Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-05T11:12:52.133Z Has data issue: false hasContentIssue false
  • English
  • Français

Acoustic energy flux from shock-turbulence interaction

Published online by Cambridge University Press:  28 March 2006

H. S. Ribner
H. S. Ribner
Affiliation:
Institute for Aerospace Studies, University of Toronto, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

The analysis of the sound field generated by the passage of isotropic turbulence through a shock of finite strength (Ribner 1953, 1954) has been extended to provide the flux of acoustic energy emanating from unit area on the downstream side of the shock. This is motivated by the problem of estimating the sound power emerging from a supersonic jet containing shock waves. The energy flux is found to vary almost linearly with shock density ratio, reaching a maximum at infinite Mach number of 0[sdot ]062 of the flux of turbulence kinetic energy convected into unit area of the shock.

Direct comparison with a result obtained by Lighthill (1953) is misleading. His energy relations, reckoned relative to a frame moving with the fluid, must be converted to the shock-fixed frame used herein. The converted results of his theory (weak shocks) and the results of our theory (arbitrary shocks) appear to show a similar asymptotic behaviour for vanishing shock strength; they diverge with increasing shock strength.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 35 , Issue 2 , 16 January 1969 , pp. 299 - 310
Copyright
© 1969 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

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Blokhintsev, D. I. 1946 Acoustics of a nonhomogeneous moving medium. NACA TM no. 1399 Feb. 1956 (translation of 1946 Russian paper).Google Scholar
Liepmann, H. W. & Roshko, A. 1957 Elements of Gasdynamics. New York: John Wiley.
Lighthill, M. J. 1953 On the energy scattered from the interaction of turbulence with sound or shock waves Proc. Camb. Phil. Soc. 49, 531–51.Google Scholar
Lowson, M. V. 1966 The fluctuating pressures due to shock interactions with turbulence and sound. Wyle Laboratories, Huntsville, Ala., Res. Staff Rep. WR 66–35.Google Scholar
Moore, F. K. 1953 Unsteady oblique interaction of a shock wave with a plane disturbance. NACA Rep. no. 1165, 1954 (supersedes TN no. 2879, 1953).Google Scholar
Ollerhead, J. 1966 Some shadowgraph experiments with a cold supersonic jet. Wyle Laboratories, Huntsville, Ala., Res. Staff Rep. WR 66–44.Google Scholar
Ribner, H. S. 1953 Convection of a pattern of vorticity through a shock wave. NACA TN no. 2864, Jan. 1953; NACA Rep. no. 1164, 1954.Google Scholar
Ribner, H. S. 1954 Shock-turbulence interaction and the generation of noise. NACA TN no. 3255, July 1954; NACA Rep. no. 1233, 1955.Google Scholar
Ribner, H. S. 1958 Note on acoustic energy flow in a moving medium. Univ. of Toronto, Inst. for Aerospace Studies, UTIA TN, no. 21.Google Scholar
Ribner, H. S. 1960 Energy flux from an acoustic source contained in a moving fluid element and its relation to jet noise J. Acoust. Soc. Am. 32, 1159–60.Google Scholar
Ribner, H. S. & Tucker, M. 1952 Spectrum of turbulence in a contracting stream. NACA TN no. 2606, Jan. 1952; NACA Rep. no. 1113, 1953.Google Scholar
Tatarski, V. I. 1961 Wave Propagation in a Turbulent Medium. New York: McGraw-Hill.