Anomalous lewis number effects in tribrachial flames

Abstract

Tribrachial (three-armed) flames are generated when a premixed flame propagates into a nonuniform mixture, and consist of a fuel-rich branch joined to a fuel-lean branch, with a diffusion flame trailing from the junction (the stoichiometric point). They are important in the context of ‘laminar flamelet’ models of turbulent non-premixed flames. We provide a theoretical description of these flames, valid when the upstream concentration gradient is small. In addition, we assume that the Lewis number of the oxidizer is 1, but that of the fuel (Le f ) is greater than 1. Solutions are sought corresponding to steady, unbounded propagation into unburnt mixture, where we would expect—nominally—that all three arms of the flame trail behind the junction, so that to the left of some plane perpendicular to the oncoming flow there is everywhere no reaction. Instead, we find that the fuel-rich branch necessarily extends ahead of any plane, penetrating to upstream infinity. This corresponds to an anchored flame rather than one that is freely propagating, and appears to be a consequence of the stretch effects that are possible when Le f >1; a decrease in the mixture strength does not necessarily lead to a decrease in the local flame speed if flame curvature generates negative stretch. If we assume that extinction occurs at sufficiently low flame temperatures, the flame is bounded and our solution can be reinterpreted as a freely-propagating flame, albeit with unexpected shape.