Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

Skene, Calum S.; Taira, Kunihiko

doi:10.1017/jfm.2021.1093

Cited by 9 publications

(7 citation statements)

References 49 publications

(81 reference statements)

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“…Recently, an approach based on forced synchronization (Sec. V.2) of limit cycle oscillator has been used to explain the mitigation of thermoacoustic instabilities through openloop controls 119,190,274,285,287,322,323 . In Fig.…”

Section: B Open-loop Control Via Asynchronous Quenchingmentioning

confidence: 99%

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: B Open-loop Control Via Asynchronous Quenchingmentioning

confidence: 99%

Rijke tube: A nonlinear oscillator

Manoj,

Pawar,

Kurths

et al. 2022

Preprint

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“…This is achieved by performing the forward simulation that solves the incompressible Navier-Stokes equations, Eqs. ( 38), (39), and (40). In this example, we obtain the time-periodic von Karman vortex street that forms behind the circular cylinder.…”

Section: Circular Cylinder Wakementioning

confidence: 99%

“…In addition, phase reduction analysis is also sensor friendly as it only requires temporal measurements capturing the phase of the limit-cycle oscillation. Hence phase-based analysis is remarkably useful for analysis and control of periodic fluid flows, however such applications have been very recent [29,30,31,32,33,34,35,36,37,40,38,39].…”

Section: Introductionmentioning

confidence: 99%

“…Thereby, adjoint-based method results in spatial phase sensitivity fields corresponding to perturbations with respect to various state variables through a single pair of the forward computation of governing equations resulting in limit-cycle oscillations and the backward computation of adjoint equation for the corresponding time period. Adjoint method has seen a few applications in periodic flows but limited to Hele-Shaw convection [29,30,31], Rayleigh-Bernard convection [32] and thermoacoustic oscillations [40]. However, most of these applications are based on the adjoint formulation of reduced-order governing equations of incompressible flows.…”

Section: Introductionmentioning

confidence: 99%

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Adjoint-based phase reduction analysis of incompressible periodic flows

Kawamura¹,

Godavarthi²,

Taira³

2022

Preprint

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We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and backward direct numerical simulations, as opposed to the impulse-based method that requires a very large number of simulations. Phase-based analysis involves perturbation analysis about a periodically varying base state and hence is tailored for the analysis of periodic flows. We formulate the phase description of periodic flows with respect to the potential and vortical perturbations in the flow field. The current phase-reduction analysis can also be implemented consistently in the immersed boundary projection method, which facilitates the analysis over arbitrarily-shaped bodies. We demonstrate the strength of the phase-based analysis for periodic flows over circular cylinder and symmetric airfoils at high incidence angles. The critical regions for phase modification in the cylinder flow are investigated and the locations of flow separation are shown to be the most sensitive regions. Further, the results reveal the influence of the angle of attack and airfoil thickness on the phase-sensitivity distribution of flows over various airfoils. The phase for such flows is defined based on the lift coefficient, and hence is influenced by the vortical structures responsible for lift production. The present framework sheds light on the connection between phase-sensitivity and vortex formation dynamics.

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“…While the method is more commonly used in studies of biological systems 25 , 26 , it has gained much interest in the fluid physics community in the recent years 22 , 27 , 28 . Other studies have expanded its usage to fluid–structure interactions 29 and thermoacoustic systems 30 .…”

Section: Introductionmentioning

confidence: 99%

Controlling fluidic oscillator flow dynamics by elastic structure vibration

Loe

Zheng

Kotani

et al. 2023

Sci Rep

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In this study, we introduce a design of a feedback-type fluidic oscillator with elastic structures surrounding its feedback channel. By employing phase reduction theory, we extract the phase sensitivity function of the complex fluid–structure coupled system, which represents the system’s oscillatory characteristics. We show that the frequency of the oscillating flow inside the fluidic oscillator can be modulated by inducing synchronization with the weak periodic forcing from the elastic structure vibration. This design approach adds controllability to the fluidic oscillator, where conventionally, the intrinsic oscillatory characteristics of such device were highly determined by its geometry. The synchronization-induced control also changes the physical characteristics of the oscillatory fluid flow, which can be beneficial for practical applications, such as promoting better fluid mixing without changing the overall geometry of the device. Furthermore, by analyzing the phase sensitivity function, we demonstrate how the use of phase reduction theory gives good estimation of the synchronization condition with minimal number of experiments, allowing for a more efficient control design process. Finally, we show how an optimal control signal can be designed to reach the fastest time to synchronization.

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Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

Cited by 9 publications

References 49 publications

Rijke tube: A nonlinear oscillator

Rijke tube: A nonlinear oscillator

Adjoint-based phase reduction analysis of incompressible periodic flows

Controlling fluidic oscillator flow dynamics by elastic structure vibration

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