Tipping of thermoacoustic systems with secondary bifurcation in colored noise environments: Effects of rate

Xiaoyu Zhang; Yong Xu; Qi Liu; Jürgen Kurths

doi:10.1063/5.0245575

journal article Mar 01, 2025

Tipping of thermoacoustic systems with secondary bifurcation in colored noise environments: Effects of rate

Xiaoyu Zhang

Yong Xu

Qi Liu

Jürgen Kurths

Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 35 No. 3 · AIP Publishing

View at Publisher Save 10.1063/5.0245575

Abstract

Rate-dependent tipping that concerns the effects of the rate of parameter change on the sudden transitions has been revealed in thermoacoustic systems. However, the conventional models cannot accurately portray the intermittent oscillations observed in experiments. This study explores the tipping behaviors in a thermoacoustic system with a secondary bifurcation, simultaneously accounting for the coupling effects of rate and colored noise. Particularly, the model contains higher-order nonlinearities, which lead to the emergence of both supercritical and subcritical bifurcations. It can qualitatively reproduce the intermittent dynamics of the system. We perform a transient analysis for the system via a stochastic averaging method and explore the influence mechanisms of colored noise and rate on the tipping phenomenon. The results show that the system exhibits a tipping phenomenon from the desired state to thermoacoustic instability through the state of intermittency. Interestingly, the rate causes the delay of tipping, while its increase enlarges the amplitude of intermittent oscillations. In addition, the system changes from an abrupt tipping to a smooth tipping for large noise intensities.

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References

29

[1]

(2012)

[2]

"A review of active control of combustion instabilities" Prog. Energy Combust. Sci. (1993) 10.1016/0360-1285(93)90020-f

[3]

Sensitivity and Nonlinearity of Thermoacoustic Oscillations

Matthew P. Juniper, R.I. Sujith

Annual Review of Fluid Mechanics 2018 10.1146/annurev-fluid-122316-045125

[4]

"On the sound produced by a current of hydrogen gas passing through a tube" J. Nat. Philos. Chem. Arts (1802)

[5]

(1896)

[6]

"Experimental investigation of limit-cycle oscillations in an unstable gas turbine combustor" J. Propul. Power (2002) 10.2514/2.5898

[7]

"Change of criticality in a prototypical thermoacoustic system" Chaos (2017) 10.1063/1.4975822

[8]

"A PINN approach for identifying governing parameters of noisy thermoacoustic systems" J. Fluid Mech. (2024) 10.1017/jfm.2024.219

[9]

"Early detection of thermoacoustic instability in an O2/CH4 single-injector rocket combustor using analysis of chaos and deep learning models" Phys. Fluids (2024) 10.1063/5.0187918

[10]

"Deep learning-based state prediction of the Lorenz system with control parameters" Chaos (2024) 10.1063/5.0187866

[11]

"Intermittency route to thermoacoustic instability in turbulent combustors" J. Fluid Mech. (2014) 10.1017/jfm.2014.468

[12]

"Flame dynamics during intermittency and secondary bifurcation to longitudinal thermoacoustic instability in a swirl-stabilized annular combustor" Proc. Combust. Inst. (2021) 10.1016/j.proci.2020.08.053

[13]

"Intermittency, secondary bifurcation and mixed-mode oscillations in a swirl-stabilized annular combustor: Experiments and modeling" J. Eng. Gas Turbines Power (2021) 10.1115/1.4049407

[14]

(2020)

[15]

"Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview" Chaos (2022) 10.1063/5.0093478

[16]

"Complex dynamics of a conceptual airfoil structure with consideration of extreme flight conditions" Nonlinear Dyn. (2023) 10.1007/s11071-023-08636-y

[17]

"Deep learning for early warning signals of tipping points" Proc. Natl. Acad. Sci. U.S.A. (2021) 10.1073/pnas.2106140118

[18]

"Using machine learning to anticipate tipping points and extrapolate to post-tipping dynamics of non-stationary dynamical systems" Chaos (2023) 10.1063/5.0131787

[19]

"Tipping points in open systems: Bifurcation, noise-induced and rate-dependent examples in the climate system" Philos. Trans. R. Soc. A (2012) 10.1098/rsta.2011.0306

[20]

"Another reason for concern: Regional and global impacts on ecosystems for different levels of climate change" Global Environ. Change (2004) 10.1016/j.gloenvcha.2004.04.009

[21]

"Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise" Sci. China Technol. Sci. (2020) 10.1007/s11431-020-1589-x

[22]

"Rate-dependent bifurcation dodging in a thermoacoustic system driven by colored noise" Nonlinear Dyn. (2021) 10.1007/s11071-021-06368-5

[23]

"Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment" Chaos (2021) 10.1063/5.0071977

[24]

"Rate-induced tipping: Thresholds, edge states and connecting orbits" Nonlinearity (2023) 10.1088/1361-6544/accb37

[25]

"Rate-induced tipping in complex high-dimensional ecological networks" Proc. Natl. Acad. Sci. U.S.A. (2023) 10.1073/pnas.2308820120

[26]

"Rate-induced tipping cascades arising from interactions between the Greenland Ice Sheet and the Atlantic Meridional Overturning Circulation" Earth Syst. Dyn. (2024) 10.5194/esd-15-635-2024

[27]

"Rate and noise-induced tipping working in concert" Chaos (2023) 10.1063/5.0129341

[28]

"Rate and memory effects in bifurcation-induced tipping" Phys. Rev. E (2023) 10.1103/physreve.108.024203

[29]

"Abrupt transitions in turbulent thermoacoustic systems" J. Sound Vib. (2023) 10.1016/j.jsv.2022.117478

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Details

Published: Mar 01, 2025
Vol/Issue: 35(3)

Authors

X

Xiaoyu Zhang

School of Science, Qingdao University of Technology 1 , Qingdao 266520,; Department of Systems and Control Engineering, Institute of Science Tokyo 2 , Tokyo 152-8552,

Y

Yong Xu

School of Mathematics and Statistics, Northwestern Polytechnical University 3 , Xi’an 710072,; MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University 4 , Xi’an 710072,

Q

Qi Liu

Department of Systems and Control Engineering, Institute of Science Tokyo 2 , Tokyo 152-8552,

J

Jürgen Kurths

Potsdam Institute for Climate Impact Research 5 , Potsdam 14412,

Funding

National Natural Science Foundation of China Award: 12302036

China Scholarship Council Award: 202106290175

Natural Science Foundation of Shandong Province Award: ZR2023QA094

Cite This Article

Xiaoyu Zhang, Yong Xu, Qi Liu, et al. (2025). Tipping of thermoacoustic systems with secondary bifurcation in colored noise environments: Effects of rate. Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(3). https://doi.org/10.1063/5.0245575

Tipping of thermoacoustic systems with secondary bifurcation in colored noise environments: Effects of rate

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