Ivanov M F, Kiverin A D, Liberman M A
Joint Institute for High Temperatures, Russian Academy of Science, Moscow, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056313. doi: 10.1103/PhysRevE.83.056313. Epub 2011 May 13.
The features of flame acceleration in channels with wall friction and the deflagration to detonation transition (DDT) are investigated theoretically and using high resolution numerical simulations of two-dimensional reactive Navier-Stokes equations, including the effects of viscosity, thermal conduction, molecular diffusion, and a detailed chemical reaction mechanism for hydrogen-oxygen gaseous mixture. It is shown that in a wide channel, from the beginning, the flame velocity increases exponentially for a short time and then flame acceleration decreases, ending up with the abrupt increase of the combustion wave velocity and the actual transition to detonation. In a thin channel with a width smaller than the critical value, the exponential increase of the flame velocity is not bounded and ends up with the transition to detonation. The transition to detonation occurs due to the pressure pulse, which is formed at the tip of the accelerating flame. The amplitude of the pressure pulse grows exponentially due to a positive feedback coupling between the pressure pulse and the heat released in the reaction. Finally, large amplitude pressure pulse steepens into a strong shock coupled with the reaction zone forming the overdriven detonation. The evolution from a temperature gradient to a detonation via the Zeldovich gradient mechanism and its applicability to the deflagration-to-detonation transition is investigated for combustible materials whose chemistry is governed by chain-branching kinetics. The results of the high resolution simulations are fully consistent with experimental observations of the flame acceleration and DDT.
通过对二维反应性纳维 - 斯托克斯方程进行高分辨率数值模拟，包括粘性、热传导、分子扩散的影响以及氢氧气体混合物的详细化学反应机理，从理论上研究了存在壁面摩擦的通道内火焰加速以及爆燃向爆轰转变（DDT）的特征。结果表明，在宽通道中，从一开始火焰速度在短时间内呈指数增加，然后火焰加速减小，最终燃烧波速度突然增加并实际转变为爆轰。在宽度小于临界值的窄通道中，火焰速度的指数增加没有界限，最终转变为爆轰。爆轰转变是由于在加速火焰尖端形成的压力脉冲引起的。由于压力脉冲与反应中释放的热量之间的正反馈耦合，压力脉冲的幅度呈指数增长。最后，大幅度压力脉冲陡化为与反应区耦合的强激波，形成过驱动爆轰。对于化学过程由链分支动力学控制的可燃材料，研究了通过泽尔多维奇梯度机制从温度梯度到爆轰的演化及其对爆燃 - 爆轰转变的适用性。高分辨率模拟结果与火焰加速和DDT的实验观测结果完全一致。
