Upward buoyant filtration combustion

Heterogeneous combustion in a porous sample with only the top and bottom ends of the sample open to gas flow is considered. Gas enters the sample due to buoyant upward convection. That is, ignition at the bottom produces an upwardly propagating filtration combustion wave which induces hot gas to rise, thus pulling cool, fresh gas containing oxidizer in through the bottom of the sample. The gas moves through the solid products to reach the reaction zone just as in forced forward filtration combustion. In contrast to forced forward filtration combustion, in which the incoming gas flux is fixed by an external source, here the incoming gas flux is determined by the combustion process itself. That is, the incoming gas flux is determined by the burning temperature which in turn is affected by the incoming gas flux. Thus, a feedback mechanism exists which hinders ignition of the samples, but also makes the wave hard to extinguish, once it has formed. A one-dimensional model is analyzed and two types of wave structure, termed reaction-leading and reaction-trailing according as the reaction occurs at the leading or trailing edge of the heated region of the sample, respectively, are determined. For each structure, two solution modes are described, termed stoichiometric and kinetically controlled, according as the rate of oxygen supply or the kinetics controls propagation of the wave. In each of these four situations, expressions are derived for the evolution of the burning temperature, propagation velocity, incoming gas flux, degree of oxidizer consumption and degree of fuel conversion as the wave moves through the sample. In addition, profiles for the temperature are described. Analysis of the case where significant heat is lost through the sides of the sample leads to extinction limits and demonstrates the sensitivity of the wave structure to changes in external heat losses.