Role of chemical kinetics on detonation stability and cell sizes

爆轰室宽度在包括安全在内的许多应用中是一个重要的参数，因为它相对容易通过实验获得，而且许多实用的特征和属性被发现随室宽而变化。晶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，即使是简单的动力学方案，也包括许多标度，其中一些标度对温度也非常敏感，因此由动力学确定的标度范围非常大。我们假设晶胞宽度与最不稳定的横向稳定模有关。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。我们最初建议通过将数值模拟获得的晶胞尺寸与三步链支化方案的稳定性结果进行比较来验证这一点，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通常是这样的，稳定的平面波长有效地由引发决定，并且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，尝试分解这两个区域可能是不可行的：与引发长度相比，分解已知引发不稳定性的反应区的波长非常短。然而，这种情况是非常典型的，需要加以解决，从而激励拟议的工作。此外，众所周知，主要来自实验，单元宽度总是比稳定的平面波厚度大得多。因此，如果单元尺寸和横向稳定性之间确实存在关系，那么如果不稳定横模的波长远远大于稳定的平面波厚度，而稳定的平面波厚度本身也比反应区大得多，因此纵模波长，则需要基于多尺度模型进行分析，预计这将是一项非常具有挑战性的工作。假设结果验证了当前的假设，下一步，稳定性分析将扩展到任意复杂的方案，其中的结构也具有比主反应区域长得多的结构。稳定性分析涉及到定常平面解的摄动的特征值问题，这是首先确定的。因此，与具有高激活能的动力学步骤有关的刚度问题可以通过局部地使用沿平面定常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定常平面解时获得并一劳永逸地对角化，也许可以使用符号包。然后，这些结果已经可用，并且简单地用于迭代搜索稳定模式。

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.