Flame Stabilization in a Layered Medium

Abstract

We analyze the steady-state structure of a l1ame stabilized on a burner which is fed by a nonuniform mixture. Our diffusional-thermal model is based on the assumption of large overall activation energy, and the nonuniformity in the feed is treated as a perturbation of the uniform case. The flame shape for a given inflow enthalpy profile depends on Lewis number, inflow velocity, and conductance of the burner, and for sufficiently small Lewis number, we exhibit the onset of cellular flame formation. Unlike previously encountered flame instabilities, the transition to a cellular name occurs here in a gradual, rather than an abrupt, fashion through an "imperfect bifurcation."

Nonlinear Stability and Bifurcation in the Transition from Laminar to Turbulent Flame Propagation

“…A multidimensional stability analysis was performed by Buckmaster (1983) and Margolis and Kerstein (1983). There it was shown that the nonadiabaticity of the flame resulted in a nonmonotonicity of the cellular stability boundary, allowing one to isolate cellular modes of flame propagation much as we did for the pulsating flames in Sections 4.1-4.3.…”