Abstract
Dynamical systems theory has emerged as an interdisciplinary area of research to characterize the complex dynamical transitions in real-world systems. Various nonlinear dynamical phenomena and bifurcations have been discovered over the decades using different reduced-order models of oscillators. Different measures and methodologies have been developed theoretically to detect, control, or suppress the nonlinear oscillations. However, obtaining such phenomena experimentally is often challenging, time-consuming, and risky mainly due to the limited control of certain parameters during experiments. With this review, we aim to introduce a paradigmatic and easily configurable Rijke tube oscillator to the dynamical systems community. The Rijke tube is commonly used by the combustion community as a prototype to investigate the detrimental phenomena of thermoacoustic instability. Recent investigations in such Rijke tubes have utilized various methodologies from dynamical systems theory to better understand the occurrence of thermoacoustic oscillations and their prediction and mitigation, both experimentally and theoretically. The existence of various dynamical behaviors has been reported in single and coupled Rijke tube oscillators. These behaviors include bifurcations, routes to chaos, noise-induced transitions, synchronization, and suppression of oscillations. Various early warning measures have been established to predict thermoacoustic instabilities. Therefore, this review article consolidates the usefulness of a Rijke tube oscillator in terms of experimentally discovering and modeling different nonlinear phenomena observed in physics, thus transcending the boundaries between the physics and the engineering communities.
The occurrence of various nonlinear self-sustained oscillations in different systems observed in our day-to-day life has been studied from a dynamical system’s perspective. Many such systems that mesmerize the human mind have been modeled as an oscillator. Theoretical reduced-order models have been developed for oscillators, e.g., Stuart-Landau, Van der Pol, Rossler, Lorenz, etc., to study and predict a plethora of dynamical behaviors observed in natural systems. The experimental validations of these theoretically discovered dynamical phenomena, however, are limited to oscillators involving electronic circuits including Chua’s circuit, lasers, pendulums, chemical oscillators, etc. In the present study, we introduce the Rijke tube as a paradigmatic member to the family of nonlinear oscillators. Rijke tube systems are prototypical thermoacoustic oscillators and have been extensively studied to understand the occurrence of complex thermoacoustic instabilities observed in gas turbines and rocket engines used for propulsion and power generation applications. Recent studies on the Rijke tube have shown the existence of numerous dynamical states, bifurcations, and nonlinear behaviors such as synchronization and oscillation quenching in coupled systems that are often observed in nonlinear oscillators. Different nonlinear measures have been used to predict critical transitions in a Rijke tube system. Therefore, through this review article, we introduce the dynamical systems’ community to the Rijke tube oscillator to experimentally validate their novel theoretical findings and, thus, bridge the gap between the physics and the engineering communities.
