An analytical model for predicting the flame length of fire lines and tree crown scorching

Abstract

In forest fires, the fire plume can heat tree crowns and cause the mortality of live vegetation, even though the surface fire spread is of low burning intensity. A lot of empirical or semi-empirical correlations have been built to link the fire intensity and flame height to the crown scorch height. These correlations lack the basic physical processes of heat transfer and thermal response of needles and leaves. Besides the flame height, the fire plume temperature and velocity are also of great importance to quantify the heat transfer to the tree crown. Accordingly, an analytical model, derived from a system of differential equations, describing the conservation of mass, momentum, energy, and chemical composition, is proposed to predict the properties of a fire plume from a line fire. The flame height predicted by the analytical model matches experimental measurements of small, medium, and large line fires, showing a considerable robustness of the proposed model. With an assumption of the lethal temperature of live vegetation, the analytical model can also predict the crown scorch height against available empirical correlations and experimental data. In addition, an analysis of the effect on the flame length of the distance between the fire and the ground surface indicates that it would be better to simulate the wildland fire front by a gaseous line fire above the ground surface. The effect of ambient air temperature and fireline residence time (or heating time of foliage) on the crown scorch height is also quantified. It is found that the hot plume can heat the live foliage to reach a lethal temperature of 60°C under a heating time of 60 s.