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Analytical and experimental investigation into the effects of leading-edge radius on gust–aerofoil interaction noise

  • Lorna J. Ayton (a1) and Paruchuri Chaitanya (a2)


This paper investigates the effects of local leading-edge geometry on unsteady aerofoil interaction noise. Analytical results are obtained by extending previous work for parabolic leading edges to leading edges of the form $x^{m}$ for $0<m<1$ . Rapid distortion theory governs the interaction of an unsteady vortical perturbation with a rigid aerofoil in compressible steady mean flow that is uniform far upstream. For high-frequency gusts interacting with aerofoils of small total thickness this allows a matched asymptotic solution to be obtained. This paper mainly focusses on obtaining the analytic solution in the leading-edge inner region, which is the dominant term in determining the total far-field acoustic directivity, and contains the effects of the local leading-edge geometry. Experimental measurements for the noise generated by aerofoils with different leading-edge nose radii in uniform flow with approximate homogeneous, isotropic turbulence are also presented. Both experimental and analytic results predict that a larger nose radius generates less overall noise in low-Mach-number flow. By considering individual terms in the analytic solution, this paper is able to propose reasons behind this result.


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Allampalli, V., Hixon, R., Nallasamy, M. & Sawyer, S. D. 2009 High-accuracy large-step explicit Runge–Kutta (HALE-RK) schemes for computational aeroacoustics. J. Comput. Phys. 228, 38373850.
Amiet, R. K. 1975 Acoustic radiation from an airfoil in a turbulent stream. J. Sound Vib. 41, 407420.
Ayton, L. J. 2016 An analytic solution for gust-aerofoil interaction noise including effects of geometry. IMA J. Appl. Maths 00, 125.
Ayton, L. J., Gill, J. R. & Peake, N. 2016 The Importance of the unsteady Kutta condition when modelling gust-aerofoil interaction. J. Sound Vib. 378, 2837.
Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.
Chaitanya, P., Gill, J., Narayanan, S., Joseph, P., Vanderwel, C., Zhang, X. & Ganapathisubramani, B. 2015 Aerofoil geometry effects on turbulence interaction noise. In 21st AIAA/CEAS Aeroacoustics Conference, Dallas, TX, AIAA Paper 2015-2830.
Chong, T. P., Joseph, P. F. & Davis, P. O. A. L. 2008 A parametric study of passive flow control for a short, high area ratio 90° curved diffuser. Trans. ASME J. Fluids Engng 130, 111104-12.
Crighton, D. G. 1985 The Kutta condition in unsteady flow. Annu. Rev. Fluid Mech. 17, 411445.
Devenport, W. J., Staubs, J. K. & Glegg, S. A. L. 2010 Sound radiation from real airfoils in turbulence. J. Sound Vib. 329, 34703483.
Gill, J., Zhang, X. & Joseph, P. 2013 Symmetric airfoil geometry effects on leading edge noise. J. Acoust. Soc. Am. 134, 26692680.
Gill, J., Zhang, X. & Joseph, P. 2014 Reduced dimension modeling of leading edge turbulent interaction noise. In 20th AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, AIAA Paper 2014-2321.
Glegg, S. A. L. & Devenport, W. 2009 Unsteady loading on an airfoil of arbitrary thickness. J. Sound Vib. 319, 12521270.
Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433468.
Grace, S. M. 2001 Unsteady blade response: the BVI model versus the gust model. In 7th AIAA/CEAS Aeroacoustics Conference, Maastricht, AIAA Paper 2001-2209.
Hall, A. M., Atassi, O. V. & Gilson, J. 2011 Effects of leading-edge thickness on high-speed aerofoil-turbulence interaction noise. In 17th AIAA/CEAS Aeroacoustics Conference, Portland, Oregon, AIAA Paper 2011-2861.
Hinze, J. O. 1959 Turbulence. McGraw-Hill.
Lockard, D. P. & Morris, P. J. 1998 Radiated noise from airfoils in realistic mean flows. AIAA J. 36, 907914.
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.
Myers, M. R. & Kerschen, E. J. 1997 Influence of camber on sound generation by airfoils interacting with high-frequency gusts. J. Fluid Mech. 353, 221259.
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.
Olsen, W. & Wagner, J. 1982 Effect of thickness on airfoil surface noise. AIAA J. 20, 437439.
Peake, N. & Parry, A. B. 2012 Modern challenges facing turbomachinery aeroacoustics. Annu. Rev. Fluid Mech. 44, 227248.
Roach, P. E. 1987 The generation of nearly isotropic turbulence by mean of grid. Intl J. Heat Fluid Flow 8, 8292.
Sears, W. R. 1941 Some aspects of non-stationary airfoil theory and its practical applications. J. Aero. Sci. 8, 104188.
Thwaites, B. 1960 Incompressible Aerodynamics: An Account of the Theory and Observation of the Steady Flow of Incompressible Fluid Past Aerofoils, Wings, and Other Bodies. Dover Publications.
Tsai, C-T.1992 Effect of airfoil thickness on high-frequency gust interaction noise. PhD thesis, University of Arizona.
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic Press.
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Analytical and experimental investigation into the effects of leading-edge radius on gust–aerofoil interaction noise

  • Lorna J. Ayton (a1) and Paruchuri Chaitanya (a2)


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