Evolution Equations in Modeling Chemically Reacting Flows

马塔隆9703716建议的工作目标是通过渐近和摄动方法并辅之以数值计算来推导和分析简单的反应流动系统的数学模型。将要解决的问题与实验中观察到的、尚未完全理解的现象有关。它们分为两类：第一类问题涉及预混火焰在管道中的传播，第二类问题涉及液体燃料蒸发引起的扩散火焰(非预混燃烧)。这些问题的数学表述可以归结为一个或几个演化方程，这些方程包含物理问题的主要成分，并需要用数值方法求解。对于预混火焰在管道中的传播，演化方程采用积分-微分方程组的形式，描述了火焰锋面的瞬时形状和位置。对于液膜的燃烧，人们通常可以找到两个方程：一个是液气两相界面的动力学方程，另一个是扩散火焰片的方程，扩散火焰是燃料蒸汽与环境氧化剂燃烧的界面。燃烧过程极其复杂；它们包括与能量产生和热传递、化学反应的速率和机制、流体流动和质量传输有关的主题。它们涵盖了广泛的重要工程技术以及主要的社会和环境问题。了解人们在各种燃烧系统中观察到的复杂现象的基本方法是通过数学建模。这种方法使人们能够确定导致观察到的现象的潜在物理机制，研究各种物理参数之间的相互作用，并探索这种相互作用是否导致了观察到的行为。对实验和设计的深入理解往往会带来新的实验和设计方向的建议。这项研究中的问题涉及预混火焰，涉及内燃机和航空航天推进系统，其中燃料和氧化剂在点火前紧密混合，以及液体燃料的燃烧，与意外溢出和火灾蔓延有关，在特殊情况下，可用环境氧化剂可能发生燃烧。

Matalon 9703716 The objectives of the proposed work is to derive and analyze simple mathematical models of reacting flow systems by means of asymptotic and perturbation methods supplemented by numerical computations. The problems that will be addressed are related to phenomena that have been observed experimentally and are not yet completely understood. They fall in two categories: the first class of problems is concerned with premixed flames propagating in tubes, while the second class is concerned with diffusion flames (non-premixed combustion) that result from evaporating liquid fuels. The mathematical formulation of these problems can be reduced to a single, or a couple, of evolution equations that contain the main ingredients of the physical problem and are to be solved numerically. For premixed flames propagating in tubes the evolution equation takes the form of an integro-differential equation that describes the instantaneous shape and location of the flame front. For the burning of liquid films one finds, in general, two equations: one for the dynamics of the interface between the liquid and gas phases, and the other for the diffusion flame sheet which is the interface where the fuel vapor burns with the ambient oxidant. Combustion processes are extremely complicated; they encompass subjects concerned with energy generation and heat transfer, rates and mechanisms of chemical reactions, fluid flow and mass transport. They cover a broad range of important engineering technologies as well as topics of primary societal and environmental concerns. A fundamental way to gain understanding into the complex phenomena that one observe in various combustion systems is through mathematical modeling. This approach enables one to identify the underlying physical mechanisms responsible for the observed phenomenon, to study the interaction between the various physical parameters and to explore whether this interaction leads to the observed behavior. A deep understandin g often leadq to suggestions of new directions for experiments and design. The problems in this study are concerned with premixed flames, relevant to internal combustion engines and aerospace propulsion systems where the fuel and oxidant are intimately mixed prior to ignition, and combustion of liquid fuels, relevant to accidental spillage and fire spread where, under special circumstances, burning may occur with the available ambient oxidant.