An ignition-temperature model with two free interfaces in premixed flames†
An ignition-temperature model with two free interfaces in premixed flames†
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DOI：
10.1080/13647830.2016.1220625
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发表时间：
2016-09
影响因子：
1.3
通讯作者：
C. Brauner;P. Gordon;Wen Zhang
中科院分区：
文献类型：
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作者：
C. Brauner;P. Gordon;Wen Zhang
本文考虑了热扩散燃烧的着火温度零级反应模型。该模型描述了厚火焰的动力学，最近在物理和工程文献中受到了相当大的关注。该模型承认一个唯一的（平移）平面行波解。这种行波解与通常在燃烧理论中研究的行波解有很大的不同。这种行波的主要定性特征是它有两个界面：达到点火温度的点火界面和不足反应物浓度达到零的拖尾界面。我们给出了一个新的数学框架，研究细胞的不稳定性，这样的旅行前的解决方案。我们的方法允许自由边界问题的分析转换为具有完全非线性抛物方程组的边值问题的分析。后者非常适合于数学和数值分析。我们证明了存在一个临界刘易斯数，使行波解是稳定的刘易斯数低于临界值，是不稳定的刘易斯数超过这个临界值。最后，我们讨论了一个完全非线性系统，描述了扰动动力学的平面前的数值模拟结果。这些模拟揭示，特别是，一些非常有趣的“双细胞”稳定模式的弯曲燃烧锋。
In this paper we consider an ignition-temperature zero-order reaction model of thermo-diffusive combustion. This model describes the dynamics of thick flames, which have recently received considerable attention in the physical and engineering literature. The model admits a unique (up to translations) planar travelling wave solution. This travelling wave solution is quite different from those usually studied in combustion theory. The main qualitative feature of this travelling wave is that it has two interfaces: the ignition interface where the ignition temperature is attained and the trailing interface where the concentration of deficient reactants reaches zero. We give a new mathematical framework for studying the cellular instability of such travelling front solutions. Our approach allows the analysis of a free boundary problem to be converted into the analysis of a boundary value problem having a fully nonlinear system of parabolic equations. The latter is very suitable for both mathematical and numerical analysis. We prove the existence of a critical Lewis number such that the travelling wave solution is stable for values of Lewis number below the critical one and is unstable for Lewis numbers that exceed this critical value. Finally, we discuss the results of numerical simulations of a fully nonlinear system that describes the perturbation dynamics of planar fronts. These simulations reveal, in particular, some very interesting ‘two-cell’ steady patterns of curved combustion fronts.