Hostname: page-component-599cfd5f84-z6fpd Total loading time: 0 Render date: 2025-01-07T08:00:07.724Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytic solution for aerodynamic noise generated by plates with spanwise-varying trailing edges

Published online by Cambridge University Press:  21 June 2018

Lorna J. Ayton Open the ORCID record for Lorna J. Ayton [Opens in a new window]
Lorna J. Ayton*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents an analytic solution for aerodynamic noise generated by an unsteady wall pressure gust interacting with a spanwise-variable trailing edge in a background steady uniform flow. Viscous and nonlinear effects are neglected. The Wiener–Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to permit analytical progress. The solution is obtained in terms of a tailored modal expansion in the spanwise coordinate; however, only finitely many modes are cut-on, therefore the far-field noise can be quickly evaluated. The solution gives insight into the potential mechanisms behind the reduction of noise for plates with serrated trailing edges compared to those with straight edges. The two mechanisms behind the noise reduction are an increased destructive interference in the far field, and a redistribution of acoustic energy from low cut-on modes to higher cut-off modes. Five different test-case trailing-edge geometries are considered. The analytic solution identifies which geometries are most effective in different frequency ranges: geometries which promote destructive interference are best at low frequencies, whilst geometries which promote a redistribution of energy are better at high frequencies.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 448 - 466
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

