Hostname: page-component-cb9f654ff-5kfdg Total loading time: 0 Render date: 2025-08-07T12:39:13.321Z Has data issue: false hasContentIssue false
  • English
  • Français

The influence of vortex shedding on the generation of sound by convected turbulence

Published online by Cambridge University Press:  11 April 2006

M. S. Howe
M. S. Howe
Affiliation:
Engineering Department, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses the theory of the generation of sound which occurs when a frozen turbulent eddy is convected in a mean flow past an airfoil or a semi-infinite plate, with and without the application of a Kutta condition and with and without the presence of a mean vortex sheet in the wake. A sequence of two-dimensional mathematical problems involving a prototype eddy in the form of a line vortex is examined, it being argued that this constitutes the simplest realistic model. Important effects of convection are deduced which hitherto have not been revealed by analyses which assume quadrupole sources to be at rest relative to the plate or airfoil. It is concluded that, to the order of approximation to which the sound from convected turbulence near a scattering body is usually estimated, the imposition of a Kutta condition at the trailing edge leads to a complete cancellation of the sound generated when frozen turbulence convects past a semi-infinite plate, and to the cancellation of the diffraction field produced by the trailing edge in the case of an airfoil of compact chord.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 4 , 25 August 1976 , pp. 711 - 740
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Bechert, D. & Michel, U. 1975 Acustica. 33, 287.
Crighton, D. G. 1972 Proc. Roy. Soc. A 330, 185.
Crighton, D. G. 1975 J. Fluid Mech. 72, 209.
Crighton, D. G. & Leppington, F. G. 1970 J. Fluid Mech. 43, 721.
Crighton, D. G. & Leppington, F. G. 1971 J. Fluid Mech. 46, 577.
Crighton, D. G. & Leppington, F. G. 1974 J. Fluid Mech. 64, 393.
Curle, N. 1955 Proc. Roy. Soc. A 231, 505.
Davies, S. S. 1975 A.I.A.A. J. 13, 375.
Dowling, A. 1976 J. Fluid Mech. 74, 529.
Ffowcs Williams, J. E. 1969 Ann. Rev. Fluid Mech. 1, 197.
Ffowcs Williams, J. E. 1974 J. Fluid Mech. 66, 791.
Ffowcs Williams, J. E. & Hall, L. H. 1970 J. Fluid Mech. 40, 657.
Ffowcs Williams, J. E. & Howe, M. S. 1975 J. Fluid Mech. 70, 605.
Ffowcs Williams, J. E. & Lovely, J. 1975 J. Fluid Mech. 71, 689.
Filotas, L. T. 1969 Toronto Univ. UTIAS Rep. no. 139.
Garabedian, P. R. 1964 Partial Differential Equations. Wiley.
Garabedian, P. R. & Lieberstein, H. M. 1958 J. Aero. Sci. 27, 109.
Goldstein, M. E. 1974 N.A.S.A. Special Publication, no. 346.
Graham, J. M. R. 1970 Aero. Quart. 21, 182.
Hadamard, J. 1952 Lectures on Cauchy's Problem in Linear Partial Differential Equations. Dover.
Howe, M. S. 1967 J. Fluid Mech. 30, 497.
Howe, M. S. 1974 Proc. Roy. Soc. A 337, 413.
Howe, M. S. 1975a J. Fluid Mech 67, 597.
Howe, M. S. 1975b J. Fluid Mech 71, 625.
Jones, D. S. 1972 J. Inst. Math. Appl. 9, 114.
Jones, D. S. & Morgan, J. D. 1972 Proc. Camb. Phil. Soc. 72, 465.
Jones, D. S. & Morgan, J. D. 1974 Proc. Roy. Soc. A 338, 17.
Kármán, T. von & Sears, W. R. 1938 J. Aero. Sci. 5, 397.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Levine, H. 1975 Philips Res. Rep. 30, 240.
Lieberstein, H. M. 1959 MRC Tech. Summ. Rep. no. 81. Madison, Wisconsin.
Lighthill, M. J. 1952 Proc. Roy. Soc. A 221, 564.
Lighthill, M. J. 1960 Phil. Trans. A 252, 397.
Möhring, W. 1975 J. Sound Vib. 38, 403.
Morfey, C. L. 1973 J. Sound Vib. 31, 391.
Morgan, J. D. 1974 Quart. J. Mech. Appl. Math. 27, 465.
Mugridge, B. D. 1971 Aero. Quart. 22, 301.
Morse, P. M. & Ingard, K. U. 1968 Theoretical Acoustics. McGraw Hill.
Noble, B. 1958 Methods Based on the Wiener-Hopf Technique. Pergamon.
Orszag, S. A. & Crow, S. C. 1970 Stud. Appl. Math. 49, 167.
Rayleigh, Lord 1945 Theory of Sound. Dover.