Nonlinear analysis of an acoustically excited laminar premixed flame

The nonlinear effects of the fully coupled two-way interactions between a disturbance field defined by an amplitude variation of the inflow velocity distribution and a laminar premixed flame incorporating gas expansion effects are investigated by numerically solving the conservation equations of a compressible fluid. Results of the higher harmonics of the flame front perturbation for two burnt to unburnt temperature ratios show how the nonlinear transfer of flame response is affected by the hydrodynamic instability and the shear layer effect. The flame response at the fundamental forcing frequency, i.e., the flame-describing function can be well predicted by the reduced-order model (ROM) for both investigated temperature ratios at low Markstein length values, where the balance between the flame stretch effects and the hydrodynamic instability is insignificant. However, at high Markstein lengths the balance between the flame stretch and the hydrodynamic instability influences the flame response characteristics at all excitation amplitudes. The nonlinear study of the flame front perturbation indicates that differences in the higher harmonic content of the overall nonlinear flame response between the detailed computation and the ROM predictions are located at the flame front just before the flame pockets separate. Thus, the shear layer and the hydrodynamic instability effect determine the nonlinear character of the flame response through the nonlinearity introduced at the flame base, the location of flame pocket separation, and the annihilation process at the flame tip especially at high Markstein length values. In addition, the flame base movement response is compared to a recent developed reduced-order flame base model to understand the findings with respect to the assumption of flame attachment at the burner lips.