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Acoustic resonance in annular cascades in the presence of background mean flow

Published online by Cambridge University Press:  03 March 2025

Zihan Shen Open the ORCID record for Zihan Shen [Opens in a new window] ,
Xiaoyu Wang Open the ORCID record for Xiaoyu Wang [Opens in a new window] ,
Jia Li ,
Guangyu Zhang Open the ORCID record for Guangyu Zhang [Opens in a new window]  and
Xiaofeng Sun
Zihan Shen
Affiliation:
School of Energy and Power Engineering, Beihang University, Beijing 100191, PR China
Xiaoyu Wang*
Affiliation:
Research Institute of Aero-Engine, Beihang University, Beijing 100191, PR China
Jia Li
Affiliation:
School of Energy and Power Engineering, Beihang University, Beijing 100191, PR China
Guangyu Zhang
Affiliation:
Research Institute of Aero-Engine, Beihang University, Beijing 100191, PR China
Xiaofeng Sun
Affiliation:
School of Energy and Power Engineering, Beihang University, Beijing 100191, PR China
*
Corresponding author: Xiaoyu Wang, bhwxy@buaa.edu.cn
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Abstract

Acoustic resonances in cascade structures may cause structural damage and instability problems in aero-engines and other industrial plants; thus, developing corresponding prediction methods is important. However, works published in the open literature mostly focus on the special case of the stationary Parker modes and provide little knowledge into the rotating resonances in annular cascades, especially in the presence of non-zero background mean flows. This paper develops a three-dimensional semi-analytic model to study the acoustic resonances in an annular cascade in the presence of axial mean flow. The model applies an unsteady cascade response based on the three-dimensional lifting surface method to construct a matrix equation. Characteristic frequencies are solved in the complex domain by numerically searching for singular points. Both the oscillation frequency and the growth rate of the three-dimensional resonance modes are theoretically calculated for the first time under non-zero mean flow conditions. The results reveal an organised distribution with varying inter-blade phase angle and show obvious change with the background flow speed. It is found that the unsteady vortex shedding from the trailing edges of the cascade is a key factor influencing the dissipation rate of the resonance modes. In addition, the important effects of acoustic scattering by the cascade during resonances are examined, which qualitatively corroborate some previous experimental observations.

JFM classification

Acoustics: Aeroacoustics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1006 , 04 January 2025 , A7
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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References

