Hostname: page-component-6bf8c574d5-rwnhh Total loading time: 0 Render date: 2025-02-25T17:11:41.806Z Has data issue: false hasContentIssue false
  • English
  • Français

The low frequency sound from multipole sources in axisymmetric shear flows, with applications to jet noise

Published online by Cambridge University Press:  29 March 2006

M. E. Goldstein
M. E. Goldstein
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, Ohio 44135
Get access Rights & Permissions [Opens in a new window]

Abstract

We have obtained a closed-form solution for the sound radiation from multipole sources imbedded in an infinite cylindrical jet with an arbitrary velocity profile. It is valid in the limit where the wavelength is large compared with the jet radius. Simple formulae for the acoustic pressure field due to convected point sources are also obtained. The results show (in a simple way) how the mean flow affects the radiation pattern from the sources. For convected lateral quadrupoles it causes the exponent n of the Doppler factor (1 - M cosθ)−n multiplying the far-field pressure signal to be increased from the value of 3 used by Lighthill to 5.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 3 , 12 August 1975 , pp. 595 - 604
Copyright
© 1975 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.)

References

Berman, C. H. 1974 Noise from nonuniform turbulent flow. A.I.A.A. 12th Aerospace Sci. Meeting, paper 74–2.Google Scholar
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Blaisdell.
Csanady, G. T. 1966 The effect of mean velocity variations on jet noise. J. Fluid Mech. 26, 183.Google Scholar
Erdélyi, A. 1956 Asymptotic Expansions. Dover.
Ffowcs Williams, J. E. 1960 Some thoughts on the effects of aircraft motion and eddy convection on the noise from air jets. Southampton University Rep. USAA-155.Google Scholar
Goldstein, M. E. 1974 Aeroacoustics. N.A.S.A. Special Publ. no. 364.Google Scholar
Goldstein, M. E. & Howes, W. 1973 New aspects of subsonic aerodynamic noise theory. N.A.S.A. Tech. Note, D-7158.Google Scholar
Graham, E. W. & Graham, B. B. 1971 A note on theoretical acoustic sources in motion. J. Fluid Mech. 49, 481.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. I. General theory. Proc. Roy. Soc. A 211, 564.Google Scholar
Lighthill, M. J. 1954 On sound generated aerodynamically. II. Turbulence as a source of sound. Proc. Roy. Soc. A 222, 1.Google Scholar
Lush, P. A. 1971 Measurements of subsonic jet noise and comparison with theory. J. Fluid Mech. 46, 477.Google Scholar
Mani, R. 1972 A moving source problem relevant to jet noise. J. Sound Vib. 25, 337.Google Scholar
Mani, R. 1974 The jet density exponent issue for the noise of heated subsonic jets. J. Fluid Mech. 64, 611.Google Scholar
Morse, P. M. & Ingard, K. U. 1968 Theoretical Acoustics. McGraw-Hill.
Phillips, O. M. 1960 On the generation of sound by supersonic turbulent shear layers. J. Fluid Mech. 9, 1.Google Scholar
Ribner, H. S. & Macgregor, G. R. 1968 The elusive Doppler shift in jet noise. Proc. 6th Int. Congr. Acoust., Tokyo, Japan.Google Scholar
Slutsky, S. & Tamagno, J. 1961 Sound field distribution about a jet. Gen. Appl. Sci. Lab., New York, Tech. Rep. no. 259.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.