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On the laminar flow in a free jet of liquid at high Reynolds numbers

Published online by Cambridge University Press:  28 March 2006

J. P. K. Tillett
J. P. K. Tillett
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

This paper is concerned with the jet of liquid, open to the atmosphere, that emerges from a two-dimensional channel in which there is Poiseuille flow far upstream, the flow being driven by an applied pressure gradient. The problem is discussed with the aid of the method of matched asymptotic expansions; the small parameter involved is the inverse Reynolds number. A boundary layer forms adjacent to the free surface, and a classical boundary-layer analysis is applied to find the flow there (for moderate distances downstream); the influence of this boundary layer on the flow in the core of the jet is then investigated. Higher-order boundary-layer effects, such as indeterminacy and eigensolutions, are also discussed. The first few terms are found of an asymptotic expansion for the equation of the free surface, and considerations of momentum balance are applied to find the asymptotic contraction ratio of the jet.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 2 , 3 May 1968 , pp. 273 - 292
Copyright
© 1968 Cambridge University Press

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References

Abbott, D. E. & Kline, S. J. 1961 Stanford Univ. Rept. MD-5.
Bursnal, W. J. & Loftin, L. K. 1951 NACA TN 2338.
Clauses, F. H. 1954 J. Aero. Sci. 21, 91–108.
Finn, C. L. & Sandborn, V. A. 1967 International Symposium on Hot Wire Anemometry, University of Maryland.
Gault, D. E. 1955 NACA TN 3505.
Kline, S. J. 1957 J. Aero. Sci. 21, 470–1.
Landwebber, L. 1960 Proceedings of Ninth International Towing Tank Conference, Paris.
Liu, C. Y. 1967 Ph.D. dissertation, Colorado University.
Liu, C. Y. & Sandborn, V. A. 1967a Evaluation of the Separation Properties of Laminar Boundary Layers. (To be published.)
Liu, C. Y. & Sandborn, V. A. 1967b Calculation of Laminar Boundary Layers near Separation. (To be published.)
Moon, I. MAN 1962 Symposium on Measurements in Unsteady Flow, ASME, Worchester, Mass.
Mueller, T. J., Korst, H. H. & Chow, W. L. 1964 J. Basic Engr. 86, 221–6.
Plate, E. J. & Lin, C. W. 1965 Colorado State Univ. Tech. Rept. CER 65 EJP 14.
Rotta, J. C. 1962 Prog. Aero. Sci. 2 (ed. Ferri, Kuchemann & Sterne). New York: Pergamon Press.
Rotta, J. C. 1965 Fluid Mech. of Internal Flow (ed. Sovran). American Elsevier Publ. Co.
Sandborn, V. A. 1959 NASA Memo 2-5-59E.
Sandborn, V. A. 1967 International Symposium on Hot Wire Anemometry. University of Maryland.
Sandborn, V. A. & Kline, S. J. 1961 J. Basic Engr. (Ser. D), 83, 317.
Schubauer, G. B. & Scramstead, H. K. 1948 NACA TR 909.
Stratford, D. S. 1959 J. Fluid Mech. 5, 1–16.
Townsend, A. A. 1962 J. Fluid Mech. 12, 143–55.