含支链动力学的Fickett模型中激波诱导点火动力学：$χ$的影响
Dynamics of shock induced ignition in Fickett's model with chain-branching kinetics: influence of $χ$
摘要：
在Fickett的反应性可压缩流模型框架内讨论了由活塞引起的激波点火问题，即，Burgers方程的反应形式。采用诱导-反应两步链式分支模型研究了激波点火过程中能量释放与可压缩流体动力学之间的耦合。由于该模型的简单性，使用该模型承认的两族特征来解释点火和加速机制。沿着粒子路径的能量释放提供了向前行进的压力波的放大。这些波预压缩反应区前面的诱导层中的介质，因此改变连续粒子的诱导延迟。通过控制压力波在反应区中的停留时间，感应延迟的变化提供了对向前行进的压力波的放大的调制。用特征线法和高活化能渐近法得到了封闭形式的解析解。发现反应区的加速与活化能、诱导与反应时间之比和放热的乘积成正比。这一发现提供了一个理论上的理由，以前使用这个无量纲数来表征实验观察到的点火制度，在爆震和冲击引起的点火现象。数值模拟和分析。亚音速和超音速内部火焰传播制度的观察，与实验和以前的反应欧拉模型。
英文摘要：
The problem of shock induced ignition by a piston is addressed in the framework of Fickett's model for reactive compressible flows, i.e., the reactive form of Burgers' equation. An induction-reaction two-step chain-branching model is used to study the coupling between the energy release and the compressible hydrodynamics occurring during the shock ignition transient leading to a detonation. Owing to the model's simplicity, the ignition and acceleration mechanism is explained using the two families of characteristics admitted by the model. The energy release along the particle paths provides the amplification of forward-travelling pressure waves. These waves pre-compress the medium in the induction layer ahead of the reaction zone, therefore changing the induction delays of successive particles. The variation of the induction delay provides the modulation of the amplification of the forward travelling pressure waves by controlling the residence time of the pressure waves in the reaction zone. A closed form analytical solution is obtained by the method of characteristics and high activation energy asymptotics. The acceleration of the reaction zone was found to be proportional to the product of the activation energy, the ratio of the induction to reaction time and the heat release. This finding provides a theoretical justification for the previous use of this non-dimensional number to characterize the ignition regimes observed experimentally in detonations and shock induced ignition phenomena. Numerical simulations are presented and analysed. Both subsonic and supersonic internal flame propagation regimes are observed, consistent with experiment and previous reactive Euler models.
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