Bifurcation Phenomena in Burner-Stabilized Premixed Flames

Abstract

The one-dimensional stability of an isobaric burner-stabilized premixed flame is investigated for arbitrary Lewis number and stoichiometry in the asymptotic limit of large activation energy. Assuming a one-step irreversible chemical reaction in which fuel and oxidizer react to form a product, a linear stability analysis is Used to calculate the neutral stability boundary in Lewis number-activation energy space as a function of incoming flow velocity (or equivalently, the burned temperature) The major result is that although a steady-state adiabatic flame is likely to be stable for typical parameter values, a value of the incoming flow velocity sufficiently less than the adiabatic flame speed is destabilizing to the extent that the unstable region becomes feasible for many flames. Consequently, if all other parameters are fixed, there exists for such flames a critical value of the incoming flow velocity at which the time-asymptotic solution to the time-dependent problem bifurcates from the nontrivial steady state solution. Time-oscillating burner-stabilized flames are observable experimentally, and realistic numerical calculations of a fuel-rich H2IO2 premixed flame are presented which further verify the existence of such time-periodic solutions for sufficiently small incoming flow velocities. In addition, the numerical results indicate the existence of a secondary instability phenomenon in which a singly periodic pulsating solution abruptly becomes doubly periodic.