THEORY OF FLAME SPREAD OVER A SOLID FUEL INCLUDING FINITE-RATE CHEMICAL-KINETICS

A theory for the steady-state flame spread over a thermally thin solid fuel is developed in this study. The model considers a laminar diffusion flame in a uniform opposed flow and includes the two-dimensional, elliptic, gas-phase energy, and species equations with one-step overall chemical reaction and second-order, finite-rate Arrhenius kinetics. The unsteady, solid-fuel equations neglect heat conduction ahead of the flame but include transient heating and Arrhenius pyrolysis kinetics and are coupled to the quasisteady gas phase. The equations are solved in the laboratory coordinate system. In this study the two-dimensional distributions of temperature and species are obtained, including the low reactivity zone in the flame region. The solid-fuel surface profiles indicate a region of almost uniform temperature (vaporization temperature) during pyrolysis for some parameter values; however, the value is not universally constant for the fuel and does depend on the ambient parameters (pressure, oxygen mass fraction, and magnitude of opposed velocity). The dependence of the flame-spread rate on the ambient parameters is investigated, and qualitative agreement is obtained with experimental results in the near-extinction-limit region. Quantitative agreement with experimental data depends on the choice of parameter values, especially the gas-phase kinetics model parameters, which are generally unknown. The flame-extinction limits due to increased opposed velocity, reduced pressure, and reduced ambient oxygen mass fraction are all obtained in the results calculated from this theory. © 1979.