Multiscale Modeling and Computation of Multiphase Energetic Materials

多相含能材料的多尺度建模与计算

• 批准号: 0609874
• 负责人: Donald Schwendeman
• 金额: --
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0609874&HistoricalAwards=false
• 关键词: Multiscale; Modeling; Computation; Multiphase; Energetic

Multiscale systems abound in science and engineering. Their comprehensive treatment requiresaccurate mathematical modeling of processes at the fine scales and a mathematical framework forflow of information across scales. This proposal addresses this problem in the context of heterogeneousexplosives. These have a complex microstructure with fragments of the energetic material, voids andpores existing within the granular aggregate. When subjected to a sufficiently strong shock, a detonationis initiated. Although the crystalline homogeneous explosive has a high ignition threshold, relativelyweaker stimuli are sufficient to initiate the heterogeneous aggregate. This is caused by the appearanceof discrete sites, or hot spots, where burning commences and then spreads to consume the entire bulk.The multi-scale nature of the system is a daunting obstacle in the way of any attempt at ab-initio modelingof the detonation phenomena, at least at the present time. Two major approaches to mathematicalmodeling have been proposed. Both generate continuum equations at the macro scale, wherein a certaindegree of homogenization is implicit and fine-scale processes have been included as subgrid models.The first approach, typified by the ignition-and-growth model, treats the explosive as a homogeneousmixture of two distinct constituents, the unreacted explosive and the products of reaction, at pressure andtemperature equilibrium. To each constituent is assigned an equation of state, and a single reaction-ratelaw is postulated for the conversion of the explosive to products. The second approach explicitlyrecognizes the two-phase character of the explosive mixture. The resulting model has separatebalance laws of mass, momentum and energy for each phase, plus a rule that allows compaction ofthe solid phase driven by pressure difference between the phases. Terms representing interfacialexchange of mass, momentum and energy appear, corresponding to the nonequilibrium processes ofreaction, drag and heat transfer. These models are systems of hyperbolic partial differential equationsthat can be considered as generalizations of the Euler equations of gasdynamics. This proposal is aimedat studies of existing continuum models as well as the investigation of fine-scale phenomena. The primaryobjective will be to study how the strength and distribution of hot spots depend, in a quantitative way,upon the constitutive properties of the explosive and the size of the igniting stimulus, thus providingimportant information that can be used in attempts at multi-scale descriptions.Many areas in science and engineering, including weather, combustion, pollution, and biological systems,among others, involve behavior at the scale of observation that is determined by the events occurring atmicro scales. A thorough treatment of such systems requires, on the one hand, a fundamentalunderstanding and accurate mathematical modeling of processes at the micro scales, and on the other, development of a theoretical and computational framework that would facilitate flow of informationacross scales, so that behavior at the scale of observation can be predicted reliably and accurately.Attention to such systems is particularly timely and apt in the context of science-based stewardship ofexplosive devices, and it is problems from this arena that form the core of this proposal.

多尺度系统在科学和工程中比比皆是。 它们的综合治疗需要精确的数学建模过程中的精细尺度和数学框架的信息流跨尺度。 本提案针对的是非均质炸药的这一问题。 这些具有复杂的微观结构，其中含有含能材料的碎片、存在于颗粒状聚集体内的空隙和孔隙。 当受到足够强的冲击时，就会发生爆炸。 虽然晶体均质炸药具有较高的点火阈值，但相对较弱的刺激足以引发非均质聚集体。 这是由于出现了离散点或热点，在那里燃烧开始，然后蔓延到消耗整个bulk.The多尺度系统的性质是一个令人生畏的障碍，在ab-initio modelingof爆炸现象的任何尝试的方式，至少在目前的时间。 已经提出了两种主要的方法来进行物理建模。 这两种方法都是在宏观尺度上生成连续介质方程，其中一定程度的均匀化是隐式的，而细尺度过程被包括为亚网格模型。第一种方法，以点燃-增长模型为代表，将炸药视为两种不同成分的混合物，即未反应的炸药和反应产物，在压力和温度平衡下。 每一种组分都有一个状态方程，炸药转化为产品的反应速率定律也只有一个。 第二种方法明确地认识到爆炸混合物的两相特征。 由此产生的模型有单独的质量，动量和能量平衡定律的每一个阶段，加上一个规则，允许压实的固相驱动的压力差之间的阶段。 出现了代表质量、动量和能量的界面交换的术语，对应于反应、阻力和传热的非平衡过程。这些模型是双曲型偏微分方程组，可以被认为是气体动力学欧拉方程的推广。 这一建议旨在研究现有的连续介质模型以及细尺度现象的调查。 主要目的是研究热点的强度和分布如何以定量的方式依赖于炸药的本构性质和点火刺激的大小，从而提供可用于多尺度描述的重要信息。科学和工程的许多领域，包括天气、燃烧、污染和生物系统等，涉及由微观尺度上发生的事件所决定的观察尺度上的行为。 对这些系统的彻底处理一方面需要对微观尺度的过程有基本的理解和精确的数学建模，另一方面需要发展一个理论和计算框架，以促进跨尺度的信息流动，这样，在观测尺度上的行为就可以被可靠而准确地预测。在科学的背景下，对这种系统的关注特别及时和恰当-这一竞技场的问题构成了本提案的核心。