Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T10:24:17.092Z Has data issue: false hasContentIssue false
  • English
  • Français

Sound radiation into uniformly flowing fluid by compact surface vibration

Published online by Cambridge University Press:  29 March 2006

J. E. Ffowcs Williams  and
D. J. Lovely
J. E. Ffowcs Williams
Affiliation:
Engineering Department, University of Cambridge
D. J. Lovely
Affiliation:
Department of Mathematics, Imperial College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper describes a model problem where compact surface vibration radiates sound into a subsonically flowing fluid. There are two distinct acoustic effects. First, the radiation is increased by flow by an amount proportional to 5M2 and that increase is shown by a general argument to arise from an enhanced surface damping and work done by the flow to overcome drag in the ratio 2:1. Second, the acoustic source strength is affected and resonance frequencies are significantly modified by flow. The main effect is that flow induces on the surface a force proportional to the displacement which opposes the action of natural surface elasticity. A critical velocity exists beyond which the surface is unstable; the stability limit is determined. The surface motion might be regarded as an acoustic monopole, but since aerodynamic fields are determined by the rate of change of the rate of mass outflow, the frequency dependence is more that of a quadrupole. Convective amplification of the sound is also shown to be that characteristic of quadrupole sources. This result indicates that real simple fields may be more sensitive to convection than might be expected from past studies of simple inhomogeneities satisfying a convected wave equation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 4 , 28 October 1975 , pp. 689 - 700
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

Batchelor, G. K. 1967 Introduction to Fluid Dynamics. Cambridge University Press.
Benjamin, T. B. 1963 The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flow. J. Fluid Mech. 16, 436.Google Scholar
Copson, E. T. 1947 On the problem of the electrified disk. Proc. Edin. Math. Soc. 3 (8), 14.Google Scholar
Dean, P. 1972 Attenuation and in situ impedance measurements in flow ducts. ISVR Flow Duct Acoustic Symp.Google Scholar
Ffowcs Williams, J. E. 1963 The noise from turbulence convected at high speed. Phil. Trans. A 255, 469.Google Scholar
Ffowcs Williams, J. E. 1974 Sound production at the edge of a steady flow. J. Fluid Mech. 66, 791.Google Scholar
Ffowcs Williams, J. E. & Hawkings, D. L. 1969 Sound generated by turbulence and surfaces in arbitrary motion. Phil. Trans. A 264, 321.Google Scholar
Hoch, R. & Hawkins, R. 1974 Recent studies into Concorde noise reduction. AGARD Conf. Proc. no. 131.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. Proc. Roy. Soc. A 211, 564.Google Scholar
Lowson, M. V. 1965 The sound field of singularities in motion. Proc. Roy. Soc. A 286, 559.Google Scholar
Mani, R. 1974 The jet density exponent issue for the noise of heated subsonic jets. J. Fluid Mech. 63, 611.Google Scholar
Tester, B. 1973 The propagation and attenuation of sound in lined ducts containing uniform or plug flow. J. Sound Vib. 28, 151.Google Scholar