Role of chemical kinetics on detonation stability and cell sizes

爆轰池宽度在包括安全性在内的许多应用中是一个至关重要的参数，因为它相对容易通过实验获得，而且许多实际特征和性能都与爆轰池宽度成比例。细胞宽度最终是表征反应混合物的化学动力学的函数，但没有明确的方法直接确定它知道动力学方案。事实上，动力学方案，即使是简单的，也包括许多尺度，其中一些对温度也非常敏感，因此动力学决定的尺度范围非常大。我们假设电池宽度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态都是横向尺度，并且没有其他明显的横向尺度可以定义。我们最初建议通过比较数值模拟得到的细胞尺寸与三步链支化方案的稳定性结果来验证这一点，在三步链支化方案中，包括氢-空气在内的现实链支化动力学中，稳定的平面波长有效地由起始决定，反应区本身要薄得多。在这种情况下，稳定性分析变得困难，我们的经验是，由于尺度差异，试图解决两个区域可能是不可行的：解决反应区域的波长，在已知的不稳定性开始，与开始长度相比非常短。然而，这种情况是相当典型的，需要解决，激励所提议的工作。此外，主要从实验中也知道，胞体宽度总是比稳定的平面波厚度大得多。因此，如果确实存在细胞尺寸和横向稳定性之间的关系，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，则分析将需要基于多尺度模型，这一练习预计将是相当具有挑战性的。假设结果证实了目前的假设，接下来，稳定性分析将扩展到任意复杂方案，也具有起爆区远长于主反应区的结构。稳定性分析包括一个扰动对稳定平面解的特征值问题，它首先被确定。因此，与具有高活化能的动力学步骤相关的刚度问题可以通过局部使用沿平面稳定波的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定平面解时一劳永逸地得到并对角化，可能使用符号包。然后，这些结果已经可用，并简单地用于稳定模态的迭代搜索。

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.