Amiet, R. K. 1976 Noise due to turbulent flow past a trailing edge. J. Sound Vib. 47, 387–393.Google Scholar
Avallone, F., Probsting, S. & Ragni, D. 2016 Three-dimensional flow field over a trailing-edge serration and implications on broadband noise. Phys. Fluids 28, 117101.Google Scholar
Avallone, F., van der Velden, W. C. P. & Ragni, D. 2017 Benefits of curved serrations on broadband trailing-edge noise reduction. J. Sound Vib. 400, 167–177.Google Scholar
Ayton, L. J. & Kim, J. W.2018 An analytic solution for the noise generated by gust–aerofoil interaction for plates with serrated leading edges. arXiv:1805.05118.Google Scholar
Cavalieri, A. V. G., Wolf, W. R. & Jaworski, J. W. 2016 Numerical solution of acoustic scattering by finite perforated elastic plates. Proc. R. Soc. Lond. A 427, 20150767.Google Scholar
Chase, D. M. 1987 The character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model. J. Sound Vib. 112, 125–147.Google Scholar
Chong, T. P. & Vathylakis, A. 2015 On the aeroacoustic and flow structures developed on a flat plate with a serrated sawtooth trailing edge. J. Sound Vib. 354, 65–90.Google Scholar
Chong, T. P., Vathylakis, A., Joseph, P. F. & Gurber, M. 2016 Self-noise produced by an airfoil with nonflat plate trailing-edge serrations. AIAA J. 51, 2665–2677.Google Scholar
Clark, I. A., Daly, C. A., Devenport, W., Alexander, W. N., Peake, N., Jaworski, J. W. & Glegg, S. 2016 Bio-inspired canopies for the reduction of roughness noise. J. Sound Vib. 385, 33–54.Google Scholar
Clark, I. A., Devenport, W., Jaworski, J. W., Daly, C. A., Peake, N. & Glegg, S.2014 The noise generating and suppressing characteristics of bio-inspired rough surfaces. In 20th AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2014–2911.Google Scholar
Crighton, D. G., Dowling, A. P., Williams, J. F., Heckl, M. & Leppington, F. G. 1996 Modern Methods in Analytical Acoustics. Springer.Google Scholar
Dassen, T., Parchen, R., Bruggeman, J. & Hagg, F.1996 Results of a wind tunnel study on the reduction of airfoil self-noise by the application of serrated blade trailing edges. In European Union Wind Energy Conference and Exhibition, Gothenburg. NLR TP 96350.Google Scholar
Envia, E.1988 Influence of vane sweep on rotor–stator interaction noise. PhD thesis, University of Arizona.Google Scholar
European Commission 2011 Flightpath 2050: Europe’s vision for aviation. In Report of the High Level Group on Aviation Research, Publications Office of the European Union.Google Scholar
Graham, R. R. 1934 The silent flight of owls. J. R. Aero. Soc. 38, 837–843.Google Scholar
Gruber, M.2012 Airfoil noise reduction by edge treatments. PhD thesis, University of Southampton.Google Scholar
Herr, M. 2006 Experimental study on noise reduction through trailing-edge brushes. Notes Numer. Fluid Mech. 92, 365–372.Google Scholar
Howe, M. S. 1991a Aerodynamic noise of a serrated trailing edge. J. Fluids Struct. 5, 33–45.Google Scholar
Howe, M. S. 1991b Noise produced by a sawtooth trailing edge. J. Acoust. Soc. Am. 90, 482–487.Google Scholar
Howe, M. S. 1998 Acoustics of fluid–structure interactions. Cambridge University Press.Google Scholar
Huang, X. 2017 Theoretical model of acoustic scattering from a flat plate with serrations. J. Fluid Mech. 819, 228–257.Google Scholar
Jaworski, J. W. & Peake, N. 2013 Aerodynamic noise from a poroelastic edge with implications for the silent flight of owls. J. Fluid Mech. 723, 456–479.Google Scholar
Jones, L. & Sandberg, R. D.2010 Numerical investigation of airfoil self-noise reduction by addition of trailing edge serrations. In 16th AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2010-3703.Google Scholar
Jones, L. & Sandberg, R. D. 2012 Acoustic and hydrodynamic analysis of the flow around an aerofoil with trailing-edge serrations. J. Fluid Mech. 706, 295–322.Google Scholar
Karimi, M., Croaker, P., Kinns, R. & Kessissoglou, N. 2017 Effect of a serrated trailing edge on sound radiation from nearby quadrupoles. J. Acoust. Soc. Am. 141, 2997–3010.Google Scholar
Koegler, K. U., Herr, S. & Fisher, M.2009 Wind turbine blades with trailing edge serrations. US Patent App. 11/857,844.Google Scholar
Leon, C. A., Merino-Martínez, R., Ragni, D., Avallone, F., Scarano, F., Probsting, S., Snellen, M., Simons, D. G. & Madsen, J. 2017 Effect of trailing edge serration-flow misalignment on airfoil noise emissions. J. Sound Vib. 406, 19–33.Google Scholar
Lyu, B., Azarpeyvand, M. & Sinayoko, S. 2016 Prediction of noise from serrated trailing edges. J. Fluid Mech. 793, 556–588.Google Scholar
Moreau, D. J. & Doolan, C. J. 2013 Noise-reduction mechanism of a flat-plate serrated trailing edge. AIAA J. 51, 2513–2522.Google Scholar
Noble, B. 1958 Methods Based on the Wiener–Hopf Technique for the Solution of Partial Differential Equations. Pergamon Press.Google Scholar
Oerlemans, S.2016 Reduction of wind turbine noise using blade trailing edge devices. In 22nd AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2016-3018.Google Scholar
Oerlemans, S. & Olsen, A. S.2014 A wind turbine blade with a noise reducing device. US Patent App. 14/427,326.Google Scholar
Roger, M. & Moreau, S. 2005 Back-scattering correction and further extensions of Amiet’s trailing-edge noise model. Part 1. Theory. J. Sound Vib. 286, 477–506.Google Scholar
Roger, M. & Moreau, S. 2009 Backscattering correction and further extensions of Amiet’s trailing-edge noise model. Part II. Application. J. Sound Vib. 323, 397–425.Google Scholar
Roger, M., Schram, C. & De Santana, L.2013 Reduction of airfoil turbulence-impingement noise by means of leading-edge serrations and/or porous material. In 19th AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2013-2108.Google Scholar
Sanjose, M., Meon, C., Masson, V. & Moreau, S.2014 Direct numerical simulation of acoustic reduction using serrated trailing-edge on an isolated airfoil. In 20th AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2014–2324.Google Scholar
Schlanderer, S. C. & Sandberg, R. D.2016 DNS of noise radiation from a turbulent flow convecting over an elastic trailing-edge. In 22nd AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2016–2836.Google Scholar
van der Velden, W. C., Avallone, F. & Ragni, D.2017 Numerical analysis of noise reduction mechanisms of serrated trailing edges under zero lift condition. In 23rd AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2017-4173.Google Scholar
Winkler, J., Moreau, S. & Carolus, T.2010 Airfoil trailing edge noise prediction from large-eddy simulation: influence of grid resolution and noise model formulation. In 16th AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2010–3704.Google Scholar
Wolf, A., Lutz, T., Würz, W., Krämer, E., Stalnov, O. & Seifert, A. 2014 Trailing edge noise reduction of wind turbine blades by active flow control. Wind Energy 18, 909–923.Google Scholar