Duality, Pulsating Instability, and Product Dissociation in Burner-Stabilized Flames

Abstract

The stabilization and diffusional-thermal pulsating instability of burner-stabilized flames, with and without product dissociation, are studied via activation energy asymptotics. The steady solution is characterized by the existence of two flame speeds either for the same heat loss rate or for the same flame standoff distance, while the stability analysis shows that the dual solutions for both cases can be stable, These provide a unified theoretical interpretation of the experimental observations of Spalding and Yumlu for the existence of two flame speeds with the same heat loss rate, and of Ferguson and Keck for the existence of two flame speeds for the same flame standoff distance.

Additional results show that the flame speed can exceed the adiabatic value for a highly mobile dissociated product, that the effect of product dissociation is mostly stabilizing, and that the preferential diffusion of the deficient reactant and the dissociated product can be either stabilizing or destabilizing, depending on the specific system parameter which is varied.

The study also emphasizes the need for renormalization to a fixed reference state for an unambiguous interpretation of the results.