Thermoacoustic Instability

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, tonaloscillations 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.

Autorentext

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.

Inhalt

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 subcri…