Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T22:06:28.059Z Has data issue: false hasContentIssue false
  • English
  • Français

The influence of mean shear on unsteady aperture flow, with application to acoustical diffraction and self-sustained cavity oscillations

Published online by Cambridge University Press:  20 April 2006

M. S. Howe
M. S. Howe
Affiliation:
Bolt Beranek and Newman, Inc., 50 Moulton Street, Cambridge, MA 02138, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses the linearized theory of unsteady flow through a two-dimensional aperture in a thin plate in the presence of a grazing mean flow on one side of the plate. The mean shear layer is modelled by a vortex sheet, and it is predicted that at low mean-flow Mach numbers there is a transfer of energy from the mean flow to the disturbed motion of the vortex sheet provided (i) the Kutta condition is imposed at the leading edge of the aperture, resulting in the unsteady shedding of vorticity from the edge, and (ii) the width of the aperture 2s satisfies ½ < 2s/λ < 1.1, where λ is the hydrodynamic wavelength of the disturbance on the vortex sheet within the aperture. The theory is used to examine the effect of mean shear on the diffraction of sound by a perforated screen, and to predict the spontaneous excitation and suppression of self-sustained oscillations in a wall-cavity beneath a nominally steady mean flow. In the latter case support for the proposed theory is provided by a favourable comparison of theoretical results with experimental data available in the literature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 125 - 146
Copyright
© 1981 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

Ashley, H. & Landahl, M. 1965 Aerodynamics of Wings and Bodies. Addison-Wesley.
Barthel, F. 1958 Investigations on nonlinear Helmholtz resonators. Frequenz 12, 1–11.Google Scholar
Bechert, D. 1979 Sound absorption caused by vorticity shedding, demonstrated with a jet flow. A.I.A.A. paper 79–0575.
Bechert, D., Michel, U. & Pfizenmaier, E. 1977 Experiments on the transmission of sound through jets. A.I.A.A. paper 77–1278.
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable. McGraw-Hill.
Covert, E. E. 1970 An approximate calculation of the onset velocity of cavity oscillations. A.I.A.A. J. 8, 2189–2194.Google Scholar
Crighton, D. G. & Innes, D. 1981 Analytical models for shear layer feed-back cycles. A.I.A.A. paper 81–0061.
Demetz, F. C. & Farabee, T. M. 1977 Laminar and turbulent shear flow induced resonances. A.I.A.A. paper 77–1293.
Elder, S. A. 1978 Self-excited depth mode resonance for a wall-mounted cavity in turbulent flow. J. Acoust. Soc. Am. 64, 877–890.Google Scholar
Fletcher, N. H. 1979 Air flow and sound generation in musical instruments. Ann. Rev. Fluid Mech. 11, 123–146.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Table of Integrals, Series and Products. Academic.
Heller, H. H. & Bliss, D. B. 1975 The physical mechanism of flow-induced pressure fluctuations in cavities and concepts for their suppression. A.I.A.A. paper 75–491.
Hersh, A. S. & Walker, B. 1979 Effect of grazing flow on the acoustic impedance of Helmholtz resonators consisting of single and clustered orifices. N.A.S.A. CR 3177.
Howe, M. S. 1979a Attenuation of sound in a low Mach number nozzle flow. J. Fluid Mech. 91, 209–230.Google Scholar
Howe, M. S. 1979b On the theory of unsteady high Reynolds number flow through a circular aperture. Proc. Roy. Soc. A 366, 205–223.Google Scholar
Howe, M. S. 1980a The influence of vortex shedding on the diffraction of sound by a perforated screen. J. Fluid Mech. 97, 641–653.Google Scholar
Howe, M. S. 1980b On the diffraction of sound by a screen with circular apertures in the presence of a low Mach number grazing flow. Proc. Roy. Soc. A 374, 543–568.Google Scholar
Howe, M. S. 1980c The dissipation of sound at an edge. J. Sound Vib. 70, 407–411.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th edn. Macmillan.
Möhring, W. 1975 On flows with vortex sheets and solid plates. J. Sound Vib. 38, 403–412.Google Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Ann. Rev. Fluid Mech. 11, 67–94.Google Scholar
Ronneberger, D. 1972 The acoustical impedance of holes in the wall of flow ducts. J. Sound Vib. 24, 133–150.Google Scholar
Rossiter, J. E. 1962 The effect of cavities on the buffeting of aircraft. Royal Aircraft Est. Tech. Memo. Aero 754.
Tam, C. K. W. & Block, P. J. W. 1978 On the tones and pressure oscillations induced by flow over rectangular cavities. J. Fluid Mech. 89, 373–399.Google Scholar