Multiplicity and stability of burner stabilized premixed laminar flames: A general proof

Abstract

The stability of a one-dimensional burner-stabilized premixed flame is investigated for an arbitrary Lewis number and general N-species mass action kinetic laws. The flame is assumed to be radially adiabatic. The existence of unsteady solutions is proved via fixed point theory for nonlinear operators acting on closed bounded spaces. The stability and multiplicity of steady states is studied with the help of bifurcation theory. The major result is that for an N-species system, 2 N+1 steady states are possible, N of which are unstable. This result is recast in experimental terms for burner-stabilized flames. There exist critical values of experimentally controlled parameters—e.g. incoming flow velocity, heat transfer rate at the burner plugs, and species mass fraction in the feed—for which the time-asymptotic solution bifurcates from the nontrivial steady state solution. These bifurcations lead to burner extinction but periodic solutions cannot be excluded. The present conclusions are, believed to be the first generalization of recent specific results obtained by Margolis, Joulin and Clavin, and Hennemann et al, on bifurcation in premixed laminar flames. A discussion of the extension to multidimensional flames is presented, together with the limitations of the present technique.