Amplitude death and growth in a pair of nonidentical thermoacoustic oscillators interacting via time-delay and dissipative coupling

Abstract

We numerically explore the effect of asymmetric limit-cycle amplitudes on the quenching and growth of self-excited thermoacoustic oscillations in two nonidentical Rijke tubes interacting via time-delay and dissipative coupling. When either type of coupling is applied separately, we find that increasing the asymmetry of the (uncoupled) limit-cycle amplitudes can shrink the regions of amplitude death (AD) in both oscillators, while producing a new region in which one of the oscillators becomes amplified, a state we refer to here as amplitude growth (AG). We find that the AG region resembles a 1:1 Arnold tongue when only dissipative coupling is applied, but that it splits into two discrete branches when only time-delay coupling is applied. When both types of coupling are applied simultaneously, we find that the AD and AG regions change in ways that depend sensitively on the detuning between the two oscillators. The findings of this study could be used to gain a better understanding of the can-to-can acoustic interactions in modern gas turbines, facilitating the development of both passive and active strategies to control thermoacoustic instability.