Effect of spatial discretization of energy on detonation wave propagation
Effect of spatial discretization of energy on detonation wave propagation
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DOI：
10.1017/jfm.2017.81
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发表时间：
2016-08
影响因子：
3.7
通讯作者：
X. Mi;E. Timofeev;A. Higgins
中科院分区：
文献类型：
--
作者：
X. Mi;E. Timofeev;A. Higgins
研究了空间高度离散化能量源极限下的爆轰波传播。这个问题的模型从一种介质开始，该介质由具有规定的每单位质量能量释放的热量理想气体组成。释放的能量被收集到片状源中，片状源嵌入在填充它们之间空间的惰性气体中。第一层中的能量释放会产生平面爆炸波，传播到下一个源，在规定的延迟后触发，产生新的爆炸，等等。通过数值求解实验室固定参考系中的一维欧拉方程，计算模拟了锋面穿过数百个此类源时产生的波动动力学。使用两种不同的求解器：一个固定的均匀网格，另一个使用非结构化的，自适应细化的网格，使高度集中，空间离散的源的限制进行检查。两个不同的求解器生成一致的结果，在测量的波速的精度范围内一致。一旦波传播达到准周期解，就测量每个模拟的平均波速。研究了源延迟时间、源能量密度、比热比和源的空间离散性对波速的影响。源固定在实验室参考框架与源对流与流进行了比较。模拟使用Arrhenius率依赖的能量释放进行。将平均波速与等效均匀化介质的理想Chapman-Jouguet（CJ）速度进行比较。超过CJ速度的速度被发现作为源越来越离散，与CJ以上的偏差高达15%。CJ值以上的偏差随着比热比$\unicode[STIX]{x1 D 6 FE}$值的减小而增大。总的能量释放，延迟时间，以及是否源保持实验室固定或对流的流量没有显着的影响偏离CJ的平均波速。一个简单的，特设的分析模型，提出了治疗的情况下，零延迟时间（即源能量释放在冲击波阵面），表现出定性的协议与计算的解决方案，并可以解释为什么偏离CJ随着减少$\unicode[STIX]{x1 D 6 FE}$增加。当震源充分分散，使介质的能量释放接近连续时，得到了平均波速的经典CJ解。这种连续波也可以被证明具有与经典的Zel'dovich-von Neumann-Döring（ZND）爆轰结构一致的时间平均结构。在高度离散源的限制下，波结构的时间平均表明有效声面不对应于平衡状态。在这种情况下，离开波的流动的平均状态最终确实达到平衡Hugoniot，但只有在有效音速面被越过之后。因此，在高度离散源的极限下观测到的超CJ波可以理解为由于有效声速面处的非平衡态而引起的弱爆轰。这些结果的有效性CJ标准适用于高度不稳定的爆轰气体和非均匀爆轰在凝聚相和多相介质的影响。
Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The energy release is collected into sheet-like sources that are embedded in an inert gas that fills the spaces between them. The release of energy in the first sheet results in a planar blast wave that propagates to the next source, which is triggered after a prescribed delay, generating a new blast, and so forth. The resulting wave dynamics as the front passes through hundreds of such sources is computationally simulated by numerically solving the governing one-dimensional Euler equations in the laboratory-fixed reference frame. Two different solvers are used: one with a fixed uniform grid and the other using an unstructured, adaptively refined grid enabling the limit of highly concentrated, spatially discrete sources to be examined. The two different solvers generate consistent results, agreeing within the accuracy of the measured wave speeds. The average wave speed for each simulation is measured once the wave propagation has reached a quasi-periodic solution. The effect of source delay time, source energy density, specific heat ratio and the spatial discreteness of the sources on the wave speed is studied. Sources fixed in the laboratory reference frame versus sources that convect with the flow are compared. Simulations using an Arrhenius-rate-dependent energy release are performed as well. The average wave speed is compared to the ideal Chapman–Jouguet (CJ) speed of the equivalent homogenized media. Velocities in excess of the CJ speed are found as the sources are made increasingly discrete, with the deviation above CJ being as great as 15 %. The deviation above the CJ value increases with decreasing values of specific heat ratio $\unicode[STIX]{x1D6FE}$ . The total energy release, delay time and whether the sources remain laboratory-fixed or are convected with the flow do not have a significant influence on the deviation of the average wave speed away from CJ. A simple, ad hoc analytic model is proposed to treat the case of zero delay time (i.e. source energy released at the shock front) that exhibits qualitative agreement with the computational solutions and may explain why the deviation from CJ increases with decreasing $\unicode[STIX]{x1D6FE}$ . When the sources are sufficiently spread out so as to make the energy release of the media nearly continuous, the classic CJ solution is obtained for the average wave speed. Such continuous waves can also be shown to have a time-averaged structure consistent with the classical Zel’dovich–von Neumann–Döring (ZND) structure of a detonation. In the limit of highly discrete sources, temporal averaging of the wave structure shows that the effective sonic surface does not correspond to an equilibrium state. The average state of the flow leaving the wave in this case does eventually reach the equilibrium Hugoniot, but only after the effective sonic surface has been crossed. Thus, the super-CJ waves observed in the limit of highly discretized sources can be understood as weak detonations due to the non-equilibrium state at the effective sonic surface. These results have implications for the validity of the CJ criterion as applied to highly unstable detonations in gases and heterogeneous detonations in condensed phase and multiphase media.