Asymptotic analysis of flame propagation in weakly-strained mixing layers under a reversible chemical reaction

We present an asymptotic study of triple-flames in a strained mixing layer under a reversible reaction, which extends analytical descriptions of these flames beyond the common framework of a single irreversible Arrhenius reaction and constitutes a first step towards accounting for real chemistry effects. The study is carried out in the twodimensional counterflow configuration and adopts a constant-density assumption along with a generalization of the near-equidiffusional flame (NEF) approximation to the case of a reversible reaction. This generalization involves a convenient and physically motivated distinguished limit comprising a specific scaling of the difference in the activation energies of the forward and backward reactions and of the degree of reversibility. The resulting model yields an extensive set of results for weakly strained triple-flames characterizing the combined influence of the stoichiometry and reversibility of the reaction, the strain rate, and the Lewis numbers of the reactants. The findings include the determination of the local burning speed, temperature and Markstein length along the flame-front, the shape, leading edge and curvature of the latter, and the propagation speed of the triple-flame. In particular, it is found that the Markstein length is affected by the reversibility parameter and the local coordinate along the flame-front whenever the Lewis numbers of the fuel and oxidizer are unequal and is independent of them otherwise; in all cases, however, its value at the leading-edge, which features in the formula derived for the propagation speed, is found to be unaffected by the reversibility. Several features of triple-flames specifically associated with the reversibility of the reaction are described analytically, including the decrease in the propagation speed and flame-front curvature and the increased shift of the location of the leading edge away from the stoichiometric surface with increased reversibility. Some of these features have no counterparts in the irreversible case. For example, whereas the maximum temperature of the triple-flame front occurs at the stoichiometric location in the irreversible case, irrespective of the location of the leading edge, it is typically found to be sandwiched between these two locations in the reversible case.