Forced cocurrent smoldering combustion

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An analytic model of the propagation of smoldering combustion through a very porous solid fuel is presented. Here smoldering is initiated at the top of a long, radially insulated, uniform fuel cylinder, so that the smolder wave propagates downward, opposing an upward forced flow of oxidizer. Because the solid fuel and the gaseous oxidizer enter the reaction zone from the same direction, this configuration is referred to as cocurrent (or premixed-flame-like). It is assumed that the propagation of the smolder wave is one-dimensional and steady in a frame of reference moving with the wave. Buoyancy is included and shown to be negligible in the proposed application of a smoldering combustion experiment for use on the Space Shuttle. Radiation heat transfer is incorporated using the diffusion approximation and smoldering combustion is modeled by a finite rate, one-step reaction mechanism. Because the solid and the gas move at different velocities, both the downstream temperature, T f, and the smolder velocity, ν, are eigenvalues. The dimensionless equations are very similar to those governing the propagation of a laminar premixed flame. A straightforward extension of the activation energy asymptotics analysis presented by Williams for premixed flames yields an expression for a dimensionless eigenvalue determining T f. A global energy balance provides a relation for the smolder velocity, ν. Predictions are compared with the experimental findings of Rogers and Ohlemiller and with the numerical results of Ohlemiller, Bellan, and Rogers. Key results include (1) for a given solid fuel, T f depends only on the initial oxygen mass flux, m ̇ oi ″ , and increases logarithmically with m ̇ oi ″ ; (2) ν increases linearly with m ̇ oi ″ and at fixed m ̇ oi ″ , increasing the initial oxygen mass fraction, Y oi, increases ν; (3) steady smolder propagation is possible only for Y oi ≥ c eff (T f − T i ) Q , with extinction occurring when all of the energy released in the reaction zone is used to heat the incoming gas. General explicit expressions for T f and ν are presented.