An analysis is presented for the Burke–Schumann flame established when a fuel tank discharges with mean velocity U along a circular duct of radius a filled initially with air. Attention is focused on effects of interactions of shear with transverse diffusion resulting in enhanced longitudinal dispersion. The analysis accounts for preferential-diffusion effects arising for non-unity values of the fuel Lewis number , with the Peclet number based on the thermal diffusivity taken to be of order unity for generality. The solution to the associated Taylor-dispersion problem is described for times much larger than the characteristic diffusion time across the pipe , when the flame is embedded in a mixing region of increasing longitudinal extent moving with the mean velocity. At leading order in the limit , the longitudinal flame location, the burning rate, and the peak temperature are found to be a function of the effective Lewis number , whose value changes from for to for . As a result of this variation, the flame exhibits preferential-diffusion effects that depend fundamentally on , with important implications in designs of microcombustion devices employing narrow channels and pipes.

中文翻译：

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管道中的泰勒扩散控制燃烧

当燃料箱沿半径为 a 的圆形管道以平均速度 U 排放时，建立了伯克-舒曼火焰的分析，该管道最初充满空气。注意力集中在剪切与横向扩散的相互作用导致增强的纵向扩散的影响上。该分析考虑了燃料刘易斯数 的非统一值引起的优先扩散效应，为了一般性，基于热扩散率的佩克莱特数被认为是统一的。当火焰嵌入随着平均速度移动的纵向范围增加的混合区域中时，相关泰勒色散问题的解决方案被描述为远大于管道特征扩散时间的时间。在极限的领先顺序，纵向火焰位置，燃烧速度，并且发现峰值温度是有效路易斯数的函数，其值从 for 变为 for 。由于这种变化，火焰表现出优先扩散效应，从根本上取决于 ，对采用窄通道和管道的微燃烧装置的设计具有重要意义。