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Acoustic Models for Cooled Helmholtz Resonators

Dong Yang

Imperial College London, London, England SW7 2AZ, United Kingdom

*Ph.D. Student, Department of Mechanical Engineering.

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and

Aimee S. Morgans

Imperial College London, London, England SW7 2AZ, United Kingdom

†Reader, Department of Mechanical Engineering.

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Published Online:30 May 2017https://doi.org/10.2514/1.J055854

Abstract

Helmholtz resonators are commonly used to damp thermoacoustic oscillations in aeroengine and gas turbine combustors. In practice, the Helmholtz resonator is often maintained at a cooler temperature than the combustor, but this tends to be neglected when modeling. In this work, we derive an analytical model for both the acoustic damping and the effect on the combustor thermoacoustics of Helmholtz resonators for which the volume is at a different temperature to the combustor. The energy conservation equation based on stagnation enthalpy, together with the mass and momentum conservation equations, is incorporated into a linear Helmholtz resonator sound-absorption model. These are coupled with linear wave-based models for the plane acoustic waves in the system to which the Helmholtz resonator is attached: here, a combustor. The temperature difference is found to generate an entropy wave that advects downstream of the resonator (and may generate further acoustic waves if accelerated) and to change the acoustic damping near the resonant frequency. This model for the Helmholtz resonator acoustics is then incorporated into a low-order network model for combustor thermoacoustics. The importance of capturing the effect of the Helmholtz resonator temperature difference on the overall thermoacoustic modes is clearly demonstrated.

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Volume 55, Number 9September 2017

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Copyright © 2017 by Dong Yang and Aimee S. Morgans. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the ISSN 0001-1452 (print) or 1533-385X (online) to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp.

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Acknowledgments

Dong Yang is supported by a Ph.D. scholarship from the Chinese Scholarship Council and Imperial College London, which is gratefully acknowledged. The financial support of Aimee S. Morgans’s European Research Council (ERC) Starting Grant [ACOULOMODE (2013–2018)—advanced coupling of low order combustor simulations with thermoacoustic modelling and controller design] is also acknowledged.

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Received22 November 2016
Accepted1 March 2017
Published online30 May 2017

Acoustic Models for Cooled Helmholtz Resonators

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