A model of opposed-flow flame spread over charring materials

Abstract

This paper presents a theoretical description of a diffusion flame spreading against the wind on a semiinfinite charring solid. It extends the previous flame spread models on “vaporizing” solids to charring materials like wood and provides a realistic description of the gas phase. To make the problem analytically tractable, a mixture fraction approach is used in the gas phase and the no-slip boundary condition is satisfied only for x >0. In the solid phase, the charring solid is assumed to decompose abruptly (endothermically or exothermically) into char and fuel gases at a specified pyrolysis temperature. The steady-state coupled elliptic equations for conservation of energy, mixture fraction, and momentum in the gas phase and conservation of energy in the char and the pristine solid are solved by using orthogonal parabolic coordinates. A general analytical solution is presented that reduces to de Ris's flame spread formula in the limit of zero char thickness and with similar assumptions. The growing char layer in the solid phase has considerable influence on the flame spread rate. It is seen that formation of a thicker char layer significantly retards the spread rate. Unique steady-state solutions for the parabolic char-material interface were found to exist only for Stefan number >−1. For Stefan number=−1 (i.e., exothermic), two solutions were found. One of these solutions corresponds to the location of the char-solid interface at infinity, indicating the likelihood of a thermal runaway. This happens regardless of the property values.