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Frequency domain and time domain analysis of thermoacoustic oscillations with wave-based acoustics


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Authors

Orchini, A 
Illingworth, SJ 
Juniper, MP 

Abstract

jats:pMany thermoacoustic systems exhibit rich nonlinear behaviour. Recent studies show that this nonlinear dynamics can be well captured by low-order time domain models that couple a level set kinematic model for a laminar flame, the jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112015001391_inline1" />jats:tex-mathG</jats:tex-math></jats:alternatives></jats:inline-formula>-equation, with a state-space realization of the linearized acoustic equations. However, so far the jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112015001391_inline2" />jats:tex-mathG</jats:tex-math></jats:alternatives></jats:inline-formula>-equation has been coupled only with straight ducts with uniform mean acoustic properties, which is a simplistic configuration. In this study, we incorporate a wave-based model of the acoustic network, containing area and temperature variations and frequency-dependent boundary conditions. We cast the linear acoustics into state-space form using a different approach from that in the existing literature. We then use this state-space form to investigate the stability of the thermoacoustic system, both in the frequency and time domains, using the flame position as a control parameter. We observe frequency-locked, quasiperiodic and chaotic oscillations. We identify the location of Neimark–Sacker bifurcations with Floquet theory. We also find the Ruelle–Takens–Newhouse route to chaos with nonlinear time series analysis techniques. We highlight important differences between the nonlinear response predicted by the frequency domain and the time domain methods. This reveals deficiencies with the frequency domain technique, which is commonly used in academic and industrial studies of thermoacoustic systems. We then demonstrate a more accurate approach based on continuation analysis applied to time domain techniques.</jats:p>

Description

Keywords

acoustics, low-dimensional models, nonlinear dynamical systems

Journal Title

Journal of Fluid Mechanics

Conference Name

Journal ISSN

0022-1120
1469-7645

Volume Title

775

Publisher

Cambridge University Press (CUP)
Sponsorship
Engineering and Physical Sciences Research Council (EP/H050310/1)
This project was funded by the European Research Council through Project ALORS 2590620.