The Mathematical Modelling of Unconfined and Confined Combustion of Explosives

炸药非密闭和密闭燃烧的数学模型

• 批准号: 1916657
• 金额: --
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1916657
• 关键词: Mathematical; Modelling; Unconfined; Confined; Combustion

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.

该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。数学建模是渐近分析和数值计算相结合之前的关键因素。第一个这样的问题是关于有限尺寸的容器，具体地说是一个长矩形，在该长矩形内存在相对少量的固体材料，并且剩余部分填充有理想气体。这里将对相互作用作一个离散的说明，并适当地加以解决。这将导致一个连续差分帐户，有更广泛的应用，然后在越来越现实的建模方面更多。高能炸药是一种低质量的大能量释放源，但这种储存的能量如果意外释放，可能会造成重大危险，甚至造成灾难。因此，安全处理和储存是一个常数。如果我们要预测可能危害的严重性并了解相关风险，就必须了解爆炸物可能点燃、燃烧和引爆的情况。当烈性炸药由于意外的严重变形引起的机械耗散或热源的直接加热而受到显著加热时，它就开始起反应。固体材料反应，即燃烧以形成高压气体产物。随着反应的进行，越来越多的气体形成。炸药的孔隙率增加，并且随着越来越多的表面积变得暴露，反应可以随着孔隙率和渗透性的增加而加速和传播，直到所有的炸药被消耗或者直到某种机制释放压力并且反应被淬灭。在某些情况下，可以实现剧烈反应甚至灾难性的爆炸。燃烧（从而分解）的固体基质和气体产物之间的相互作用仍然不清楚。很明显，在有限的位置，火焰与附近表面的火焰相互作用，可能在高度复杂的方式，以前的工作已经探讨了两相问题的反应固体和气体产品从宏观连续的观点，但详细的处理内部燃烧过程和如何热气体加热炸药是缺乏的。现代非均质炸药的复杂性使问题更加复杂，其中纯炸药的晶体嵌入聚合物粘合剂中，聚合物粘合剂本身可以是反应性的。在这种类型的炸药中火焰的产生和传播尚未被详细建模;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形状。这是爆炸性反应的模型，以支持安全的情况下，推动了这种经验和半经验模型的发展，使假设的物理和化学正在进行的化学反应的需要。它们的经验性质限制了这些模型作为进行评估所需的经验证的预测工具的适用性，而进行全面实验是昂贵的和/或不切实际的。拟议的研究开始了克服这一限制的旅程。爆炸物增材制造的最新进展为理想爆炸物几何形状的研究提供了动力，这些几何形状在实践中变得可实现，同时适合数学建模。这项跨学科的工作与EPSRC研究领域，包括连续介质力学，化学反应，流体动力学，非线性系统，工业，国防和安全方面的联系。