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Thermoacoustic Instability: A Complex Systems Perspective
ISBN-13: 9783030811341 / Angielski / Twarda / 2021 / 480 str.
Thermoacoustic Instability: A Complex Systems Perspective
ISBN-13: 9783030811341 / Angielski / Twarda / 2021 / 480 str.
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1 Introduction
1.1 Introduction to thermoacoustic instability and its consequences
1.2 Mechanisms that cause thermoacoustic instability
1.2.1 Flame surface area modulations
1.2.2 Equivalence ratio fluctuations
1.2.3 Coherent structures in the flow
1.2.4 Entropy waves
1.3 Mechanisms that damp thermoacoustic instability
1.4 Current approaches: Acoustic oscillations driven by unsteady combustion, network modelling, and eigenvalues
1.5 Why do we need a nonlinear description?
1.6 Nonlinearities in a thermoacoustic system
1.7 Thermoacoustic stability analysis: Acoustic vs dynamical systems approach
1.8 Beyond limit cycles
1.9 Thermoacoustic instability in turbulent combustors
1.10 Transition to thermoacoustic instability in turbulent reacting flow systems
1.10.1 Is combustion noise deterministic or stochastic?
1.10.2 Studying the transition to thermoacoustic instability in “noisy” systems
1.10.3 Noise induced transition, stochastic bifurcation and Fokker-Planck equation
1.10.4 Is ‘signal plus noise’ paradigm the right way to go about?
1.11 Alternate perspectives
1.11.1 Combustion noise is chaos
1.11.2 Intermittency presages the onset of thermoacoustic instability
1.11.3 Multifractal description of combustion noise and its transition to thermoacoustic instability
1.11.4 Complex networks
1.11.5 On the importance of being nonlinear
1.11.6 Reductionist vs complex systems approach
1.12 References
2 Introduction to Dynamical Systems Theory
2.1 Dynamical system
2.1.1 Conservative and dissipative dynamical systems
2.1.2 Modeling dynamical systems as discrete and continuous functions of time
2.2 Linear approximation of one-dimensional systems
2.2.1 Two-dimensional linear systems
2.3 Bifurcations and their classification
2.3.1 Saddle-node bifurcation
2.3.2 Transcritical bifurcation
2.3.3 Pitchfork bifurcation
2.3.4 Hopf bifurcation
2.4 Signals and their classification
2.4.1 Limit cycle oscillations
2.4.2 Period-= oscillations
2.4.3 Quasiperiodic oscillations
2.4.4 Chaotic oscillations
2.4.5 Difference between strange chaotic, strange nonchaotic, and chaotic nonstrange attractors
2.4.6 Intermittency
2.5 Routes to chaos
2.5.1 Period-doubling route to chaos
2.5.2 Quasiperiodic route to chaos
2.5.3 Intermittency route to chaos
2.6 Phase space reconstruction
2.6.1 Selection of optimum time delay ()
2.6.2 Selection of the minimum emending dimension (d)2.7 Poincaré map (or Poincaré section or return map)
2.8 Recurrence plots
2.8.1 Cross recurrence plots
2.8.2 Joint recurrence plot
2.8.3 Recurrence quantification analysis
2.9 References
3 Bifurcation to Limit Cycle Oscillations in Laminar Thermoacoustic Systems
3.1 A brief history of Rijke-type thermoacoustic systems
3.2 Bifurcation characteristics of a deterministic thermoacoustic system
3.3 Noise-induced transition, triggering, and stochastic bifurcation to limit cycle
3.3.1 Effect of noise on hysteresis (or bistability) of a subcritical Hopf bifurcation
3.3.2 Stochastic (or P) bifurcation
3.3.3 Triggering in thermoacoustic systems
3.4 References
4 Thermoacoustic Instability: Beyond Limit Cycle Oscillations
4.1 Bifurcation of thermoacoustic instability beyond the state of limit cycle
4.2 Other dynamical states of thermoacoustic instability
4.2.1 Strange nonchaos
4.2.2 Intermittency
4.3 Routes to chaos for thermoacoustic oscillations
4.3.1 Period-doubling route to chaos
4.3.2 Ruelle-Takens-Newhouse route to chaos
4.3.3 Intermittency route to chaos
4.4 Nonlinear nature of flame-acoustic interactions
4.5 References
5 Thermoacoustic Instability is Self-Organization in a Complex System
5.1 Examples of complex systems
5.2 Nonlinearity: The reductionist’s nightmare
5.3 Emergence
5.4 Pattern formation 5.5 Order emerging from chaos5.6 Onset of thermoacoustic instability in turbulent combustors
5.7 Fractals and multifractals
5.8 Collective interaction in complex systems
5.9 Complex networks
5.10 Why should we use complex systems approach to study thermoacoustic instability in turbulent combustors?
5.11 Practical applications
5.12 References
6 Intermittency - A State Precedes Thermoacoustic Instability and Blowout in Turbulent Combustors
6.1 Classification of sound waves generated by turbulent flame in a combustor
6.2 What is combustion noise?
6.2.1 Phase space dynamics of acoustic pressure fluctuations during combustion noise
6.2.2 0-1 test for chaos
6.3 What is thermoacoustic instability?
6.4 Transition from combustion noise to thermoacoustic instability in turbulent combustors
6.4.1 Reformulating the onset of thermoacoustic instability as a loss of chaos
