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Sound propagation using an adjoint-based method

Published online by Cambridge University Press:  31 July 2020

Étienne Spieser Open the ORCID record for Étienne Spieser [Opens in a new window]  and
Christophe Bailly Open the ORCID record for Christophe Bailly [Opens in a new window]
Étienne Spieser*
Affiliation:
Univ Lyon, École Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon I, CNRS, Laboratoire de Mécanique des Fluides et d'Acoustique, UMR 5509, F-69134Écully, France Safran Aircraft Engines, 77500 Moissy-Cramayel, France
Christophe Bailly
Affiliation:
Univ Lyon, École Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon I, CNRS, Laboratoire de Mécanique des Fluides et d'Acoustique, UMR 5509, F-69134Écully, France
*
†Email address for correspondence: etienne.spieser@ec-lyon.fr
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Abstract

In this study, a comprehensive description of the adjoint formulation based on a systematic use of Lagrange's identity is proposed to compute acoustic propagation effects induced by the presence of a mean flow. The adjoint method is a clever approach introduced by Tam & Auriault (J. Fluid Mech., vol. 370, 1998, pp. 149–174) in aeroacoustics to predict noise of distributed stochastic sources in a complex environment. A clear statement is also provided about the application of the flow reversal theorem, and its restriction to self-adjoint wave equations. As an illustration, sound propagation is computed numerically over a sheared and stratified mean flow for Lilley's and Pierce's wave equations. Acoustic solutions obtained with the adjoint approach are then compared with predictions obtained with the flow reversal theorem. Additionally Pierce's wave equation for potential acoustics is identified as an outstanding candidate to compute accurately acoustic propagation while removing possible instability waves.

JFM classification

Acoustics: Aeroacoustics

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JFM Papers
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Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A5
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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