Thermoacoustic Instability: A Complex Systems Perspective

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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.

Author(s): R. I. Sujith, Samadhan A. Pawar
Series: Springer Series in Synergetics
Publisher: Springer
Year: 2021

Language: English
Pages: 492
City: Cham

Foreword by Jürgen Kurths
Foreword by Timothy C. Lieuwen
Preface
Acknowledgments
Contents
About the Authors
1 Introduction
1.1 Introduction to Thermoacoustic Instability and itsConsequences
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 Versus Dynamical Systems Approach
1.7.1 Traditional Acoustic Approach
1.7.1.1 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
References
2 An 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
2.3.3.1 Supercritical Pitchfork Bifurcation
2.3.3.2 Subcritical Pitchfork Bifurcation
2.3.4 Hopf Bifurcation
2.3.4.1 Supercritical Hopf Bifurcation
2.3.4.2 Subcritical Hopf Bifurcation
2.4 Signals and Their Classification
2.4.1 Limit Cycle Oscillations
2.4.2 Period-n Oscillations
2.4.3 Quasiperiodic Oscillations
2.4.4 Chaotic Oscillations
2.4.4.1 Lyapunov Exponent
2.4.4.2 Correlation Dimension
2.4.5 Difference Between Strange Chaotic, Strange Nonchaotic, and Chaotic Nonstrange Signals
2.4.6 Intermittency
2.4.6.1 Types of 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 (τ)
2.6.1.1 Autocorrelation Function
2.6.1.2 Average Mutual Information
2.6.2 Selection of the Minimum Embedding Dimension (d)
2.6.2.1 False Nearest Neighbor Method
2.6.2.2 Cao's Method
2.7 Poincaré Section (or First Return Map)
2.8 Recurrence Plots
2.8.1 Cross Recurrence Plots
2.8.2 Joint Recurrence Plot
2.8.3 Recurrence Quantification Analysis
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
3.3.3.1 What Causes Triggering?
3.3.3.2 Triggering Due to Deterministic Perturbations
3.3.3.3 Noise-Induced Triggering
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 Behavior of Flame-Acoustic Interactions
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 Chaos
5.6 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
References
6 Intermittency—A State That 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 The Phase Space Reconstruction
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
6.4.2.1 Characteristics of the Intermittency Signal
6.4.2.2 Bifurcation Analysis of Intermittency Route to Thermoacoustic Instability
6.4.2.3 Phase Space and Recurrence Analysis of the Intermittency Route to Thermoacoustic Instability
6.5 Intermittency Route to Flame Blowout
6.6 Type of Intermittency En-Route to Thermoacoustic Instability and Its Scaling Laws
References
7 Spatiotemporal Dynamics of Flow, Flame, and Acoustic Fields During the Onset of Thermoacoustic Instability
7.1 Pattern Formation
7.2 Pattern Formation in Turbulent Thermoacoustic Systems
7.2.1 Emergence Versus Self-Organization
7.2.2 The Emergence of Patterns During the Onset of Thermoacoustic Instability
7.3 Collective Interaction of Large-Scale Vortices During Thermoacoustic Instability
References
8 Synchronization Between the Acoustic Field of the Confinement and the Turbulent Reacting Flow
8.1 Basics of Synchronization of Coupled Oscillators
8.2 Mutual Synchronization of the Acoustic Field and the Turbulent Reactive Flow Field in Thermoacoustic Systems
8.2.1 Temporal Dynamics of the Acoustic Pressure Field and the Heat Release Rate Field in a Turbulent Combustor
8.2.2 Temporal Synchronization of the Acoustic Pressure and the Global Heat Release RateFluctuations
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 Basics of Forced Synchronization of an Oscillator
8.3.2 Forced Response of the Self-Excited Acoustic Field
8.3.2.1 Forced Synchronization of Limit Cycle Oscillations in a Horizontal Rijke Tube
8.3.3 Forced Synchronization of the Acoustic Field and the Heat Release Rate Field in LaminarCombustors
8.3.4 Forced Synchronization of 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
References
9 Model for Intermittency Route to Thermoacoustic Instability
9.1 Model Description
9.2 Intermittency Route to Thermoacoustic Instability in Model
References
10 Multifractal Analysis of Turbulent Thermoacoustic Systems
10.1 Fractals
10.1.1 Self-Similarity, Scale-Invariance, and Self-Affinity
10.1.2 The Fractal Dimension
10.1.3 The Hurst Exponent and Properties of Fractal Signals
10.2 Multifractals
10.2.1 Methods of Multifractal Analysis
10.2.1.1 Multifractal Detrended Fluctuation Analysis (MFDFA)
10.2.1.2 Singularity Spectrum and Generalized Dimension
10.2.1.3 Modified Box-Counting Method
10.3 Multifractal Analysis of Thermoacoustic Systems
10.3.1 Loss of Multifractality Prior to Thermoacoustic Instability
10.3.2 Detection of Correlations Through Surrogate Analysis and Singularity Spectrum
10.3.3 Fractional-Order Van der Pol Model to Study Multifractality
10.3.4 Unified Multifractal Analysis During the Transition to Thermoacoustic Instability and Flame Blowout
10.3.5 Multifractal Behavior of Flame Surfaces
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 Thermoacoustic Instability as a Condensation Transition in the Phase Space
11.4.5 Recurrence Network Topologies of Different Dynamical States
11.4.6 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 Correlation Networks of the Time-Averaged Flow Field
11.5.1.1 Construction of Spatial Networks Using the Pearson Correlation
11.5.1.2 Networks Based on Dot Products
11.5.2 Weighted Time-Varying Spatial Networks Obtained Though Acoustic Power and VorticityFields
11.5.3 Weighted Time-Varying Turbulence Networks Obtained Though Vorticity Fields
References
12 Early Warning and Mitigation Strategies for Thermoacoustic Instability
12.1 Precursors for the Onset of Impending ThermoacousticInstability
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
12.3.1.1 Model for Studying Amplitude Death in Coupled Thermoacoustic Systems
12.3.1.2 Experiments for Studying Amplitude Death in Coupled Thermoacoustic Systems
12.3.2 Open-Loop Control of Thermoacoustic Instability Through Asynchronous Quenching
12.4 Identification of Critical Regions in the Spatial Reacting Field
References
13 Oscillatory Instabilities in Other Turbulent Flow Systems
13.1 Aeroacoustic Instabilities
13.2 Aeroelastic Instabilities
13.3 Scaling Behavior During the Onset of Oscillatory Instability
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 Issues
14.5 Final Thoughts
References
A Governing Equations for the One-Dimensional Fluid Flow
A.1 Continuity Equation
A.2 Momentum Equation
A.3 Energy Equation
A.4 Linearized Governing Equations for the Acoustic Field
A.4.1 Linearized Conservation of Mass Equation
A.4.2 Linearized Momentum Equation
A.4.3 Linearized Energy Equation
References
Index