Oscillatory instabilities, although ubiquitous in nature, are undesirable in many situations such as biological systems, swaying of bridges and skyscrapers, aero-acoustic flutter, prey-predator and disease spread models, and thermoacoustic systems, where they exhibit large amplitude periodic oscillations. In the present study, we aim to study the suppression mechanism of such undesired oscillations in a pair of thermoacoustic oscillators, also known as horizontal Rijke tubes. These oscillators are coupled through a connecting tube whose length and diameter are varied as coupling parameters. With the variation of these parameters, we show the first experimental evidence of rich dynamical phenomena such as synchronization, amplitude death, and phase-flip bifurcation in coupled identical thermoacoustic oscillators. We discover that when frequency and amplitude mismatch are introduced between these oscillators, quenching of oscillations in one or both the oscillators occurs with further ease, through the mechanisms of amplitude death and partial amplitude death. Finally, we show that the effectiveness of coupling is sensitive to the dimensions of the connecting tube which can be directly correlated with the time delay and coupling strength of the system. © 2019 Author(s).

R. I. Sujith

Department of Aerospace Engineering

Suraj Dange

Krishna Manoj

Samadhan A. Pawar

Fulltext

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IIT Madras

Oscillation quenching and phase-flip bifurcation in coupled thermoacoustic systems

Chaos

Coupling nonlinear dynamical systems can lead to a host of phenomena, one of which leads to the complete cessation of their oscillations. This phenomenon is referred to as amplitude death (AD) in the dynamical systems literature. Recently, there is a growing interest to mitigate oscillatory or dynamic instabilities in a variety of engineering systems using AD. Deriving impetus from the same, we investigate the possibility of cessation of oscillatory instabilities in aeroelastic systems using the concept of AD. In specific, the suppression of flutter instability that arises in aeroelastic systems due to highly nonlinear fluid–structure interactions is investigated from the purview of AD. To that end, we consider two identical airfoils that are exposed to input fluid forces along the axial directions. The airfoils, via translational and rotational springs, are allowed to oscillate in plunge and pitch degrees of freedom. To augment the findings to in-field scenarios, we consider the individual cases of the input flow to be either uniform (deterministic) or possess randomly time varying components, respectively. To promote coupled interactions, the airfoils are coupled using a linear torsional spring. The coupled interaction of the airfoils at the flutter regime are then studied by obtaining the pitch and plunge responses. Further, the strength of the coupling and the time delay between the airfoils are systematically varied to investigate its effect on the regime of AD. The ability of AD to suppress flutter instability and thereby serve as a possible flutter suppression mechanism in both deterministic and stochastic input flow cases is then demonstrated. Finally, the phase delay values between the airfoils is computed to heuristically present a relationship between the coupling parameters and the post coupling signatures. © 2020 Elsevier Ltd

International Journal of Non-Linear Mechanics

Investigating amplitude death in a coupled nonlinear aeroelastic system

Nonlinear phenomena emerging from the coupled behaviour of a pair of oscillators have attracted considerable research attention over the years, of which, amplitude death (AD) and phase-flip bifurcation (PFB) are two noteworthy examples. Although theoretical research has postulated the coexistence of AD and PFB upon variation of different control parameters, such an occurrence has not been reported in practical systems. Here, we provide the first experimental evidence of the coexistence of AD and PFB in a physical system, comprising of a coupled pair of candle-flame oscillators. As the strength of coupling between the oscillators is increased, we report a decrease in the span of AD region between the states of in-phase and anti-phase oscillations, leading up to a point of PFB. Understanding such a switching of phenomena between AD and PFB helps us to evade their undesirable occurrences such as AD in neuron and brain cells, oscillatory state in prey-predator systems, oscillatory spread of epidemics and so forth. © 2018, The Author(s).

Scientific Reports

Experimental Evidence of Amplitude Death and Phase-Flip Bifurcation between In-Phase and Anti-Phase Synchronization

