Analytical and Computational Studies of High-Speed Flows in Single-and Multi-Phase Reacting Media

提出了爆炸和起爆介质中化学反应流动的计算和分析研究。主要关注的是凝聚相含能材料，其典型特征是由惰性粘合剂粘合在一起的爆炸成分的固体颗粒组成的非均匀微观结构。这些材料在形态、热机械和化学上都很复杂。在燃烧过程中释放能量的微尺度与典型爆炸装置的尺度之间存在着巨大的差异。因此，现有的数学模型是近似的，描述平均行为，并隐式或显式地纳入一定程度的均匀化。建议的工作集中在两个可用的连续体描述。第一种称为点火和生长，将炸药视为反应和产物的均匀混合物。第二种方法采用多相方法，将反应物和生成物视为两个不同的相。在基本水平上，这两个数学模型都是双曲偏微分方程系统，由质量、动量和能量的平衡定律组成，辅以反应速率和状态方程的规定。应用适当的机械和/或热刺激导致爆震波的形成。提出的研究目标是通过数学和计算研究阐明这些波的进化行为背后的机制。我们将重点讨论它们的产生、传播、与扰动的相互作用以及对边界结构变化的响应。传统上，炸药科学的主要重点一直是可靠和可预测地引发爆炸。反过来，这需要对刺激的种类和强度（通常是机械脉冲），以及从初始冲击转变为自我持续爆炸所需的相关时间和距离有精确的了解。数学模型的使用确实考虑到了这一目的。然而，本研究建议在更广泛的背景下系统地研究这些模型。如果要合理地评估使用高能炸药的装置的安全性，这样的演习是绝对必要的。这是因为在发生事故的情况下，刺激不太可能以精确施加的强烈平面冲击的形式出现。在这种情况下，必须发现炸药在受到弱压缩脉冲或热梯度作用时的反应。我们打算通过提出和研究适合这两类数学模型的问题来做到这一点。这种详细的理解应该为进一步合理推导更适合工程计算和设计的简化或近似铺平道路。

Computational and analytical studies of chemically reacting flows in exploding and detonating media are proposed. Of primary interest are condensed-phase energetic materials, typified by a heterogeneous microstructure consisting of solid grains of the explosive component held together by an inert binder. Such materials are morphologically, thermomechanically, and chemically complex. There is a vast disparity between the microscales at which energy is released during combustion, and the scale of a typical explosive device. Accordingly, existing mathematical models are approximate, describe averaged behavior, and incorporate either implicitly or explicitly a certain degree of homogenization. The proposed work focuses on two available continuum descriptions. The first, called ignition and growth, treats the explosive as a homogeneous mixture of reacting and product species. The second employs a multiphase approach and considers the reactants and products as two distinct phases. At a fundamental level both mathematical models are systems of hyperbolic PDEs, consisting of the balance laws of mass, momentum and energy, supplemented by prescriptions for the reaction rates and the equations of state. Application of appropriate mechanical and/or thermal stimulus leads to the formation of detonation waves. The objective of the proposed research is the elucidation, via a mathematical and computational study, of the mechanisms that underlie the evolutionary behavior of these waves. We shall focus on their birth, propagation, interaction with disturbances, and response to changes in the configuration of the confining boundary. Traditionally, the major emphasis in explosives science has been to initiate a detonation reliably and predictably. That, in turn, has required a precise knowledge of the kind and strength of stimulus usually a mechanical impulse), and the associated time and distance, needed for the initial shock to transition into a self-sustained detonation. Mathematical models have indeed been employed with that end in mind. This study, however, proposes that these models be investigated systematically in a broader context. Such an exercise is absolutely essential if one is to rationally assess the safety of devices that employ high-energy explosives. This is because in case of an accident, the stimulus is unlikely to be in the form of a strong, planar shock applied with precision. For such a case, one must discover how the explosive will respond when subjected to a weak compressive pulse or thermal gradient. We intend to do so by posing and investigating suitable problems for the two classes of mathematical models. Such a detailed understanding should pave the way for the rational derivation of further reductions or approximations that are better suited for engineering computations and design.