Pattern formation in reverse smoldering combustion : a homogenization approach
Pattern formation in reverse smoldering combustion : a homogenization approach
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发表时间：
2012
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通讯作者：
Ekeoma R. Ijioma;T. Ogawa;A. Muntean
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作者：
Ekeoma R. Ijioma;T. Ogawa;A. Muntean
在反燃烧的框架下，研究了多孔薄材料表面指炭模式的发展。可燃介质的这一宏观特性也通过实验和现象学模型进行了研究。然而，基于材料特性的新兴图案的行为并没有得到足够的关注。从燃烧过程的微观描述出发，提出了应用均质化技术推导出的反燃烧宏观模型。采用适当的尺度参数e，在微观和宏观水平上的定性多尺度数值模拟证明了形式渐近过程的结果。我们考虑两种基于有效电导率对比的平衡模型，在简单的绝热情况下，研究烧焦材料表面不稳定指指模式的形成。新出现的模式的行为分析主要使用Peclet数作为控制参数。
The development of fingering char pattern on the surface of porous thin materials has been investigated in the framework of reverse combustion. This macroscopic characteristic feature of combustible media has also been studied experimentally and through the use of phenomenological models. However, much attention has not been given to the behavior of the emerging patterns based on characteristic material properties. Starting from a microscopic description of the combustion process, macroscopic models of reverse combustion that are derived by the application of the homogenization technique are presented. Using proper scaling by means of a small scale parameter, e, the results of the formal asymptotic procedure are justified by qualitative multiscale numerical simulations at the microscopic and macroscopic levels. We consider two equilibrium models that are based on effective conductivity contrasts, in a simple adiabatic situation, to investigate the formation of unstable fingering patterns on the surface of a charred material. The behavior of the emerging patterns is analyzed using primarily the Peclet number as a control parameter.