Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-29T13:09:33.068Z Has data issue: false hasContentIssue false
  • English
  • Français

The modified Myers boundary condition for swirling flow

Published online by Cambridge University Press:  29 May 2018

James R. Mathews Open the ORCID record for James R. Mathews [Opens in a new window] ,
Vianney Masson Open the ORCID record for Vianney Masson [Opens in a new window] ,
Stéphane Moreau  and
Hélène Posson
James R. Mathews
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1TN, UK
Vianney Masson
Affiliation:
Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada
Stéphane Moreau*
Affiliation:
Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada
Hélène Posson
Affiliation:
Acoustic Department, Airbus Commercial Aircraft, 31060 Toulouse, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper gives a modified Myers boundary condition in swirling inviscid flow, which differs from the standard Myers boundary condition by assuming a small but non-zero boundary layer thickness. The new boundary condition is derived and is shown to have the correct quadratic error behaviour with boundary layer thickness and also to agree with previous results when the swirl is set to zero. The boundary condition is initially derived for swirling flow with constant azimuthal velocity, but easily extends to radially varying swirling flow, with terms depending on the boundary layer model. The modified Myers boundary condition is then given in the time domain rather than in the frequency domain. The effect of the boundary layer profile is then considered, and shown to be small compared to the boundary layer thickness. The boundary condition is then used to analyse the eigenmodes and Green’s function in a realistic flow. Modelling the thickness of the boundary layer properly is shown to be essential in order to get accurate results.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics Boundary Layers: Boundary Layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , pp. 868 - 906
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

