论文标题
在两个单独的衰减时间尺度上，爆炸波的建模，汉堡方程模型及其与其混沌动力学的关系
On the two separate decay time scales of a detonation wave modelled by the Burgers equation and their relation to its chaotic dynamics
论文作者
论文摘要
这项研究使用简化的爆炸模型来研究带有疾驰的脉动爆炸的行为。反应性汉堡方程用于流体动力方程，耦合到脉冲源，从而在固定时间间隔同时消耗所有震惊的反应物。该模型模仿了冲击阵线的短期周期性放大，然后在疾驰的爆炸中看到了相对较长的衰变。数值模拟揭示了前速度的锯齿进化，其时期平均爆炸速度等于Chapman-Jouguet速度。爆炸速度表现出两组不同的衰减时间尺度，并由反应脉冲打断。在每个脉冲上，在反应阵线的最后一个位置上会产生稀疏波。一项特征调查表明，源自此稀疏负责人的特征需要1.57个时期才能到达和衰减爆炸前部，而尾部的特征则需要额外的时期。通过通过后续脉冲的反应前线，在到达冲击阵线之前，通过经过后的反应前线进行两次放大，而尾随特性则被放大了3次。这导致了在爆炸前速中看到的两个不同的时间尺度。
This study uses a simplified detonation model to investigate the behaviour of detonations with galloping-like pulsations. The reactive Burgers equation is used for the hydrodynamic equation, coupled to a pulsed source whereby all the shocked reactants are simultaneously consumed at fixed time intervals. The model mimics the short periodic amplifications of the shock front followed by relatively lengthy decays seen in galloping detonations. Numerical simulations reveal a saw tooth evolution of the front velocity with a period-averaged detonation speed equal to the Chapman-Jouguet velocity. The detonation velocity exhibits two distinct groups of decay time scales, punctuated by reaction pulses. At each pulse, a rarefaction wave is created at the reaction front's last position. A characteristic investigation reveals that characteristics originating from the head of this rarefaction take 1.57 periods to reach and attenuate the detonation front, while characteristics at the tail take an additional period. The leading characteristics are amplified twice, by passing through the reaction fronts of subsequent pulses, before arriving at the shock front, whilst the trailing characteristics are amplified three times. This leads to the two distinct groups of time scales seen in the detonation front speed.
