Rijke tube: A nonlinear oscillator
arXiv:2203.06351 · doi:10.1063/5.0091826
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.
arXiv comment34 pages, 29 figures
References in corpus (24)
- Recurrence Plots for the Analysis of Complex Systems
- Chimera States for Coupled Oscillators
- Multifractality in Human Heartbeat Dynamics
- Hierarchical group dynamics in pigeon flocks
- On the performance of different synchronization measures in real data: a case study on EEG signals
- Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system
- Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks
- Amplitude Death: The emergence of stationarity in coupled nonlinear systems
- Weak chimeras in minimal networks of coupled phase oscillators
- Experimental observation of chimera and cluster states in a minimal globally coupled network
- Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach
- Strange nonchaotic stars
- Total and partial amplitude death in networks of diffusively coupled oscillators
- Climate tipping as a noisy bifurcation: a predictive technique
- Dynamics of a Limit Cycle Oscillator under Time Delayed Linear and Nonlinear Feedbacks
- Phase-response analysis of synchronization for periodic flows
- Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise
- Effect of rate of change of parameter on early warning signals for critical transitions
- Experimental investigation on the susceptibility of minimal networks to a change in topology and number of oscillators
- Dynamics of coupled thermoacoustic oscillators under asymmetric forcing: Experiments and theoretical modeling
- Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors
- Adjoint-based linear analysis in reduced-order thermo-acoustic models
- Dynamical States and Bifurcations in Coupled Thermoacoustic Oscillators
- Self-coupling: An Effective Method to Mitigate Thermoacoustic Instability