Finite Analytic Solution of Flow over spillways
Publication: Journal of Engineering Mechanics
Volume 115, Issue 12
Abstract
In this study, two‐dimensional irrotational gravity flows over a spill‐way with a free surface are investigated numerically and compared to available experimental measurements. The difficulty of the present problem lies in that both the free surface elevation and flow rate are unknowns, even when the reservoir and spillway crest heights are given. In order to solve the problem, the boundary‐fitted coordinate system is adopted to map the complex domain into a rectangular domain with uniform meshes. The finite analytic method is used to obtain the numerical solution. In the finite analytic method, the local analytic solution of the governing equation in an element is obtained and used to formulate the algebraic representation of the governing equation. The discharge coefficient is deduced by a scan method according to the variational principle for variable domains. The prediction is made for the Waterways Experimental Station spillway, where extensive data are available for comparison. The numerical results agree well with experimental data on discharge coefficients and free surface elevation.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Betts, P. L. (1979). “A variational principle in terms of stream function for free surface flows and its application to finite element method.” Computers and Fluids, 7(2), 145–153.
2.
Cassidy, J. J. (1964). “Spillway discharge at other than design head.” Thesis presented to The University of Iowa, at Iowa City, Iowa, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
3.
Cassidy, J. J. (1965). “Irrotational flow over spillways of finite height.” J. Engrg. Mech. Div., ASCE, 91(6), 155–173.
4.
Chen, C. J. (1988). “Finite analytic method.” Handbook of Numerical Heat Transfer, W. J. Minkowycz, et al., eds., John Wiley and Sons, New York, N.Y., 723–746.
5.
Chen, C. J., and Chen, H. C. (1984). “Development of finite analytic numerical method for unsteady two‐dimensional Navier‐Stokes equations,” J. Computational Physics, 53(2), 209–226.
6.
Chow, V. T. (1959). Open‐channel hydraulics. McGraw‐Hill, New York, N.Y., 365–380.
7.
“Corps of engineers hydraulic design criteria.” (1952). Office of Chief of Engrs., U.S. Army Corps of Engrs., Waterways Exp. Station, Vicksburg, Miss.
8.
Diersch, H. J., Schiremer, A., and Busch, K. F. (1977). “Analysis of flows with initially unknown discharge.” ASCE, J. Hydraulics Div., 103(3), 213–231.
9.
Hsu, Hsieh‐Ching (1980). “A method for solution of free surface gravity flow by finite elements.” ShuiLi XueBao, Beijing, China, 1–13.
10.
Ikegawa, M., and Washizu, K. (1973). “Finite element method applied to analysis of flow over a spillway crest.” Int. J. of Nuιn. Meth. in Engrg., 6(2), 179–189.
11.
Thompson, J. F., Warsi, Z. U. A., and Mastin, C. W. (1982). “Boundary‐fitted coordinate system for numerical solution of partial differential equations.” J. Computational Physics, 47(1), 1–108.
12.
Varoglu, E., and Finn, W. D. L. (1978). “Variable domain finite element analysis of free surface gravity flow.” Computers and Fluids, 6(2), 103–114.
Information & Authors
Information
Published In
Copyright
Copyright © 1989 ASCE.
History
Published online: Dec 1, 1989
Published in print: Dec 1989
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.