Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-19T09:50:47.872Z Has data issue: false hasContentIssue false
  • English
  • Français

The generation of sound by density inhomogeneities in low Mach number nozzle flows

Published online by Cambridge University Press:  29 March 2006

J. E. Ffowcs Williams  and
M. S. Howe
J. E. Ffowcs Williams
Affiliation:
Engineering Department, University of Cambridge
M. S. Howe
Affiliation:
Engineering Department, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses the sound generated when an inhomogeneity in density is convected in a low Mach number steady flow through a contraction in a duct of infinite extent, and also when the inhomogeneity exhausts through a nozzle into free space. The analyses of Candel (1972) and Marble (1973) for the case of duct flow were based on a frequency decomposition of the incident inhomogeneity and cannot adequately deal with sharp-fronted inhomogeneities and entropy spots. However, the practical difficulties of this earlier work can be avoided at low flow Mach numbers by conducting the analysis in terms of an approximate expression for the acoustic Green's function in the manner described by Howe (1975). This method also permits a considerable extension of the range of the earlier investigations to the determination of the sound generated when the inhomogeneity is swept out of a nozzle orifice into free space. It is shown that the acoustic pressure perturbations developed in a duct at a contraction are in general proportional to the fractional difference between the density of the inhomogeneity and that of the mean flow times a typical mean flow pressure level, and are due principally to the fluctuation in thrust accompanying the passage of the inhomogeneity through the region of variable pressure gradient. The pressure waves generated at a nozzle orifice and radiated into free space are O(M0) smaller, where M0 is a mean flow Mach number based on the speed of sound in the jet.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 3 , 12 August 1975 , pp. 605 - 622
Copyright
© 1975 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

Candel, S. M. 1972 Analytical studies of some acoustic problems of jet engines. Ph.D. thesis, California Institute of Technology, Pasadena
Cumpsty, N. A. & Marble, F. E. 1974 The generation of noise by the fluctuations in gas temperature into a turbine. Cambridge University Engng Lab. Rep. CUED/A TURBO/TR57.Google Scholar
Ffowcs Williams, J. E. 1974 Sound production at the edge of a steady flow. J. Fluid Mech. 66, 791–816.Google Scholar
Ffowcs Williams, J. E. & Hawkings, D. L. 1969 Sound generation by turbulence and surfaces in arbitrary motion. Phil. Trans. A 264, 321–342.Google Scholar
Howe, M. S. 1975 The generation of sound by aerodynamic sources in inhomogeneous steady flow. J. Fluid Mech. 67, 597–610.Google Scholar
Leppington, F. G. 1971 Rep. Aero. Res. Counc. Working Party on Novel Aerodynamic Noise Source Mechanisms at Low Jet Speeds, chap. 5. Aero. Res. Counc. publ. no. 32 925 N. 742.
Marble, F. E. 1973 Acoustic disturbance from gas nonuniformities convected through a nozzle. Dep. Transportation Symp. Stanford University.
Morfey, C. L. 1973 Amplification of aerodynamic noise by convected flow inhomogeneities. J. Sound Vib. 31, 391–397.Google Scholar
Rayleigh, Lord 1945 The Theory of Sound, vol. 2. Dover.