Theory of Combustion By Analytical Methods for Real Chemistry

这项研究应用偏微分方程组的数学方法来分析实际可燃混合物中燃烧过程的结构和稳定性。扩散火焰、预混火焰和爆炸在研究的不同部分进行了讨论。基本化学步骤的速率参数是从化学动力学实验的文献中估计出来的，并通过对守恒方程的无量纲化，确定了合适的大参数和小参数。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的比率，导致速率比率渐近。参数极限值的识别简化了守恒方程，使解能够在很大程度上以解析的方式获得，而不需要对整个守恒方程进行数值积分。这些方法通常会得到感兴趣的量的公式，如燃烧速度、点火或熄灭应变率以及稳定的临界条件，并且这些公式通常包含由常微分方程组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，所以得到了完整的参数解，而不是限制在特定条件下的解。结果，更好地了解了火焰的结构和稳定性，识别了燃烧过程的基本方面，并消除了不起重要作用的非基本并发症。例如，对于甲烷和氢气燃烧，这种类型的方法现在已经完成，分别产生了良好的四步和两步记忆机制。这项新的研究将涉及更高碳氢化合物燃烧、更高酒精燃烧和火焰中氮氧化物的产生，以及固有的爆轰稳定性和应变对火焰的影响。将特别注意得出有用的简化动力学方案及其对火焰和爆轰的影响。此外，还将讨论描述卤素在氢火焰中作为抑制剂或消光促进剂的影响的简化化学。这一结果与我们对火焰传播机理、火焰结构、火焰和爆震不稳定性以及点火和熄灭的认识相一致。

This research applies mathematical methods for partial differential equations to analysis of the structure and stability of combustion processes in real combustible mixtures. Diffusion flames, premixed flames and detonations are addressed in different parts of the research. Rate parameters for elementary chemical steps are evaluated from the 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, leading to rate-ratio asymptotics. 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 methods typically lead to formulas for the quantities of interest, such as burning velocities, ignition or extinction strain rates, and critical conditions for stability, 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 and stability is developed, the essential aspects of the combustion processes are identified, and nonessential complications that play no significant role are eliminated. This type of approach has now been completed for methane and hydrogen combustion, for example, yielding good four-step and two-step memchanisms, respectively. The new research will address higher hydrocarbon combustion, higher alcohol combustion, and production of oxides of nitrogen in flames, as well as intrinsic detonation stability and influences of strain on flames. Special attention will be paid to the derivation of useful reduced kinetic schemes and to their influences on flame and detonation. In addition, reduced chemistry for describing influences of halogens as inhibitors or extinction promoters in hydrogen flames will be addressed. The results constribute to our knowledge of mechanisms of flame propagation, flame structure, flame and detonation instabilities, and ignition and extinction.