Skip to main content Accessibility help
×
Home

An analytic solution for the noise generated by gust–aerofoil interaction for plates with serrated leading edges

  • Lorna J. Ayton (a1) and Jae Wook Kim (a2)

Abstract

This paper presents an analytic solution for the sound generated by an unsteady gust interacting with a semi-infinite flat plate with a serrated leading 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 modal expansion in the spanwise coordinate; however, for low- and mid-range incident frequencies only the zeroth-order mode is seen to contribute to the far-field acoustics, 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 leading edges compared to those with straight edges, and predicts a logarithmic dependence between the tip-to-root serration height and the decrease of far-field noise. The two mechanisms behind the noise reduction are proposed to be an increased destructive interference in the far field, and a redistribution of acoustic energy from low cut-on modes to higher cut-off modes as the tip-to-root serration height is increased. The analytic results show good agreement in comparison with experimental measurements. The results are also compared against nonlinear numerical predictions where good agreement is also seen between the two results as frequency and tip-to-root ratio are varied.

Copyright

Corresponding author

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

References

Hide All
Adamczyk, J. J. 1974 Passage of a swept airfoil through an oblique gust. J. Sound Aircraft 11, 281287.
Amiet, R. K. 1975 Acoustic radiation from an airfoil in a turbulent stream. J. Sound Vib. 41, 407420.
Ayton, L. J. & Chaitanya, P. 2017 Analytical and experimental investigation into the effects of leading-edge radius on gust–aerofoil interaction noise. J. Fluid Mech. 829, 780808
Chaitanya, P., Narayanan, S., Joseph, P. F. & Kim, J. W.2016 Leading edge serration geometries for significantly enhanced leading edge noise reductions. In 22nd AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2016-2736.
Envia, E.1988 Influence of vane sweep on rotor–stator interaction noise. PhD thesis, University of Arizona.
Geyer, T. F., Wasala, S. H., Cater, J. E., Norris, S. E. & Sarradj, E.2016 Experimental investigation of leading edge hook structures for wind turbine noise reduction. In 22nd AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2016-2954.
Goldstein, M. E. & Atassi, H. 1976 A complete second-order theory for the unsteady flow about an airfoil due to a periodic gust. J. Fluid Mech. 74, 741765.
Graham, R. R. 1934 The silent flight of owls. J. R. Aero. Soc. 38, 837843.
Haeri, S., Kim, J. W. & Joseph, P.2015 On the mechanisms of noise reduction in aerofoil–turbulence interaction by using wavy leading edges. In 21st AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2015-3269.
Huang, X. 2017 Theoretical model of acoustic scattering from a flat plate with serrations. J. Fluid Mech. 819, 228257.
Kim, J. W. 2013 Quasi-disjoint pentadiagonal matrix systems for the parallelization of compact finite-difference schemes and filters. J. Comput. Phys. 241, 168194.
Kim, J. W., Haeri, S. & Joseph, P. F. 2016 On the reduction of aerofoil–turbulence interaction noise associated with wavy leading edges. J. Fluid Mech. 792, 526552.
Kim, J. W., Lau, A. S. H. & Sandham, N. D. 2010a Boundary conditions for airfoil noise due to high-frequency gusts. Periodica Engineering 6, 244253.
Kim, J. W., Lau, A. S. H. & Sandham, N. D. 2010b Proposed boundary conditions for gust–airfoil interaction noise. AIAA J. 48, 27052709.
Kim, J. W. & Morris, P. J. 2002 Computation of subsonic inviscid flow past a cone using high-order schemes. AIAA J. 40, 19611968.
Lilley, G. M.1998 A study of the silent flight of the owl. In 4th AIAA/CEAS Aeroacoustics Conference. AIAA Paper 1998-2340.
Lockard, D. P. & Morris, P. J. 1998 Radiated noise from airfoils in realistic mean flows. AIAA J. 36, 907914.
Lyu, B. & Azarpeyvand, M. 2017 On the noise prediction for serrated leading edges. J. Fluid Mech. 826, 205234.
Mathews, J. & Peake, N. 2018 An analytically-based method for predicting the noise generated by the interaction between turbulence and a serrated leading edge. J. Sound Vib. 422, 506525.
Myers, M. R. & Kerschen, E. J. 1995 Influence of incidence angle on sound generation by airfoils interacting with high-frequency gusts. J. Fluid Mech. 292, 271304.
Narayanan, S., Chaitanya, P., Haeri, S., Joseph, P. F., Kim, J. W. & Polacsek, C. 2015 Airfoil noise reductions through leading edge serrations. Phys. Fluids 27, 025109.
Peake, N. & Parry, A. B. 2012 Modern challenges facing turbomachinery aeroacoustics. Annu. Rev. Fluid Mech. 44, 227248.
Turner, J. M. & Kim, J. W. 2017 Aeroacoustic source mechanisms of a wavy leading edge undergoing vortical disturbances. J. Fluid Mech. 811, 582611.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

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