Evaluating a Simple Model for Laminar-Flame-Propagation Rates. I. Planar Geometry

Abstract

A comparison with experimental dame-speed data is made for results from a simple formulation. conveniently reducible to quadrature, of laminar isobaric flame propagation in an initially homogeneous gaseous mixture. A direct one-step irreversible bimolecular second-order chemical reaction with large Arrhenius activation energy is adopted, but account is taken of the modified exothermicity owing to partial dissociation of the product species and to other causes of incomplete oxidation. The effects arising from differing diffusivities for heat transfer and reactant-species transport arc developed to within the limitations of the model. A tractable general expression is obtained for the steady-laminar-flame-propagation speed, by exploitation of the two-zone (convective-diffusive, diffusive-reactive) deflagration-wave structure. For simple-fuel/air mixtures, the predicted variation of flame speed with equivalence ratio φ agrees fairly well with experimental data, with the provision that (1) the cold-mixture transport properties are evaluated for the pertinent value of φ, and (2) the overall activation energy, taken lo be invariant with φ, is ascribed values in the 10–15 kcal/mole range. In particular. The experimentally observed off-stoichiometric (often fuel-rich) condition for peak flame speed in simple-fuel/air premixtures is recovered. However, for simple-fuel/oxygen mixtures, the predictions deviate from the data, although the sense of the stoichiometry for which the peak speed occurs is recovered. Finally, observations concerning the transient planar deflagration wave are made, as background useful for a study of spherical flame propagation, lo be reported separately.