ACARE2012 Strategic Research Agenda: Volume 1, http://www.eurosfaire.prd.fr/7pc/doc/1349425601 _sria_acare_vol1.pdf.Google Scholar
Aurégan, Y., Starobinski, R. & Pagneux, V. 2001 Influence of grazing flow and dissipation effects on the acoustic boundary conditions at a lined wall. J. Acoust. Soc. Am. 109 (1), 59–64.Google Scholar
Bers, A. 1983 Space–time evolution of plasma instabilities-absolute and convective. In Basic Plasma Physics, vol. 1. North-Holland.Google Scholar
Brambley, E. J. 2009 Fundamental problems with the model of uniform flow over acoustic linings. J. Sound Vib. 322 (4), 1026–1037.Google Scholar
Brambley, E. J. 2011 Well-posed boundary condition for acoustic liners in straight ducts with flow. AIAA J. 49 (6), 1272–1282.Google Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT Press.Google Scholar
Driscoll, T. A., Hale, N. & Trefethen, L. N. 2014 Chebfun Guide. Pafnuty Publications.Google Scholar
European Commision2011 Flightpath 2050: Europe’s vision for aviation: Maintaining global leadership & serving societys needs.Google Scholar
Eversman, W. & Beckemeyer, R. J. 1972 Transmission of sound in ducts with thin shear layers convergence to the uniform flow case. J. Acoust. Soc. Am. 52 (1B), 216–220.CrossRefGoogle Scholar
Gabard, G. 2013 A comparison of impedance boundary conditions for flow acoustics. J. Sound Vib. 332 (4), 714–724.CrossRefGoogle Scholar
Golubev, V. V. & Atassi, H. M. 1998 Acoustic–vorticity waves in swirling flows. J. Sound Vib. 209, 203–222.CrossRefGoogle Scholar
Guan, Y., Luo, K. H. & Wang, T. Q. 2008 Sound transmission in a lined annular duct with mean swirling flow. In ASME 2008 Noise Control and Acoustics Division Conference, pp. 135–144. American Society of Mechanical Engineers.Google Scholar
Heaton, C. J. & Peake, N. 2005 Acoustic scattering in a duct with mean swirling flow. J. Fluid Mech. 540, 189–220.CrossRefGoogle Scholar
Hughes, C., Jeracki, R., Woodward, R. & Miller, C. 2002 Fan noise source diagnostic test-rotor alone aerodynamic performance results. In 8th AIAA/CEAS Aeroacoustics Conference, Breckenridge, Colorado. AIAA.Google Scholar
Ingard, U. 1959 Influence of fluid motion past a plane boundary on sound reflection, absorption, and transmission. J. Acoust. Soc. Am. 31 (7), 1035–1036.CrossRefGoogle Scholar
Joubert, L.2010 Asymptotic approach for the mathematical and numerical analysis of the acoustic propagation in a strong shear flow. PhD thesis, École Polytechnique (in French).Google Scholar
Khamis, D. & Brambley, E. J. 2016 Acoustic boundary conditions at an impedance lining in inviscid shear flow. J. Fluid Mech. 796, 386–416.Google Scholar
Maldonado, A. L. P., Astley, R. J., Coupland, J., Gabard, G. & Sutliff, D. 2015 Sound propagation in lined annular ducts with mean swirling flow. In 21st AIAA/CEAS Aeroacoustics Conference, Dallas, Texas, AIAA.Google Scholar
Masson, V.2018 Sound propagation in a possibly lined annular duct with swirling and sheared mean flow: application to fan broadband noise prediction. Thèse de doctorat de l’université de Lyon opérée au sein de l’Ecole Centrale de Lyon. http://www.theses.fr/2018LYSEC007.Google Scholar
Masson, V., Mathews, J. R., Moreau, S., Posson, H. & Brambley, E. J. 2017 The impedance boundary condition for acoustics in swirling ducted flow. J. Fluid Mech. (submitted).Google Scholar
Mathews, J. R., Masson, V., Moreau, S. & Posson, H. 2017 The modified Myers boundary condition for swirling flow. In 23rd AIAA/CEAS Aeroacoustics Conference, Denver, Colorado, AIAA.Google Scholar
Mathews, J. R. & Peake, N. 2017 The acoustic Green’s function for swirling flow in a lined duct. J. Sound Vib. 395, 294–316.Google Scholar
Myers, M. K. 1980 On the acoustic boundary condition in the presence of flow. J. Sound Vib. 71 (3), 429–434.Google Scholar
Myers, M. K. & Chuang, S. L. 1984 Uniform asymptotic approximations for duct acoustic modes in a thin boundary-layer flow. AIAA J. 22 (9), 1234–1241.CrossRefGoogle Scholar
Nayfeh, A. H., Kaiser, J. E. & Shaker, B. S. 1974 Effect of mean-velocity profile shapes on sound transmission through two-dimensional ducts. J. Sound Vib. 34 (3), 413–423.Google Scholar
Posson, H. & Peake, N. 2013 The acoustic analogy in an annular duct with swirling mean flow. J. Fluid Mech. 726, 439–475.Google Scholar
Pridmore-Brown, D. C. 1958 Sound propagation in a fluid flowing through an attenuating duct. J. Fluid Mech. 4, 393–406.Google Scholar
Renou, Y. & Aurégan, Y. 2011 Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation. J. Acoust. Soc. Am. 130 (1), 52–60.Google Scholar
Rienstra, S. W. & Darau, M. 2011 Boundary-layer thickness effects of the hydrodynamic instability along an impedance wall. J. Fluid Mech. 671, 559–573.CrossRefGoogle Scholar
Tam, C. K. W. & Auriault, L. 1998 The wave modes in ducted swirling flows. J. Fluid Mech. 371, 1–20.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
Woodward, R., Hughes, C., Jeracki, R. & Miller, C. 2002 Fan noise source diagnostic test–far-field acoustic results. In 8th AIAA/CEAS Aeroacoustics Conference, Breckenridge, Colorado, AIAA.Google Scholar
Supplementary material: File

Mathews et al. supplementary material

Mathews et al. supplementary material 1

Download Mathews et al. supplementary material(File)
File 96.5 KB