A Theoretical Description of Flame Spreading over Solid Combustibles in a Quiescent Environment at Zero Gravity

Abstract

Abstract A theoretical model is presented that can be used to predict the structure and rate of spread of an attached diffusion flame moving over a thermally thin, pyrolyzing combustible placed in a gravity-free, quiescent, oxidizing environment. The gas-phase model includes steady-state, two-dimensional momentum, energy, and species equations while the solid-phase model consists of continuity and energy equations, the solution to which provide boundary conditions for the gas-phase problem. The spread rate appears as an eigenvalue in both the gas- and solid-phase equations. The numerical procedure developed to solve the system of equations is stable even for spread rates comparable to normal velocities present at the fuel-gas interface. Solid fuel pyrolysis is modelled using a first-order Arrhenius decomposition while both finite-rate and infinite rate chemistry in the gas phase are considered. Computed spread rates increase with increasing oxygen concentration in the ambient and are generally a factor of two to three larger than those measured in drop towers due, most likely, to neglect in the model of the effects of solid-surface and/or gas-phase radiation. Results on the effects of variable gas properties and momentum sources arising from the compressible nature of the How are also presented.