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The spectral broadening of sound by turbulent shear layers. Part 2. The spectral broadening of sound and aircraft noise

Published online by Cambridge University Press:  19 April 2006

L. M. B. C. Campos
L. M. B. C. Campos
Affiliation:
Engineering Department, University of Cambridge
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Abstract

It has been observed experimentally by Candel, Julienne & Julliand (1975) that a monochromatic test tone generated by a source inside a jet is received outside as a broad frequency band of definite shape. This phenomenon of spectral broadening occurs during transmission through the shear layer, which generally has a randomly irregular and unsteady shape, contains in addition distributed turbulence, and separates the jet and the ambient medium. We show in the first place that, in the audible range of frequencies, neither the approximation which treats the shear layer as a scattering interface with a convected undulating shape nor the opposite, high frequency limit obtained by means of asymptotic estimation of integrals derived for the diffraction of rays in turbulence is sufficient to provide a satisfactory theory of the observations. The refraction integrals obtained in part 1 have to be evaluated exactly in order to account for the phenomenon of spectral broadening, the methods used possibly being of interest in other branches of wave theory. The formation of the transmitted spectrum from an incident tone can be illustrated by representing a simple shear layer as an array of elements each re-radiating energy received from the source with its own characteristic attenuation and frequency shift. A computer program is used to obtain spectra under conditions corresponding to the experiments of Candel, Guédel & Julienne (1975) and gives encouraging agreement with their measurements, which were made with high frequency sources immersed in low speed jets. The theory can also be applied to the prediction of spectra received at various angles to the axis of high subsonic jets, but depends on extrapolation when supersonic exhausts are considered. We conclude with an example of the possible relevance of spectral broadening as a means of reducing the noise disturbance from current jet-powered aircraft, such as Concorde.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 4 , 27 December 1978 , pp. 751 - 783
Copyright
© 1978 Cambridge University Press

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References

Balsa, T. F. 1976a The far field of high frequency convected singularities in sheared flows, with an application to jet-noise prediction. J. Fluid Mech. 74, 193–208.Google Scholar
Balsa, T. F. 1976b Refraction and shielding of sound from a source in a jet. J. Fluid Mech. 76, 443–456.Google Scholar
Barratt, M. J., Davies, P. O. A. L. & Fisher, M. J. 1963 The characteristics of turbulence in the mixing region of a round jet. J. Fluid Mech. 16, 337–367.Google Scholar
Beckmann, P. & Spizzichino, A. 1963 The Scattering of Electromagnetic Waves from Rough Surfaces. Pergamon.
Berry, M. V. 1973 The statistical properties of echoes diffracted from rough surfaces. Phil. Trans. Roy. Soc. A 273, 611–654.Google Scholar
Born, M. & Wolf, E. 1970 Principles of Optics, 5th edn. Pergamon.
Campos, L. M. B. C. 1977 On the generation and radiation of magneto-acoustic waves. J. Fluid Mech. 81, 529–549.Google Scholar
Campos, L. M. B. C. 1978a On the emission of sound by an ionized inhomogeneity. Proc. Roy. Soc. A 343, 65–91.Google Scholar
Campos, L. M. B. C. 1978b The spectral broadening of sound by turbulent shear layers. Part 1. On the transmission of sound through turbulent shear layers. J. Fluid Mech. 89, 723–749.Google Scholar
Candel, S. M., Guédel, A. & Julienne, A. 1975 Refraction and scattering of sound in an open wind tunnel flow. Proc. 6th Int. Cong. Instrum. in Aerospace Simulation Facilities, Ottawa, p. 288.Google Scholar
Candel, S. M., Julienne, A. & Julliand, M. 1975 Étude de l'effet de masque produit par un écran fluide. Dép. Aérodyn. Acoust., Direction Tech., SNECMA, Villaroche, Paris, Fiche Tech. YKA 869.
Chernov, L. A. 1967 Wave Propagation in a Random Medium. Dover.
Clarke, R. H. 1973 Theory of acoustic propagation in a variable ocean. Saclant ASW Res. Centre, La Spezia, Memo. SM-28.Google Scholar
Courant, R. & Hilbert, D. 1966 Methods of Mathematical Physics. Interscience.
Ffowcs Williams, J. E. 1974 Sound production at the edge of a steady flow. J. Fluid Mech. 66, 791–816.Google Scholar
Hammersley, J. M. & Handscomb, D. C. 1960 Monte Carlo Methods. Methuen.
Hermite, C. 1864 Sur un nouveau dévelopement en séries de fonctions. C. R. Acad. Sci. Paris 53, 93–100, 266–273.Google Scholar
Howe, M. S. 1974 Plane wave transmission and reflection coefficients for a two-dimensional jet. Camb. Univ. Noise Res. Unit. Memo. MSH/40.Google Scholar
Howe, M. S. 1975 Application of energy conservation to the solution of radiation problems involving uniformly convected source distributions. J. Sound Vib. 43, 77–86.Google Scholar
Howe, M. S. 1976 The attenuation of sound by a randomly irregular impedance layer. Proc. Roy. Soc. A 347, 513–535.Google Scholar
Jeffreys, H. & Jeffreys, B. S. 1946 Methods of Mathematical Physics. Cambridge University Press.
Jones, D. S. 1974 A linear model of a finite amplitude Helmholtz instability. Proc. Roy. Soc. A 338, 17–41.Google Scholar
Jones, D. S. 1977 The scattering of sound by a simple layer. Phil. Trans. Roy. Soc. A 284, 287–328.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Lighthill, M. J. 1952 On sound generated aerodynamically. I. The general theory. Proc. Roy. Soc. A 211, 564–587.Google Scholar
Lighthill, M. J. 1954 On sound generated aerodynamically. II. Turbulence as a source of sound. Proc. Roy. Soc. A 222, 1–32.Google Scholar
Lighthill, M. J. 1958 Fourier Transforms and Generalised Functions. Cambridge University Press.
Lighthill, M. J. 1962 Sound generated aerodynamically. Bakerian lecture (1961). Proc. Roy. Soc. A 252, 147–182.Google Scholar
Mani, R. 1976 The influence of flow on jet noise. J. Fluid Mech. 73, 773–778, 779–793.Google Scholar
Phillips, O. M. 1960 On the generation of sound by supersonic turbulent shear layers. J. Fluid Mech. 9, 1–28.Google Scholar
Rayleigh, Lord 1873 Note on a natural limit to the sharpness of spectral lines. Nature 8, 474–475. (See also Papers, vol. 1, pp. 83–84.)Google Scholar
Rayleigh, Lord 1889 On the limit to interference when light is emitted from moving molecules. Phil. Mag. 27, 298–304. (See also Papers, vol. 3, pp. 258–263.)Google Scholar
Rayleigh, Lord 1915 On the widening of spectrum lines. Phil. Mag. 29, 274–284. (See also Papers, vol. 6, pp. 291–299.)Google Scholar
Rayleigh, Lord 1945 The Theory of Sound. Dover.
Sholnik, M. I. 1962 Introduction to Radar Systems. McGraw-Hill.
Watson, G. N. 1927 Theory of Bessel Functions, 4th edn. Cambridge University Press.