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ON THE FAST-TIME CELLULAR INSTABILITIES OF LINAN'S DIFFUSION-FLAME REGIME

机译：扩散火焰场的快速细胞不稳定性研究

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摘要

The fast-time instability of the Linan's diffusion-flame regime is investigated asymptotically and numerically by employing the fast inner-zone time and length scales, as a model problem for the cellular instability in diffusion flames with Lewis numbers far from unity by an amount of order unity. The stability analysis revealed the full spectral nature, particularly near the saddle-node bifurcation condition corresponding to the minimum reduced Damkoehler number Δ Contrary to the conventional belief, the minimum Δ condition, commonly known as the Linan's diffusion-flame extinction condition, is not necessarily an extinction condition for flames with Lewis numbers less than unity which can survive beyond the saddle-node bifurcation condition. The cellular instability could emerge upon passing the saddle-node bifurcation condition. The cellular instability is thus observable for near-extinction diffusion flames with Lewis numbers less than unity, as predicted by the previous experimental studies and the linear stability analysis employing the NEF limit. The stable parametric regions of small wave number and Lewis number just below unity were not predicted by the fast-time instability. But these parametric regions lie in the inner parametric layer of the distinguished limit employed in this analysis, so that the leading-order behavior is not contradictory with the previous experimental and analytical results.
机译：通过使用快速的内部区域时间和长度标度，渐近地和数值地研究了Linan扩散火焰状态的快速时间不稳定性，以此作为刘易斯数远非为单位1的扩散火焰中细胞不稳定性的模型问题。秩序统一。稳定性分析揭示了完整的光谱性质，尤其是在对应于最小减小的Damkoehler数Δ的鞍节点分叉条件附近。与传统观点相反，最小Δ条件（通常称为Linan扩散火焰熄灭条件）不一定Lewis数小于1的火焰的熄灭条件，可以在鞍节点分叉条件下生存。通过鞍节点分叉条件时，可能会出现细胞不稳定性。如先前的实验研究和采用NEF极限的线性稳定性分析所预测，对于路易斯数小于1的近乎灭绝的扩散火焰，可以观察到细胞的不稳定性。小波数和刘易斯数的稳定参数区域恰好在1以下，无法通过快速时间不稳定性进行预测。但是这些参数区域位于此分析中使用的可分辨极限的内部参数层中，因此，前导行为与先前的实验和分析结果并不矛盾。

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