Rijke tube: A nonlinear oscillator

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.

Experimental Implementation of Retrospective Cost Adaptive Control for Suppressing Thermoacoustic Oscillations in a Rijke Tube

“…Pressure oscillations are created within the experimental Rijke-tube setup by supplying voltage to the heating element, as noted by Rijke in [1] and subsequently elucidated by Rayleigh [2], [30]. As explained in [30]- [32] [33, pp. 232-234], pressure oscillations are created and become selfexcited if and only if the heating element is placed in the lower half of the tube and sufficient power is provided to the heating element to overcome the acoustic damping.…”