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Sound propagation using an adjoint-based method

Published online by Cambridge University Press:  31 July 2020

Étienne Spieser*
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
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:


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.

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© The Author(s), 2020. Published by Cambridge University Press

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