Effects of curvature on triple flame propagation in fuel-oxidizer counterflow

Abstract

In this study, we analyze the propagation of an expanding triple flame in an axisymmetric counterflow of a fuel against an oxidizer. The problem is formulated as a thermo-diffusive model with one-step global reaction. An asymptotic analysis in the limit of large activation energy and weak strain rate is conducted. The study is supported and complemented by numerical simulations carried out for arbitrary values of the strain rate. In addition to the flame front curvature 1/Rt associated with the variation in the reactants concentrations transverse to the mixing layer, the propagation of the expanding triple flame also depends on the azimuthal curvature 1/Rf where Rf is the front leading edge radial distance. As the triple flame expands to large radial distances, its propagation becomes quasi-steady. Under a quasi-steady state assumption, an explicit expression is derived for the displacement speed of the triple flame, which is found to be linearly proportional to the total curvature 1/Rf+1/Rt. Two-dimensional axisymmetric simulations are conducted to validate in particular the quasi-steady assumption. These include transient simulations of the expanding triple flame which are compared to the numerical solution of the steady eigenvalue problem obtained in a frame attached to the propagating front under a quasi-steady assumption. Following a transient ignition phase, the triple flame is found to propagate in a quasi-steady manner when Rf (measured with the stoichiometric planar flame thickness) exceeds 5, approximately. Although the theoretical analysis is performed in the weak strain limit, the linear dependence of the triple flame speed on the curvature 1/Rfis found to be applicable over a wide range of strain rates. Besides, the analysis is extended for inwardly propagating triple flames (flame holes) and similar expressions describing the relationship between displacement speed of the triple flame and curvatures are obtained.