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Sound wave scattering in a flow duct with azimuthally non-uniform liners

Published online by Cambridge University Press:  02 February 2018

Hanbo Jiang ,
Alex Siu Hong Lau  and
Xun Huang Open the ORCID record for Xun Huang [Opens in a new window]
Hanbo Jiang
Affiliation:
Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong SAR, China
Alex Siu Hong Lau
Affiliation:
Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong SAR, China
Xun Huang*
Affiliation:
Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong SAR, China State Key Laboratory of Turbulence and Complex Systems, Aeronautics and Astronautics, College of Engineering, Peking University, Beijing, China
*
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Novel acoustic liner designs often incorporate new materials with non-uniform impedance distributions. Therefore, new methods are required for their modelling and analysis. In this paper, a theoretical model is developed to investigate the scattering of sound waves from an axially symmetrical flow duct with a semi-infinite, azimuthally non-uniform acoustic lining on the duct wall. More specifically, the incorporation of Fourier series expansions into the Wiener–Hopf method leads to an analytical model with a matrix kernel, which is further factorised by using the pole-removal method to obtain a closed-form solution. A new mathematical method is developed to solve the residues associated with the pole-removal technique. The proposed model has been verified and validated by comparing with corresponding computational results. In addition to shedding light on the possible physical effect of azimuthally non-uniform liners along with an axial hard–soft interface, the current model enhances the theoretical modelling capability for a complicated set-up of practical importance, and can be used to investigate new liner designs for passive noise control in flow ducts.

JFM classification

Acoustics: Aeroacoustics Acoustics: Noise control Acoustics: Waves in random media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , pp. 644 - 662
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Copyright
© 2018 Cambridge University Press 

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References

Abrahams, I. D. 1987 Scattering of sound by three semi-infinite planes. J. Sound Vib. 112 (2), 396–398.Google Scholar
Boorsma, K., Zhang, X. & Molin, N. 2010 Landing gear noise control using perforated fairings. Acta Mech. Sin. 26 (2), 159–174.Google Scholar
Brambley, E. J., Davis, A. M. J. & Peake, N. 2012 Eigenmodes of lined flow ducts with rigid splices. J. Fluid Mech. 690, 399–425.Google Scholar
Campos, L. M. B. C. & Oliveira, J. M. G. S. 2004 On the optimization of non-uniform acoustic liners on annular nozzles. J. Sound Vib. 275 (3), 557–576.Google Scholar
Campos, L. M. B. C. & Oliveira, J. M. G. S. 2013 On sound generation in cylindrical flow ducts with non-uniform wall impedance. Intl J. Aeroacoust. 12 (4), 309–347.Google Scholar
Fuller, C. R. 1984 Propagation and radiation of sound from flanged circular ducts with circumferentially varying wall admittances, i: semi-infinite ducts. J. Sound Vib. 93 (3), 321–340.Google Scholar
Gabard, G. & Astley, R. J. 2006 Theoretical model for sound radiation from annular jet pipes: far- and near-field solutions. J. Fluid Mech. 549, 315–341.Google Scholar
Huang, X. 2017 Theoretical model of acoustic scattering from a flat plate with serrations. J. Fluid Mech. 819, 228–257.Google Scholar
Huang, X., Chen, X. X., Ma, Z. K. & Zhang, X. 2008 Efficient computation of spinning modal radiation through an engine bypass duct. AIAA J. 46 (6), 1413–1423.Google Scholar
Huang, X., Zhong, S. Y. & Liu, X. 2014 Acoustic invisibility in turbulent fluids by optimised cloaking. J. Fluid Mech. 749, 460–477.Google Scholar
Idemen, M. 1979 A new method to obtain exact solutions of vector Wiener–Hopf equations. Z. Angew. Math. Mech. 59 (11), 656–658.Google Scholar
Jiang, H. B. & Huang, X. 2017a Efficient impedance eductions for liner tests in grazing flow incidence tube. J. Vib. Acoust. 139 (3), 031002.Google Scholar
Jiang, H. B., Lau, A. & Huang, X. 2017b An efficient algorithm of Wiener–Hopf method with graphics processing unit for duct acoustics. J. Vib. Acoust. 139 (5), 054501.Google Scholar
Koch, W. & Möhring, W. 1983 Eigensolutions for liners in uniform mean flow ducts. AIAA J. 21 (2), 200–213.Google Scholar
Liu, X., Huang, X. & Zhang, X. 2014 Stability analysis and design of time-domain acoustic impedance boundary conditions for lined duct with mean flow. J. Acoust. Soc. Am. 136 (5), 2441–2452.Google Scholar
Liu, X., Jiang, H. B., Huang, X. & Chen, S. Y. 2015 Theoretical model of scattering from flow ducts with semi-infinite axial liner splices. J. Fluid Mech. 786, 62–83.Google Scholar
McAlpine, A. & Wright, M. C. M. 2006 Acoustic scattering by a spliced turbofan inlet duct liner at supersonic fan speeds. J. Sound Vib. 292 (3), 911–934.Google Scholar
Munt, R. M. 1977 The interaction of sound with a subsonic jet issuing from a semi-infinite cylindrical pipe. J. Fluid Mech. 83 (04), 609–640.Google Scholar
Noble, B. 1958 Methods Beaded on the Wiener–Hopf Technique for the Solution of Partial Differential Equations. Pergamon Press.Google Scholar
Rawlins, A. D. 1980 Simultaneous Wiener–Hopf equations. Can. J. Phys. 58 (3), 420–428.Google Scholar
Rienstra, S. W. 2007 Acoustic scattering at a hard-soft lining transition in a flow duct. J. Engng Maths 59, 451–475.Google Scholar
Rienstra, S. W. & Eversman, W. 2001 A numerical comparison between the multiple-scales and finite-element solution for sound propagation in lined flow ducts. J. Fluid Mech. 437, 367–384.Google Scholar
Tester, B. J. 1973 Some aspects of sound attenuation in lined ducts containing inviscid mean flows with boundary layers. J. Sound Vib. 28 (2), 217–245.Google Scholar
Veitch, B. & Peake, N. 2008 Acoustic propagation and scattering in the exhaust flow from coaxial cylinders. J. Fluid Mech. 613, 275–307.Google Scholar
Wright, M. C. M. & McAlpine, A. 2007 Calculation of modes in azimuthally non-uniform lined ducts with uniform flow. J. Sound Vib. 302 (3), 403–407.Google Scholar
Zhang, Q. & Bodony, D. J. 2016 Numerical investigation of a honeycomb liner grazed by laminar and turbulent boundary layers. J. Fluid Mech. 792, 936–980.Google Scholar
Zhang, X. 2012 Aircraft noise and its nearfield propagation computations. Acta Mecha. Sin. 28 (4), 960–977.Google Scholar
Zhao, X. C., Liu, G. M., Zhao, C. M. & Grosh, K. 2014 Broadband noise attenuation using a variable locally reacting impedance. J. Acoust. Soc. Am. 141 (1), 147–158.Google Scholar