, we propose a reduced Burgers-type model for the evolution of the post-shock compression-wave packet, incorporating particle drag, particle heat absorption, and delayed particle heat release. The model predicts a leading-order quadratic scaling of the wave-merging time with particle diameter, and clarifies how drag and heat absorption shape the upstream trapping effect while delayed heat release drives packet amplification and secondary-shock formation. Comparison with full Eulerian two-phase simulations over a range of conditions shows that this scaling captures the dominant particle-size dependence of the merging time, while finite transport, drag, and particle-state effects introduce systematic deviations. The reduced description therefore provides a leading-order basis for interpreting and estimating secondary-front formation and wave-merging times in particle-laden detonation systems, with relevance to detonation propulsion and explosion hazard assessment. Novelty and significance statement The novelty of this work is a weakly nonlinear reduced-order Burgers-type model that links post-SPFD compression-wave evolution to a leading-order quadratic scaling of the wave-merging time in H2-Al detonations. Rather than treating DFD, quasi-DFD, and wave merging as independent front structures, the present simulations and analysis interpret them as transiently connected stages of delayed particle-energy-release coupling. The model identifies the distinct roles of particle drag, heat absorption, and delayed heat release, and provides a leading-order basis for interpreting and estimating the dominant merging timescale within the parameter range examined.