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Aerodynamic sound generation in a pipe

Published online by Cambridge University Press:  28 March 2006

H. G. Davies  and
J. E. Ffowcs Williams
H. G. Davies
Affiliation:
Department of Mathematics, Imperial College, London
J. E. Ffowcs Williams
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

The paper deals with the problem of estimating the sound field generated by a limited region of turbulence in an infinitely long, straight, hard-walled pipe. The field is analysed in a co-ordinate system moving with the assumed uniform mean flow, and the possibility of eddy convection relative to that reference system is considered. Large-scale turbulence is shown to induce plane acoustic waves of intensity proportional to the sixth power of flow velocity. The same is true of small-scale turbulence of low characteristic frequency. In both cases convective effects increase the acoustic output and distribute the bulk of the energy in a mode propagating upstream against the mean flow. Small-scale turbulence of higher frequency excites more modes, the sound increasing with very nearly the eighth power of velocity (U7.7) as soon as the second mode is excited. In the limit, when more than about 20 modes are excited, the energy output is unaffected by the constraint of the pipe walls, increasing with the eighth power of velocity, and being substantially amplified by convective motion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 4 , 18 June 1968 , pp. 765 - 778
Copyright
© 1968 Cambridge University Press

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References

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