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Entry flow in a channel

Published online by Cambridge University Press:  29 March 2006

Milton Van Dyke
Milton Van Dyke
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, California
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Abstract

A uniformly valid asymptotic solution for large Reynolds number is constructed for plane steady laminar flow of a liquid into the channel between two semi-infinite parallel plates. The entry condition is taken as either that for a cascade of plates in a uniform oncoming stream, or uniform flow directly at the inlet. A paradox in the standard solution of Schlichting—that near the inlet the flow due to displacement would not be the accelerated uniform core on which his expansion is based—is resolved by showing that his series for small as well as large distance actually applies only to conditions far downstream, and matches with another expansion valid near the inlet. Good agreement is found with three independent numerical solutions of the full Navier-Stokes equations, except for a discrepancy in one solution for uniform entry that is traced to erroneous neglect of inlet vorticity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 44 , Issue 4 , 16 December 1970 , pp. 813 - 823
Copyright
© 1970 Cambridge University Press

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References

Atkinson, B., Zdzislaw, K. & Smith, J. M. 1967 A.I.Ch.E. J. 13, 1.
Atkinson, G. S. & Goldstein, S. 1938 Unpublished work described in Modern Developments in Fluid Dynamics, vol. 1, 304 (ed. S. Goldstein). Oxford: Clarendon.
Blankenship, V. D. & Chung, P. M. 1967 J. Heat Transf., Trans. ASME 89, Ser. C, 281.
Bodoia, J. R. 1959 Ph.D. Diss., Dep. Mech. Engng, Carnegie Inst. Tech.
Brandt, J. R. & Osterle, J. F. 1961 Appl. Sci. Res. 10, 26.
Boussinesq, J. 1891 Comptes Rendus, 113, 9.
Brandt, A. & Gillis, J. 1966 Phys. Fluids, 9, 690.
Collins, M. & Schowalter, W. R. 1962 Phys. Fluids, 5, 1122.
Collins, M. & Schowalter, W. R. 1963 A.I.Ch.E. J. 9, 9.
Conti, R. & Van Dyke, M. 1969 J. Fluid Mech. 38, 51.
Davis, R. T. 1967 J. Fluid Mech. 27, 69.
Friedmann, M., Gillis, J. & Liron, N. 1968 Appl. Sci. Res. 19, 42.
Gillis, J. & Brandt, A. 1964 Air Force European Office of Aerospace Res. Sci. Rep. 63–73 (AD 614 915).
Hahneman, E., Freeman, J. C. & Finston, M. 1948 J. Aeron. Sci. 15, 49.
Hornbeck, R. W. 1964 Appl. Sci. Res. 13 A, 224.
Horton, T. E. & Yuan, S. W. 1964 Appl. Sci. Res. 14 A, 233.
Johnson, M. W. & Reissner, E. 1960 J. Soc. Indus. Appl. Math. 8, 38.
Kaplun, S. 1954 Z. angew. Math. Phys. 5, 11.
Kovasznay, L. S. G. 1948 Proc. Camb. Phil. Soc. 44, 5.
Langhaar, H. L. 1942 J. Appl. Mech., Trans. ASME, 64, A 55.
Lighthill, M. J. 1958 Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press.
Mccomas, S. T. 1967 J. Basic. Engng, Trans. ASME 89, Ser. D, 847.
Metzner, A. B. & White, J. L. 1965 A.I.Ch.E. J. 11, 98.
Roidt, M. & Cess, R. D. 1962 J. Appl. Mech., Trans. ASME, 84, Ser. E, 171.
Rosenhead, L.(ed.)1963 Laminar Boundary Layers. Oxford: Clarendon.
Schiller, L. 1922 Z. angew. Math. Mech. 2, 9.
Schlichting, H. 1934 Z. angew. Math. Mech. 14, 36.
Shercliff, J. A. 1956 Proc. Camb. Phil. Soc. 52, 57.
Van Dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic.
Van Dyke, M. D. 1969 Ann. Rev. Fluid Mech. 1, 26.
Vrentas, J. S., Duda, J. L. & Bargeron, K. G. 1966 A.I.Ch.E. J. 12, 83.
Wang, Y. L. 1963 Part 2 of Ph.D. Diss., Calif. Inst. Tech.
Wang, Y. L. & Longwell, P. A. 1964 A.I.Ch.E. J. 10, 323. Additional tables of results: Document 7846, Amer. Documentation Inst., Photoduplication Service, Library of Congress, Washington, D.C.
Wilson, S. 1969 J. Fluid Mech. 38, 79.
Wilson, S. 1970 Unpublished.