Numerical modelling of spillway flow with free drop and initially unknown discharge

The difficulties in solving the spillway flow arise not only from the determination of the critical point, which has been used to divide the subcritical and supercritical flows, but also from the fact that either the boundary or the discharge is not known a priori. It is much more difficult to deal...

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Bibliographic Details
Published in:Journal of hydraulic research 1998-01, Vol.36 (5), p.785-801
Main Authors: Yakun, Guo, Xianyun, Wen, Chigong, Wu, Duo, Fang
Format: Article
Language:English
Subjects:
Boundary value problems
Discharge (fluid mechanics)
Earth sciences
Earth, ocean, space
Engineering and environment geology. Geothermics
Engineering geology
Exact sciences and technology
Flow of water
Flow patterns
Hydrology
Hydrology. Hydrogeology
Integral equations
Iterative methods
Mathematical models
Pressure
Velocity
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Summary:The difficulties in solving the spillway flow arise not only from the determination of the critical point, which has been used to divide the subcritical and supercritical flows, but also from the fact that either the boundary or the discharge is not known a priori. It is much more difficult to deal with such flow pattern with free drop. In this paper, by using the analytic functional boundary-value theory and the substitution of variables, the nonsingular boundary integral equations in the physical plane are derived. A synchronous iterative method for the discharge and the flow pattern is presented according to the consistency between the discharge and the uniform velocity at far upstream. Flows over different spillway profiles are treated. The discharge, the profiles of the free drop and the pressure distributions on the walls are calculated. The numerical results are in good agreement with the measured ones.
ISSN:0022-1686
1814-2079
DOI:10.1080/00221689809498603