The present study analyses the flame extinction of timber under different levels of external heating and oxygen contents in the surrounding atmosphere. An existing theoretical framework conceived initially for the analysis of a counter-flow diffusion flame established above the surface of a condensed fuel is extended for charring materials to deliver a fundamental understanding of the self-extinction of timber. This study shows that the energy balance at the burning surface is influenced primarily by the magnitude of external heating conditions, which directly influences the evolution of bulk properties such as flame temperature, location, and stagnation plane position. Variations in the oxygen content had a lesser influence over these bulk properties. For all investigated conditions, the limits of the strain rate range where a flame can be sustained were shown to vary substantially, and critical Damköhler number (Da) analyses were conducted. Blow-off at high strain rates (low Da) occurs for all investigated conditions. The value of this critical Da decreases when increasing either the magnitude of the external heating or the oxygen content as flame temperature increases. Quenching at low strain rates (high Da) is only found for sufficiently low magnitudes of external heating. There, the associated critical Da increases when increasing either the external heating or the oxygen content. Above a certain degree of external heating, the flame can be theoretically sustained even at infinitely-low strain rates. By comparing these results to experimental data, the experimental critical Da at quenching was found to behave like the theoretical results but with a lower sensitivity to variations in the parameters studied. To account for this discrepancy, a fuel dilution parameter is introduced to incorporate the complex dependencies of timber decomposition and surface reactions not captured by the theoretical framework.

本研究分析了木材在不同程度的外部加热和周围大气中的氧气含量下的火焰熄灭情况。现有的理论框架最初设想用于分析在冷凝燃料表面上方建立的逆流扩散火焰，扩展到炭化材料，以提供对木材自熄的基本理解。该研究表明，燃烧表面的能量平衡主要受外部加热条件大小的影响，外部加热条件直接影响火焰温度、位置和停滞平面位置等整体特性的演变。氧含量的变化对这些整体特性的影响较小。对于所有调查条件，显示可以维持火焰的应变率范围的极限变化很大，并进行了临界 Damköhler 数 (Da) 分析。在所有研究条件下都会发生高应变率（低 Da）的吹气。随着火焰温度的增加，当增加外部加热的幅度或氧气含量时，该临界 Da 的值会降低。低应变率（高 Da）下的淬火仅在足够低的外部加热量下发现。在那里，当增加外部加热或氧含量时，相关的临界 Da 会增加。超过一定程度的外部加热，即使在无限低的应变率下，火焰理论上也可以持续。通过将这些结果与实验数据进行比较，发现淬灭时的实验临界 Da 表现得与理论结果相似，但对所研究参数的变化具有较低的敏感性。为了解决这种差异，引入了燃料稀释参数，以结合理论框架未捕获的木材分解和表面反应的复杂依赖性。