The asymptotic structure of counterflow diffusion flames for large activation energies

Abstract

The structure of steady state diffusion flames is investigated by analyzing the mixing and chemical reaction of two opposed jets of fuel and oxidizer as a particular example. An Arrhenius one-step irreversible reaction has been considered in the realistic limit of large activation energies. The entire range of Damköhler numbers, or ratio of characteristic diffusion and chemical times, has been covered. When the resulting maximum temperature is plotted in terms of the Damköhler number (which is inversely proportional to the flow velocity) the characteristic S curve emerges from the analysis, with segments from the curve resulting from: 1. (a) A nearly frozen ignition regime where the temperature and concentrations deviations from its frozen flow values are small. The lower branch and bend of the S curve is covered by this regime. 2. (b) A partial burning regime, where both reactants cross the reaction zone toward regions of frozen flow. This regime is unstable. 3. (c) A premixed flame regime where only one of the reactants leaks through the reaction zone, which then separates a region of frozen flow from a region of near-equilibrium. 4. (d) A near-equilibrium diffusion controlled regime, covering the upper branch of the S curve, with a thin reaction zone separating two regions of equilibrium flow. Analytical expressions are obtained, in particular, for the ignition and extinction conditions.