Role of chemical kinetics on detonation stability and cell sizes

爆轰单元宽度在包括安全性在内的许多应用中是关键参数，因为它相对容易通过实验获得，并且因为发现许多实际特征和性质与单元宽度成比例。泡孔宽度最终是表征反应性混合物的化学动力学的函数，但是没有明确的方法直接知道动力学方案来确定它。事实上，动力学的计划，即使是简单的，包括许多尺度，其中一些也是非常温度敏感的，使范围内的尺度所确定的动力学是非常大的。我们假设胞宽与最不稳定的横向稳定模式有关。这样做的动机是，宽度和模式都是横向尺度，并且没有其他明显的横向尺度可以定义。我们建议最初测试这通过比较细胞大小通过数值模拟与稳定性结果为三步链分支计划，其中，经常是现实的链分支动力学，包括氢-空气的情况下，稳定的平面波长有效地确定由启动，和反应区本身是薄得多。在这种情况下，稳定性分析变得困难，我们的经验是，试图解决这两个区域可能是不可行的，因为规模的差异：波长解决反应区，不稳定性是已知的启动，然后非常短的启动长度相比。然而，这种情况是相当典型的，需要加以解决，推动拟议的工作。此外，主要从实验中也众所周知，单元宽度总是比稳定的平面波厚度大得多。因此，如果在单元尺寸和横向稳定性之间确实存在关系，那么如果不稳定横向模式的波长比稳定平面波厚度大得多，而稳定平面波厚度本身比反应区大得多，因此纵向模式波长也大得多，则分析将需要基于多尺度模型，这是一种预期相当具有挑战性的练习。假设结果验证了当前的假设，接下来，稳定性分析将扩展到任意复杂的计划，也具有结构，其中启动是远远长于主反应区。稳定性分析包括一个特征值问题的扰动稳定的平面解决方案，这是确定的第一。因此，与具有高活化能的动力学步骤相关联的刚度问题可以通过沿着平面稳态波局部地使用动力学矩阵的雅可比矩阵来处理，该雅可比矩阵可以在计算稳态平面解时一次性地获得和对角化，也许使用符号包。然后这些结果已经是可用的，并简单地用于迭代搜索的稳定模式。

The detonation cell width is a crucial parameter in many applications, including safety, because it is relatively easy to obtain experimentally and because many practical features and properties are found to scale with the cell width. The cell width is ultimately a function of the chemical kinetics characterizing the reactive mixture, but there is no clear way to determine it directly knowing the kinetic scheme. Indeed kinetic schemes, even simple ones, include many scales, some of which are also very temperature-sensitive, so that the range of scales determined by the kinetics is very large. We hypothesize that the cell width is related to the most unstable transverse stability modes. The motivation for this is that both width and modes are transverse scales, and that there are no other obvious transverse scales that can be defined. We propose initially to test this by comparing cell sizes obtained by numerical simulation with stability results for three step chain-branching schemes in which, as is often the case for realistic chain-branching kinetics including hydrogen-air, the steady planar wave length is effectively determined by initiation, and the reaction zone itself is much thinner. In that situation, stability analysis becomes difficult and our experience is that attempts to resolve both zones may not be doable because of the scale disparity: wavelengths resolving the reaction zone, where instability is known to initiate, are then very short when compared with the initiation length. Yet, such a situation is quite typical and it needs to be addressed, motivating the proposed work. Furthermore, it is also well-known, mainly from experiments, that the cell width is invariably much larger than the steady planar wave thickness. Thus, if there is indeed a relationship between cell sizes and transverse stability, then if the wavelength of unstable transverse modes is much larger than the steady planar wave thickness, which is itself much larger than the reaction zone hence longitudinal mode wavelengths, the analysis will need to be based upon a multiple scale model, an exercise which is expected to be quite challenging. Assuming results validate the current hypothesis, next, the stability analysis will be extended to arbitrary complex schemes also featuring a structure in which initiation is much longer than the zone of main reaction. Stability analysis consists in an eigenvalue problem for a perturbation to the steady planar solution, which is determined first. Thus stiffness issues associated with kinetic steps with high activation energy can be dealt with by locally using the Jacobian of the kinetics matrix along the planar steady wave, which can be obtained and diagonalized once and for all when computing the steady planar solution, perhaps using a symbolic package. Then these results are already available and simply used in the iterative search for stability modes.