Skip to main content Accessibility help
×
Home

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

  • Lorna J. Ayton (a1)

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.

Copyright

Corresponding author

Email address for correspondence: L.J.Ayton@damtp.cam.ac.uk

References

Hide All
Amiet, R. K. 1976 Noise due to turbulent flow past a trailing edge. J. Sound Vib. 47, 387393.
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.
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, 167177.
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.
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.
Chase, D. M. 1987 The character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model. J. Sound Vib. 112, 125147.
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, 6590.
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, 26652677.
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, 3354.
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.
Crighton, D. G., Dowling, A. P., Williams, J. F., Heckl, M. & Leppington, F. G. 1996 Modern Methods in Analytical Acoustics. Springer.
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.
Envia, E.1988 Influence of vane sweep on rotor–stator interaction noise. PhD thesis, University of Arizona.
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.
Graham, R. R. 1934 The silent flight of owls. J. R. Aero. Soc. 38, 837843.
Gruber, M.2012 Airfoil noise reduction by edge treatments. PhD thesis, University of Southampton.
Herr, M. 2006 Experimental study on noise reduction through trailing-edge brushes. Notes Numer. Fluid Mech. 92, 365372.
Howe, M. S. 1991a Aerodynamic noise of a serrated trailing edge. J. Fluids Struct. 5, 3345.
Howe, M. S. 1991b Noise produced by a sawtooth trailing edge. J. Acoust. Soc. Am. 90, 482487.
Howe, M. S. 1998 Acoustics of fluid–structure interactions. Cambridge University Press.
Huang, X. 2017 Theoretical model of acoustic scattering from a flat plate with serrations. J. Fluid Mech. 819, 228257.
Jaworski, J. W. & Peake, N. 2013 Aerodynamic noise from a poroelastic edge with implications for the silent flight of owls. J. Fluid Mech. 723, 456479.
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.
Jones, L. & Sandberg, R. D. 2012 Acoustic and hydrodynamic analysis of the flow around an aerofoil with trailing-edge serrations. J. Fluid Mech. 706, 295322.
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, 29973010.
Koegler, K. U., Herr, S. & Fisher, M.2009 Wind turbine blades with trailing edge serrations. US Patent App. 11/857,844.
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, 1933.
Lyu, B., Azarpeyvand, M. & Sinayoko, S. 2016 Prediction of noise from serrated trailing edges. J. Fluid Mech. 793, 556588.
Moreau, D. J. & Doolan, C. J. 2013 Noise-reduction mechanism of a flat-plate serrated trailing edge. AIAA J. 51, 25132522.
Noble, B. 1958 Methods Based on the Wiener–Hopf Technique for the Solution of Partial Differential Equations. Pergamon Press.
Oerlemans, S.2016 Reduction of wind turbine noise using blade trailing edge devices. In 22nd AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2016-3018.
Oerlemans, S. & Olsen, A. S.2014 A wind turbine blade with a noise reducing device. US Patent App. 14/427,326.
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, 477506.
Roger, M. & Moreau, S. 2009 Backscattering correction and further extensions of Amiet’s trailing-edge noise model. Part II. Application. J. Sound Vib. 323, 397425.
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.
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.
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.
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.
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.
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, 909923.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

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

  • Lorna J. Ayton (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.