Hostname: page-component-7bb8b95d7b-wpx69 Total loading time: 0 Render date: 2024-10-02T15:36:57.819Z Has data issue: false hasContentIssue false
  • English
  • Français

Sound diffraction at a trailing edge

Published online by Cambridge University Press:  20 April 2006

S. W. Rienstra
S. W. Rienstra
Affiliation:
National Aerospace Laboratory NLR, Amsterdam, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

The diffraction of externally generated sound in a uniformly moving flow at the trailing edge of a semi-infinite flat plate is studied. In particular, the coupling of the sound field to the hydrodynamic field by way of vortex shedding from the edge is considered in detail, both in inviscid and in viscous flow.

In the inviscid model the (two-dimensional) diffracted fields of a cylindrical pulse wave, a plane harmonic wave and a plane pulse wave are calculated. The viscous proess of vortex shedding is represented by an appropriate trailing-edge condition. Two specific cases are compared, in one of which the full Kutta condition is applied, and in the other no vortex shedding is permitted. The results show good agreement with Heavens’ (1978) observations from his schlieren photographs, and confirm his conclusions. It is further demonstrated, by an explicit expression, that the sound power absorbed by the wake may be positive or negative, depending on Mach number and source position. So the process of vortex shedding does not necessarily imply an attenuation of the sound.

In the viscous model a high-Reynolds-number approximation is constructed, based on a triple-deck boundary-layer structure, matching the harmonic plane wave outer solution to a known incompressible inner solution near the edge, to obtain the viscous correction to the Kutta condition.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 108 , July 1981 , pp. 443 - 460
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

Archibald, F. S. 1975 J. Aircraft 12, 545–550.
Bechert, D. 1979 A.I.A.A. paper no. 79–0575.
Bechert, D. & Pfizenmaier, E. 1975 J. Fluid Mech. 71, 123–144.
Broadbent, E. G. 1977 Prog. Aerospace Sci. 17, 231–268.
Brown, S. N. & Daniels, P. G. 1975 J. Fluid Mech. 67, 743–761.
Brown, S. N. & Stewartson, K. 1970 J. Fluid Mech. 42, 561–584.
Candel, S. M. 1973 J. Acoust. Soc. Am. 54, 1008–1016.
Carrier, G. F. 1956 Q. Appl. Math. 13, 457–461.
Crighton, D. G. 1972 J. Fluid Mech. 51, 357–365.
Crighton, D. G. 1975 Prog. Aerospace Sci. 16, 31–96.
Daniels, P. G. 1978 Q. J. Mech. Appl. Math. 31, 49–75.
Davis, S. S. 1975 A.I.A.A. J. 13, 375–380.
Fleeter, S. 1979 A.I.A.A. paper no. 79–0152.
Friedlander, F. G. 1958 Sound Pulses. Cambridge University Press.
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill.
Heavens, S. N. 1978 J. Fluid Mech. 84, 331–335.
Howe, M. S. 1976 J. Fluid Mech. 76, 711–740.
Howe, M. S. 1978 J. Sound Vib. 61, 437–465.
Howe, M. S. 1979 J. Fluid Mech. 91, 209–229.
Jones, D. S. 1964 The Theory of Electromagnetism. Pergamon.
Jones, D. S. 1972 J. Inst. Maths. Applics. 9, 114–122.
Lawrence, L. F., Schmidt, S. F. & Looschen, F. W. 1951 N.A.C.A. TN 2509.
Messiter, A. F. 1970 SIAM J. Appl. Math. 18, 241–257.
Morfey, C. L. 1971 J. Sound Vib. 14, 159–170.
Stewartson, K. 1969 Mathematika 16, 106–121.