Forced-Coupled Rijke tubes

We show that simultaneous use of mutual coupling and asymmetric forcing in a system of coupled identical Rijke tubes can enhance the parametric region of oscillation quenchingthan when the two mechanisms are utilized individually.

Mitigation strategies. Two types of synchronization methods are widely used to control oscillations in nonlinear systems: mutual coupling and external forcing. Under optimal conditions, these two methodolgies can lead to complete suppression of oscillations in the system, the phenomenon known as asynchronous quenching and amplitude death, respectively.

Best of both worlds. Information on how forcing of the thermoacoustic instability in one combustor affects the thermoacoustic instability developed in another combustor is still unknown. Similarly, mutual coupling works for two coupled oscillators; however, the parametric regime for which amplitude death is observed is limited. We implement a proof of concept capable of combining the best of both strategies — asynchronous quenching and mutual synchronization — to control thermoacoustic oscillations. To this end, we couple two Rijke tubes during the state of thermoacoustic instability and subject one to external harmonic forcing (asymmetric forcing). We demonstrate the expansion of the region of oscillation quenching of thermoacoustic instability in the system of coupled identical Rijke tubes by compounding the effect of asynchronous quenching and mutual synchronization. Finally, we develop a model where two Rijke tube oscillators are coupled through dissipative and time-delay coupling and are forced asymmetrically.

Nonlinear systems. Mutual coupling and asynchronous quenching have been used to control nonlinear systems such as lasers, DC microgrids, plasma instability, etc. The results above can be further extended to general nonlinear systms, which we demonstrate by investigating a system of coupled oscillators represented by second-order nonlinear differential equations.