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On high-frequency sound generated by gust–aerofoil interaction in shear flow

Published online by Cambridge University Press:  04 February 2015

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 constructed to predict the far-field sound generated by high-frequency gust–aerofoil interaction in steady parallel shear flow, including the effects of aerofoil thickness. Our approach is to use asymptotic analysis of the Euler equations linearised about steady parallel shear flow, in the limits of high frequency and small, but non-zero, aerofoil thickness and Mach number. The analysis splits the flow into various regions around the aerofoil; local inner regions around the leading and the trailing edges where sound is generated and scattered; a surface transition region accounting for the curvature of the aerofoil; a wake transition region downstream of the aerofoil; and an outer region through which the sound propagates to the observer. Solutions are constructed in all regions, and matched using the principle of matched asymptotic expansions to yield the first two terms in the expansion of both the amplitude and the phase of the far-field pressure. Result are computed for the particular case of scattering of a gust by a symmetric Joukowski aerofoil placed in symmetric Gaussian parallel shear flow. The introduction of mean shear is shown to have a significant effect on the far-field directivity and on the total radiated power.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 297 - 325
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Copyright
© 2015 Cambridge University Press 

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References

Ablowitz, M. J. & Fokas, A. S. 2003 Complex Variables: Introduction and Applications. Cambridge University Press.CrossRefGoogle 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.CrossRefGoogle Scholar
Amiet, R. K. 1978 Refraction of sound by a shear layer. J. Sound Vib. 58, 467–482.CrossRefGoogle Scholar
Atassi, H. M. & Grzedzinski, J. 1989 Unsteady disturbances of streaming motions around bodies. J. Fluid Mech. 209, 385–403.CrossRefGoogle Scholar
Ayton, L. J. & Peake, N. 2013 On high-frequency noise scattering by aerofoils in flow. J. Fluid Mech. 734, 144–182.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dyanmics. Cambridge University Press.Google Scholar
Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. Springer.Google Scholar
Bodony, D. J. 2009 Scattering of an entropy disturbance into sound by a symmetric thin body. Phys. Fluids 21, 096101.CrossRefGoogle Scholar
Davis, M. R. & Pan, N. H. 1993 Noise generated by a turbulent jet interacting with a rigid plate. J. Sound Vib. 167, 165–181.CrossRefGoogle Scholar
Durbin, P. A. 1983 High frequency Green function for aerodynamic noise in moving media, part I; general theory. J. Sound Vib. 91, 519–525.CrossRefGoogle Scholar
Finnigan, J. J. 1983 A streamline coordinate system for distorted two-dimensional shear flows. J. Fluid Mech. 130, 241–258.CrossRefGoogle Scholar
Goldstein, M. E. 1978a Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433–468.CrossRefGoogle Scholar
Goldstein, M. E. 1978b Characteristics of the unsteady motion on transversely sheared mean flows. J. Fluid Mech. 84, 305–329.CrossRefGoogle Scholar
Goldstein, M. E. 1979 Scattering and distortion of the unsteady motion on transversely sheared mean flows. J. Fluid Mech. 91, 601–632.CrossRefGoogle Scholar
Goldstein, M. E., Afsar, M. Z. & Leib, S. J. 2013 Non-homogeneous rapid distortion theory on transversely sheared mean flows. J. Fluid Mech. 736, 532–569.CrossRefGoogle Scholar
Hixon, R., Scott, J. R., Sawyer, S. & Nallasamy, M. 2006 Application of a nonlinear computational aeroacoustics code to the gust–airfoil problem. AIAA J. 44, 323–328.CrossRefGoogle Scholar
Mengle, V. G., Stoker, R. W., Brusniak, L., Elkoby, R. & Thomas, R. H.2007 Flaperon Modification Effect on Jet-Flap Interaction Noise Reduction for Chevron Nozzles. In 13th AIAA/CEAS Aeroacoustics Conference, 21–23 May, AIAA-2007-3666.Google Scholar
Myers, M. R. & Kerschen, E. J. 1997 Influence of camber on sound generation by airfoils interacting with high-frequency gusts. J. Fluid Mech. 353, 221–259.CrossRefGoogle Scholar
Noble, B. 1998 Methods Based on the Wiener–Hopf Technique for the Solution of Partial Differential Equations. Chelsea Publications.Google 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.CrossRefGoogle Scholar
Semiletov, V., Karabasov, S., Lyubimov, D., Faranosov, G. & Kopiev, V.2013 On the effect of flap deflection on jet flow for a jet-pylon-wing configuration: near-field and acoustic modelling results. In 19th AIAA/CEAS Conference, Berlin, 27–29 May, AIAA-2013-2215.Google Scholar
Sowyrda, A.1958 Theory of cambered Joukowsky airfoils in shear flow. Tech. Rep. Cornell University.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.CrossRefGoogle Scholar
Tsai, C.-T.1992 Effect of Airfoil Thickness on High-Frequency Gust Interaction Noise. PhD thesis, University of Arizona.Google Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic Press.Google Scholar