Brandstetter, C., Paoletti, B. & Ottavy, X. 2019 Acoustic and convective mechanisms contributing to non-synchronous-vibrations in a multistage compressor. In Proceedings of the ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. Volume 7A: Structures and Dynamics. Phoenix, Arizona, USA. ASME.CrossRefGoogle Scholar
Camp, T.R. 1999 A study of acoustic resonance in a low-speed multistage compressor. Trans. ASME J. Turbomach. 121 (1), 36–43.CrossRefGoogle Scholar
Cooper, A.J., Parry, A.B. & Peake, N. 2004 Acoustic resonance in aeroengine intake ducts. Trans. ASME J. Turbomach. 126 (3), 432–441.CrossRefGoogle Scholar
Cooper, A.J. & Peake, N. 2000 Trapped acoustic modes in aeroengine intakes with swirling flow. J. Fluid Mech. 419, 151–175.CrossRefGoogle Scholar
Crighton, D.G. 1985 The kutta condition in unsteady flow. Annu. Rev. Fluid Mech. 17 (1985), 411–445.CrossRefGoogle Scholar
Cumpsty, N.A. & Whitehead, D.S. 1971 The excitation of acoustic resonances by vortex shedding. J. Sound Vib. 18 (3), 353–369.CrossRefGoogle Scholar
Dai, X. 2024 Commonality and difference in the eigenfunctions of various types of acoustic trapped modes. J. Fluid Mech. 980, A1.CrossRefGoogle Scholar
Duan, Y. 2004 Trapped modes and acoustic resonances. PhD thesis, Loughborough University, Loughborough Leicestershire, UK.Google Scholar
Duan, Y. & McIver, M. 2004 Rotational acoustic resonances in cylindrical waveguides. Wave Motion 39 (3), 261–274.CrossRefGoogle Scholar
Fiquet, A.-L., Aubert, S., Brandstetter, C., Buffaz, N. & Vercoutter, A. 2021 Acoustic resonance in an axial multistage compressor leading to non-synchronous blade vibration. Trans. ASME J. Turbomach. 143 (9), 091014.CrossRefGoogle Scholar
Goldstein, M.E. 1976 Aeroacoustics. McGraw-Hill.Google Scholar
Hanson, D.B. 1997 Acoustic reflection and transmission of rotors and stators including mode and frequency scattering. In 3rd AIAA/CEAS Aeroacoustics Conference. AIAA 1997-1610. AIAA.CrossRefGoogle Scholar
Holzinger, F., Wartzek, F., Schiffer, H.-P., Leichtfuss, S. & Nestle, M. 2015 Self-excited blade vibration experimentally investigated in transonic compressors: acoustic resonance. Trans. ASME J. Turbomach. 138 (4), 041001.CrossRefGoogle Scholar
Hong, Z., Fu, Y., Chen, L. & Yang, M. 2023 Experimental investigation on vortex sound interaction in self-induced acoustic resonance. J. Sound Vib. 548, 117510.CrossRefGoogle Scholar
Hong, Z., Wang, X., Jing, X. & Sun, X. 2020 Frequency lock-in mechanism in flow-induced acoustic resonance of a cylinder in a flow duct. J. Fluid Mech. 884, A42.CrossRefGoogle Scholar
Howe, M.S. 1980 The dissipation of sound at an edge. J. Sound Vib. 70 (3), 407–411.CrossRefGoogle Scholar
Katasonov, M.M., Sung, H.J., H, & Bardakhanov, S.P. 2015 Wake flow-induced acoustic resonance around a long flat plate in a duct. J. Engng. Thermophys. 24 (1), 36–56.CrossRefGoogle Scholar
Koch, W. 1983 Resonant acoustic frequencies of flat plate cascades. J. Sound Vib. 88 (2), 233–242.CrossRefGoogle Scholar
Koch, W. 2009 Acoustic resonances and trapped modes in annular plate cascades. J. Fluid Mech. 628, 155–180.CrossRefGoogle Scholar
Lighthill, M.J. 1952 On sound generated aerodynamically. I. general theory. Proc. R. Soc. Lond. A 211 (1107), 564–587.Google Scholar
Linton, C.M. & McIver, P. 1998 Acoustic resonances in the presence of radial fins in circular cylindrical waveguides. Wave Motion 28 (2), 99–117.CrossRefGoogle Scholar
Maierhofer, G. & Peake, N. 2022 Acoustic and hydrodynamic power of wave scattering by an infinite cascade of plates in mean flow. J. Sound Vib. 520, 116564.CrossRefGoogle Scholar
Morfey, C.L. 1971 Acoustic energy in non-uniform flows. J. Sound Vib. 14 (2), 159–170.CrossRefGoogle Scholar
Myers, M.K. 1991 Transport of energy by disturbances in arbitrary steady flows. J. Fluid Mech. 226, 383–400.CrossRefGoogle Scholar
Namba, M. 1972 Lifting surface theory for a rotating subsonic or transonic blade row. Tech. Rep. Reports and Memoranda No. 3740. Aeronautical Research Council.Google Scholar
