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Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

Published online by Cambridge University Press:  29 December 2021

Calum S. Skene Open the ORCID record for Calum S. Skene [Opens in a new window]  and
Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]
Calum S. Skene*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
Kunihiko Taira
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: c.s.skene@leeds.ac.uk
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Abstract

Phase-reduction analysis captures the linear phase dynamics with respect to a limit cycle subjected to weak external forcing. We apply this technique to study the phase dynamics of the self-sustained oscillations produced by a Rijke tube undergoing thermoacoustic instability. Through the phase-reduction formulation, we are able to reduce these dynamics to a scalar equation for the phase, which allows us to efficiently determine the synchronisation properties of the system. For the thermoacoustic system, we find the conditions for which $m:n$ frequency locking occurs, which sheds light on the mechanisms behind asynchronous and synchronous quenching. We also reveal the optimal placement of pressure actuators that provide the most efficient route to synchronisation.

JFM classification

Acoustics: Acoustics Instability: Instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A35
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

‡

Present address: Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK.

References

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