Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

Abstract

The linear stability of freely propagating, adiabatic, planar premixed flames is investigated in the context of a simple chain-branching chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and contrasted with those from a previous purely thermal-diffusive constant density linear stability study. It is shown that when thermal expansion is properly accounted for, a region of stable flames predicted by the constant density model disappears, and instead the flame is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak effect on the critical fuel Lewis number required for instability. These effects of thermal expansion on the two-step chain-branching flame are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in the limit that the chain-branching crossover temperature tends to the adiabatic flame temperature, the two-step model can be described to leading order by the one-step model with a suitably defined effective activation energy.

Keywords:

• stability analysis
• cellular instabilities
• pulsating instabilities
• cross-over temperature
• chain branching

Acknowledgments

The author was supported by an EPSRC Advanced Fellowship. The author is also grateful to Ted Bearman, Rio Tinto Technology & Innovation for research sponsorship. Thanks also go to Tom Jackson for previously providing the one-step model data used in Jackson and Kapila [9].