Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-19T06:33:28.726Z Has data issue: false hasContentIssue false
  • English
  • Français

Acoustic wave emitted by a vortex ring passing near the edge of a half-plane

Published online by Cambridge University Press:  20 April 2006

T. Kambe ,
T. Minota  and
Y. Ikushima
T. Kambe
Affiliation:
Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan
T. Minota
Affiliation:
Department of Applied Science, Kyushu University, Hakozaki, Fukuoka 812, Japan
Y. Ikushima
Affiliation:
Department of Applied Science, Kyushu University, Hakozaki, Fukuoka 812, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

Acoustic emission by vortex–edge interaction is investigated both theoretically and experimentally. The theory of vortex sound enables us to represent the far-field pressure in terms of the vortex motion near the half-plane edge. It is found that the pressure p depends on the product of an angular factor representing directionality and a time factor representing wave profile. The pressure formula leads to the scaling law $p \propto U^{\frac{5}{2}} L^{-2}$ for the sound emitted by a vortex ring of velocity U, L being the nearest distance of the vortex path to the edge. The sound intensity is proportional to U5 and shows cardioid directionality pattern.

The vortex ring used in the experiment had radius about 4.7 mm and velocity ranging from 29 to 61 m/s. The above scaling law of the pressure and the cardioid directionality of the intensity were reproduced in the experiment with reasonable accuracy. Especially notable is the agreement between the predicted and observed wave profiles. The theoretical profile is determined by the $\frac{3}{2}\,{\rm th}$ time derivative of the volume flux (through the vortex ring) of a hypothetical potential flow around the edge.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 155 , June 1985 , pp. 77 - 103
Copyright
© 1985 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

Alblas, J. B. 1957 Appl. Sci. Res. 6A, 237–262.
Cannell, P. A. & Ffowcs Williams, J. E. 1973 J. Fluid Mech. 58, 65–80.
Crighton, D. G. 1972 J. Fluid Mech. 51, 357–362.
Crighton, D. G. & Leppington, F. G. 1970 J. Fluid Mech. 43, 721–736.
Curle, N. 1955 Proc. R. Soc. Lond. A 231, 505–514.
Ffowcs Williams, J. E. & Hall, L. H. 1970 J. Fluid Mech. 40, 657–670.
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill.
Howe, M. S. 1975 J. Fluid Mech. 71, 625–673.
Jones, D. S. 1972 J. Inst. Maths. Applics. 9, 114–122.
Kambe, T. 1984 J. Sound Vib. 95 (3), 351–360.
Kambe, T. & Minota, T. 1983 Proc. R. Soc. Lond. A 386, 277–308.
Kambe, T. & Mya Oo, U. 1984 J. Phys. Soc. Jpn. 53, 2263–2273.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, §74. Pergamon.
Lighthill, M. J. 1952 Proc. R. Soc. Lond. A 211, 564–587.
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Macdonald, H. M. 1915 Proc. Lond. Math. Soc. (2) 14, 410–427.
Möhring, W. 1978 J. Fluid Mech. 85, 685–691.
Noble, B. 1958 Methods based on the Wiener–Hopf Technique. Pergamon.
Obermeier, F. 1979 Acustica 42, 56–61.
Obermeier, F. 1980 J. Sound Vib. 72, 39–49.