Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-19T18:29:25.568Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence generated by the interaction of entropy fluctuations with non-uniform mean flows

Published online by Cambridge University Press:  19 April 2006

M. E. Goldstein
M. E. Goldstein
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, Ohio 44135
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is primarily concerned with the turbulence generated by the interaction of random entropy fluctuations with non-uniform mean flows. The results are obtained by using rapid distortion theory in conjunction with a high frequency solution of a previously developed wave equation that governs the small amplitude unsteady vortical and entropic motion on steady potential flows (Goldstein 1978). The analysis is applied to symmetric contractions or expansions (or combinations of the two) and comparisons are made with a corresponding theory of Batchelor & Proudman (1954) for the rapid distortion of upstream turbulence by a contraction of this type. It is shown that the energy of the entropy-generated turbulence increases much more rapidly with contraction ratio than that of the imposed upstream turbulence. Turbulence of the former type can therefore dominate the latter even when the upstream entropy fluctuations are weak relative to the imposed turbulent intensities. Moreover the structure of the entropy-generated turbulence is found to be quite different from that of the contracted upstream turbulence.

A secondary purpose of the paper is to discuss some effects of compressibility on rapid distortion theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 93 , Issue 2 , 26 July 1979 , pp. 209 - 224
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

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. & Proudman, I. 1954 The effect of rapid distortion of a fluid in turbulent motion. Quart. J. Mech. Appl. Math. 1, 83.Google Scholar
Candel, S. M. 1972 Analytical studies of some acoustic problems of jet engines. Ph.D. Thesis, Calif. Inst. Technology, Pasadena.
Corrsin, S. 1952 Effect of wind-tunnel nozzle on steady flow non-uniformities. J. Aeronaut. Sci. 19 (2), 135.Google Scholar
Cumpsty, N. A. & Marble, F. E. 1974 The generation of noise by the fluctuations in gas temperature into a turbine. Cambridge University, Engineering Dept.
Darwin, C. G. 1953 A note on hydrodynamics. Proc. Camb. Phil. Soc. 49, 342.Google Scholar
Ffowcs Williams, J. E. & Howe, M. S. 1975 J. Fluid Mech. 70, 605.
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill.
Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433.Google Scholar
Hinze, J. O. 1959 Turbulence. McGraw-Hill.
Hunt, J. C. R. 1973 A theory of turbulent flow round two-dimensional bluff bodies. J. Fluid Mech. 61, 625.Google Scholar
Hunt, J. C. R. 1977 A review of the theory of rapidly distorted flow and its application. Presented at the XIII Biennial Fluid Dyn. Symp., Poland, Sept. 1977
Kovàsznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aero. Sci. 20, 657.Google Scholar
Lamb, H. 1932 Hydrodynamics. Dover.
Landahl, M. T. 1961 Unsteady Transonic Flow. Pergamon.
Lighthill, M. J. 1956 Drift. J. Fluid Mech. 1, 31.Google Scholar
Myers, M. K. & Callegari, A. J. 1978 Transmission of sound through high-subsonic flows in non-uniform flows. A.I.A.A. paper no. 78–1155 (presented at A.I.A.A. 11th Fluid and Plasma Dyn. Conf., Seattle, Wash., July 1978).Google Scholar
Pickett, G. F. 1974 Turbine noise due to turbulence and temperature fluctuations. Pratt and Whitney Aircraft Corp. (presented at the 8th Int. Cong, on Acoustics, London).
Prasad, P. & Krishnan, E. V. 1977 Nonlinear wave propagation in a two-dimensional steady transonic flow. J. Fluid Mech. 82, 17.Google Scholar
Ribner, H. S. & Tucker, M. 1953 Spectrum of turbulence in a contracting stream. N.A.C.A. Rep. 1113.Google Scholar