Dynamics of two mutually coupled thermoacoustic oscillators under external dual forcing

Abstract While non-resonant external forcing has proven effective in suppressing self-excited thermoacoustic oscillations in single oscillators, its application to systems consisting of multiple coupled oscillators remains poorly understood. This numerical study investigates external dual forcing for oscillation suppression in a system of two mutually coupled thermoacoustic oscillators, each modeled as a horizontal electrically heated Rijke tube. We demonstrate that symmetric dual forcing (equal energy distribution) achieves superior oscillation suppression, reducing global thermoacoustic amplitudes by up to 60% compared to single forcing at equivalent total energy. Spectral power analysis reveals that this enhancement arises from additional energy dissipation during inter-oscillator transfer under single forcing conditions. Furthermore, the control effectiveness can be enhanced—achieving an additional amplitude reduction of up to 5 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> —by carefully modulating the phase difference between the two forcing inputs. In contrast, detuning the forcing frequencies degrades suppression performance. These findings establish a theoretical basis for developing effective dual-forcing control strategies in coupled thermoacoustic systems and offer new insights into the underlying control mechanisms.