Flame spread over fuel beds: solid-phase energy considerations

Abstract

This paper reports on an analytical and experimental investigation of flame spread over the surface of a solid-fuel bed in an oxygen-inert environment. It is postulated that the processes controlling the flame-spreading phenomenon occur in a very small “ignition region” at the leading edge of the spreading flame adjacent to the surface, and attention is focused on this small region. The solid-phase energy equation is uncoupled from the gas-phase conservation equations and solved separately, retaining as a boundary condition the heat flux into the surface from the adjacent gas phase. The resulting solutions, in the form of simple algebraic equations, show clearly the different relationships between the physically important parameters associated with flame propagation over: (1) a “thick” fuel bed (thermal wave penetration into the solid beneath the ignition region much less than the fuel-bed depth), and (2) a “thin” fuel bed (subsurface temperature gradients negligible). The “critical thickness” criterion for separating the regions of thin and thick fuel-bed flame-spreading characteristics evolves as a naturally occurring parameter of the problem. The main dependence of heat flux on environmental parameters is obtained from consideration of the gas-phase conservation equations in a quiescent environment. By combining the results from the gas-phase and solid-phase analyses, simple algebraic relationships are obtained between flame-spreading velocity and parameters of theoretical and practical interest. Experimentally, using the techniques described in Ref. 1, the dependence of flame-spreading velocity on pressure level, oxidant mole fraction, diluent gas, initial temperature and fuel-bed depth is determined for polymeric and cellulosic materials. In addition, the influence of forced convective motion of the environment on flame spreading velocity is investigated experimentally. The analytical results provide excellent correlation for all data obtained in a quiescent environment, with the exception of the influence of initial temperature. Data obtained by other investigators are shown to be correlated as well. It is concluded that the role played by the solid phase in the over-all flame-spreading mechanism is generally understood, but the gas-phase processes require further definition.