The Dynamics of Flame Fronts - Asymptotics and Computations

这项研究的目的是通过数学建模从根本上了解实际燃烧系统中发生的复杂过程。这项工作涉及多维火焰锋面的传播，重点是它们与底层流动的相互作用。一组问题涉及火焰在通道和裂缝中的传播，这在火焰穿透可能是有利的，如在微型燃烧装置中，或有害的，如内燃机的缝隙体积的许多应用中具有相当大的兴趣。第二组问题涉及边缘火焰，它对许多应用中发生的火焰稳定和升空现象至关重要，例如家用燃烧器和炉子。由于高应变或过多的热损失，边缘火焰在火焰界面上形成的孔洞的演化中起着重要的作用，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手头问题必要的物理成分的模型，利用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进行比较来实现。燃烧提供了我们今天消耗的大部分能源。重要的是要确保以最有效的方式利用燃烧过程，并将其对环境的不利影响降至最低。这项研究将对火焰锋面的动力学、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提供基本的理解。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和减少污染物。通过参与这一研究项目培训的学生将成为国家教育和研究需求的有价值的人。

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.