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Applicability of the isotropic vorticity theory to an adverse pressure gradient flow

Published online by Cambridge University Press:  19 April 2006

S. C. Arora  and
R. S. Azad
S. C. Arora
Affiliation:
Department of Mechanical Engineering, The University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 Permanent address: Structures Analysis Turbine Department, Pratt & Whitney Aircraft of Canada Ltd., Longueuil, Quebec, Canada J4K 4X9.
R. S. Azad
Affiliation:
Department of Mechanical Engineering, The University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
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Abstract

An examination of the isotropic vorticity theory was made in an adverse pressure gradient flow based on experimental data obtained in a conical diffuser having a total divergence angle of 8° and an area ratio of 4:1 with fully-developed pipe flow at entry. The results showed that the rates and the ratio of production and dissipation of the turbulent vorticity were constant in the core region of the diffuser but increase significantly in the wall layer. The overall vorticity balance was essentially the same at all axial stations. The analysis of Batchelor & Townsend (1947) for isotropic vorticity was found to be valid in the core region of the diffuser for an order-of-magnitude higher Rλ (200 [les ] Rλ 600) than in grid turbulence. The magnitude of the skewness of ∂u1/∂t was constant in the core region and comparable to that for grid turbulence. Also, this region of constant skewness extended over a larger portion of the flow cross-section compared to pipe flow. On the basis of these results, it was concluded that assumptions of isotropy in the fine structure are valid in the core region of the diffuser.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 97 , Issue 2 , 25 March 1980 , pp. 385 - 404
Copyright
© 1980 Cambridge University Press

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References

Arora, S. C. & Azad, R. S. 1978a Univ. Manitoba, Winnipeg, Canada, Dept. Mech. Engng, Rep. no ER25.27.
Arora, S. C. & Azad, R. S. 1978b Univ. Manitoba, Winnipeg, Canada, Dept. Mech. Engng, Rep. no ER25.28.
Azad, R. S. & Hummel, R. H. 1971 Can. J. Phys. 49, 2917.
Azad, R. S. & Hummel, R. H. 1979 A.I.A.A. J. 17, 884.
Batchelor, G. K. 1947 Proc. Camb. phil. Soc. 43, 533.
Batchelor, G. K. & Townsend, A. A. 1947 Proc. Roy. Soc. A 191, 534.
Betchov, R. 1956 J. Fluid Mech. 1, 497.
Corrsin, S. & Kistler, A. L. 1955 N.A.C.A. Rep. 1244.
Elena, M. 1977 Int. J. Heat & Mass Transfer 20, 935.
Frenkiel, F. N. & Klebanoff, P. S. 1975 Boundary-Layer Meteorol. 8, 173.
Kolmogoroff, A. N. 1941 Comptes rendus de l'Académie des sciences de l'U.R.S.S. 30, 301.
(English translation: 1961 Turbulence, Classical Papers on Statistical Theory (ed. S. K. Friedlander & L. Topper), paper 7, p. 151. Interscience.)
Kuo, A. Y. S. & Corrsin, S. 1971 J. Fluid Mech. 50, 285.
Lumley, J. L. 1970 J. Fluid Mech. 41, 413.
Okwuobi, P. A. C. & Azad, R. S. 1973 J. Fluid Mech. 57, 603.
Saffman, P. G. 1963 J. Fluid Mech. 16, 545.
Sovran, G. & Klomp, E. D. 1967 Gen. Motors Symp. on Internal Flow. Elsevier.
Tatsumi, T., Kida, S. & Mizushima, J. 1978 J. Fluid Mech. 85, 97.
Taylor, G. I. 1935 Proc. Roy. Soc. A 151, 421.
Taylor, G. I. 1938 Proc. Roy. Soc. A 164, 15.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. M.I.T. Press.
Ueda, H. & Hinze, J. O. 1975 J. Fluid Mech. 67, 125.
Ueda, H. & Mizushina, T. 1977 5th Biennial Symp. on Turbulence, University of Missouri-Rolla.
Wyngaard, J. C. 1969 J. Phys. E Sci. Instr. 2, 983.
Wyngaard, J. C. & Tennekes, H. 1970 Phys. Fluids 13, 1962.