A model for the wind-blown flame from a line fire

Abstract

A one-dimensional model is developed for the structure of the wind-blown, turbulent flame from a line fire in which buoyancy is the principal source of vertical momentum. A one-step, second-order bimolecular reaction between fuel and air is used, with rate proportional to the strain rate of the mean streamlines of the flame fluid flow. Air accretion into the flame fluid flow is assumed to be proportional to incident windspeed. The flame tip is defined to occur at the height at which the mean temperature falls to 500°K. Numerical examples are presented for flames in uniform wind, and approximate expressions are found for flame height, length, and tilt angle. The flame height is found to correspond within ± 30% to the height at which 10 times the stoichiometric requirement of air is incorporated into the flow, and the flame tilt angle is found to be nearly constant with height. The square of the tangent of the flame tilt angle from vertical is found to be 3 2 the Froude number based on flame height, the numerical factor being dependent only on the flame tip temperature. Generally satisfactory agreement is found with experimental work on flame geometries. An additional model is invoked to relate the thermochemical properties, and the rate of generation, of fuel gas released from burning pine needle beds to the moisture content of the pine needles and the fuelbed weight loss rate. These relations permit comparison of predicted and observed flame dimensions for pine needle beds burned in a wind tunnel. The predictions of the model presented here match observed flame dimensions somewhat better than do the predictions of available empirical relations.