Dynamics of Laminar Premixed Flames Forced by Harmonic Velocity Disturbances

This paper describes the dynamics of constant-burning-velocity premixed flames responding to harmonic velocity disturbances. Results are derived from analytical and computational solutions of the nonlinear G equation and compared with available experimental data. It is shown that the flame dynamics are controlled by the superposition of two waves propagating along the flame sheet: those originating at the flame-anchoring point and from flow nommiformities; along the flame. They may either constructively or destructively superpose, and so the overall linear flame response depends upon two Strouhal numbers, St(2) and St(c), related to the amount of time taken for a flow (St(c)) and flame-front (St(2)) disturbance to propagate the flame length, normalized by the acoustic period. The nonlinear flame response is controlled by flame propagation normal to itself, which smoothens out the wrinkles induced by the forcing at an amplitude-dependent rate. The flame's nonlinear response is shown to exhibit two qualitatively different behaviors. For parameter values at which these disturbances constructively interfere, the nonlinear flame response saturates. When the flame disturbances destructively interfere, the nonlinear transfer function may actually exceed its linear value before saturating. This result explains experimentally observed variations of the nonlinear flame response with frequency.