A Model for Combustion of Firebrands of Various Shapes

The lifetime of a firebrand before burning out controls the maximum distance a firebrand can travel to cause spotting. Thus, combustion of firebrands of various shapes and sizes and their burnout time during transport is studied. The analysis assumes “quasi-steady” burning. In the present context, “quasi-steady” means that the rate processes controlling the gas phase fuel consumption and energy release are much faster than the particle fuel depletion time or the gas phase transport times. The Reynolds number based on the overall particle dimension and velocity relative to the ambient flow is assumed to be small. The gas phase combustion processes are represented by the evolution of a mixture fraction variable. It is shown that the velocity field near the particle can be described by a potential flow whose functional form is determined by the mass conservation equation and that this flow satisfies the particle surface boundary conditions. Gas phase solutions are obtained for two-parameter family of firebrand shapes composed of oblate and prolate ellipsoids of revolution. Prolate ellipsoids range from a thin needle to a sphere and oblate ellipsoids range from a sphere to a thin disc. Thus, they cover all possible firebrand shapes. The ambient velocity field does not need to be aligned with the firebrand axis of symmetry, so that the composite velocity and mixture fraction fields are three-dimensional. While a variety of steady-state condensed phase models are compatible with this picture, results are first presented for an ablating solid describable by the Spalding B number. B-numbers representative of flaming combustion of wood firebrands and glowing combustion of remaining char are used. All quantities are calculated as a function of ellipsoidal aspect ratio, B number, and the Reynolds number. Surprisingly, it is found that the firebrand burnout time is shape independent. All possible shapes were considered by using oblate and prolate ellipsoids of different sizes and aspect ratios. The burnout time depends only on the firebrand mass under the assumptions used.