Rijke tube: A nonlinear oscillator

TL;DR

This paper reviews the Rijke tube oscillator as a versatile and accessible experimental platform for studying complex nonlinear dynamical phenomena, including bifurcations, chaos, and instability mitigation, bridging physics and engineering.

Contribution

It introduces the Rijke tube as an easily configurable experimental model for nonlinear dynamics research, highlighting its utility in discovering and modeling diverse phenomena.

Findings

Rijke tube exhibits bifurcations, chaos, and synchronization.

Various early warning measures can predict thermoacoustic instabilities.

The Rijke tube bridges physics and engineering in nonlinear dynamics studies.

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, their prediction and mitigation, both experimentally and theoretically. The existence of various dynamical behaviors has been reported in single as well as 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 paper 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.