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The interaction of sound with a subsonic jet issuing from a semi-infinite cylindrical pipe

Published online by Cambridge University Press:  12 April 2006

R. M. Munt
R. M. Munt
Affiliation:
Mathematics Department, University of Dundee, Scotland
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Abstract

The transmission of sound out of a semi-infinite circular jet pipe in the presence of subsonic flow from the pipe is investigated. An unstable cylindrical vortex layer attached to the edge of the pipe is considered across which differences in mean subsonic flow, density and temperature are included. A solution satisfying the Kutta condition and causality is found which possesses an instability wave term that dominates within a region of approximately 45° to the downstream jet axis. It is shown that when an exterior flow is imposed the noise level increases upstream whilst the instability wave weakens downstream. The stable part of the solution is shown to agree very well with some recent experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 4 , 21 December 1977 , pp. 609 - 640
Copyright
© 1977 Cambridge University Press

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References

Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529–551.Google Scholar
Bechert, D. & Pfizenmaier, E. 1975 Optical compensation measurements on the unsteady exit condition at a nozzle discharge edge. J. Fluid Mech. 71, 123–144.Google Scholar
Candel, S. M. 1973 Acoustic radiation from the end of a two-dimensional duct, effects of uniform flow and duct lining. J. Sound Vib. 28, 1–13. Quart. Appl. Math. 13, 457–461.Google Scholar
Carrier, G. F. 1956 Sound transmission from a tube with flow.
Chan, Y. Y. & Westley, R. 1973 Directional acoustic radiation generated by spatial jet instability. C.A.S.I. Trans. 6, 36–41.Google Scholar
Crighton, D. G. 1972a Radiation properties of the semi-infinite vortex sheet. Proc. Roy. Soc. A 330, 185.Google Scholar
Crighton, D. G. 1972b The excess noise field of subsonic jets. J. Fluid Mech. 56, 683–694.Google Scholar
Crighton, D. G. & Leppington, F. G. 1974 Radiation properties of the semi-infinite vortex sheet: the initial-value problem. J. Fluid Mech. 64, 393–414.Google Scholar
Crow, S. C. 1972 Acoustic gain of a turbulent jet. Am. Phys. Soc. Meeting, Boulder, Colorado, paper IE.6.
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591.Google Scholar
Hardisty, N. 1975 The instability of two vortex sheets enclosing a subsonic jet due to an acoustic point source. Proc. Roy. Soc. Edin. A 73, 215–229.Google Scholar
Homicz, G. F. & Lordi, J. A. 1975 A note on the radiative directivity patterns of duct acoustic modes. J. Sound Vib. 41, 283–290.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
Jacques, J. R. 1975 The noise from moving aircraft; some relevant models. Ph.D. thesis, Cambridge University.
Jones, D. S. 1973 The convolution of generalised functions. Quart. J. Math. 24, 145–163.Google Scholar
Jones, D. S. 1977 The scattering of sound by a simple shear layer. Phil. Trans. Roy. Soc. A 284, 287–328.Google Scholar
Jones, D. S. & Morgan, J. D. 1972 The instability of a vortex sheet on a subsonic stream under acoustic radiation. Proc. Camb. Phil. Soc. 72, 465–488.Google Scholar
Jones, D. S. & Morgan, J. D. 1974 A linear model of a finite Helmholtz instability. Proc. Roy. Soc. A 338, 17–41.Google Scholar
Lansing, D. L., Drischler, J. A. & Pusey, C. G. 1970 Radiation of sound from an unflanged circular duct with flow. 79th Meeting Acoust. Soc. Am.
Lee, B. H. K. & Jones, D. J. 1973 Transmission of upstream sound through a subsonic jet. A.I.A.A. Paper no. 73–630.Google Scholar
Mani, R. 1973 Refraction of acoustic duct waveguide modes by exhaust jets. Quart. Appl. Math. 30, 501–520.Google Scholar
Mani, R. 1974 The jet density exponent issue for the noise of heated subsonic jets. J. Fluid Mech. 64, 611–622.Google Scholar
Morgan, J. D. 1974 The interaction of sound with a semi-infinite vortex sheet. Quart. J. Mech. Appl. Math. 27, 465–487.Google Scholar
Morgan, J. D. 1975 The interaction of sound with a subsonic cylindrical vortex sheet. Proc. Roy. Soc. A 344, 341–362.Google Scholar
Munt, R. M. 1975 Acoustic radiation from a circular cylinder in a subsonic stream. J. Inst. Math. 16, 1–10.Google Scholar
Noble, B. 1958 Methods based on the Wiener — Hopf Technique. Pergamon.
Orszag, S. A. & Crow, S. C. 1970 Instability of a vortex sheet leaving a semi-infinite plate. Stud. Appl. Math. 49, 167–181.Google Scholar
Pinker, R. A. & Bryce, W. D. 1976 The radiation of plane wave duct noise from a jet exhaust, statically and in flight. A.I.A.A. Paper no. 76–581.Google Scholar
Plumblee, H. E. & Dean, P. D. 1973 Sound measurements within and in the radiated field of an annular duct with flow. J. Sound Vib. 28, 715–735.Google Scholar
Savkar, S. D. 1975 Radiation of cylindrical duct acoustic modes with flow mismatch. J. Sound Vib. 42, 363–386.Google Scholar
Tam, C. K. W. 1971 Directional acoustic radiation from a supersonic jet generated by a shear layer instability. J. Fluid Mech. 46, 757–768.Google Scholar
Watson, G. N. 1966 Theory of Bessel Functions. Cambridge University Press.