| Abstract: | An asymptotic analysis is presented for the ignition of a solid fuel that gasifies endothermically then reacts exothermically in the gas phase through a one-step Arrhenius process. The endothermic gasification was analyzed in an earlier paper; the present paper employs those results in treating the gas-phase reaction. It is shown that depending on values of the chemical parameters, the gas-phase ignition reaction may begin either at the time that gasification begins or during the later stage of transport-controlled gasification. In the former case, results for the gas-phase ignition time are similar to those for condensed-phase ignitions. In the latter case, a mixing layer develops in the gas-phase and moves away from the surface, the exothermic reaction being negligible until thermal runaway occurs somewhere within the mixing layer. Both early-time and late-time ignitions within the mixing layer are analyzed by solving partial differential equations derived from perturbations for large activation energies and a small ratio of gas to solid thermal responsivity. The theory serves to indicate how ignition by gas-phase reactions may be distinguished experimentally from ignition by condensed-phase or heterogenous reactions. |
