Asymptotic Analyses of Flames with Real Chemistry

这个程序应用渐近方法-参数的大值和小值出现在微分方程参数展开-在实际可燃混合物的火焰结构的分析。从化学动力学实验文献中获取基本化学步骤的速率参数，通过对守恒方程的无量纲化，确定适当的大、小参数。这些参数通常涉及活化能，导致活化能渐近，或基本步骤的反应速率比，产生速率比渐近。参数极限值的识别简化了守恒方程，并允许在很大程度上用解析方法获得解，而无需对整个守恒方程进行数值积分。这些方法通常会得到有关量的公式，例如燃烧速度和消光应变率，这些公式通常包含由常微分方程两点边值问题的数值积分确定的参数。由于这些方程比初始方程简单得多，因此得到了全参数解，而不是局限于特定条件的解。因此，对火焰结构的更好理解得到了发展，燃烧过程的基本方面得到了识别，并且消除了不起重要作用的非必要并发症。这种方法已经在之前的臭氧分解火焰、甲烷火焰和氢火焰的研究中完成，例如，对后两种火焰分别产生了良好的四步和两步机制。目前的计划将解决高碳氢化合物火焰、含卤素的氢火焰、涉及氮化学的火焰和甲醇火焰，以及解决内在稳定性和应变对火焰的影响问题。本课程将特别关注简化动力学格式的推导，以供实践工程师在燃烧设计应用中使用。此外，这些结果将有助于我们对火焰传播，火焰结构和熄灭机制的一般知识。

This program applies asymptotic methods--parameter expansions for large and small values of parameters appearing in differential equations--to the analysis of structures of flames in real combustible mixtures. Rate parameters for elementary chemical steps are taken from literature on chemical-kinetic experiments, and through nondimensionalization of the conservation equations, appropriate large and small parameters are identified. These parameters typically involve activation energies, leading to activation-energy asymptotics, or ratios of reaction rates of elementary steps, yielding rate-ratio asymptotics. Identification of limiting values of the parameters simplifies the conservation equations and allows solutions to be obtained largely analytically, without resort to numerical integration of the full set of conservation equations. The methods typically lead to formulas for the quantities of interest, such as burning velocities and extinction strain rates, and the formulas usually contain parameters determined by numerical integrations of two-point boundary-value problems for ordinary differential equations. Since these equations are much simpler than the starting equations, full parametric solutions are obtained, rather than solutions restricted to specific conditions. As a consequence, better understanding of flame structure is developed, the essential aspects of the combustion process are identified, and non-essential complications that play no significant role are eliminated. This type of approach has been completed in a previous study for the ozone decomposition flame, for methane flames, and for hydrogen flames, for example, yielding good four-step and two-step mechanisms for the last two flames, respectively. The current program will address higher hydrocarbon flames, hydrogen flames containing halogens, flames involving nitrogen chemistry, and methanol flames, as well as addressing issues of intrinsic stability and influences of strain on flames. Special attention will be paid to the derivation of reduced kinetic schemes of use to the practicing engineer in combustion design applications. In addition, the results will contribute to our general knowledge of mechanisms of flame propagation, flame structure, and extinction.