Nonlinear Forced Response of a Self-Excited Hydrogen-Enriched Swirling Flame

The nonlinear interactions between the self-excited and forcing frequencies in the open-loop control of thermoacoustic oscillations remain insufficiently understood. In this experimental study, we investigate the nonlinear forced response of a self-excited hydrogen-enriched swirling flame. First, a theoretical analysis is performed based on the perturbed [Formula: see text] equation and reveals that changes in the flame’s response at the self-excited frequency arise not only from the self-excited mode itself but also from nonlinear interactions between the self-excited and forced modes. To quantify these contributions, data-driven bispectral mode decomposition is then applied, which uncovers that interactions involving the sum frequency and the forcing frequency, as well as those between the second harmonic and the self-excited frequency, amplify the self-excited mode. In contrast, the interaction between the difference frequency and the forcing frequency has a suppressive effect on it. At last, the flame’s forced response is analyzed spatially, and the flame tip is identified as the region most receptive to external forcing, whereas the flame root remains relatively insensitive. This study advances the understanding of nonlinear flame dynamics under dual-frequency excitation, providing new physical insights for optimizing open-loop control strategies, particularly the selection of forcing frequencies.