Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T06:57:04.244Z Has data issue: false hasContentIssue false
  • English
  • Français

Sound generation by a supersonic aerofoil cutting through a steady jet flow

Published online by Cambridge University Press:  26 April 2006

Y. P. Guo
Y. P. Guo
Affiliation:
St John's College, Cambridge CB2 1TP, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper examines the sound generation process when a supersonic aerofoil cuts through a steady jet flow. It is shown that the principal sound is generated by the leading edge of the aerofoil when it interacts with the streaming jet. To the leading order in terms of the jet velocity, no trailing-edge sound is generated. This is not the result of the cancellation of a trailing-edge sound by that from vortex shedding through the imposition of the Kutta condition. Instead, the null acoustic radiation from the trailing edge is entirely because, to the leading order, there is no interaction between the trailing edge and the jet. The effect of the trailing edge is to diffract sound waves generated by the leading edge. It is shown that the diffracted field (as well as the incident field) is regular at the trailing edge and the issue of satisfying the Kutta condition does not arise during the diffraction process. Thus, there is no extra vortex shedding from the trailing edge owing to its interaction with the flow, apart from those resulting from the discontinuity across the aerofoil, generated by the flow-leading edge interaction. This is in sharp contrast to the case of subsonic aerofoils where the removal of the singularity in the diffracted field at the trailing edge through the imposition of the Kutta condition results in vortex shedding from the sharp edge and energy exchange between the sound field and the vortical wake.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 216 , July 1990 , pp. 193 - 212
Copyright
© 1990 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

Amiet, R. K. 1986a Airfoil gust response and the sound produced by aerofoil-vortex interaction. J. Sound Vib. 107, 487–506.Google Scholar
Amiet, R. K. 1986b Intersection of a jet by an infinite span aerofoil. J. Sound Vib. 111, 499–503.Google Scholar
Amiet, R. K. 1988 Comment on the surface pressure produced by an aerofoil—gust interaction. J. Sound Vib. 121, 571–572.Google Scholar
Cargill, A. M. 1982 Low-frequency sound radiation and generation due to the interaction of unsteady flow with a jet pipe. J. Fluid Mech. 121, 59–105.Google Scholar
Crighton, D. G. 1972 Radiation properties of the semi-infinite vortex sheet.. Proc. R. Soc. Lond. A 330, 185–198.Google Scholar
Crighton, D. G. 1981 Acoustics as a branch of fluid mechanics. J. Fluid Mech. 106, 261–298.Google Scholar
Crighton, D. G. 1985 The Kutta condition in unsteady flow. Ann. Rev. Fluid Mech. 17, 411–445.Google Scholar
Ffowcs Williams, J. E. & Guo, Y. P. 1988 Sound generated from the interruption of a steady flow by a supersonically moving aerofoil. J. Fluid Mech. 195, 113–135.Google Scholar
Ffowcs Williams, J. E. & Hall, L. H. 1970 Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane. J. Fluid Mech. 40, 657–670.Google Scholar
Ffowcs Williams, J. E. & Hawkings, D. L. 1969 Sound generation by turbulence and surfaces in arbitrary motion.. Phil. Trans. R. Soc. Lond. A 264, 321–342.Google Scholar
Gradshtevn, I. S. & Ryzhik, I. M. 1980 Table of Integrals, Series and Products (Corrected and enlarged edition). Academic.
Guo, Y. P. 1989 On sound generation by a jet flow passing a semi-infinite aerofoil. AIAA Paper 89–1070.Google Scholar
Howe, M. S. 1976 The influence of vortex shedding on the generation of sound by convected turbulence. J. Fluid Mech. 76, 711–740.Google Scholar
Howe, M. S. 1980 The dissipation of sound at an edge. J. Sound Vib. 70, 407–411.Google Scholar
Howe, M. S. 1988 Contributions to the theory of sound production by vortex-aerofoil interactions, with applications to vortices with finite axial velocity defect.. Proc. R. Soc. Lond. A 420, 157–182.Google Scholar
Jones, D. S. 1972 Aerodynamic sound due to a source near a half plane. J. Inst. Maths Applics. 9, 114–122.Google Scholar
Jones, D. S. 1982 The Theory of Generalized Functions. Cambridge University Press.
Lighthill, M. J. 1952 On sound generated aerodynamically. I. General theory. Proc. R. Soc. Lond. A 211, 1–32.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Miles, J. E. 1959 The Potential Theory of Unsteady Supersonic Flow. Cambridge University Press.
Morgan, J. D. 1974 The interaction of sound with a semi-infinite vortex sheet. Q. J. Mech. Appl. Maths 27, 465–487.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Rienstra, S. W. 1981 Sound diffraction at a trailing edge. J. Fluid Mech. 108, 443–460.Google Scholar