Stoichiometry and Flameholder Effects on a One-Dimensional Flame

Abstract

The steady one-dimensional isobaric combustion of a gaseous premixture of fuel and oxidant under a direct one-step irreversible Arrhenius-type exothermic chemical reaction is studied analytically for constant, but general, Lewis-Semenov number. Limit-process expansions are used to obtain solutions in the physically interesting limit of activation temperature large relative to the hot-boundary temperature. The eigenvalue or critical flow speed for an adiabatic system is established as a function of departure from stoichiometry. It is emphasized that, for relatively small departures from stoichiometry, the bimolecular system behaves as a monopropellant decomposition, to lowest order of approximation, because the richer reactant is effectively undepleted. The porous-disk-type flameholder for a flat-flame burner is modeled as a (nonadiabatic) heat source (supercritical flow speed) or heat sink (subcritical flow speed). The flame stand-off distance and the amount of departure of the hot-boundary temperature from the adiabatic flame temperature are obtained as functions of flow speed and stoichiometry. It is noted that for a nonidistributed heat source/sink, the heat transfer to/from the flameholder is a unique function of flow speed, provided only that the heat transfer is less than that derived from combustion of the premixture. The reliability of evidence for two flame speeds for spatially distributed heat losses is critically reviewed.