Effects of selective diffusion on the stability of burner-stabilized premixed flames

Abstract

The effects of selective diffusion, or multiple Lewis numbers, on the one-dimensional stability of an isobaric burner-stabilized premixed flame is investigated for arbitrary stoichiometry and reaction order in the asymptotic limit of large activation energy. Utilizing a global reaction model of the form ν f F+ν o O→ν p P, the author has recently shown that, unlike most adiabatic flames, many burner-stabilized flames are unstable to arbitrarily small “normal mode” disturbances under easily achievable conditions. In particular, when certain parameters pass through critical values, the nontrivial steady-state solution undergoes a supercritical Hopf bifurcation to a pulsating, or time-oscillating, solution branch. In the present work, the previous restrictive assumption that Le f =Le o is relaxed to allow for unequal diffusion of fuel and oxidizer. This results in a number of interesting and significant effects (which are absent when Le f =Le o ) on the location of the stability boundary in parameter space and which are particularly relevant for complex hydrocarbon flames, where the heavier hydrocarbon fuel may have a significantly higher Lewis number than the oxidizing species. The bifurcation phenomenon is illustrated by a computer-generated movie which shows the transient response of a realistic H 2 /O 2 flame when parameter values lie on either side of the neutral stability boundary.