Non-Steady Solutions of Models Describing Smoldering Combustion

DMS-9971881描述阴燃燃烧模型的非稳态解Daniel SchultColgate大学摘要弥漫燃烧指的是主要反应过程涉及固体和气体反应物，而不是常见火焰中的气体/气体反应的燃烧。阴燃通常发生在向反应提供的氧化剂有限的情况下，例如，因为氧化剂必须流经多孔介质才能到达反应地点。阴燃燃烧模型需要描述多孔流体流动以及反应过程。由此产生的偏微分方程是高度非线性的，使得解的描述变得困难。采用自适应方法的数值模拟能够更详细地逼近这些模型的定常解，这些方法随着过程的发展而改变分辨率。渐近方法也成功地描述了这些模型的稳定和缓慢变化的近似解。提出的项目包括将渐近和数值方法扩展到非定常解的研究，然后使用这些技术来描述这些解的动力学和转变的细节。这个项目应该会引起科学家的兴趣，他们使用渐近方法，使用自适应数值方法，研究具有多个解的系统，对多个时间尺度的解的稳定性问题感兴趣，或者对混沌解的发展感兴趣。火灾安全专家特别感兴趣的是，他们希望了解接近灭火极限的阴燃动力学、从阴燃到火焰的转变以及阴燃在材料中传播的模式。阴燃燃烧是指没有空气传播火焰的固体的燃烧。它不仅是火灾的前兆，而且往往会释放大量有毒气体，因此引起了人们对消防安全的兴趣。阴燃也被用于正时装置(点火引线)的设计，以及材料合成过程，如自蔓延高温合成。了解阴燃背后的机理和过程可以提高火灾安全，并可以更好地控制阴燃燃烧的工程用途。阴燃过程的模型涉及高度非线性的偏微分方程组，使得解的描述变得困难。对于稳定的均匀传播和缓慢变化的传播有近似的描述，但阴燃通常涉及复杂的非稳定行为。了解驱动这种动态行为的机制应该有助于我们控制阴燃系统，甚至可以设计出理想的阴燃动力学。该项目包括开发和扩展高性能计算算法以及分析渐近方法来研究非稳态阴燃，然后使用这些技术来描述这些复杂阴燃波的动力学和转变的细节。这项工作介绍的解决方法和阴燃动力学的具体描述将增加我们对阴燃过程和向燃烧过渡的理解。此外，这些技术很可能适用于其他燃烧领域和多孔介质中的流动问题。这个项目应该引起科学家的兴趣，他们使用渐近方法，使用高性能计算的自适应数值方法，研究具有多个解的系统，对多个时间尺度的解的稳定性问题感兴趣，或者对混沌解的发展感兴趣。消防安全专家和燃烧控制工程师将特别感兴趣，他们希望了解接近灭火极限的阴燃动力学，从阴燃到燃烧的转变以及阴燃在材料中传播的模式。

DMS - 9971881Non-steady Solutions of Models Describing Smoldering CombustionDaniel SchultColgate UniversityAbstractSmoldering combustion refers to combustion in which the primary reaction process involves both solid and gaseous reactants instead of the gas/gas reactions seen in common flames. Smoldering often occurs when oxidizer supply to the reaction is limited, for example because it must flow through porous media to reach the reaction site. Models of smoldering combustion require a description of porous fluid flow as well as a description of the reaction process. The resulting partial differential equations are highly nonlinear, making description of solutions difficult. Numerical simulations involving adaptive methods which change resolution as the process evolves have been able to approximate steady solutions to these models in some detail. Asymptotic methods have also been successful in describing steady and slowly varying approximate solutions to these models. The proposed project involves extending both asymptotic and numerical methods to the study of non-steady solutions and then using these techniques to describe the details of the dynamics and transitions of these solutions. This project should be of interest to scientists using asymptotic methods, using adaptive numerical methods, studying systems with multiple solutions, interested in issues of stability of solutions with many time scales, or interested in the development of chaotic solutions. It will be of particular interest to fire safety experts who wish to understand dynamics of smoldering near extinction limits, transitions from smoldering to flaming and patterns of smolder propagation through materials.Smoldering combustion is the burning of a solid without an airborne flame. It is of interest for fire safety not only as a precursor to flaming, but also because it tends to release large quantities of toxic gases. Smoldering is also used in the design of timing devices (ignition fuses), and material synthesis processes such as self-propagating high-temperature synthesis. Understanding the mechanisms and processes behind smoldering can enhance fire safety as well as allow better control for engineering uses of smoldering combustion. Models of smolder processes involve highly nonlinear partial differential equations making description of solutions difficult. Approximate descriptions exist for steady uniform propagation and slowly varying propagation, but smoldering often involves complicated non-steady behavior. Understanding the mechanisms which drive this dynamical behavior should help us control smoldering systemsand may even allow design of desirable smolder dynamics. The proposed project involves developing and extending high-performance computingalgorithms as well as analytical asymptotic methods to the study of non-steady smolder and then using these techniques to describe the details of the dynamics and transitions of these complex smolder waves. The solution methods introduced by this work and the specific descriptions of the dynamics of smoldering will increase our understanding of the smoldering process and transitions to flaming. In addition, the techniques will likely be applicable in other areas of combustion and problems of flow in porous media. This project should be of interest to scientists using asymptotic methods, using adaptive numerical methods for high-performance computing, studying systems with multiple solutions, interested in issues of stability of solutions with many time scales, or interested in the development of chaotic solutions. It will be of particular interest to fire safety experts and combustion control engineers who wish to understand dynamics of smoldering near extinction limits, transitions from smoldering to flaming and patterns of smolder propagation through materials.