Skip to main content Accessibility help

On the reduction of aerofoil–turbulence interaction noise associated with wavy leading edges

  • Jae Wook Kim (a1), Sina Haeri (a1) and Phillip F. Joseph (a2)


An aerofoil leading-edge profile based on wavy (sinusoidal) protuberances/tubercles is investigated to understand the mechanisms by which they are able to reduce the noise produced through the interaction with turbulent mean flow. Numerical simulations are performed for non-lifting flat-plate aerofoils with straight and wavy leading edges (denoted by SLE and WLE, respectively) subjected to impinging turbulence that is synthetically generated in the upstream zone (free-stream Mach number of 0.24). Full three-dimensional Euler (inviscid) solutions are computed for this study thereby eliminating self-noise components. A high-order accurate finite-difference method and artefact-free boundary conditions are used in the current simulations. Various statistical analysis methods, including frequency spectra, are implemented to aid the understanding of the noise-reduction mechanisms. It is found with WLEs, unlike the SLE, that the surface pressure fluctuations along the leading edge exhibit a significant source-cutoff effect due to geometric obliqueness which leads to reduced levels of radiated sound pressure. It is also found that there exists a phase interference effect particularly prevalent between the peak and the hill centre of the WLE geometry, which contributes to the noise reduction in the mid- to high-frequency range.


Corresponding author

Email address for correspondence:


Hide All
Amiet, R. K. 1975 Acoustic radiation from an airfoil in a turbulent stream. J. Sound Vib. 41, 407420.
Arndt, R. E. A. & Nagel, R. T.1972 Effect of leading edge serrations on noise radiation from a model rotor. AIAA Paper 72-655; doi:10.2514/6.1972-655.
Atassi, H. M., Subramaniam, S. & Scott, J. R.1990 Acoustic radiation from lifting airfoils in compressible subsonic flow. AIAA 90-3911, Washington, DC, USA.
Ayton, L. J. & Peake, N. 2013 On high-frequency noise scattering by aerofoils in flow. J. Fluid Mech. 734, 144182.
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189214.
Clair, V., Polacsek, C., Garrec, T. L., Reboul, G., Gruber, M. & Joseph, P. 2013 Experimental and numerical investigation of turbulence-airfoil noise reduction using wavy edges. AIAA J. 51, 26952713.
Devenport, W. J., Staubs, J. K. & Glegg, S. A. L. 2010 Sound radiation from real airfoils in turbulence. J. Sound Vib. 329, 34703483.
Evers, I. & Peake, N. 2002 On sound generation by the interaction between turbulence and a cascade of airfoils with non-uniform mean flow. J. Fluid Mech. 463, 2552.
Farassat, F.2007 Derivation of formulation 1 and 1a of farassat. NASA Tech. Rep. TM-2007-214853.
Fish, F. E. & Battle, J. M. 1995 Hydrodynamic design of the humpback whale flipper. J. Morphol. 225 (1), 5160.
Garrick, I. E. & Watkins, C. E.1953 A theoretical study of the effect of forward speed on the free-space sound-pressure field around propellers. NACA Tech. Rep. TN-3018.
Gill, J., Zhang, X. & Joseph, P. 2013 Symmetric airfoil geometry effects on leading edge noise. J. Acoust. Soc. Am. 134, 26692680.
Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows around arbitrary obstacles. J. Fluid Mech. 89, 433468.
Guerreiro, J. L. E. & Sousa, J. M. M. 2012 Low-Reynolds-number effects in passive stall control using sinusoidal leading edges. AIAA J. 50, 461469.
Hansen, K., Kelso, R. & Doolan, C. 2012 Reduction of flow induced airfoil tonal noise using leading edge sinusoidal modifications. Acoust. Australia 40 (3), 172177.
Hansen, K. L., Kelso, R. M. & Dally, B. D. 2011 Performance variations of leading-edge tubercles for distinct airfoil profiles. AIAA J. 49, 185194.
Hersh, A. S., Soderman, P. T. & Hayden, R. E. 1974 Investigation of acoustic effects of leading-edge serrations on airfoils. J. Aircraft 11, 4.
Johari, H., Henoch, C., Custodio, D. & Levshin, L. 2007 Effects of leading-edge protuberances on airfoil performance. AIAA J. 45, 26342642.
Kim, D., Lee, G.-S. & Cheong, C. 2015 Inflow broadband noise from an isolated symmetric airfoil interacting with incident turbulence. J. Fluids Struct. 55, 428450.
Kim, J. W. 2007 Optimised boundary compact finite difference schemes for computational aeroacoustics. J. Comput. Phys. 225, 9951019.
Kim, J. W. 2010 High-order compact filters with variable cut-off wavenumber and stable boundary treatment. Comput. Fluids 39, 11681182.
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. 2015 An advanced synthetic eddy method for the computation of aerofoil–turbulence interaction noise. J. Comput. Phys. 287, 117.
Kim, J. W., Lau, A. S. H. & Sandham, N. D. 2010 Proposed boundary conditions for gust–airfoil interaction noise. AIAA J. 48, 27052710.
Kim, J. W. & Lee, D. J. 2000 Generalized characteristic boundary conditions for computational aeroacoustics. AIAA J. 38 (11), 20402049.
Kim, J. W. & Morris, P. J. 2002 Computation of subsonic inviscid flow past a cone using high-order schemes. AIAA J. 40 (10), 19611968.
Lau, A.S.H, Haeri, S. & Kim, J. W. 2013 The effect of wavy leading edges on aerofoil-gust interaction noise. J. Sound Vib. 332 (24), 62346253.
Lockard, D. & Morris, P. 1998 Radiated noise from airfoils in realistic mean flows. AIAA J. 36, 907914.
Longhouse, R. E. 1977 Vortex shedding noise of low tip speed, axial flow fans. J. Sound Vib. 53, 2546.
Migliore, P. & Oerlemans, S. 2004 Wind tunnel aeroacoustic tests of six airfoils for use on small wind turbines. J. Sol. Energy Eng. 126, 974985.
Miklosovic, D. S., Murray, M. M., Howle, L. E. & Fish, F. E. 2004 Leading-edge tubercles delay stall on humpback whale flippers. Phys. Fluids 16, 3942.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press.
Narayanan, S., Chaitanya, P., Haeri, S., Joseph, P., Kim, J. W. & Polacsek, C. 2015 Airfoil noise reductions through leading edge serrations. Phys. Fluids 27, 025109.
Roger, M. & Carazo, A.2010 Blade-geometry considerations in analytical gust–airfoil interaction noise models. In 16th AIAA/CEAS Aeroacoustics Conference, AIAA 2010-3799, Stockholm, Sweden.
Roger, M. & Moreau, S. 2010 Extensions and limitations of analytical airfoil broadband noise models. Intl J. Aeroacoust. 9, 273305.
Skillen, A., Revell, A., Pinelli, A., Piomelli, U. & Favier, J. 2014 Flow over a wing with leading-edge undulations. AIAA J. 53 (2), 464472.
Yoon, H. S., Hung, P. A., Jung, J. H. & Kim, M. C. 2011 Effect of the wavy leading edge on hydrodynamic characteristics for flow around low aspect ratio wing. Comput. Fluids 49, 276289.
Zhang, M. M., Wang, G. F. & Xu, J. Z. 2013 Aerodynamic control of low-Reynolds-number airfoil with leading-edge protuberances. AIAA J. 51 (8), 19601971.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

On the reduction of aerofoil–turbulence interaction noise associated with wavy leading edges

  • Jae Wook Kim (a1), Sina Haeri (a1) and Phillip F. Joseph (a2)


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.