The deflagration-to-detonation transition via the interaction of a weak shock with a series of discrete laminar flames is analyzed computationally based on the unsteady reactive Navier–Stokes equations with one-step Arrhenius chemistry. For comparison, simulations with the Euler equations are also performed. The numerical setup aims to mimic an array of laminar flames ignited at different spark times, artificially inducing chemical activity to stimulate the coupling between the gas dynamics and the chemical energy release for the deflagration-to-detonation transition. The interaction of the weak shock with the first cylindrical flame demonstrates a very good agreement with the results in the literature and that a single weak shock–flame interaction is insufficient to cause a prompt DDT. However, a high degree of Richtmyer–Meshkov instabilities induced by repetitive shock–flame and shock–boundary interactions generate turbulence that accelerates the flame surface, referred to as the flame brush, until eventually a hot spot ignition in the unreacted material develops into a multi-headed detonation wave. In the absence of physical diffusion in the Euler simulation, the enhanced burning rate of the turbulent flame brush is suppressed. Nevertheless, the intense flow fluctuations generated by the interactions of shocks, boundary and flames create the conditions under which a deflagration-to-detonation transition can potentially occur at later times. A parametric study is also reported in this paper to assess the influence of various physical parameters on the transition event and to explore scaling relationships among these parameters.

基于不稳定的反应性Navier-Stokes方程和一步法Arrhenius化学反应，通过计算分析了通过弱冲击与一系列离散层流火焰相互作用而引起的爆燃-爆轰过渡。为了进行比较，还使用欧拉方程进行了仿真。该数值设置旨在模拟在不同火花时间点燃的一系列层流火焰，人为地诱导化学活性，以激发气体动力学与化学能释放之间的耦合，从而实现爆燃-爆轰过渡。弱冲击与第一个圆柱火焰的相互作用与文献中的结果非常吻合，而且单个弱冲击与火焰的相互作用不足以引起迅速的滴滴涕。然而，反复的冲击-火焰和冲击-边界相互作用引起的高度的Richtmyer-Meshkov不稳定性会产生湍流，从而加速火焰表面（称为火焰刷），直到最终未反应材料中的热点点火发展为多头爆震波。在欧拉模拟中没有物理扩散的情况下，湍流火焰刷的燃烧速率得到了抑制。然而，由冲击，边界和火焰的相互作用产生的强烈的流量波动创造了条件，在这种条件下，爆燃到爆轰的过渡可能在以后发生。本文还报道了一项参数研究，以评估各种物理参数对过渡事件的影响，并探索这些参数之间的比例关系。