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On a solution of the Lavrentiev wake model and its cascade

Published online by Cambridge University Press:  11 April 2006

Anching Lin  and
Louis Landweber
Anching Lin
Affiliation:
University of Utah, Salt Lake City
Louis Landweber
Affiliation:
Institute of Hydraulic Research, University of Iowa, Iowa City
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Abstract

A Lavrentiev model of the flow about a blunt two-dimensional body with a separation bubble is considered. Physical bases of the model are discussed in relation to other wake models. The Lavrentiev wake bubble contains a pair of closed free streamlines enclosing the regions of vorticity. It is shown, by means of conformal mapping, that the complex potential can be expressed in terms of elliptic functions, and a one-parameter family of exact solutions has been constructed for a normal flat plate and truncated wedges, for both an unbounded and a bounded stream. A procedure for relating the value of the parameter to the Reynolds number of the real fluid flow is indicated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 4 , 23 March 1977 , pp. 801 - 823
Copyright
© 1977 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. E. 1964 Handbook of Mathematical Functions. Washington: Nat. Bur. Stand.
Acrivos, A., Leal, G., Snowden, D. D. & Pan, F. 1968 Further experiments on steady separated flows past bluff objects. J. Fluid Mech. 34, 25–48.Google Scholar
Acrivos, A., Snowden, D. D., Grove, A. S. & Petersen, E. E. 1965 The steady separated flow past a circular cylinder at large Reynolds numbers. J. Fluid Mech. 21, 737–60.Google Scholar
Arie, M. & Rouse, H. 1956 Experiments on two-dimensional flow over a normal wall. J. Fluid Mech. 1, 129–41.Google Scholar
Batchelor, G. K. 1956 A proposal concerning laminar wakes behind bluff bodies at large Reynolds numbers. J. Fluid Mech. 1, 388–98.Google Scholar
Dutta, M. & Debnath, L. 1965 Theory of Elliptic and Associated Functions. Calcutta: The World Press Private, Ltd.
Grove, A. S., Shair, F. H., Petersen, E. E. & Acrivos, A. 1964 An experimental investigation of the steady separated flows past a circular cylinder. J. Fluid Mech. 19, 60–80.Google Scholar
Landweber, L. 1970 A note on blockage effect. In Jubilee Memorial W.P.A. Van Lammeren Volume, pp. 49–51. Netherlands Ship Model Basin, Wageningen.
Lavrentiev, M. A. 1962 Variational Methods for Boundary Value Problems for Systems of Elliptic Functions. Noordhoff.
Lighthill, M. J. 1960 Fourier Analysis and Generalised Functions. Cambridge University Press.
Lin, A. 1966 Effect of channel walls on base pressure and flow of a blunt body. M.S. thasis, University of Iowa, Iowa City.
Lin, A. 1970 A free-streamline model of two-dimensional wake. Ph.D. dissertation, University of Iowa, Iowa City.
Lin, A. & Sha, P. Y. 1975 Some flow characteristics in the vicinity of reattachment point behind a flat plate. Proc. 2nd U.S. Nat. Con. Wind Engng. Res., vol. IV-24, pp. 1–3.Google Scholar
Nehari, Z. 1952 Conformal Mapping. McGraw-Hill.
Sedov, L. I. 1965 Two Dimensional Problems in Hydrodynamics and Aerodynamics. Wiley.
Whittaker, E. T. & Watson, G. N. 1950 A Course of Modern Analysis. Cambridge University Press.
Wu, T. Y. 1972 Cavity and wake flows. Ann. Rev. Fluid Mech. 4, 243–84.Google Scholar
Wu, T. Y., Whitney, A. K. & Brennan, C. 1971 Cavity-flow wall effects and correction rules. J. Fluid Mech. 49, 223–56.Google Scholar