Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-04T18:20:27.819Z Has data issue: false hasContentIssue false
  • English
  • Français

Attenuation of sound in a low Mach Number nozzle flow

Published online by Cambridge University Press:  19 April 2006

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

Abstract

This paper examines the energy conversion mechanisms which govern the emission of low frequency sound from an axisymmetric jet pipe of arbitrary nozzle contraction ratio in the case of low Mach number nozzle flow. The incident acoustic energy which escapes from the nozzle is partitioned between two distinct disturbances in the exterior fluid. The first of these is the free-space radiation, whose directivity is equivalent to that produced by monopole and dipole sources. Second, essentially incompressible vortex waves are excited by the shedding of vorticity from the nozzle lip, and may be associated with the large-scale instabilities of the jet. Two linearized theoretical models are discussed. One of these is an exact linear theory in which the boundary of the jet is treated as an unstable vortex sheet. The second assumes that the finite width of the mean shear layer of the real jet cannot be neglected. The analytical results are shown to compare favourably with recent attenuation measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 2 , 23 March 1979 , pp. 209 - 229
Copyright
© 1979 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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Washington: Nat. Bur. Stand.
Barthel, Von F. 1958 Untersuchungen uber nichtlineare Helmholtzresonatoren. Frequenz 12.Google Scholar
Bechert, D., Michel, U. & Pfizenmaier, E. 1977 Experiments on the transmission of sound through jets, A.I.A.A. Paper no. 77–1278.Google Scholar
Bechert, D. & Pfizenmaier, E. 1975a On the amplification of broad band jet noise by a pure tone excitation. J. Sound Vib. 43, 581–587.Google Scholar
Bechert, D. & Pfizenmaier, E. 1975b Optical compensation measurements on the unsteady exit condition at a nozzle discharge edge. J. Fluid Mech. 71, 123–144.Google Scholar
Blokhintsev, D. I. 1946 Acoustics of a nonhomogeneous moving medium. N.A.C.A. Tech. Memo. no. 1399.Google Scholar
Brown, G. B. 1935 On vortex motion in gaseous jets and the origin of their sensitivity to sound. Proc. Phys. Soc. 47, 703.Google Scholar
Crighton, D. G. 1972 The excess noise field of subsonic jets. Aero. Res. Counc. Rep. no. 33714 N. 781.Google Scholar
Crow, S. C. 1972 Acoustic gain of a turbulent jet. Acoustic gain of a turbulent jet, paper IEG.
Davies, P. O. A. L., Fisher, M. J. & Barratt, M. J. 1963 The characteristics of the turbulence in the mixing region of a round jet. J. Fluid Mech. 15, 337–367.Google Scholar
Dean, P. D. & Tester, B. J. 1975 Duct wall impedance control as an advanced concept for acoustic suppression. N.A.S.A. Contractor Rep. no. 134998.Google Scholar
Ffowcs Williams, J. E. & Howe, M. S. 1975 The generation of sound by density inhomogeneities in low Mach number nozzle flows. J. Fluid Mech. 70, 605–622.Google Scholar
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683–704.Google Scholar
Gerend, R. P., Kumasaka, H. P. & Roundhill, J. P. 1973 Core engine noise, A.I.A.A. Paper no. 73–1027.Google Scholar
Howe, M. S. 1975 Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. J. Fluid Mech. 71, 625–673.Google Scholar
Jones, D. S. 1972 Aerodynamic sound due to a source near a half-plane. J. Inst. Math. Appl. 9, 114–122.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Liepmann, H. W. & Roshko, A. 1957 Elements of Gasdynamics. Wiley.
Lighthill, M. J. 1952 On sound generated aerodynamically. I. General theory Proc. Roy. Soc. A221, 564–587.Google Scholar
Lighthill, M. J. 1960 Studies on magneto-hydrodynamic waves and other anisotropic wave motions. Phil. Trans. Roy. Soc. A252, 397–430.Google Scholar
Moore, C. J. 1977 The role of shear-layer instability waves in jet exhaust noise. J. Fluid Mech. 80, 321–367.Google Scholar
Munt, R. M. 1977 The interaction of sound with a subsonic jet issuing from a semi-infinite cylindrical pipe. J. Fluid Mech. 83, 609–640.Google Scholar
Noble, B. 1958 Methods based on the Wiener-Hopf Technique. Pergamon.
Pinker, R. A. & Bryce, W. D. 1976 The radiation of plane wave duct noise from a jet exhaust, statically and in flight. U.K. Nat. Gas Turbine Est. Note no. NT-1024.Google Scholar
Rayleigh, Lord 1945 The Theory of Sound. Dover.
Saffman, P. G. 1975 On the formation of vortex rings. Stud. Appl. Math. 54, 261–268.Google Scholar
Savkar, S. D. 1975 Radiation of cylindrical duct acoustic modes with flow mismatch. J. Sound Vib. 42, 363–386.Google Scholar
Stratton, J. A. 1941 Electromagnetic Theory. McGraw-Hill.