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The impedance boundary condition for acoustics in swirling ducted flow

  • Vianney Masson (a1), James R. Mathews (a2), Stéphane Moreau (a1), Hélène Posson (a3) and Edward J. Brambley (a4)...

The acoustics of a straight annular lined duct containing a swirling mean flow is considered. The classical Ingard–Myers impedance boundary condition is shown not to be correct for swirling flow. By considering behaviour within the thin boundary layers at the duct walls, the correct impedance boundary condition for an infinitely thin boundary layer with swirl is derived, which reduces to the Ingard–Myers condition when the swirl is set to zero. The correct boundary condition contains a spring-like term due to centrifugal acceleration at the walls, and consequently has a different sign at the inner (hub) and outer (tip) walls. Examples are given for mean flows relevant to the interstage region of aeroengines. Surface waves in swirling flows are also considered, and are shown to obey a more complicated dispersion relation than for non-swirling flows. The stability of the surface waves is also investigated, and as in the non-swirling case, one unstable surface wave per wall is found.

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Atassi, H. M., Ali, A. A., Atassi, O. V. & Vinogradov, I. V. 2004 Scattering of incident disturbances by an annular cascade in a swirling flow. J. Fluid Mech. 499, 111138.
Bers, A. 1983 Space-time evolution of plasma instabilities-absolute and convective. In Basic Plasma Physics, vol. 1. North-Holland.
Brambley, E. J. 2009 Fundamental problems with the model of uniform flow over acoustic linings. J. Sound Vib. 322 (4), 10261037.
Brambley, E. J. 2011 Well-posed boundary condition for acoustic liners in straight ducts with flow. AIAA J. 49 (6), 12721282.
Brambley, E. J. 2013 Surface modes in sheared boundary layers over impedance linings. J. Sound Vib. 332 (16), 37503767.
Brambley, E. J. & Gabard, G. 2016 Time-domain implementation of an impedance boundary condition with boundary layer correction. J. Comput. Phys. 321, 755775.
Brambley, E. J. & Peake, N. 2006 Classification of aeroacoustically relevant surface modes in cylindrical lined ducts. Wave Motion 43 (4), 301310.
Brambley, E. J. & Peake, N 2008 Sound transmission in strongly curved slowly varying cylindrical ducts with flow. J. Fluid Mech. 596, 387412.
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT Press.
Cooper, A. J. & Peake, N. 2005 Upstream-radiated rotorstator interaction noise in mean swirling flow. J. Fluid Mech. 523, 219250.
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), 216220.
Gabard, G. 2013 A comparison of impedance boundary conditions for flow acoustics. J. Sound Vib. 332 (4), 714724.
Gabard, G. 2016 Boundary layer effects on liners for aircraft engines. J. Sound Vib. 381, 3047.
Golubev, V. V. & Atassi, H. M. 2000a Unsteady swirling flows in annular cascades, part 1: evolution of incident disturbances. AIAA J. 38 (7), 11421149.
Golubev, V. V. & Atassi, H. M. 2000b Unsteady swirling flows in annular cascades, part 2: aerodynamic blade response. AIAA J. 38 (7), 11501158.
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. 135144. American Society of Mechanical Engineers.
Heaton, C. J. & Peake, N. 2005 Acoustic scattering in a duct with mean swirling flow. J. Fluid Mech. 540, 189220.
Heaton, C. J. & Peake, N. 2006 Algebraic and exponential instability of inviscid swirling flow. J. Fluid Mech. 565, 279318.
Hughes, C. E., Jeracki, R. J., Woodward, R. P. & Miller, C. J. 2002 Fan noise source diagnostic test-rotor alone aerodynamic performance results. In 8th AIAA/CEAS Aeroacoustics Conference, Breckenridge (CO), USA, AIAA.
Ingard, U. 1959 Influence of fluid motion past a plane boundary on sound reflection, absorption, and transmission. J. Acoust. Soc. Am. 31 (7), 10351036.
Khamis, D. & Brambley, E. J. 2016 Acoustic boundary conditions at an impedance lining in inviscid shear flow. J. Fluid Mech. 796, 386416.
Khamis, D. & Brambley, E. J. 2017 Acoustics in a two-deck viscothermal boundary layer over an impedance surface. AIAA J. 55 (10), 33283345.
Khorrami, R., Malik, M. R. & Ash, R. L. 1989 Application of spectral collocation techniques to the stability of swirling flows. J. Comput. Phys. 81 (1), 206229.
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 (TX), USA, AIAA.
Masson, V., Mathews, J. R., Sanjose, M., Moreau, S. & Posson, H. 2017 Liner behavior in an annular duct with swirling and sheared mean flow. In 23rd AIAA/CEAS Aeroacoustics Conference, Denver (CO), USA, AIAA.
Masson, V., Posson, H., Sanjose, M., Moreau, S. & Roger, M. 2016 Fan-OGV interaction broadband noise prediction in a rigid annular duct with swirling and sheared mean flow. In 22nd AIAA/CEAS Aeroacoustics Conference, Lyon, France, AIAA.
Mathews, J. R., Masson, V., Moreau, S. & Posson, H. 2018 The modified Myers boundary condition for swirling flow. J. Fluid Mech. 847, 868906.
Mathews, J. R. & Peake, N. 2017 The acoustic Green’s function for swirling flow in a lined duct. J. Sound Vib. 395, 294316.
Meyer, E., Mechel, F. & Kurtze, G. 1958 Experiments on the influence of flow on sound attenuation in absorbing ducts. J. Acoust. Soc. Am. 30 (3), 165174.
Myers, M. K. 1980 On the acoustic boundary condition in the presence of flow. J. Sound Vib. 71 (3), 429434.
Myers, M. K. & Chuang, S. L. 1984 Uniform asymptotic approximations for duct acoustic modes in a thin boundary-layer flow. AIAA J. 22 (9), 12341241.
Podboy, G. G., Krupar, M. J., Hughes, C. E. & Woodward, R. P. 2002 Fan noise source diagnostic test-LDV measured flow field results. In 8th AIAA/CEAS Aeroacoustics Conference, Breckenridge (CO), USA, AIAA.
Posson, H. & Peake, N. 2012 Acoustic analogy in swirling mean flow applied to predict rotor trailing-edge noise. In 18th AIAA/CEAS Aeroacoustics Conference, Colorado Springs (CO), USA, AIAA.
Posson, H. & Peake, N. 2013a The acoustic analogy in an annular duct with swirling mean flow. J. Fluid Mech. 726, 439475.
Posson, H. & Peake, N. 2013b Swirling mean flow effect on fan-trailing edge broadband noise in a lined annular duct. In 19th AIAA/CEAS Aeroacoustics Conference, Berlin, Germany, AIAA.
Renou, Y. & Aurégan, Y. 2010 On a modified Myers boundary condition to match lined wall impedance deduced from several experimental methods in presence of a grazing flow. In 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, AIAA.
Rienstra, S. W. 2003 A classification of duct modes based on surface waves. Wave Motion 37 (2), 119135.
Rienstra, S. W. & Darau, M. 2011 Boundary-layer thickness effects of the hydrodynamic instability along an impedance wall. J. Fluid Mech. 671, 559573.
Woodward, R. P., Hughes, C. E., Jeracki, R. J. & Miller, C. J. 2002 Fan noise source diagnostic test-far-field acoustic results. In 8th AIAA/CEAS Aeroacoustics Conference, Breckenridge (CO), USA, AIAA.
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