Namba, M. 1977 Three-dimensional analysis of blade force and sound generation for an annular cascade in distorted flows. J. Sound Vib. 50 (4), 479–508.CrossRefGoogle Scholar
Namba, M. 1987 Three dimensional flows, AGARD manual on aeroelasticity in axial-flow turbomachinery aerodynamics, volume 1: unsteady turbomachinery aerodynamics. Tech. Rep. AGARD-AG-298. Advisory Group for Aerospace Research and Development.Google Scholar
Parker, R. 1966 Resonance effects in wake shedding from parallel plates: some experimental observations. J. Sound Vib. 4 (1), 62–72.CrossRefGoogle Scholar
Parker, R. 1967 Resonance effects in wake shedding from parallel plates: calculation of resonant frequencies. J. Sound Vib. 5 (2), 330–343.CrossRefGoogle Scholar
Parker, R. 1968 An investigation of acoustic resonance effects in an axial flow compressor stage. J. Sound Vib. 8 (2), 281–297.CrossRefGoogle Scholar
Parker, R. 1983 A note on frequency ratios for acoustic resonances of flat plate cascades with plate spacing less than half the longitudinal wavelength. J. Sound Vib. 86 (4), 594–596.CrossRefGoogle Scholar
Parker, R. & Pryce, D.C. 1974 Wake excited resonances in an annular cascade: an experimental investigation. J. Sound Vib. 37 (2), 247–261.CrossRefGoogle Scholar
Parker, R. & Stoneman, S. 1989 The excitation and consequences of acoustic resonances in enclosed fluid flow around solid bodies. Proc. Inst. Mech. Engrs C 203, 9–19.CrossRefGoogle Scholar
Rienstra, S.W. 1981 Sound diffraction at a trailing edge. J. Fluid Mech. 108, 443–460.CrossRefGoogle Scholar
Rienstra, S.W. 1984 Acoustic radiation from a semi-infinite annular duct in a uniform subsonic mean flow. J. Sound Vib. 94 (2), 267–288.CrossRefGoogle Scholar
Rienstra, S.W. 1992 A note on the Kutta condition in Glauert’s solution of the thin aerofoil problem. J. Engng Maths, 26, 61–69.Google Scholar
Rienstra, S.W. 2022 Acoustic energy balances for sound radiated from duct exit with mean flow. Intl. J. Aeroacoust. 21 (5-7), 410–429.CrossRefGoogle Scholar
Shen, Z., Wang, X. & Sun, X. 2022 a Noise reduction by perforated cascades in annular ducts. Proceedings of Internoise 2022 – 51st International Congress and Exposition on Noise Control Engineering, vol. 599. Institute of Noise Control Engineering.Google Scholar
Shen, Z., Wang, X., Sun, Y., Zhang, G. & Sun, X. 2022 b Three-dimensional effects of cascade perforations on rotor–stator interaction noise. J. Fluid Mech. 952, A7.CrossRefGoogle Scholar
Sun, X. & Wang, X. 2021 Fundamentals of Aeroacoustics with Applications to Aeropropulsion Systems. Academic Press.Google Scholar
Tyler, J.M. & Sofrin, T.G. 1962 Axial flow compressor noise studies. SAE Technical Papers 620532. SAE International.CrossRefGoogle Scholar
Welsh, M.C., Stokes, A.N. & Parker, R. 1984 Flow-resonant sound interaction in a duct containing a plate, part I: Semi-circular leading edge. J. Sound Vib. 95 (3), 305–323.CrossRefGoogle Scholar
Whitehead, D.S. 1962 Force and moment coefficients for vibrating aerofoils in cascade. Tech. Rep. Reports and Memoranda No. 3254. Aeronautical Research Council.Google Scholar
Woodley, B.M. & Peake, N. 1999 a Resonant acoustic frequencies of a tandem cascade. Part 1. Zero relative motion. J. Fluid Mech. 393, 215–240.CrossRefGoogle Scholar
Woodley, B.M. & Peake, N. 1999 b Resonant acoustic frequencies of a tandem cascade. Part 2. Rotating blade rows. J. Fluid Mech. 393, 241–256.CrossRefGoogle Scholar
Worth, N.A. & Dawson, J.R. 2017 Effect of equivalence ratio on the modal dynamics of azimuthal combustion instabilities. Proc. Combust. Inst. 36 (3), 3743–3751.CrossRefGoogle Scholar
Zhang, G., Wang, X., Li, L. & Sun, X. 2020 Effects of perforated liners on controlling combustion instabilities in annular combustors. AIAA J. 58 (7), 3100–3114.CrossRefGoogle Scholar
Zhang, W., Wang, X., Du, L. & Sun, X. 2019 Mutual effect between swept-and-leaned vanes and acoustic liners on fan interaction-noise reduction. AIAA J. 57 (6), 2479–2488.CrossRefGoogle Scholar