Effective Lewis number of smoldering spread over a thin solid in a narrow channel

Smoldering combustion occurs when a solid is burned in a narrow channel between two parallel plates. A fingering pattern is then formed owing to the instability of smoldering front. The objective of this paper is to modify the theory proposed by Kagan and Sivashinsky and assess its validity by comparing its predictions with experimental data. A heat loss term that depends on channel height is newly added to the Kagan-Sivashinsky theory because the channel height is known to influence fingering instability. A linear stability analysis is then conducted, leading to the definition of an effective Lewis number, which is proposed to be the governing parameter. A series of experiments are conducted in which channel height, oxidizer velocity, and oxygen concentration are varied. Obtained fingering patterns are quantified by image analysis; the average finger width, the fraction burned, and the number of fingertip splits are calculated under each experimental condition. It is confirmed that all the experimental data can be expressed by the single parameter, i.e., the effective Lewis number. Further, theoretically predicted finger width agrees reasonably well with experimental data. (C) 2016 by The Combustion Institute. Published by Elsevier Inc.