A Review on Noise-Induced Dynamics of Thermoacoustic Systems

Kabiraj, Lipika; Vishnoi, Neha; Saurabh, Aditya

doi:10.1007/978-981-15-0536-2_12

Cited by 9 publications

(9 citation statements)

References 57 publications

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“…Most systems in nature are inherently noisy and, therefore, exhibit many noise-induced phenomena and bifurcations [204][205][206][207][208][209] . These dynamical changes include modification in the stability margins, occurrence of coherence and stochastic resonance, and excitation of new dynamical states [209][210][211][212] . In this section, we discuss various noise-induced dynamics in the sub-threshold and bistable regimes of Rijke tube oscillators 107,161,[213][214][215][216][217][218][219][220] .…”

Section: Noise-induced Dynamics In the Subthreshold And Bistable Regi...mentioning

confidence: 99%

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Rijke tube: A nonlinear oscillator

Manoj,

Pawar,

Kurths

et al. 2022

Preprint

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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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Section: Noise-induced Dynamics In the Subthreshold And Bistable Regi...mentioning

confidence: 99%

“…15a) and the fold point (saddle-node) in subcritical Hopf bifurcation (Fig. 15b), is referred as the subthreshold regime 210 . A bistable region is observed for subcritical Hopf bifurcation and lies between the Hopf and fold points of the system parameter space (Fig.…”

Section: Noise-induced Dynamics In the Subthreshold And Bistable Regi...mentioning

confidence: 99%

Rijke tube: A nonlinear oscillator

Manoj,

Pawar,

Kurths

et al. 2022

Preprint

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“…The presence of noise in the system can induce different phenomena, such as triggering (when the system behavior is in the excitable region of operation, see Sect. 3.3.3) and coherence resonance (when the system behavior is in the nonexcitable region of operation) [54]. In the case of subcritical Hopf bifurcation, the excitable region is the bistable (hysteresis) region in the parameter space and the non-excitable region (also called the subthreshold region by Kabiraj et al [52]) is the parameter space prior to the hysteresis region (or prior to the fold point).…”

Section: Noise-induced Transition Triggering and Stochastic Bifurcation To Limit Cyclementioning

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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“…Random disturbances in thermoacoustic systems may be generated directly by the unsteady combustion processes or indirectly by flow separation and turbulence [24]. It has been found that [25,26] these random disturbances occurring in the combustion response, frequency, and damping rate may work as additive or multiplicative excitation sources to the acoustic propagation system inside the combustors.…”

Section: Introductionmentioning

confidence: 99%

Experimental Investigation on the Stochastically Forced Rijke-Type Supercritical Thermoacoustic Systems

Zhang¹,

WANG²,

Li³

et al. 2023

Preprint

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Intense thermoacoustic oscillations may lead to severe deterioration due to the induced intolerable damage to combustors. A better understanding of unstable behaviors is important to prevent or suppress these oscillations. Active thermoacoustic coupling in practical combustors is caused primarily by two approaches: inherent turbulent fluctuations and the flame response to acoustic waves. Turbulent fluctuations are generally characterized by random noise. This paper experimentally expands on previous analytic studies regarding the influence of colored disturbances on the thermoacoustic response near the supercritical bifurcation point. Therein, a laboratory-scale Rijke-type thermoacoustic system is established, and both supercritical and subcritical bifurcations are observed. Then, Ornstein–Uhlenbeck (OU)-type external colored noise is introduced near the supercritical bifurcation point, and the effects of the corresponding correlation time τc and noise intensity D are studied. The experimental results show that these variables of the colored noise significantly influence the dynamics of thermoacoustic oscillations in terms of the most probable amplitude, autocorrelation, and correlation time. A resonance-like behavior is observed as the noise intensity or the autocorrelation time of the colored noise is continuously varied, which means that the coherent resonance occurs in the thermoacoustic system. Finally, when the system is configured closer to the stability boundary, the extent of the coherence motion is intensified in the stochastic system response. Meanwhile, the Signal to Noise Ratios (SNRs) of the colored-noise-induced response are found to become more distinguished, the optimal colored noise intensity decreases, and the optimal autocorrelation time increases. This provides valuable guidance to predict the onset of thermoacoustic instabilities.

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A Review on Noise-Induced Dynamics of Thermoacoustic Systems

Cited by 9 publications

References 57 publications

Rijke tube: A nonlinear oscillator

Rijke tube: A nonlinear oscillator

Bifurcation to Limit Cycle Oscillations in Laminar Thermoacoustic Systems

Experimental Investigation on the Stochastically Forced Rijke-Type Supercritical Thermoacoustic Systems

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