层焰系统奇点结构的研究

在一定的假设条件下，将气体燃烧的物理模型简化为层焰系统．借助于热力学理论和相关的守恒定律建立了层焰系统的数学模型并对其进行了深入地分析．利用常微分方程的定性理论和方法，结合燃烧的实际需要，对应于参数的不同取值，研究了位于瑞利线上奇点的个数和位置，确定了暴燃区和爆炸区内不同奇点的定性结构及其稳定性，给出了在反应速度-滞止焓平面及燃烧速度-滞止焓平面内层焰系统轨线的相图．

Study on the Structure of Singular Points of Laminar Flame System

Under some certain assumptions, the physical model of the air combustion system was simplified to a laminar flame system. The mathematical model of the laminar flame system, which was built according to thermodynamics theory and the corresponding conservative laws, was studied. With the aid of qualitative theory and method of ordinary differential equations, the location of singular points on the Rayleigh curves is determined, the qualitative structure and the stability of the singular points of the laminar flame system, which are located in the areas of deflagration and detonation, are given for different parameter values and uses of combustion. The phase portraits of the laminar flame system in the reaction_stagnation enthalpy and combustion velocity_stagnation enthalpy planes are shown in the corresponding figures.