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On high-frequency noise scattering by aerofoils in flow

Published online by Cambridge University Press:  08 October 2013

Lorna J. Ayton  and
N. Peake
Lorna J. Ayton*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
N. Peake
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

A theoretical model is developed for the sound scattered when a sound wave is incident on a cambered aerofoil at non-zero angle of attack. The model is based on the linearization of the Euler equations about a steady subsonic flow, and is an adaptation of previous work which considered incident vortical disturbances. Only high-frequency sound waves are considered. The aerofoil thickness, camber and angle of attack are restricted such that the steady flow past the aerofoil is a small perturbation to a uniform flow. The singular perturbation analysis identifies asymptotic regions around the aerofoil; local ‘inner’ regions, which scale on the incident wavelength, at the leading and trailing edges of the aerofoil; Fresnel regions emanating from the leading and trailing edges of the aerofoil due to the coalescence of singularities and points of stationary phase; a wake transition region downstream of the aerofoil leading and trailing edge; and an outer region far from the aerofoil and wake. An acoustic boundary layer on the aerofoil surface and within the transition region accounts for the effects of curvature. The final result is a uniformly-valid solution for the far-field sound; the effects of angle of attack, camber and thickness are investigated.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 734 , 10 November 2013 , pp. 144 - 182
Copyright
©2013 Cambridge University Press 

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Courier Dover.Google Scholar
Agarwal, A., Dowling, A. P., Shin, H.-C., Graham, W. & Sefi, S. 2007 Ray tracing approach to calculate acoustic shielding by a flying wing airframe. AIAA J. 44, 1080–1090.Google Scholar
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, 3837–3850.Google Scholar
Atassi, H. M. 1984 The Sears problem for a lifting aerofoil revisited – new results. J. Fluid Mech. 141, 109–122.Google Scholar
Atassi, H. M., Fang, J. & Patrick, S. 1993 Direct calculation of sound radiated from bodies in non-uniform flows. J. Fluids Engng 115 (4), 573–579.Google Scholar
Bleistein, N. & Handelsman, R. A. 1975 Asymptotic Expansions of Integrals. Ardent Media.Google Scholar
Crighton, D G 1985 The Kutta condition in unsteady flow. Annu. Rev. Fluid Mech. 17, 411–445.CrossRefGoogle Scholar
Evers, I. & Peake, N. 2002 On sound generation by the interaction between turbulence and a cascade of aerofoils with non-uniform mean flow. J. Fluid Mech. 463, 25–52.Google Scholar
Ffowcs Williams, J. E. & Hawkings, D. L. 1969 Sound generation by turbulence and surfaces in arbitrary motion. Phil. Trans. R. Soc. 264, 321–342.Google Scholar
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill.Google Scholar
Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433–468.Google Scholar
Goldstein, M. E. & Atassi, H. 1976 A complete second-order theory for the unsteady flow about an aerofoil due to a periodic gust. J. Fluid Mech. 74, 741–765.CrossRefGoogle Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Table of Integrals, Series, and Products, 6th edn. Academic.Google Scholar
Hixon, R., Scott, J. R., Sawyer, S. & Nallasamy, M. 2006 Application of a nonlinear computational aeroacoustics code to the gust–aerofoil problem. AIAA J. 44, 323–328.Google Scholar
Howe, M. S. 1978 A review of the theory of trailing edge noise. J. Sound Vibr. 61, 437–465.CrossRefGoogle Scholar
Hunt, J. C. R. 1973 A theory of turbulent flow round two-dimensional bluff bodies. J. Fluid Mech. 61, 625–706.Google Scholar
Jones, D. S. 1966 Generalised Functions. McGraw-Hill.Google Scholar
Jones, D. S. 1986 Acoustic and Electromagnetic Waves. Clarendon.Google Scholar
Kerschen, E. J. & Balsa, T. F. 1981 Transformation of the equation governing disturbances of a two-dimensional compressible flow. AIAA J. 19, 1367–1370.CrossRefGoogle Scholar
Kerschen, E. J. & Myers, M. R. 1987 Perfect gas effects in compressible rapid distortion theory. AIAA J. 25, 504–507.Google Scholar
Myers, M. R. & Kerschen, E. J. 1995 Influence of incidence angle on sound generation by aerofoils interacting with high-frequency gusts. J. Fluid Mech. 292, 271–304.Google Scholar
Myers, M. R. & Kerschen, E. J. 1997 Influence of camber on sound generation by aerofoils interacting with high-frequency gusts. J. Fluid Mech. 353, 221–259.CrossRefGoogle Scholar
Peake, N. & Kerschen, E. J. 1997 Influence of mean loading on noise generated by the interaction of gusts with a flat-plate cascade: upstream radiation. J. Fluid Mech. 347, 315–346.CrossRefGoogle Scholar
Peake, N. & Kerschen, E. J. 2004 Influence of mean loading on noise generated by the interaction of gusts with a cascade: downstream radiation. J. Fluid Mech. 515, 99–133.CrossRefGoogle Scholar
Peake, N. & Parry, A. B. 2012 Modern challenges facing turbomachinery aeroacoustics. Annu. Rev. Fluid Mech. 44, 227–248.Google Scholar
Scott, J. R. & Atassi, H. M. 1995 A finite-difference, frequency-domain numerical scheme for the solution of the gust response problem. J. Comput. Phys. 119 (1), 75–93.Google Scholar
Sears, W. R. 1941 Some aspects of non-stationary aerofoil theory and its practical applications. J. Aeronaut. Sci. 8, 104–188.Google Scholar
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.Google Scholar
Tsai, C.-T. 1992 Effect of airfoil thickness on high-frequency gust interaction noise. PhD thesis, University of Arizona.Google Scholar
Van der Waerden, B. L. 1952 On the method of saddle points. Appl. Sci. Res., Section B 2, 33–45.Google Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic Press.Google Scholar