燃烧不稳定性是燃烧室中非定常的热释放和声波相互耦合、放大而产生的大幅度压力脉动现象，具有超强的破坏性。而伴随着燃烧不稳定性，熵波和涡波往往会在燃烧室中产生和传播。理论上已经证明，某些条件下熵波和涡波对燃烧不稳定性会产生关键性的影响。但目前对燃烧不稳定性导致的熵波和涡波的产生机制和规律还未研究透彻，现有的研究尤其无法包含流动马赫数和燃烧区域厚度的影响，而真实条件下流动马赫数和火焰区域厚度很可能对熵波和涡波的生成具有重要影响。因此本申请拟采取量级分析和渐近分析方法，深入研究流动马赫数和火焰厚度对熵波和涡波的影响。在此基础之上进一步的研究熵波和涡波影响下的燃烧不稳定性问题。这项工作不仅能够加深我们对于燃烧、流动和声波相互作用的物理机制的理解，也对认识发动机当中发生的燃烧不稳定性问题提供新的理论指导。

Combustion instabilities may occur in the combustors of energy systems, which can lead to large pressure fluctuations and structural damages, even catastrophic failure of a combustor. Therefore it is always meaningful to study the mechanisms and the suppressing methods of the combustion instabilities. The combustion instability is induced by the coupling of the unsteady heat release and the acoustic waves. In fact the interaction of the flame and the flow can also produce other two kinds of fluctuations, i.e., entropy and vorticity fluctuations. It has been proved that entropy and vorticity waves may have significant effects on the combustion instabilities. However the production mechanisms of the entropy and vorticity waves by the interaction of unsteady heat release, flow and acoustic waves are not clearly investigated. In the previous work the effects of the mean flow Mach number and the length of the flame area on the generation of these two kinds of waves have not yet been studied. In the present project, the generation of the entropy and vorticity fluctuations under the effects of flow Mach number and the length of the heat source region will be studied through order analysis method and asymptotic analysis method. Then the effects of entropy and vorticity waves on the combustion instabilities will be further investigated. Through the investigation, we can gain more insight into the interaction of the combustion, flow and the acoustic waves, and we will also get a better understanding and improved design tools for problems of combustion instabilities.