Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T05:33:40.787Z Has data issue: false hasContentIssue false
  • English
  • Français

The acoustic field of sources in shear flow with application to jet noise: convective amplification

Published online by Cambridge University Press:  11 April 2006

T. F. Balsa
T. F. Balsa
Affiliation:
Corporate Research and Development, General Electric Company, Schenectady, New York 12301
Get access Rights & Permissions [Opens in a new window]

Abstract

Lighthill, in his elegant and classic theory of jet noise, showed that the far-field acoustic pressure of noise generated by turbulence is proportional to the integral over the jet volume of the second time derivative of the Lighthill stress tensor, the integrand being evaluated at a retarded time. The purpose of this paper is to generalize the above results to include the effects of mean flow (velocity and temperature) surrounding the source of sound. It is shown quite generally that the integrand is now a certain functional of the Lighthill stress tensor evaluated at a retarded time. More important, however, at low and high frequencies this functional assumes an extremely simple form, so that the acoustic field can once more be given by integrals of the time derivatives of the Lighthill tensor. Both the self- and the shear-noise contributions to the pressure are evaluated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 1 , 20 January 1977 , pp. 33 - 47
Copyright
© 1977 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

Balsa, T. F. 1975 J. Fluid Mech. 70, 17.
Balsa, T. F. 1976a J. Fluid Mech. 74, 193.
Balsa, T. F. 1976b J. Fluid Mech. 76, 443.
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable. McGraw-Hill.
Csanady, G. T. 1966 J. Fluid Mech. 26, 183.
Davies, P. O. A. L., Fisher, M. J. & Barratt, M. J. 1963 J. Fluid Mech. 15, 337.
Ffowcs Williams, J. E. 1963 Phil. Trans. A 255, 58.
Ffowcs Williams, J. E. 1973 AGARD Conf Proc. no. 131 (Noise Mechanisms), paper 1–1.
Ffowcs Williams, J. E. 1974 J. Fluid Mech. 66, 791.
Friedman, B. 1956 Principles and Techniques of Applied Mathematics. Wiley.
Goldstein, M. E. 1975 J. Fluid Mech. 70, 595.
Gottlieb, P. 1960 J. Acoust. Soc. Am. 32, 1117.
Hoch, R. G. et al. 1973 J. Sound Vib. 28, 649.
Lighthill, M. J. 1952 Proc. Roy. Soc. A 211, 564.
Lilley, G. M. 1972 AFAPL-TR-72-53, vol. 4.
Mani, R. 1972 J. Sound Vib. 25, 337.
Mani, R. 1974 J. Fluid Mech. 64, 611.
Mani, R. 1975a J. Fluid Mech. 73, 753.
Mani, R. 1975b J. Fluid Mech. 73, 779.
Pao, S. 1973 J. Fluid Mech. 59, 451.
Proudman, I. 1952 Proc. Roy. Soc. A 214, 119.
Ribner, H. S. 1962 Univ. Toronto, Inst. Aerophys. Rep. UTIA 86.
Ribner, H. S. 1969 J. Fluid Mech. 38, 1.