Oscillation quenching and phase-flip bifurcation in coupled thermoacoustic systems

Dange, Suraj; Manoj, Krishna; Banerjee, Subham; Pawar, Samadhan A.; Mondal, Sirshendu; Sujith, R. I.

doi:10.1063/1.5114695

Cited by 45 publications

(52 citation statements)

References 29 publications

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“…3 and 4 bear some similarity to the studies found in Refs. [33,67,100] where phase-flip bifurcations are studied. The difference is that the referenced works consider transient bifurcations which occur during operation as some parameter is varied, while our investigation is focused on steadystate phenomena with all parameters constant during operation.…”

Section: Discussionmentioning

confidence: 99%

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Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Pedergnana

Noiray

2022

Nonlinear Dyn

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Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work, we analytically and numerically study a symmetric ring of N coupled self-oscillators of van der Pol type under external stochastic forcing. The system is proposed as a model of the thermo- and aeroacoustic interactions of sound fields in rigid enclosures with compact source regions in a can-annular combustor. The oscillators are connected via linear resistive coupling with nonlinear saturation. After transforming the system to amplitude-phase coordinates, deterministic and stochastic averaging is performed to eliminate the fast oscillating terms. By projecting the potential of the slow-flow dynamics onto the phase-locked quasi-limit cycle solutions, we obtain a compact, low-order description of the (de-)synchronization transition for an arbitrary number of oscillators. The stationary probability density function of the state variables is derived from the Fokker–Planck equation, studied for varying parameter values and compared to time series simulations. We leverage our analysis to offer explanations for the intermittent energy transfer between Bloch waves observed in acoustic pressure spectrograms observed of real-world gas turbines.

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Section: Discussionmentioning

confidence: 99%

“…[29]. We also mention that nonlinear phenomena in can-annular configurations, such as amplitude death and quenching, have drawn increased interest in recent years [30][31][32][33].…”

Section: Thermoacoustic Instabilities In Can-annular Combustorsmentioning

confidence: 99%

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Pedergnana

Noiray

2022

Nonlinear Dyn

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“…Using similar concepts, Dange et al. (2019) observed experimentally in-phase/anti-phase synchronization, phase-flip bifurcations and partial amplitude death in two coupled Rijke tubes powered by electric heaters. Similarly, Biwa, Tozuka & Yazaki (2015), Hyodo & Biwa (2018) and Hyodo, Iwasaki & Biwa (2020) observed experimentally in-phase/anti-phase synchronization and amplitude death in two coupled thermoacoustic oscillators powered by electric heaters and laminar Bunsen flames.…”

Section: Introductionmentioning

confidence: 96%

Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

et al. 2022

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We take a complex systems approach to investigating experimentally the collective dynamics of a network of four self-excited thermoacoustic oscillators coupled in a ring. Using synchronization metrics, we find a wide variety of emergent multi-scale behaviour, such as (i) a transition from intermittent frequency locking on a $\mathbb {T}^{3}$ quasiperiodic attractor to a breathing chimera, (ii) a two-cluster state of anti-phase synchronization on a periodic limit cycle, and (iii) a weak anti-phase chimera. We then compute the cross-transitivity from recurrence networks to identify the dominant direction of the coupling between the heat-release-rate ( $q^{\prime }_{\mathbb {X}}$ ) and pressure ( $p^{\prime }_{\mathbb {X}}$ ) fluctuations in each individual oscillator, as well as that between the pressure ( $p^{\prime }_{\mathbb {X}}$ and $p^{\prime }_{\mathbb {Y}}$ ) fluctuations in each pair of coupled oscillators. We find that networks of non-identical oscillators exhibit circumferentially biased $p^{\prime }_{\mathbb {X}}$ – $p^{\prime }_{\mathbb {Y}}$ coupling, leading to mode localization, whereas networks of identical oscillators exhibit globally symmetric $p^{\prime }_{\mathbb {X}}$ – $p^{\prime }_{\mathbb {Y}}$ coupling. In both types of networks, we find that the $p^{\prime }_{\mathbb {X}}$ – $q^{\prime }_{\mathbb {X}}$ coupling can be symmetric or asymmetric, but that the asymmetry is always such that $q^{\prime }_{\mathbb {X}}$ exerts a greater influence on $p^{\prime }_{\mathbb {X}}$ than vice versa. Finally, we show through a cluster analysis that the $p^{\prime }_{\mathbb {X}}$ – $p^{\prime }_{\mathbb {Y}}$ interactions play a more critical role than the $p^{\prime }_{\mathbb {X}}$ – $q^{\prime }_{\mathbb {X}}$ interactions in defining the collective dynamics of the system. As well as providing new insight into the interplay between the $p^\prime_{\mathbb{X}}\text{--}p^\prime_{\mathbb{Y}}$ and $p^\prime_{\mathbb{X}}\text{--}q^\prime_{\mathbb{X}}$ coupling, this study shows that even a small network of four ring-coupled thermoacoustic oscillators can exhibit a wide variety of collective dynamics. In particular, we present the first evidence of chimera states in a minimal network of coupled thermoacoustic oscillators, paving the way for the application of oscillation quenching strategies based on chimera control.

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“…They also confirmed that AD can be observed even in situations where white noise is applied [32]. Dange et al experimentally examined AD in coupled Rijke tube oscillators [33]. Hyodo et al experimentally confirmed the effectiveness of multiple delayed connections in coupled Rijke tube oscillators [34].…”

Section: Discussionmentioning

confidence: 83%

Delay-induced stabilization of coupled oscillators

Sugitani

Konishi

2021

NOLTA

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Delays can have a negative impact on the stability of various systems. However, it was reported that the transmission delays of signals among oscillators can stabilize unstable equilibrium points in coupled oscillators, which is called amplitude death (AD). AD caused by delays has been extensively researched in the field of nonlinear science and has attracted attention for various engineering applications. In this article, we review the latest studies on AD caused by delays in oscillator networks, in particular those that considered heterogeneous delays and time-varying networks.

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Oscillation quenching and phase-flip bifurcation in coupled thermoacoustic systems

Cited by 45 publications

References 29 publications

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

Delay-induced stabilization of coupled oscillators

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