The Near-Stoichiometric Behavior of Combustible Mixtures Part I: Diffusion of the Reactants†

Abstract

s-The burning rate of a fuel-oxidant mixture is invariably found by experiment to have a maximum slightly on the fuel-rich side of stoichiometry. The usual explanation is that the maximum adiabatic flame temperature is shifted there by dissociation of the products. However, several aspects of this explanation are unsatisfactory: the burning rate depends on other factors than the flame temperature, especially near stoichiometry; verification is always numerical and hence for a limited range of parameters; and cool flames, where dissociation is negligible, are excluded. The present paper is an analysis of a two-reactant model, with not necessarily equal Lewis numbers K and L for oxidant and fuel (respectively), in the absence of dissociation. In particular, it is found that the phenomenon occurs whenever K is large enough and L small enough, the precise conditions nearly always being met in practice. In other words, diffusion alone provides a satisfactory explanation. Part 11 will incorporate dissociation to show that, while it does explain the shift in maximum temperature, it has a subsidiary effect on the maximum burning rate.

Hydrodynamic theory of premixed flames: effects of stoichiometry, variable transport coefficients and arbitrary reaction orders

“…Among the earlier studies that have used a two-reactant model are the works of Sen & Ludford (1979) and Mitani (1980) who examined the dependence of the laminar flame speed on stoichiometry, and of Joulin & Mitani (1981) and Jackson (1987) who studied the stability of a planar flame in the context of a constant density model. Effects of variable transport, which are easily accounted for when studying the structure of a planar flame, have been incorporated in more general circumstances by Clavin & Garcia (1983) when examining the stability of a premixed flame and by Keller & Peters (1994) when examining transient pressure effects on the evolution of premixed flames.…”

Effects of stoichiometry on premixed flames propagating in narrow channels: symmetry-breaking bifurcations

“…The factor s L ensures that, for a given value of Φ, the burning velocity of the flame propagating in the channel, u f , equals one when the flame acquires the planar shape. This factor represents the ratio between the planar flame speed obtained with finite activation energy, S L , and the flame speed calculated by assuming infinite activation energy [21,20]…”

“…Previous theoretical analyses using the two-reactant combustion model [21,22,19] have not considered the dependence of the adiabatic temperature, the activation energy or the Lewis numbers of the reactants with the stoichiometric ratio. This was partially justified because the analysis was carried out at near-stoichiometric conditions, although the assumption can also be justified in some cases for off-stoichiometric mixtures.…”

“…, where Y Nu stands for the mass fraction of the inert gas in the fresh unburnt mixture; see [21]. Changing Y Nu in an adequate proportion (or alternatively the parameter c) the adiabatic temperature can be held constant in the experiments.…”

Asymptotic Analysis of Laminar Flame Propagation with Variable Transport Coefficients

“…Thus, although a number of analyses have allowed for either variable properties or more complicated chemistry (e.g., Clavin and Garcia, 1983;Sen and Ludford, 1979, 1981a, 1981b, in carrying the expansion only t o leading order they d o not uncover the effects sought herein. The simplification in burning-velocity evaluation no longer occurs at higher orders in j3-1 since variations in transport coefficients through the reactive-diffusive zone then become important.…”