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The effect of finite turbulence spatial scale on the amplification of turbulence by a contracting stream

Published online by Cambridge University Press:  19 April 2006

M. E. Goldstein  and
P. A. Durbin
M. E. Goldstein
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, Ohio 44135
P. A. Durbin
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3-9EW
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Abstract

An alternative to Hunt's (1973) extension of classical rapid distortion theory is used to calculate the turbulence downstream of a rapid contraction. This problem was originally studied by Batchelor & Proudman (1954) and Ribner & Tucker (1953), but their analyses were restricted to flows in which the characteristic turbulence scales were small compared to the spatial scales of the mean flow (usually the characteristic dimension of the apparatus). We now consider the case where the turbulence scale can have the same magnitude as the mean-flow spatial scale. Relatively simple formulae are obtained by calculating the turbulence only in the downstream region where the mean flow is no longer affected by the potential field of the contraction.

The results are then further simplified by assuming that the contraction is large and expanding in inverse powers of the contraction ratio. The calculations show that effects of finite turbulence scale can be quite significant. We also obtain some important new results for small-scale turbulence by expanding the solutions in inverse powers of the turbulence spatial scale.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 3 , 12 June 1980 , pp. 473 - 508
Copyright
© 1980 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions. Washington: National Bureau of Standards.
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. 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. 7, 83.Google Scholar
Britter, R. E., Hunt, J. C. R. & Mumford, J. C. 1979 The distortion of turbulence by a circular cylinder. J. Fluid Mech. 92, 269.Google Scholar
Darwin, C. G. 1953 A note on hydrodynamics. Proc. Camb. Phil. Soc. 49, 342.Google Scholar
Durbin, P. 1979 Ph.D. thesis, Cambridge University. (See also J. Inst. Math. Appl. (1979) 23, 181).
Erdélyi, A. 1956 Asymptotic Expansion, p. 51. Dover.
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill.
Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows around arbitrary obstacles. J. Fluid Mech. 89, 433.Google Scholar
Goldstein, M. E. 1979 Turbulence generated by the interaction of entropy fluctuations with non-uniform mean flows. J. Fluid Mech. 93, 209.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. & Graham, J. M. R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 89, 209.Google Scholar
Kovasznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aero. Sci. 20, 657.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lighthill, M. J. 1956 Drift. J. Fluid Mech. 1, 31.Google Scholar
Loehrke, R. E. & Nagib, H. M. 1976 Control of free-stream turbulence by means of honey. combs: A balance between suppression and generalism. Trans. A.S.M.E. I, J. Fluids Engng 98, 342.Google Scholar
Phillips, O. M. 1955 The irrotational motion outside of a free boundary layer. Proc. Camb. Phil. Soc. 51, 220.Google Scholar
Ribner, H. S. & Tucker, M. 1953 Spectrum of turbulence in a contracting stream. N.A.C.A. Rep. 1113.Google Scholar
Taylor, G. I. 1935 Turbulence in a contracting stream. Z. angew. Math. Mech. 15, 91.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Tucker, H. J. & Reynolds, A. J. 1968 The distortion of turbulence by irrotational plane strain. J. Fluid Mech. 32, 657.Google Scholar