Understanding flame extinction in timber under external heating using high-activation energy asymptotics

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.