The Mathematical Modelling of Unconfined and Confined Combustion of Explosives

这个博士项目基于一系列相互关联的数学模型问题，这些问题涉及增加对敏感的复杂燃烧特性及其对人类安全的相关影响的理解和量化。数学模型是应用渐近分析和数值计算相结合的关键要素。第一个这样的问题是关于有限大小的容器，特别是一个长方形，其中有相对少量的固体物质，其余的装满了理想气体。这里将对相互作用进行离散的描述，并适当地加以解决。这应该会导致一个应用更广泛的连续统差异账户，然后在越来越现实的建模方面带来更多的东西。进一步的细节如下：烈性炸药提供了大量释放能量的低质量来源，但这些储存的能量如果意外释放，可能会构成重大危险，甚至造成灾难。因此，安全搬运和储存是一种常态。如果我们要预测可能危险的严重程度并了解相关危险，了解炸药可能引燃、燃烧和引爆的情况是至关重要的。当烈性炸药由于意外严重变形引起的机械耗散或来自热源的直接加热而受到显著加热时，它开始发生反应。固体物质发生反应，即燃烧形成高压气态产物。随着反应的进行，会形成越来越多的气体。炸药的孔隙率增加，随着暴露的表面积越来越大，反应会随着孔隙率和渗透率的增加而加速和传播，直到所有炸药用完，或者直到某种机制释放压力，反应被熄灭。在某些情况下，可能会发生剧烈反应甚至灾难性的爆炸。燃烧(并因此解体)的固体基质和气体产品之间的相互作用仍然不太清楚。显然，火焰与附近表面的火焰相互作用的地方是有限的，可能是以非常复杂的方式。以前的工作从宏观连续介质的角度探索了固体和气体产物反应的两相问题，但缺乏对内部燃烧过程和热气体如何加热炸药的详细处理。现代非均质炸药的复杂性使问题变得更加复杂，在这种炸药中，纯炸药的晶体嵌入到聚合物粘结剂中，而聚合物粘结剂本身可能是反应性的。这类炸药中火焰的产生和传播没有详细的模型；目前使用的燃烧模型通常是基于经验的宏观模型，而不是基于第一原理。它们的校准通常取决于所模拟的实验或几何图形。正是对爆炸反应模型的需求支撑了安全案例，推动了这种经验和半经验模型的发展，这些模型对化学反应中正在进行的物理和化学做出假设。它们的经验性限制了这些模型作为评估所需的经验证的预测工具的适用性，在这种情况下，进行全面的实验是昂贵的和/或不切实际的。这项拟议的研究开始了克服这一限制的旅程。炸药添加剂制造的最新进展为研究理想化的炸药几何形状提供了动力，这些几何形状在实践中正在变得可实现，同时也服从于数学模型。这项跨学科的工作与EPSRC的研究领域联系在一起，包括连续介质力学、化学反应、流体动力学、非线性系统、工业、国防和安全方面。

This doctoral project is based on a sequence of interrelated mathematical model problems that are concerned with increasing the understanding and quantifying of sensitive complex combustion properties and their associated implications in regard to human safety. The mathematical modelling is the key element prior to a combination of asymptotic analysis and numerical computation being applied. The first such problem is in terms of a finite-sized container specifically a long rectangle within which there is a comparatively small amount of solid material and the remainder is filled with an ideal gas. A discrete account of the interaction here will be formulated and solved appropriately. This should lead on to a continuum differential account which has wider application and then on to much more in terms of increasingly realistic modelling. Further details are as follows.High explosives provide a low mass source of massive energy release, but this stored energy can pose a major hazard and even cause disaster if released accidently. Thus safe handling and storage is a constant. Understanding the circumstances in which an explosive can ignite, burn and detonate is essential if we are to predict the severity of likely hazards and understand the associated risks. When a high explosive is subject to significant heating as a result of either mechanical dissipation caused by accidental severe deformation or direct heating from a heat source it begins to react. The solid material reacts, i.e. burns to form high pressure gaseous products. As the reaction proceeds more and more gas is formed. The porosity of the explosive increases and as more and more surface area becomes exposed the reaction can accelerate and propagate with the increasing porosity and permeability until all the explosive is consumed or until some mechanism releases the pressure and the reaction is quenched. Violent reaction or even disastrous detonation can be achieved in some cases. The interplay between the burning (and thereby disintegrating) solid matrix and gaseous products is still ill-understood. Plainly there are confined locations where flames are interacting with flames from nearby surfaces, probably in highly complex ways.Previous works have explored the two-phase problem of reacting solid and gaseous products from a macroscopic continuum viewpoint, but detailed treatments of the internal burning process and of how the hot gas heats the explosive up are lacking. The problem is compounded by the complexity of modern heterogeneous explosives in which crystals of pure explosive are embedded in polymer binders, which themselves can be reactive. The creation and propagation of flames in this type of explosive have not been modelled in detail; burn models in current use are generally empirically based macroscopic models rather than being based upon first principles. Their calibration often depends on the experiment or geometry being modelled. It is the need for models of explosive response to underpin safety cases that has driven the development of such empirical and semi-empirical models, which make assumptions about the physics and chemistry ongoing in a chemical reaction. Their empirical nature limits the applicability of such models as the validated predictive tools needed to make assessments where undertaking full experiments is costly and/or impractical. The proposed research begins the journey to overcoming this limitation. The recent advances in additive manufacturing of explosives provide motivation for the investigation of idealised explosive geometries, which are becoming realisable in practice while amenable to mathematical modelling. This interdisciplinary work links with EPSRC Research Areas including continuum mechanics, chemical reactions, fluid dynamics, non-linear systems, with industrial, defence and security aspects.