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Acoustic scattering by density gradients

Published online by Cambridge University Press:  12 April 2006

A. J. Kempton
A. J. Kempton
Affiliation:
Engineering Department, University of Cambridge
Present address: Noise Department, Rolls-Royce Limited, P.O. Box 31, Derby, England.
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Abstract

In this paper we solve some model problems by the method of matched expansions and deduce some features of Green's function using the reciprocal theorem to demonstrate that scattering by density gradients can enhance the radiation efficiency of quadrupoles to that of dipoles. If a fluid is subjected to body forces close to and on both sides of a density interface, then the source system degenerates to a quadrupole only if the components of the forces perpendicular to the interface are equal in magnitude and opposite in direction and, additionally, the components of the forces per unit fluid density parallel to the interface are equal but opposite. In other cases dipole rather than quadrupole radiation efficiency is achieved. But we also show that, despite published assertions to the contrary, the radiation efficiency is not enhanced further and there is no monopole contribution to the radiated sound.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 3 , 5 December 1977 , pp. 495 - 508
Copyright
© 1977 Cambridge University Press

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References

Candel, S. M. 1972 Analytical studies of some acoustic problems of jet engines. Ph.D. thesis, Cal. Inst. Tech., Pasadena.
Cumpsty, N. A. & Marble, F. E. 1974 The generation of noise by the fluctuations in gas temperature into a turbine. Camb. Univ. Engng Dept. Rep. A Turbo/TR 57.Google Scholar
Ffowcs Williams, J. E. 1974 Sound production at the edge of a steady flow. J. Fluid Mech. 66, 791–816.Google Scholar
Ffowcs Williams, J. E. 1975 Aerodynamic noise notebook. A.I.A.A. Prof. Study Ser.Google Scholar
Ffowcs Williams, J. E. & Howe, M. S. 1975 The generation of sound by density inhomogeneities in low Mach number nozzle flows. J. Fluid Mech. 70, 605–622.Google Scholar
Hicks, W. M. 1880 On the motion of two spheres in a fluid. Phil. Trans. Roy. Soc. 171, 454–492.Google Scholar
Hoch, R. G., Duponchell, J. P., Cocking, B. J. & Bryce, W. D. 1973 Studies of the influence of density on jet noise. J. Sound Vib. 28, 649–668.Google Scholar
Howe, M. S. 1975 Contribution to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. J. Fluid Mech. 71, 625–673.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Course of Theoretical Physics. vol. 6. Pergamon.
Lighthill, M. J. 1952 On sound generated aerodynamically. Part I. General theory. Proc. Roy. Soc. A 211, 564–587.Google Scholar
Lighthill, M. J. 1954 On sound generated aerodynamically. Part II. Turbulence as a source of sound. Proc. Roy. Soc. A 222, 1–32.Google Scholar
Lush, P. M. & Fisher, M. J. 1973 Noise from hot jets. AGARD Rep. CP 131, paper 12.Google Scholar
Mani, R. 1976 The influence of jet flow on jet noise. Part 2. The noise of heated jets. J. Fluid Mech. 73, 779–793.Google Scholar
Morfey, C. L. 1973 Amplification of aerodynamic noise by convected flow inhomogeneities. J. Sound Vib. 31, 391–397.Google Scholar
Morfey, C. L. & Szewczyk, V. M. 1977 Jet noise modelling using geometrical acoustics. Part I. Theory and prediction outside the cone of silence. Univ. Southampton, Inst. Sound Vib. Res. Tech. Rep. no. 91.Google Scholar
Tanna, H. D., Dean, P. D. & Fisher, M. J. 1975 The influence of temperature on shock-free supersonic jet noise. J. Sound Vib. 39, 429–460.Google Scholar
Tanna, H. K., Fisher, M. J. & Dean, P. D. 1973 Effect of temperature on supersonic jet noise. A.I.A.A. Paper no. 73–991.Google Scholar
Tester, B. J. & Morfey, C. L. 1976 Developments in jet noise modelling — theoretical predictions and comparisons with measured data. J. Sound Vib. 46, 79–103.Google Scholar