Low-frequency thermoacoustic instability induced by nonlinear interactions of high-frequency dual modes and its open-loop control

This study investigates low-frequency thermoacoustic instability induced by nonlinear coupling between high-frequency dual modes and further explores an open-loop control strategy tailored to such complex dynamics. Time-domain simulations of a laminar premixed hydrogen–air flame in a Rijke tube are performed using a low-order network model coupled with the G-equation scheme. Results show that high-frequency Mode 3 is initially excited, followed by the growth of Mode 2; their nonlinear interaction gives rise to a dominant low-frequency difference mode. Conventional flame describing functions (FDFs) prove inadequate in this context, as they neglect nonlinear mode coupling. To overcome this limitation, a dual-input FDF derived from the G-equation is employed and incorporated into frequency-domain modeling to predict modal frequencies and growth rates. Comparison with time-domain results demonstrates that this approach effectively captures both the high-frequency interactions and the emergence of the low-frequency mode. The open-loop control strategy is evaluated by applying external acoustic forcing at various frequencies. Although the system is dominated by low-frequency dynamics, effective suppression is achieved only when the forcing targets higher frequencies near the second and third acoustic modes—the actual source of the instability. Novelty and significance statement Thermoacoustic instabilities dominated by a low-frequency mode that does not originate from a self-excited instability, but rather emerges from nonlinear coupling between high-frequency acoustic modes, were numerically investigated and analyzed in detail in the present study. Using a dual-input flame describing function (FDF) combined with a low-order frequency-domain model, the study enables accurate frequency-domain prediction of this complex mode interaction. Comparison with time-domain simulations confirms that the low-frequency mode results from high-frequency dynamics. Furthermore, open-loop control results reveal that effective suppression cannot be achieved by targeting the dominant low-frequency response alone, but must instead address its high-frequency sources. This work establishes a predictive and control framework for identifying and mitigating such non-traditional multi-mode thermoacoustic instabilities.