Strained premixed flames: Effect of heat-loss, preferential diffusion and reversibility of the reaction

Abstract

We provide an analytical description of the effect of preferential diffusion and volumetric heat-loss on strained premixed flames within a reversible chemistry model. The model comprises a single reversible reaction of the form F⇌P whose forward and backward rates follow an Arrhenius law. An asymptotic analysis of the problem is carried out in the limit of infinitely large activation energy of the forward reaction. The study allows for non-unit Lewis numbers for the fuel F and the product P. Two main contributions are made.

The first contribution consists in identifying the fundamental differences in the asymptotic description of the non-adiabatic flame between the reversible and irreversible cases, and resolving the difficulties by a suitable generalization of the so-called near-equidiffusion flame approximation to the reversible case, including the derivation of appropriate jump conditions at the reaction sheet. This is used to demonstrate that the one-step reversible chemistry model is reducible to the classical irreversible chemistry model, provided that an effective reduced Lewis number and an effective heat-loss parameter are used.

The second contribution is the determination of the domain of the solutions and their multiplicity, for selected values of , in the -ε plane, where ε is a non-dimensional measure of the strain rate. For , the diagrams are found to consist of four regions with one, two, three, and four solutions respectively, including the frozen solution. For , an additional region with three solutions is identified. For larger values of , the two regions with three solutions merge, and the region with four solutions is of insignificant size. Our diagrams are found to be in good agreement with, and complementary to, numerically determined diagrams in flammability limit studies based on one-step and detailed chemistry models. They are also a valuable component in studying non-adiabatic premixed edge-flames.

Keywords:

• premixed flames
• reversible reaction
• large activation energy asymptotics
• flammability limits
• non-adiabatic flames
• edge-flames

Notes

1. See Equation (39) below.

2. To avoid possible confusion, we note that superscripts on the variables Y_F , Y_P , θ or any function of these, such as φ in (11), indicates orders of expansion in terms of the small parameter β⁻¹.

3. The reader who is not interested in reversibility needs only set and .

4. A decreasing equivalence ratio in these references corresponds to an increasing non-dimensional heat-loss in the present paper.

5. Compare in particular the large Lewis number case of Figure 16 of [5] to the bottom subfigure of Figure 5 of the present paper.