Forced forward smolder combustion

Abstract

We consider porous cylindrical samples closed to the surrounding environment except at the ends, with gas forced into the sample through one of the ends. A smolder wave is initiated at that end and propagates in the same direction as the flow of the gas. We employ asymptotic methods to find smolder wave solutions with two different structures. Each structure has two interior layers, i.e., regions of relatively rapid variation in temperature separated by longer regions in which the temperature is essentially constant. One layer is that of the combustion reaction, while the other is due to heat transfer between the solid and the gas. The layers propagate with constant, though not necessarily the same, velocity, and are separated by a region of constant high temperature. A so-called reaction leading wave structure occurs when the velocity of the combustion layer exceeds that of the heat transfer layer, while a so-called reaction trailing wave structure is obtained when the combustion layer is slower than the heat transfer layer. The former (latter) occurs when the incoming oxygen concentration is sufficiently high (low). Reaction trailing structures allow for the possibility of quenching if the gas mass influx is large enough; that is, incomplete conversion can occur due to cooling of the reaction by the incoming gas. For each wave structure there exist stoichiometric, and kinetically controlled solutions in which the smolder velocity is determined, respectively, by the rate of oxygen supply to the reaction site and by the rate of consumption in the reaction, i.e., by the kinetic rate. Stoichiometric (kinetically controlled) solutions occur when the incoming gas flux is sufficiently low (high). For each of the four solution types, we determine analytical expressions for the propagation velocities of the two layers, the burning temperature, and the final degree of solid conversion. We also determine analytical expressions for the spatial profiles of temperature, gas flux, and oxygen concentration. Gravitational forces are considered and are shown to have a minimal effect provided the ambient pressure is large compared to the hydrostatic pressure drop. The solutions obtained provide qualitative theoretical descriptions of various experimental observations of forward smolder. In particular, the reaction trailing stoichiometric solution corresponds to the experimental observations of Ohlemiller and Lucca, while the reaction leading stoichiometric solution corresponds to the experimental observations of Torero et al.