Correlation of Burning Rate with Spread Rate for Downward Flame Spread Over PMMA

Abstract

Burning rate of solid fuel and laminar flame spread rate are both well studied topics for flame spread in downward configuration. Yet, despite well-developed theories, not much experimental data is available to correlate the two. In this work, experiments are performed under ambient conditions in downward spread configuration for a wide range of thicknesses (2 mm to 24 mm) for flat samples of Poly-Methyl Methacrylate (PMMA). The samples are held by two ceramic plates in order to obtain a two-dimensional propagation that is independent on the sample width. By analyzing videos of the experiments, the instantaneous spread rate is obtained using a recently developed MATLAB based tool. The shape of the pyrolyzing fuel is carefully measured after extinguishing the flame during a steady propagation. The spread rate and the burn angle, which is defined as the angle subtended by the pyrolyzing surface with respect of the fuel surface, are correlated, producing an expression for the burning rate in terms of the burn angle and flame spread rate. As the fuel thickness is increased, the burn angle and burning rate decrease and reach asymptotic limits for thermally thick fuels, in analogy with the spread rate limit. The comparison with data from literature suggests that in the thick limit the value of mass flux for PMMA (about 10 g/m² s) tends to the one of non-spreading flames. The presented geometrical approach to study the downward spread problem avoids the use of the B number and local gradients in order to calculate the mass burning rate of the fuel.