Theoretical and Computational Aspects of Premixed Laminar Flames

Abstract

In this paper two aspects of burner-stabilized premixed laminar flames are considered: the effects of multiple chemical time scales on the nontrivial steady-state solution and the existence of a bifurcation phenomena which, under certain readily achievable conditions, leads to a time-oscillating solution. To study the first problem, attention is directed at the global two-step reaction mechanism v r R-*^tI 9 j^/-« p P. The general solution properties are characterized and explicit asymptotic results are obtained which show that the governing differential system admits both spatially growing and decaying solutions whose relative growth and decay rates are directly related to the disparity in reaction rates. This spatial instability causes extreme difficulties for steady-state numerical methods of the shooting type, and it is shown how the various time-dependent approaches circumvent this difficulty. The success of this latter technique rests on the stability of the nontrivial steady-state solution, which is studied by considering the one-step mechanism VJ-F+VQ®-* v p P. Utilizing large activation energy asymptotics, a linear stability analysis yields the neutral stability boundary in Lewis number/activation energy space as a function of the 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 timedependent problem bifurcates from the unique nontrivial steadystate solution. The existence of a time-oscillating solution for sufficiently small incoming flow velocities is illustrated by realistic calculations of an H 2 /O 2 premixed flame utilizing the timedependent numerical technique.