An Asymptotic Model of Nonadiabatic Catalytic Flames in Stagnation-Point Flow

Abstract

A formal asymptotic model is derived for a nonadiabatic catalytic flame in stagnation-point flow. In the present context, the premixed reaction in the bulk gas is augmented by a surface catalytic reaction on the stagnation plane, where conductive heat losses are allowed to occur. In addition, the thermal effects of a finite-volume combustor are accounted for by allowing for volumetric heat losses from the bulk gas. The analysis exploits the near-equidiffusional limit corresponding to near-unity Lewis numbers, and yields a general nonsteady nonplanar model for the reactionless outer flow subject to boundary conditions that reflect both surface catalysis and distributed chemical reaction in a thin boundary layer. For the case of steady planar combustion, the surface-temperature response indicates the possibility of multiple solution branches, which are shown to be linearly stable, and a corresponding extension of the extinction limit that demonstrates how the presence of a surface catalyst can counterbalance the extinguishing effects of heat loss and stretch in nonadiabatic strained flames. The present model is particularly relevant for small-volume combustors, where the increased surface-to-volume ratio can lead to extinction of the nonadiabatic flame in the absence of a catalyst.