Nonlinear responses of the premixed V-flame subjected to dual-frequency disturbances

The two-way interaction between the unsteady flame heat release rate (HRR) and acoustic waves can lead to combustion instability within combustors. Previous studies have typically characterised premixed flame responses to pure harmonic forcing, assuming dynamically linear or weakly nonlinear behaviour, to quantify flame-acoustic interactions. By combining third-order asymptotic analysis with numerical simulations of the G-equation, this study investigates the nonlinear response of laminar premixed V-flames subjected to dual-frequency velocity perturbations (St1 and St2, dimensionless frequencies). The positive correlation between disturbance propagation speed uc and frequency St is captured by integrating a velocity-potential model with calibration against existing experimental data. The mechanism by which the disturbance at one forcing frequency, say St2, affects the flame dynamic response at the other forcing frequency, St1, is studied in detail. The perturbation at St2 couples with that at St1 to induce third-order nonlinear terms, giving rise to a non-monotonic suppression mechanism that smooths out the flame's spatial wrinkling owing to the positive correlation between uc and St. As a result, excitation at St2 modifies the HRR response at St1, delineating an effective region bounded on the left by the frequency threshold of the linear response and on the right by the aforementioned non-monotonicity. Within this region, excitation at St2 can markedly attenuate the HRR gain at St1 compared with the case where the flame is driven solely by the perturbation at St1. For instance, once both perturbation amplitudes exceed a certain threshold, excitation at St2 can attenuate the flame response at St1 by more than 40% compared with the case without excitation at St2.