Interaction of a Planar Premixed Flame with a Parallel Adiabatic End Wall

Abstract

The unsteady one-dimensional interaction of a planar laminar isobaric flame (propagating at Lewis number unity through a fuel-lean uniform premixture) with a parallel end wall is described. The reaction rate is characterized by large dimensionless Arrhenius activation energy, such that the reaction zone of the flame structure is very thin. Accordingly, the reaction zone is modeled for convenience as a planar interface that is a Dirac-delta-function-type sink for reactants and a source for chemical heat. The result is a tractable Stefan-type problem, in which regions of unsteady convective diffusion are solved subject to suitable continuity conditions holding at a moving boundary (the flame). The increase in flame speed as the wall is approached is quantitatively described. A'systematic program for utilizing this thin-flame formulation for investigation of more general flame/wall interactions in premtxtures, analogous to the adoption of the Burke-Schumann diffusion flame for vigorously burning unpremixed reactants, is outlined.