Sound transmission through a finite-lined section in a rigid annular duct with swirling and sheared mean flow is analyzed with a new mode-matching method based on the conservation of the total enthalpy and the mass flow, which does not reduce to the conservation of the pressure and the axial velocity when the swirl is non-zero. It relies on a new projection method based on the property of the Chebyshev polynomials and on the scattering matrix formalism to yield transmission losses. This new method is first validated against a finite elements method tool in the uniform axial flow case, and then provides a parametric study of the effect of swirl. At low azimuthal mode order , the swirl amplifies the attenuation of the contra-rotating modes and makes the attenuation of the co-rotating modes decrease with a trend of a general shift of the transmission loss curve toward contra-rotating modes. A small rotation of the transmission loss curves at low is also generally observed. The boundary condition in the lined section has a small effect on the transmission loss, except close to the cut-on thresholds. Finally, the duct boundary-layer thickness has a significant effect on the cut-on modes and the transmission loss but not its profile.
MoreauS. A review of turbomachinery noise: from analytical models to high-fidelity simulations, volume Fundamentals of High Lift for Future Civil Aircraft. Springer Nature Switzerland AG, 2020. DOI:10.3813/AAA.918372.
4.
MassonVPossonHSanjoséM, et al.Fan-OGV interaction broadband noise prediction in a rigid annular duct with swirling and sheared mean flow. In: 22nd AIAA/CEAS Aeroacoustics Conference.AIAA 2016-2944 paper, Lyon, France, ■■■.
5.
GabardG. Mode-matching techniques for sound propagation in lined ducts with flow. In: 16th AIAA/CEAS Aeroacoustics Conference.AIAA 2010-3940 paper, Stockholm, Sweden, ■■■.
6.
BouleyS. Modélisations analytiques du bruit tonal d’interaction rotor/stator par la technique de raccordement modal. PhD Thesis. École Centrale de Lyon, 2017.
7.
GabardGAstleyR. A computational mode-matching approach for sound propagation in three-dimensional ducts with flow. J Sound Vib2008; 315(4): 1103–1124.
8.
BrooksCJMcAlpineA. Sound transmission in ducts with sheared mean flow. In: 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference).AIAA 2007-3545 paper, Rome, Italy, ■■■.
9.
GuanYLuoKHWangTQ. Sound transmission in a lined annular duct with mean swirling flow. In: ASME 2008 Noise Control and Acoustics Division Conference, ■■■, ■■■. ■■■: American Society of Mechanical Engineers.
10.
OppeneerMRienstraSWSijtsmaP. Efficient mode matching based on closed-form integrals of pridmore-brown modes. AIAA J2015; 54(1): 266–279.
PossonHPeakeN. The acoustic analogy in an annular duct with swirling mean flow. J Fluid Mech2013; 726: 439–475.
13.
Ffowcs WilliamsJEHawkingsDL. Sound generation by turbulence and surfaces in arbitrary motion. Philosophical Transactions of the Royal Society of London Series A, Mathematical and Physical Sciences1969; 264: 321–342.
14.
FarassatF.Discontinuities in aerodynamics and aeroacoustics: the concept and applications of generalized derivatives. J Sound Vib1977; 55(2): 165–193.
15.
GoldsteinME. Aeroacoustics. New York: McGraw-Hill International Book Compagny, 1976.
16.
LilleyGM. On the noise from jets. AGARD CP-1311974; ■■■: 13–21.
17.
KhorramiRMalikMRAshRL. Application of spectral collocation techniques to the stability of swirling flows. J of Comp Phys1989; 81(1): 206–229.
18.
KhorramiMR. A Chebyshev spectral collocation method using a staggered grid for the stability of cylindrical flow. Int J for Num Meth in Fluids1991; 12(9): 825–833.
19.
MathewsJPeakeN. The acoustic Green’s function for swirling flow in a lined duct. J of Sound and Vib2017; 395: 294–316.
20.
HeatonCJPeakeN. Acoustic scattering in a duct with mean swirling flow. J of Fluid Mech2005; 540: 189–220.
21.
MyersMK. On the acoustic boundary condition in the presence of flow. J Sound Vib1980; 71(3): 429–434.
22.
KhamisDBrambleyEJ. Acoustic boundary conditions at an impedance lining in inviscid shear flow. J Fluid Mech2016; 796: 386–416.
23.
