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Closed-form solution of the potential flow in a contracted flume

Published online by Cambridge University Press:  06 March 2008

G. BELAUD  and
X. LITRICO
G. BELAUD
Affiliation:
UMR G-EAU, IRD, Maison des Sciences de l'Eau, 300 av. Emile Jeanbrau34095 Montpellier Cedex 5, Francebelaud@msem.univ-montp2.fr
X. LITRICO
Affiliation:
UMR G-EAU, Cemagref, B.P. 5095, 34196 Montpellier Cedex 5, Francexavier.litrico@cemagref.fr
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Abstract

The potential flow upstream from a contraction in a rectangular flume is analysed. In order to calculate the potential function, the flow is considered as the superposition of sinks uniformly distributed in the contraction. The effect of boundaries is taken into account by introducing virtual sinks. The calculation is performed in the complex plane and provides a closed-form solution of the complex potential function. As an illustration, the effect of contraction size and position is analysed, and the solution is compared to experimental measurements and other numerical solutions for vertical sluice gates.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 599 , 25 March 2008 , pp. 299 - 307
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. US Department of Commerce.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Benjamin, T. B. 1956 On the flow in channels when rigid obstacles are placed in the stream. J. Fluid Mech. 1, 227–248.CrossRefGoogle Scholar
Binder, B. J. & Vanden-Broeck, J. M. 2007 The effect of disturbances on the flows under a sluice gate and past an inclined plate. J. Fluid Mech. 576, 475–490.CrossRefGoogle Scholar
Chung, Y. K. 1972 Solution of flow under sluice gates. ASCE J. Engng Mech. Div. 98, 121–140.CrossRefGoogle Scholar
Clamond, D. 2006 Complex dilogarithm. Tech. Rep. Available from Matlab exchange central, http://www.mathworks.com.Google Scholar
Finnie, J. & Jeppson, W. 1991 Solving turbulent flows using finite elements. J. Hydraul. Engng 117, 1513–1530.CrossRefGoogle Scholar
Larock, B. 1969 Gravity-affected flow sluice gate. ASCE J. Hyd. Div. 95, 153–176.Google Scholar
Montes, J. S. 1997 Irrotational flow and real fluid effects under planar sluice gates. J. Hydraul. Engng 123, 219–232.Google Scholar
Rajaratnam, N. & Humphries, J. A. 1982 Free flow upstream of vertical sluice gates. J. Hydraul. Res. 20, 427–437.CrossRefGoogle Scholar
Roth, A. & Hager, W. 1999 Underflow of standard sluice gate. Exps. Fluids 27, 339–350.CrossRefGoogle Scholar
Shammaa, Y., Zhu, D. Z. & Rajaratnam, N. 2005 Flow upstream of orifices and sluice gates. J. Hydraul. Engng 131, 127–133.CrossRefGoogle Scholar
Vanden-Broeck, J. M. 1997 Numerical calculations of the free-surface flow under a sluice gate. J. Fluid Mech. 130, 339–347.CrossRefGoogle Scholar