We present a systematic investigation of the effect of external noise on the dynamics of a system of two coupled prototypical thermoacoustic oscillators, horizontal Rijke tubes, using a mathematical model. We focus on the possibility of amplitude death (AD), which is observed in the deterministic model of coupled thermoacoustic oscillators as studied by Thomas et al. [Chaos 28, 033119 (2018)], in the presence of noise. Although a complete cessation of oscillations or AD is not possible in the stochastic case, we observe a significant reduction in the amplitude of coupled limit cycle oscillations (LCOs) with the application of strong coupling. Furthermore, as we increase the noise intensity, a sudden drop in the amplitude of pressure oscillations at the transition from LCO to AD, observed in the noise free case, is no longer discernible because of the amplification of noise in AD state. During this transition from LCO to AD, we notice a qualitative change in the distribution of the pressure amplitude from bimodal to unimodal. Furthermore, in order to demarcate the boundary of the transition from LCO and AD in the noisy case, we use 80 % suppression in the amplitude of LCO, which generally occurs in the parameter range over which this qualitative change in the pressure distribution happens, as a threshold. With the help of bifurcation diagrams, we show a qualitative change as well as a reduction in the size of amplitude suppression zones that happen due to the increase in noise intensity. We also observe the relative ease of suppressing the amplitude of LCO with time-delay coupling when detuning and dissipative couplings are introduced between the two thermoacoustic oscillators in the presence of noise. © 2018 Author(s).

Effect of noise amplification during the transition to amplitude death in coupled thermoacoustic oscillators

The occurrence of thermoacoustic instability has been a major concern in the combustors used in power plants and propulsive systems such as gas turbine engines, rocket motors. A positive feedback between the inherent processes such as the acoustic field and the unsteady heat release rate of the combustor can result in the occurrence of large-amplitude, self-sustained pressure oscillations. Prior to the state of thermoacoustic instability, intermittent oscillations are observed in turbulent combustors. Such intermittent oscillations are characterized by an apparently random appearance of bursts of large-amplitude periodic oscillations interspersed between epochs of low-amplitude aperiodic oscillations. In most of the earlier studies, the pressure oscillations alone have been analyzed to explore the dynamical transition to thermoacoustic instability. The present chapter focuses on the instantaneous interaction between the acoustic field and the unsteady heat release rate observed during such a transition in a bluff-body-stabilized turbulent combustor. The instantaneous interaction of these oscillations will be discussed using the concepts of synchronization theory. First, we give a brief introduction to the synchronization theory so as to summarize the concepts of locking of phase and frequency of the oscillations. Then, the temporal and spatiotemporal aspects of the interaction will be presented in detail. We find that, during stable operation, aperiodic oscillations of the pressure and the heat release rate remain desynchronized, whereas synchronized periodic oscillations are noticed during the occurrence of thermoacoustic instability. Such a transition happens through intermittent phase-synchronized oscillations, wherein synchronization and desynchronization of the oscillators are observed during the periodic and the aperiodic epochs of the intermittent oscillations, respectively. Further, the spatiotemporal analysis reveals a very interesting pattern in the reaction zone. Phase asynchrony among the local heat release rate oscillators is observed during the stable operation, while they become phase-synchronized during the onset of thermoacoustic instability. Interestingly, the state of intermittent oscillations corresponds to a simultaneous existence of synchronized periodic and desynchronized aperiodic patterns in the reaction zone. Such a coexistence of synchrony and asynchrony in the reactive flow field mimics a chimera state. © 2018, Springer Nature Singapore Pte Ltd.

Green Energy and Technology

Synchronization transition in a thermoacoustic system: Temporal and spatiotemporal analyses

Analysis of thermoacoustic instabilities were dominated by modal (eigenvalue) analysis for many decades. Recent progress in nonmodal stability analysis allows us to study the problem from a different perspective, by quantitatively describing the short-term behavior of disturbances. The short-term evolution has a bearing on subcritical transition to instability, known popularly as triggering instability in thermoacoustic parlance. We provide a review of the recent developments in the context of triggering instability. A tutorial for nonmodal stability analysis is provided. The applicability of the tools from nonmodal stability analysis are demonstrated with the help of a simple model of a Rjike tube. The article closes with a brief description of how to characterize bifurcations in thermoacoustic systems. © The Author(s) 2016.

International Journal of Spray and Combustion Dynamics

Non-normality and nonlinearity in thermoacoustic instabilities

The influence of system parameters such as heater power, heater location and mass flow rate on the hysteresis characteristics of a horizontal Rijke tube is presented in this paper. It is observed that a hysteresis zone is present for all the mass flow rates considered in the present study. A power law relation is established between the non-dimensional hysteresis width and the Strouhal number, defined as the ratio between convective time scale and acoustic time scale. The transition to instability in a horizontal Rijke tube is found to be subcritical in all the experiments performed in this study. When heater location is chosen as the control parameter, period-2 oscillations are found for specific values of mass flow rate and heater power.

Journal	Data powered by TypesetChaos
Publisher	Data powered by TypesetAmerican Institute of Physics Inc.
ISSN	10541500
Open Access	No