Asymptotic Analysis of Flame Structure with Real Chemistry

这项研究将渐近方法应用于实际可燃混合物中火焰结构的分析，该方法涉及到微分方程中出现的参数的大小展开。通过对守恒方程进行无量纲化，识别出大小参数。这些参数包括导致活化能渐近的活化能，导致Damkohler数渐近的反应速率的大小，以及导致速率比渐近的反应速率比。基本步骤的速率参数取自关于反应速率实验的文献。参数极限值的识别简化了守恒方程，使解在很大程度上可以解析获得，而不需要对整个守恒方程进行数值积分。这项研究将针对涉及一氧化碳、氢和氧的碳氢氮系统的预混火焰和扩散火焰的结构差异，以及这些火焰的内在稳定性和应变的影响进行研究。将特别注意氢-氧系统、含卤素系统、较高碳氢化合物以及可能还有甲醇的有用简化方案的推导和应用。这些方法通常会得到感兴趣的量的公式，如燃烧速度，并且这些公式通常包含由常微分方程组的两点边值问题的数值积分确定的参数。由于这些微分方程式比初始微分方程式简单得多，所以可以得到完整的参数解，而不是局限于特定条件的解。因此，更好地了解火焰结构，识别燃烧过程的基本方面，消除不起重要作用的不必要的并发症。

This research applies asymptotic methods, involving expansions for large and small values of parameters appearing in differential equations, to the analysis of structures of flames in real combustible mixtures. Through nondimensionalization of the conservation equations, large and small parameters are identified. These parameters involve activation energies leading to activation-energy asymptotics, magnitudes of reaction rates leading to Damkohler-number asymptotics, and ratios of reaction rates leading to rate- ratio asymptotics. Rate parameters for elementary steps are taken from the literature on reaction rate experiments. The identification of limiting values of the parameters simplifies the conservation equations and enables solutions to be obtained largely analytically without resort to numerical integration of the full set of conservation equations. The research will address structural differences between premixed flames and diffusion flames for hydrocarbon-oxygen-nitrogen systems for systems involving carbon monoxide, hydrogen and oxygen, as well as the intrinsic stability and influences of strain for these flames. Special attention will be paid to the derivation and application of useful reduced schemes for hydrogen-oxygen systems, for systems containing halogens, for higher hydrocarbons, and possibly also for methanol. The methods typically lead to formulas for the quantities of interest, such as burning velocities, and the formulas usually contain parameters determined by numerical integrations of two-point boundary-value problems for ordinary differential equations. Since these differential equations are much simpler than the starting differential equations, full parametric solutions are obtained, rather than solutions restricted to specific conditions. As a consequence, a better understanding of flame structure ensues, the essential aspects of the combustion processes are identified, and inessential complications that play no significant role are eliminated.