6.4.2 Intermittency route to thermoacoustic instability
6.4.3 Characteristics of the intermittency signal
6.4.4 Bifurcation analysis of intermittency route to thermoacoustic instability
6.5 Phase space and recurrence analysis of the intermittency route to thermoacoustic instability
6.6 Intermittency route to flame blowout
6.7 Type of intermittency en-route to thermoacoustic instability and its scaling laws
6.8 References
7 Spatiotemporal Dynamics of Flow, Flame, and Acoustic Fields during the Onset of Thermoacoustic Instability
7.1 Pattern formation
7.2 The emergence of patterns during the onset of thermoacoustic instability
7.3 Collective interaction of large-scale vortices during thermoacoustic instability
7.4 References
8 Synchronization of Self-excited Acoustics and Turbulent Reacting Flow Dynamics
8.1 Basics of synchronization of coupled oscillators
8.2 Mutual synchronization of the acoustic and turbulent reactive flow fields during the transition to thermoacoustic instability
8.2.1 Coupled behavior of the acoustic field and the heat release rate field in a turbulent combustor
8.2.2 Synchronization of the acoustic pressure and the global heat release rate signals during the onset of thermoacoustic instability
8.2.3 Spatiotemporal synchronization of the turbulent reacting flow field with the duct acoustics
8.3 Forced synchronization of limit cycle oscillations in thermoacoustic systems
8.3.1 Forced response of the self-excited acoustic field
8.3.2 Forced synchronization of limit cycle oscillations in a horizontal Rijke tube
8.3.3 Characteristics of the acoustic field and the heat release rate field during forced synchronization in a laminar combustor
8.3.4 Forced synchronization of multi-frequency (quasiperiodic and chaotic) thermoacoustic oscillations
8.3.5 Characteristics of forced synchronization of limit cycle oscillations in turbulent combustors
8.3.6 Forced synchronization of self-excited oscillations in the hydrodynamic field
8.4 References
9 Model for Intermittency Route to Thermoacoustic Instability
9.1 Governing equations for the one-dimensional fluid flow.
9.1.1 Continuity equation
9.1.2 Momentum equation
9.1.3 Energy equation
9.1.4 Linearized governing equations for the acoustic field
9.2 Model for intermittency route to thermoacoustic instability
9.3 References
10 Multifractal Analysis of a Turbulent Thermoacoustic System
10.1 Fractals
10.2 The Hurst exponent and fractal properties
10.3 Multifractals
10.4 Methods of multifractal analysis
10.4.1 Multifractal detrended fluctuation analysis (MFDFA)
10.4.2 Box-counting method
10.5 Combustion noise is multifractal and thermoacoustic instability is a loss of multifractality
10.6 Multifractal analysis during the transition to a flame blowout
10.7 Multifractal analysis of spatial flame structures during stable and unstable operation
10.8 References
11 Complex Network Approach to Thermoacoustic Systems
11.1 An introduction to complex networks
11.2 Measures of complex networks
11.3 Types of complex networks
11.3.1 Regular networks
11.3.2 Random network
11.3.3 Small-world networks
11.3.4 Scale-free networks
11.4 Complex network approach to study temporal dynamics of thermoacoustic systems
11.4.1 Combustion noise is scale-free
11.4.2 The onset of thermoacoustic instability as a transition from scale-free to regular networks
11.4.3 Small-world-like behavior of thermoacoustic instability using cycle network
11.4.4 Recurrence network topologies of different dynamical states of a thermoacoustic system
11.4.5 Directional dependence between the coupled acoustic pressure and heat release rate fluctuations using recurrence networks
11.5 Complex network approach to study spatial dynamics of thermoacoustic systems
11.5.1 Unweighted spatial networks of the time-averaged flow field using the Pearson coefficient
11.5.2 Weighted time-varying spatial networks obtained though acoustic power and vorticity fields
11.5.3 Weighted time-varying turbulence networks obtained though vorticity fields
11.6 References
12 Early Warning and Mitigation Strategies for Thermoacoustic Instability
12.1 Precursors for the onset of impending thermoacoustic instability . . . 418
12.2 Traditional approaches for passive and active controls of thermoacoustic instability
12.3 Control of thermoacoustic instability using methodologies from synchronization theory
12.3.1 Mitigation of thermoacoustic instability using amplitude death phenomenon
12.3.2 Open-loop control of thermoacoustic instability through asynchronous quenching
12.4 Identification of critical regions in the spatial reacting field
12.5 References
13 Oscillatory Instabilities in Other Fluid Systems
13.1 Aeroacoustic instabilities
13.2 Aeroelastic instabilities
13.3 References
14 Summary and Perspective
14.1 Temporal analysis
14.2 Spatiotemporal analysis
14.3 Mitigation Strategies
14.3.1 Evasion 14.3.2 Strategies based on the framework of synchronization theory 14.3.3 Smart passive control 14.4 Future issues14.5 Final thoughts
