Premixed edge-flames under transverse enthalpy gradients

Abstract

We describe flame propagation between two opposed reactive streams which may differ in their composition and temperature. A two-dimensional counterflow configuration and an irreversible Arrhenius reaction are adopted, along with the constant density approximation. Attention is focused on the influence of two nondimensional parameters. The first one, denoted by γ, represents the difference in the enthalpy of the feed streams. The second one, ε, quantifies the ratio between the characteristic chemical time and the strain time. After a general formulation of the problem, we begin by an analysis of the one-dimensional case consisting of two parallel planar flames of unequal strength. The flames behavior is described analytically and numerically. In particular, two extinction regimes are identified: for values of γ smaller than a critical value γ*, the flames extinguish by quenching against each other at the stagnation plane; for γ > γ* they extinguish while at a finite distance from each other which increases with γ. These behaviors are similar to those, known in the literature, associated with the influence of Lewis numbers on the extinction of twin-flames. We then describe the propagation of two-dimensional flame fronts along the stagnation line, in a direction perpendicular to the plane of strain. The flame front is thus curved under the combined effects of the flow field and the transverse enthalpy gradient in the frozen mixture ahead of it; far behind the state of the gas is that of the pair of flat flames introduced above. The problem is studied numerically and complemented by an analytical description of the fast-chemistry situations corresponding to small values of ε. In particular we describe, for different fixed values of γ, the evolution of ignition fronts, characterized by a positive propagation speed, to extinction fronts, characterized by negative speeds, as ε is increased. In addition to the marked change in the flame shape, the most noticeable effect of an increase in γ is the decrease in the propagation speed of the flame front. These effects are associated with the increased front curvature for higher values of γ, along with a shift of the front leading edge towards the stream with higher enthalpy.