Nonlinear response of laminar premixed flames to dual-input harmonic disturbances

The two-way interaction between the flame and acoustic waves leads to combustion instability. To understand and quantify the response of the flame to acoustic waves, studies have typically considered single-harmonic forcing of the flame, which assumes a dynamically linear or weakly nonlinear flame response. This study extends this approach by introducing an additional disturbance at the frequency S t₂ to influence the flame nonlinear response to the first perturbation at the frequency S t₁ to gain further insight into these associated combustion instabilities. The spatial front-tracking of premixed flames were derived from the analytical and numerical solutions of the G-equation model. The nonlinear behavior of flame response was presented and the related mechanism of that was also elucidated. Due to the flame propagating forward normal to itself, from the near-order asymptotic analysis point of view, the third-order nonlinear interaction of the additional and first perturbations induces an external flame response related to S t₁. It significantly affects the first fundamental frequency response of the flame.