Natural convection effects on thermal ignition in a porous medium. I. Semenov model

V. Balakotaiah, P. Pourtalet
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引用次数: 7

Abstract

A one-dimensional diffusion-convection-reaction model is formulated to account for natural convection effects on thermal ignition in an open system consisting of a porous medium. Various limiting cases of the model are considered. A detailed analysis of the Semenov (lumped) model is presented. Explicit relations are derived for the dependence of the critical Semenov number (ψc) on the Rayleigh number (R*). It is shown that for R* → 0, ψc approaches the classical (conduction) limit e-1, while for R* ≫ 1, the ignition locus is given by the convection asymptote ψc/R* = 4 e-2. Inclusion of reactant consumption shows that the conduction asymptote disappears at B = 4 while the convection asymptote ceases to exist for B Ls < 3 + 2√2, where Ls is a modified Lewis number and B is the heat of reaction parameter. It is shown that the Semenov model has five different types of bifurcation diagrams of temperature against Rayleigh number (particle size), (single-valued, inverse S, isola, inverse S + isola and mushroom). This behaviour is found to be qualitatively identical to that of the forced convection problem investigated by Zeldovich & Zysin.
多孔介质中自然对流对热点火的影响。1 . Semenov模型
本文建立了一维扩散-对流-反应模型,以解释由多孔介质组成的开放系统中自然对流对热着火的影响。考虑了模型的各种极限情况。详细分析了Semenov(集总)模型。导出了临界塞门诺夫数(ψc)与瑞利数(R*)的显式关系。证明了当R*→0时,ψc接近经典(传导)极限e-1,而当R*→1时,点火轨迹由对流渐近线ψc/R* = 4 e-2给出。包含反应物消耗表明,当B = 4时,传导渐近线消失,当B Ls < 3 + 2√2时,对流渐近线不存在,其中Ls为修正路易斯数,B为反应热参数。结果表明,Semenov模型具有五种不同类型的温度与瑞利数(粒径)的分岔图(单值、逆S、孤立体、逆S +孤立体和蘑菇)。这种行为被发现与Zeldovich & Zysin研究的强迫对流问题的性质相同。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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