Abstract
In this paper we investigate the linear stability and properties of the travelling premixed combustion waves in a model with two-step chain-branching reaction mechanism in the adiabatic limit in one spatial dimension. It is shown that the Lewis number for fuel has a significant effect on the properties and stability of premixed flames, whereas the Lewis number for the radicals has only quantitative (but not qualitative) effect on the combustion waves. We demonstrate that when the Lewis number for fuel is less than unity the flame speed is unique and is a monotonically decreasing function of the dimensionless activation energy. The combustion wave is stable and exhibits extinction for finite values of activation energy as the flame speed decreases to zero. For fuel Lewis number greater than unity the flame speed is a double-valued function. The slow solution branch is shown to be unstable whereas the fast solution branch is either stable or exhibits the onset of pulsating instabilities via the Hopf bifurcation. The evolution of these instabilities leads to flame extinction.
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