The Dynamics of Flame Fronts - Asymptotics and Computations

本研究的目的是通过数学建模来获得对实际燃烧系统中发生的复杂过程的基本理解。该工作关注的是多维火焰锋面的传播，重点是它们与下伏流的相互作用。一组问题涉及火焰在通道和裂缝中的传播，这在许多应用中是相当有趣的，在这些应用中，火焰的穿透可能是有利的，如在小型燃烧装置中，或有害的，如在内燃机的缝隙体积中。第二组问题与边缘火焰有关，它对许多应用中出现的火焰稳定和升起现象至关重要，例如家用燃烧器和炉子。由于高应变或热损失过大，边缘火焰在火焰界面上形成孔洞的演化中起着重要作用，因此是湍流扩散火焰动力学的基础。对这些复杂现象的理解将通过构建包含当前问题的必要物理成分的模型，通过渐近技术和数值方法构建数学模型的解，并将结果与实验观察结果进行比较来实现。燃烧提供了我们今天消耗的大部分能量。重要的是要确保以最有效的方式利用燃烧过程，并以这种方式尽量减少其对环境的不利影响。这项研究将提供对火焰锋面动力学、火焰与底层流场的相互作用、可燃性极限以及与燃烧过程相关的内在不稳定性的基本理解。这些知识将对未来的工业燃烧设计和新兴的微推进技术产生影响，从而提高能源利用率，减少污染物。通过参与这项研究项目所培养的学生将对国家的教育和研究需求有价值。

The objective of this research is to gain fundamental understanding of the complex processes occurring in practical combustion systems through mathematical modeling. The work is concerned with the propagation of multi-dimensional flame fronts with emphasis on their interaction with the underlying flow. One set of problems address the propagation of flames in channels and cracks, which is of considerable interest in a number of applications where the penetration of the flame may be favorable, as in miniaturized combustion devices, or detrimental, as in crevice volumes of an internal combustion engine. The second set of problems is concerned with edge-flames, which are of fundamental importance to the phenomena of flame stabilization and liftoff occurring in many applications such as household burners and furnaces. Edge-flames play an important role in the evolution of holes created on the flame interface because of high strain or excessive heat loss, and thus are fundamental to the dynamics of turbulent diffusion flames. Understanding of these complex phenomena will be achieved by constructing models that contain the necessary physical ingredients of the problem at hand, constructing solutions to the mathematical models by means of asymptotic techniques and numerical methods, and comparing the results with experimental observations. Combustion provides the majority of the energy that we consume today. It is important to ensure that combustion processes are utilized in the most efficient way and in such a way to minimize their adverse effect on the environment. This research will provide fundamental understanding of the dynamics of flame fronts, the interaction of a flame with the underlying flow field, inflammability limits, and intrinsic instabilities associated with the burning process. This knowledge will have an effect on future industrial combustion design and emerging micropropulsion technologies, resulting in improved energy utility and reduction of pollutants. Students trained through involvement in this research project will become valuable to the educational and research needs of the country.