Pulsations in a Burner-Stabilized Premixed Plane Flame

We employ a model for an edge-cooled flat flame burner to obtain expressions for the flame speed, flame temperature, standoff distance as well as the quenching distance for a plane flame front. For a given standoff distance there is a low-temperature as well as a high-temperature solution. We show by a linear stability analysis of the plane front that the high-temperature solution is unstable when the Lewis number is sufficiently large and the inflow velocity sufficiently less than the adiabatic flame speed. We also show that this instability is the type that will lead to a bifurcating time-periodic solution describing a pulsating flame.