PossonHPeakeN. Swirling mean flow effect on fan-trailing edge broadband noise in a lined annular duct. In: 19th AIAA/CEAS Aeroacoustics Conference and Exhibit.AIAA 2013-2150 Paper, Berlin, Germany, ■■■.
24.
MaldonadoALPAstleyRJCouplandJ, et al.Sound propagation in lined annular ducts with mean swirling flow. In: 21st AIAA/CEAS Aeroacoustics Conference.AIAA 2015-2522 paper, Dallas, TX, ■■■.
25.
RenouYAuréganY. 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.AIAA 2010-3945 paper, Stockholm, Sweden, ■■■.
26.
BrambleyEJ. Models for acoustically-lined turbofan ducts. In: 14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference).AIAA 2008-2879 paper, Cambridge, CA, ■■■.
27.
RienstraSWDarauM. Boundary-layer thickness effects of the hydrodynamic instability along an impedance wall. J Fluid Mech2011; 671: 559–573.
28.
BrambleyEJ. Well-posed boundary condition for acoustic liners in straight ducts with flow. AIAA J2011; 49(6): 1272–1282.
29.
AuréganYStarobinskiSPagneuxV. Influence of grazing flow and dissipation effects on the acoustic boundary conditions at a lined wall. J of the Acous Soc of America2001; 109(1): 59–64.
30.
GabardG. A comparison of impedance boundary conditions for flow acoustics. J Sound Vib2013; 332(4): 714–724.
31.
EversmanWBeckemeyerRJ. Transmission of sound in ducts with thin shear layers. convergence to the uniform flow case. J of the Acous Soc of America1972; 52(1B): 216–220.
32.
MassonVMathewsJMoreauS, et al.The impedance boundary condition for acoustics in swirling flow. J Fluid Mech2018; 849: 645–675.
33.
MathewsJMassonVMoreauS, et al.The modified Myers boundary condition for swirling flow. J Fluid Mech2018; 847: 868–906.
34.
AuréganYLerouxM. Experimental evidence of an instability over an impedance wall in a duct with flow. J Sound Vib2008; 317(3): 432–439.
35.
BiWPagneuxVLafargeD, et al.Modelling of sound propagation in a non-uniform lined duct using a multi-modal propagation method. J Sound Vib2006; 289(4): 1091–1111.
36.
DruonY.Etude de la propagation guidée et du rayonnement acoustiques par les conduits d’éjection de turboréacteur: Modélisations analytiques et numériques. PhD Thesis. Ecully: Ecole centrale de Lyon, 2006.
37.
LansingDLZorumskiWE. Effects of wall admittance changes on duct transmission and radiation of sound. J Sound Vib1973; 27(1): 85–100.
38.
PagneuxVAmirNKergomardJ. A study of wave propagation in varying cross-section waveguides by modal decomposition. Part i. theory and validation. J of the Acous Soc of America1996; 100(4): 2034–2048.
39.
BouleySFrançoisBRogerM, et al.On a two-dimensional mode-matching technique for sound generation and transmission in axial-flow outlet guide vanes. J Sound Vib2017; 403: 190–213.
RedhefferR. On a certain linear fractional transformation. Studies in Applied Mathematics1960; 39(1–4): 269–286.
42.
FoiaşCFrazhoAE. Redheffer products and the lifting of contractions on hilbert space. J of Operator Theor1984; ■■■: 193–196.
43.
RienstraSWHirschbergA. An Introduction to Acoustics. ■■■: ■■■, 2004.
44.
MyersM. An exact energy corollary for homentropic flow. J Sound Vib1986; 109(2): 277–284.
45.
PossonHPeakeN. Acoustic analogy in swirling mean flow applied to predict rotor trailing-edge noise. In: 18th AIAA/CEAS Aeroacoustics Conference.AIAA 2012-2267 paper, Colorado Springs, CO, ■■■.
46.
MöhringW. A well posed acoustic analogy based on a moving acoustic medium. In: KöltzschPKalitzinN (eds) Proceedings of Aeroacoustics Workshop SWING. ■■■: ■■■.
47.
Free Field Technologies. Actran 17.0 User Guide, Vol. 1: Installation, Operations, Theory and Utilities. ■■■: ■■■, October2016.
48.
Nodé-LangloisTFicat-AndrieuVDetandtY. CFD/CAA coupling strategies for rearward fan noise. In: AIAA aviation Forum. AIAA 2018-4089 paper, Atlanta, GA, ■■■.
