Dynamical States and Bifurcations in Coupled Thermoacoustic Oscillators

TL;DR

This paper provides a comprehensive theoretical analysis of coupled thermoacoustic oscillators, revealing how various dynamical phenomena like synchronization and amplitude death occur and can be controlled in gas turbine systems.

Contribution

It introduces a reduced-order model that captures complex dynamical behaviors of coupled Rijke tube oscillators, including bifurcations and amplitude death, supported by analytical and numerical analysis.

Findings

Model reproduces experimentally observed phenomena

Identifies conditions for synchronization and amplitude death

Provides insights for controlling thermoacoustic oscillations

Abstract

The emergence of rich dynamical phenomena in coupled self-sustained oscillators, primarily synchronization and amplitude death, has attracted considerable interest in several fields of science and engineering. Here, we present a comprehensive theoretical study on the manifestation of these exquisite phenomena in a reduced-order model of two coupled Rijke tube oscillators, which are prototypical thermoacoustic oscillators. We characterize the dynamical behaviors of two such identical and non-identical oscillators by varying both system parameters (such as the uncoupled amplitudes and the natural frequencies of the oscillators) and coupling parameters (such as coupling strength and coupling delay). The present model captures all the dynamical phenomena -- namely synchronization, phase-flip bifurcation, amplitude death, and partial amplitude death -- observed previously in experiments on coupled Rijke tubes. By performing numerical simulations and deriving approximate analytical solutions, we systematically decipher the conditions and the bifurcations underlying the aforementioned phenomena. The insights provided by this study can be used to understand the interactions between multiple cans in gas turbines combustors and develop suitable control strategies to avert undesirable thermoacoustic oscillations in them.