Bursting during intermittency route to thermoacoustic instability: Effects of slow–fast dynamics

Tandon, Shruti; Pawar, Samadhan A.; Banerjee, Subham; Varghese, Alan J.; Premraj, D.; Sujith, R. I.

doi:10.1063/5.0005379

Cited by 33 publications

(14 citation statements)

References 46 publications

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“…Hence, in Sec. I of the Supplemental Material, we modify the nonlinear terms in the model of delay coupled thermoacoustic oscillators so that the oscillators individually exhibit supercritical Hopf bifurcation [62]. We observe that delay coupled thermoacoustic oscillators with supercritical Hopf points exhibit second-order (i.e., continuous) change in the amplitude of acoustic pressure fluctuations during the transition from LCO to AD state and vice-versa, without hysteresis.…”

Section: Comparison Of Bifurcations In Isolated and Delay Coupled Rij...mentioning

confidence: 95%

Dynamical States and Bifurcations in Coupled Thermoacoustic Oscillators

Srikanth,

Pawar,

Manoj

et al. 2021

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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 coupling strength and coupling delay). The present model captures all of 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 nature of bifurcations underlying the aforementioned phenomena. This study provides insights into how the interplay between system and coupling parameters determines the dynamical behavior of coupled nonlinear oscillators in natural and engineering systems.

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Section: Comparison Of Bifurcations In Isolated and Delay Coupled Rij...mentioning

confidence: 95%

Dynamical States and Bifurcations in Coupled Thermoacoustic Oscillators

Srikanth,

Pawar,

Manoj

et al. 2021

Preprint

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“…Unlike direct transitions observed from steady state to thermoacoustic instability through Hopf bifurcation in the previous subsections, we come across a few studies on Rijke tube systems that report the transition to occur via an intermediate dynamical state. Various types of oscillatory dynamics such as intermittency 117 , bursting 106,113 , beating 171 , and mixed-mode oscillations 113 have been observed as the intermediate state in different Rijke tube systems. Intermittency is characterized by the occurrence of bursts of high amplitude periodic oscillations amidst epochs of low amplitude aperiodic ones.…”

Section: Transition From Steady State To Limit Cycle Via Intermittent...mentioning

confidence: 99%

“…Tandon et al 106 systematically investigated the role of slow and fast timescales on the occurrence of intermittent oscillations prior to thermoacoustic instability in a horizontal Rijke tube system. Towards this purpose, they modeled slow oscil-FIG.…”

Section: Transition From Steady State To Limit Cycle Via Intermittent...mentioning

confidence: 99%

“…8. Different types of intermediate states observed in acoustic pressure fluctuations (p ) during the transition from steady state to limit cycle oscillations such as (a) intermittency in the spray combustor 117 , (b) beating dynamics in the Rijke-type burner 171 , (c) bursting in the multiple flames matrix burner 113 , and (d) bursting in the horizontal Rijke tube 106 . Reproduced with permission from Tandon et al 106 .…”

Section: Transition From Steady State To Limit Cycle Via Intermittent...mentioning

confidence: 99%

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Rijke tube: A nonlinear oscillator

Manoj,

Pawar,

Kurths

et al. 2022

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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.

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“…3.1 Schematics of (a) a vertical Rijke tube system and (b) a horizontal Rijke tube system. (b)Reproduced with permission from Tandon et al[98]…”

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confidence: 99%

Bifurcation to Limit Cycle Oscillations in Laminar Thermoacoustic Systems

Sujith

Pawar

2021

Springer Series in Synergetics

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In this chapter, we study the bifurcation characteristics of a laminar thermoacoustic system through the application of dynamical system theory. We restrict our discussions to two simple prototypes of real thermoacoustic systems (known as Rijke-type thermoacoustic systems): a horizontal Rijke tube with an electrical heater and a ducted premixed flame combustor, both having a laminar flow field. We describe the transition of a thermoacoustic system from a state of stable operation (called stable fixed point) to unstable operation (called stable limit cycle) on variation of any control parameter. First, we will present the dynamical transitions and characteristics of the dynamical states observed in laminar thermoacoustic systems in the absence of any stochastic background fluctuations in the flow field. Subsequently, we will study the effect of external stochastic perturbations on the occurrence of different dynamical transitions in such systems. These investigations performed on simple laminar thermoacoustic systems can be considered as a baseline study before we attempt to understand the complex dynamics exhibited by turbulent thermoacoustic systems in Chap. 6.As mentioned in Chap. 1, the occurrence of thermoacoustic instability has been a concern for most practical combustion systems used in power generating units and propulsion engines. Traditionally, both linear and nonlinear methodologies have been used to explain the occurrence and the characteristics of thermoacoustic oscillations observed in such systems. In linear analysis, the equations describing flame-acoustic interactions are subjected to small amplitude perturbations for calculating the eigenvalues [12]. When all the eigenvalues are negative, the system is considered to be linearly stable, and when one of the eigenvalues is positive, the system is considered to be linearly unstable. For a linearly unstable system, an infinitesimally small perturbation introduced in the system grows in time and asymptotically approaches another stable state that is different from the initial state. As seen in Chap. 2, for the case of subcritical Hopf bifurcation, a finite amplitude perturbation (or initial condition) in the regime of bistability (hysteresis) can alter

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Bursting during intermittency route to thermoacoustic instability: Effects of slow–fast dynamics

Cited by 33 publications

References 46 publications

Dynamical States and Bifurcations in Coupled Thermoacoustic Oscillators

Dynamical States and Bifurcations in Coupled Thermoacoustic Oscillators

Rijke tube: A nonlinear oscillator

Bifurcation to Limit Cycle Oscillations in Laminar Thermoacoustic Systems

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