Srikanth Sneha, Pawar Samadhan A, Manoj Krishna, Sujith R I
Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Chaos. 2022 Jul;32(7):073129. doi: 10.1063/5.0085273.
The emergence of rich dynamical phenomena in coupled self-sustained oscillators, primarily synchronization and amplitude death, has attracted considerable interest in several fields of science and engineering. Here, we present a comprehensive theoretical study on the manifestation of these exquisite phenomena in a reduced-order model of two coupled Rijke tube oscillators, which are prototypical thermoacoustic oscillators. We characterize the dynamical behaviors of two such identical and non-identical oscillators by varying both system parameters (such as the uncoupled amplitudes and the natural frequencies of the oscillators) and coupling parameters (such as the coupling strength and the coupling delay). The present model captures all the dynamical phenomena-namely, synchronization, phase-flip bifurcation, amplitude death, and partial amplitude death-observed previously in experiments on coupled Rijke tubes. By performing numerical simulations and deriving approximate analytical solutions, we systematically decipher the conditions and the bifurcations underlying the aforementioned phenomena. The insights provided by this study can be used to understand the interactions between multiple cans in gas turbine combustors and develop control strategies to avert undesirable thermoacoustic oscillations in them.
耦合自持振荡器中丰富动力学现象的出现，主要是同步和振幅死亡，已在科学和工程的多个领域引起了相当大的兴趣。在这里，我们对两个耦合的里吉克管振荡器的降阶模型中这些精妙现象的表现进行了全面的理论研究，里吉克管振荡器是典型的热声振荡器。我们通过改变系统参数（如振荡器的非耦合振幅和固有频率）和耦合参数（如耦合强度和耦合延迟）来表征两个这样相同和不同的振荡器的动力学行为。本模型捕捉到了先前在耦合里吉克管实验中观察到的所有动力学现象，即同步、相位翻转分岔、振幅死亡和部分振幅死亡。通过进行数值模拟并推导近似解析解，我们系统地解读了上述现象背后的条件和分岔。本研究提供的见解可用于理解燃气轮机燃烧室中多个罐之间的相互作用，并制定控制策略以避免其中不希望出现的热声振荡。
