An Asymptotic Analysis of Unsteady Diffusion Flames for Large Activation Energies

Abstract

The limit of large activation energy is studied for the process of simultaneous mixing and chemical reaction of two reactants undergoing a one-step irreversible Arrhenius reaction. Consideration is restricted to problems of the evolution type—like unsteady mixing and boundary-layer combustion—for which the solution is uniquely determined in terms of the initial conditions. The continuous transition from the nearly-frozen to the near-equilibrium regimes is described. The analysis uncovers the existence of: (i) An ignition regime, in which a mixing layer develops with only minor effects of the chemical reaction, until a thermal runaway occurs somewhere within the mixing region; at this location chemical equilibrium then is established rapidly, (ii) A deflagration regime, in which premixed flames originate from the ignition point and move through the mixing region to burn completely the reactant not in excess. And (iii) a diffusion-flame regime, in which a thin diffusion flame, that is established when the deflagration wave crosses the surface where the reactants are present in stoichiometric proportions, consumes the excess reactants that could not be burned by the premixed flame. This is accomplished by a process in which the reactants diffuse through a thick layer of reaction products. There exists experimental evidence to support this rather complex picture deduced theoretically.