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 引用本文: 陈正. 奇异摄动在层流预混火焰理论研究中的应用[J]. 力学学报, 2018, 50(6): 1418-1435.
Chen Zheng. APPLICATION OF SINGULAR PERTURBATION IN THE ANALYSIS OF LAMINAR PREMIXED FLAMES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1418-1435.
 Citation: Chen Zheng. APPLICATION OF SINGULAR PERTURBATION IN THE ANALYSIS OF LAMINAR PREMIXED FLAMES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1418-1435.

## APPLICATION OF SINGULAR PERTURBATION IN THE ANALYSIS OF LAMINAR PREMIXED FLAMES

• 摘要: 奇异摄动被广泛应用于求取力学问题的近似解.一个典型问题就是流体力学中的边界层.郭永怀先生曾发展了适用于平板黏性流动边界层问题的奇异摄动理论.类似于流体力学中的边界层,燃烧研究中的层流预混火焰也可以通过奇异摄动理论进行分析,在燃烧研究中通常称其为大活化能渐近分析.本文介绍了大活化能渐近分析在一维平面预混火焰和球形传播火焰中的应用及相关研究进展.首先介绍了预混火焰结构及其涉及的不同特征尺度,分析了大活化能条件下出现的特征尺度分离,并给出了关于平面预混火焰大活化能渐近分析的详细推导,讨论了热辐射对火焰传播的影响;然后介绍了大活化能渐近分析在点火与球形传播火焰方面的应用,指出了只有能够同时描述点火与球形火焰传播的理论才能准确地预测临界点火条件,并讨论了考虑链式反应的点火与火焰传播理论,分析了热辐射对球形火焰传播的影响,给了关于火焰稳定性理论研究的发展趋势.最后,基于当前研究进展对未来的研究方向进行了展望,其中涉及多步化学反应、低温冷火焰、复杂流动、辐射重吸收等.

Abstract: Singular perturbation is widely used to obtain the approximate solutions for mechanical problems. A typical problem is the boundary layer in fluid mechanics. Yung-Huai Kuo has developed the singular perturbation theory for the boundary layer over a plate. Similar to the boundary layer in fluid mechanics, the laminar premixed flame in combustion can also be analyzed by the singular perturbation method, which is usually called as the large-activation-energy asymptotics. The laminar premixed flame structure consists of the preheat zone, reaction zone, and equilibrium zone. Under the limit of the large activation energy, the chemical reaction rate is very sensitive to the temperature and thereby chemical reaction only occurs in the very thin reaction zone. The ratio between the reaction zone thickness and the preheat zone thickness is a small parameter, based on which the asymptotic analysis can be conducted for a laminar premixed flame. This paper reviews the application and progress of the large-activation-energy asymptotic analysis in the one-dimensional planar premixed flame and spherically propagating flame. First, the structure of the premixed flame and its different characteristic length scales are introduced. The length scale separation due to large activation energy is analyzed. The detailed derivation of the large-activation-energy asymptotic analysis of a planar premixed flame is presented. The analytical solutions for the preheat zone, reaction zone, and equilibrium zone are first sepratedly obtained and then matched aound the interfaces among these three zones. The effects of radiation heat loss on premixed planar flames are discussed. Then, the application of the large-activation-energy asymptotic analysis to the ignition and spherically propagating flame is introduced. It is pointed out that in order to accurately predict the critical ignition conditions, the theory should be able to describe both the ignition kernel development and the spherical flame propagation afterwards. The ignition and flame propagation theory considering chain reactions is discussed, and the trend of theoretical research on flame instability is described. Moreover, the effects of radiation heat loss on spherical flame propagation are discussed. Finally, the future research directions are prospected based on the current research progress, which includes multi-step chemistry, low-temperature cool flame, complicated flow and radiation reabsorption.

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