Nonlinear response of an intrinsically pulsating laminar flame to harmonic disturbances in the flow field

Chaotic behaviour of flame can arise due to interactions of forcing frequency with that of intrinsic osicllations. Instrinsic instability of flame due to thermo-diffusive mechnaism is observed in laminar flames with large value of Lewis number greater than unity. This results in flame pulsating with unique natural frequency which is function of othe parmaters. This work extended previous numerical study of oscillatory behavior in laminar flames observed in a co-flow burner for a range of premixedness and low Damköhler numbers. In this study, harmonic perturbations at the forcing frequency to the flow velocity in the upstream of the flame are applied. The resulting oscillation in the flame is calculated by numerically solving the thermo-diffusive model of the laminar flame in a 2D co-flow configuration. The oscillation of flame is tracked using the fluctuations in the value of heat release integrated over the entire domain. Using this the nonlinear response function of the flow fluctuations to the heat release fluctuations are observed over a range of frequencies. The FFT plot of flame oscillations shows peaks predominantly at both the forcing frequency as well as the forcing frequency. Along with this, smaller peaks were also observed for a range of frequencies. These frequencies can be related to the linear combination of the forcing frequency and the natural frequency. This behavior over a range of Damköhler number and premixedness is also studied.