Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-06-10T22:02:59.242Z Has data issue: false hasContentIssue false

The influence of vortex shedding on the diffraction of sound by a perforated screen

Published online by Cambridge University Press:  19 April 2006

M. S. Howe
Affiliation:
Bolt Beranek and Newman, Inc., 50 Moulton Street, Cambridge, MA 02138, USA

Abstract

This paper examines the theory of the interaction of sound with a slit-perforated screen in the presence of a uniform, subsonic tangential mean flow on both sides of the screen. The sound induces vortex shedding from sharp edges of the screen. The coupling of this vorticity with the mean flow leads to a significant modification in the predicted acoustic properties as compared with those predicted by the classical treatments of Rayleigh (1897) and Lamb (1932). In particular a considerable portion of the incident acoustic energy can be lost during the interaction, and is convected away in the mean flow in the form of localized vortical disturbances. The analytical results provide theoretical support for the use of perforated plates to inhibit the onset of cavity resonances in, for example, cross-flow heat exchangers.

Type
Research Article
Copyright
© 1980 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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Washington: National Bureau of Standards.
Ashley, H. & Landahl, M. 1965 Aerodynamics of Wings and Bodies. Reading, Mass.: Addison-Wesley.
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable. McGraw-Hill.
Ffowcs Williams, J. E. 1972 The acoustics of turbulence near sound absorbent liners. J. Fluid Mech. 51, 737749.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Table of Integrals, Series and Products. Academic.
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw-Hill.
Howe, M. S. 1979a On the theory of unsteady high Reynolds number flow through a circular aperture. Proc. Roy. Soc. A 366, 205223.Google Scholar
Howe, M. S. 1979b Attenuation of sound in a low Mach number nozzle flow. J. Fluid Mech. 91, 209230.Google Scholar
Howe, M. S. 1979c The dissipation of sound at an edge. J. Sound Vib. (in the press).Google Scholar
Ingard, U. & Ising, H. 1967 Acoustic nonlinearity of an orifice. J. Acoust. Soc. Am. 42, 617.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Leppington, F. G. & Levine, H. 1973 Reflexion and transmission at a plane screen with periodically arranged circular or elliptical apertures. J. Fluid Mech. 61, 109127.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. I. General theory. Proc. Roy. Soc. A 211, 564587.Google Scholar
Lighthill, M. J. 1958 Fourier Series and Generalised Functions. Cambridge University Press.
Rayleigh, Lord 1897 On the passage of waves through apertures in plane screens, and allied problems. Phil. Mag. 43, (5), 259272.Google Scholar
Walker, W. M. & Reising, G. F. S. 1968 Flow induced vibrations in cross-flow heat exchangers. Chem. Process Engng 49, 95103.Google Scholar