Flame Propagation with a Sequential Reaction Mechanism

Abstract

The steady propagation of a flame through a premixed combustible mixture is studied for the case in which the flame is characterized by the production and depletion of a significant intermediate species. The overall chemical reaction mechanism is of the sequential type and is represented by $A + \nu_A O \to \mu _I I,I + \nu_1 O \to \mu _p P$, where A is the fuel, O is the oxidizer, I is the intermediate species, P is the product, and $\nu _A ,\mu _I ,\nu_I ,\mu _p $ are stoichiometric coefficients. We employ the method of matched asymptotic expansions to derive a solution for large activation energies, in which case both chemical reactions are confined to a thin layer. The (small) separation distance H between the points where the two reactions go to completion and the propagation velocity U play the role of eigenvalues and are determined as functions of standard flame parameters. The formula for H also represents the effective spatial distance between production and depletion of the intermediate species and is thus a measure of the flame thickness. It may also be interpreted as a measure of the maximum concentration of the intermediate species.