Manoj Krishna, Pawar Samadhan A, Kurths Jürgen, Sujith R I
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Chaos. 2022 Jul;32(7):072101. doi: 10.1063/5.0091826.
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.
动力系统理论已成为一个跨学科研究领域，用于刻画现实世界系统中复杂的动态转变。在过去几十年里，人们使用不同的振荡器降阶模型发现了各种非线性动力学现象和分岔。理论上已经开发出不同的方法和手段来检测、控制或抑制非线性振荡。然而，通过实验获得这些现象往往具有挑战性、耗时且有风险，主要原因是实验过程中某些参数的控制有限。通过这篇综述，我们旨在向动力系统领域介绍一种典型且易于配置的里吉克管振荡器。燃烧领域通常将里吉克管用作研究热声不稳定性有害现象的原型。最近对这种里吉克管的研究利用了动力系统理论中的各种方法，以便在实验和理论上更好地理解热声振荡的发生及其预测和缓解。在单个和耦合的里吉克管振荡器中已经报道了各种动力学行为。这些行为包括分岔、通向混沌的路径、噪声诱导的转变、同步以及振荡的抑制。已经建立了各种早期预警措施来预测热声不稳定性。因此，这篇综述文章巩固了里吉克管振荡器在通过实验发现和建模物理中观察到的不同非线性现象方面的实用性，从而跨越了物理和工程领域之间的界限。
