Thermal-diffusion instability of premixed flames for a simple chain-branching chemistry model with finite activation energy

A linear stability of freely propagating, adiabatic premixed flames is investigated in the context of a thermal-diffusive or constant density model, together with a simple two-step chain-branching model of the chemistry. This study considers the case of realistic, finite activation energy of the chain-branching step, and emphasis is on comparing with previous high activation energy asymptotic results. It is found that for realistic activation energies, a pulsating instability is absent in regimes predicted to be unstable by the asymptotic analysis. For the cellular instability, however, the finite activation energy results are in qualitative agreement with the asymptotic results, in that the flame is unstable only below a critical Lewis number of the fuel and becomes more unstable as the Lewis number is decreased. However, it is shown that very high activation energies would be required for the asymptotic analysis to be quantitatively predictive. The flame is less unstable for finite activation energies than predicted by the asymptotic analysis, in that a lower fuel Lewis number is required for instability. It is also shown that the flame structure and stability can have nonmonotonic dependencies on the activation energy.