14.6 References
Prof. R. I. Sujith received his Ph. D. adorned with the “top graduate student in the college of engineering” award from Georgia Institute of Technology in 1994 under the supervision of Prof. Ben T Zinn. He is currently the D. Srinivasan Chair Professor at the Department of Aerospace Engineering at the Indian Institute of Technology Madras. He is a recipient of the prestigious Alexander von Humboldt Fellowship and the Hans Fischer Senior Fellowship of the Institute for Advanced Study (IAS) at the Technical University of Munich. Prof. Sujith was the founding Editor-in-Chief of the International Journal of Spray and Combustion Dynamics from 2009-2015, and is at present a member of the editorial advisory board of the interdisciplinary journal Chaos. He won the Young Engineer Award of the Indian National Academy of Engineering. He has also been awarded the Swarnajayanti Fellowship and the J. C. Bose Fellowship by the Department of Science and Technology India. He is a fellow of the Indian National Academy of Engineering and the Indian Academy of Sciences, and has been conferred the title of “TUM Ambassador” by the Technical University of Munich. Prof. Sujith currently works on the application of dynamical systems and complex systems theory to study and mitigate thermoacoustic instability.
Dr. Samadhan A. Pawar received his Ph. D. from the Indian Institute of Technology Madras under the supervision of Prof. R. I. Sujith and Prof. Mahesh V. Panchagnula. He was conferred the ‘Institute Research Award’ from IIT Madras (2018) in recognition of his doctoral research work on the application of synchronization theory to thermoacoustic systems. Dr. Pawar has also been awarded the ‘Young Scientist Award 2021’ by the International Society for Energy, Environment and Sustainability (ISEES) in view of his impressive contributions to the research field at a very young age. Currently, he is a Postdoctoral Fellow in Prof. Sujith’s lab at IIT Madras. His work highlights the maiden experimental and theoretical characterization of the onset of thermoacoustic instability and its control using dynamical systems theory and complex systems theory.
This book systematically presents the consolidated findings of the phenomenon of self-organization observed during the onset of thermoacoustic instability using approaches from dynamical systems and complex systems theory. Over the last decade, several complex dynamical states beyond limit cycle oscillations such as quasiperiodicity, frequency-locking, period-n, chaos, strange non-chaos, and intermittency have been discovered in thermoacoustic systems operated in laminar and turbulent flow regimes. During the onset of thermoacoustic instability in turbulent systems, an ordered acoustic field and large coherent vortices emerge from the background of turbulent combustion. This emergence of order from disorder in both temporal and spatiotemporal dynamics is explored in the contexts of synchronization, pattern formation, collective interaction, multifractality, and complex networks.
For the past six decades, the spontaneous emergence of large amplitude, self-sustained, tonal oscillations in confined combustion systems, characterized as thermoacoustic instability, has remained one of the most challenging areas of research. The presence of such instabilities continues to hinder the development and deployment of high-performance combustion systems used in power generation and propulsion applications. Even with the advent of sophisticated measurement techniques to aid experimental investigations and vast improvements in computational power necessary to capture flow physics in high fidelity simulations, conventional reductionist approaches have not succeeded in explaining the plethora of dynamical behaviors and the associated complexities that arise in practical combustion systems. As a result, models and theories based on such approaches are limited in their application to mitigate or evade thermoacoustic instabilities, which continue to be among the biggest concerns for engine manufacturers today. This book helps to overcome these limitations by providing appropriate methodologies to deal with nonlinear thermoacoustic oscillations, and by developing control strategies that can mitigate and forewarn thermoacoustic instabilities.
The book is also beneficial to scientists and engineers studying the occurrence of several other instabilities, such as flow-induced vibrations, compressor surge, aeroacoustics and aeroelastic instabilities in diverse fluid-mechanical environments, to graduate students who intend to apply dynamical systems and complex systems approach to their areas of research, and to physicists who look for experimental applications of their theoretical findings on nonlinear and complex systems.
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