Finite-Element Analysis of Double-Free-Surface Flow through Slit in Dam
Publication: Journal of Engineering Mechanics
Volume 126, Issue 5
Abstract
The fluid loads on some hydraulic structures and the free-surface profiles of the flow need to be determined for design purposes. This is a difficult task because the governing equations have nonlinear boundary conditions. The goal of the present work is to develop a suitable and accurate numerical procedure for the computation of free-surface profiles, velocity and pressure distributions, and flow rate for a 2D gravity fluid flow through a conduit in the pattern of a free jet. The problem involves two highly curved unknown free surfaces and arbitrary curve-shaped boundaries. These features make the problem more complicated than the flow under a sluice gate or over a weir. A combination of a variable domain and a fixed domain finite-element method is used to solve the problem. The results of the calculations show good agreement with previous flow solutions for the water surface profiles and pressure distributions throughout the flow domain and on the gate. Results are also confirmed by conducting a hydraulic model test.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Asavanant, J., and Vanden-Broek, J. M. (1996). “Nonlinear free surface flows emerging from a vessel and flows under a sluice gate.” J. Australian Mathematics Soc., B38, 63–86.
2.
Birkhoff, G., and Zarantonello, E. H. (1957). Jets, wakes and cavities. Academic, New York.
3.
Brebbia, C. A., and Connor, J. J. (1977). Finite element techniques for fluid flow. Newnes-Butterworths, London.
4.
Brno Technical University. ( 1994). “The bottom outlet Twin Gate, Marun.” Water Management Research Institute, Czech Republic.
5.
Cassidy, J. J. (1965). “Irrotational flow over spillways of finite height.”J. Engrg. Mech. Div., ASCE, 91(6), 155.
6.
Chan, S. T. K., Larock, B. E., and Herrmann, L. R. (1973). “Free-surface ideal fluid flows by finite elements.”J. Hydr. Div., ASCE, 99(6), 959–974.
7.
Cheng, A. H.-D., Liu, P. L.-F., and Liggett, J. A. (1981). “Boundary calculations of sluice and spillway flows.”J. Hydr. Div., ASCE, 107(10), 1163–1178.
8.
Dias, F., Elcrat, A. R., and Trefethen, L. N. (1987). “Ideal jet flow in two dimensions.” J. Fluid Mech., Cambridge, U.K., 185, 275.
9.
Diersch, H.-J., Busch, K.-F., and Schirmer, A. (1977). “Analysis of flows with initially unknown discharge.”J. Hydr. Div., ASCE, 103(3), 213–232.
10.
Fangmeier, D. D., and Strelkoff, T. S. (1968). “Solution for gravity flow under a sluice gate.”J. Engrg. Mech. Div., ASCE, 94(1), 153–176.
11.
Goh, M. K., and Tuck, E. O. (1985). “Thick waterfalls from horizontal slots.” J. Engrg. Mathematics, 19, 341–349.
12.
Guo, Y., Wen, X., and Wu, C. (1996). “Flow through slit in dam.”J. Hydr. Engrg., ASCE, 122(11), 662–669.
13.
Gurvich, M. I. (1965). Theory of jets in ideal fluids. Academic, New York.
14.
Ikegawa, M., and Washizu, K. (1973). “Finite element method applied to analysis of flow over a spillway crest.” Int. J. Numer. Methods in Engrg., 6, 179–189.
15.
Issacs, L. T. (1977). “Numerical solution for flow under sluice gates.”J. Hydr. Div., ASCE, 103(5), 473–481.
16.
Larock, B. E. (1969). “Gravity affected flow from planner sluice gates.”J. Hydr. Div., ASCE, 95(4), 1211–1226.
17.
Larock, B. E. (1970). “A theory for free outflow beneath radial gates.” J. Fluid Mech., Cambridge, U.K., 41, 851.
18.
Leanau, C. W., and Cassidy, J. J. (1969). “Flow through spillway flip bucket.”J. Hydr. Div., ASCE, 95(2), 633.
19.
Lee, J., and Vanden-Broeck, J. M. (1993). “Two dimensional jets from funnels and nozzles.” Phys. of Fluids, A5(10), 2454–2460.
20.
Li, W., Xie, Q., and Chen, C. J. (1989). “Finite analytic solution of flow over spillways.”J. Engrg. Mech., ASCE, 115(12), 2635–2648.
21.
Locher, F. A., and Hsu, S. T. ( 1984). “Energy dissipation at high dams.” Developments in hydraulic engineering—2, P. Novak, ed.
22.
McCorquodale, J. A., and Li, C. Y. (1971). “Finite element analysis of sluice gate flow.” Trans. Engrg. Inst. of Canada, 14, C-2.
23.
McNown, J. S., Hsu, E. Y., and Yih, C. S. (1955). “Applications of relaxation technique in fluid mechanics.” Trans. ASCE, 120, 650–686.
24.
Roberson, J. A., and Clayton, T. C. (1997). Engineering fluid mechanics, 6th Ed., Wiley, New York.
25.
Sadid-Tadbir Co. (1997). “Hydraulic model test of the orifice spillway for Karun III Dam.” Rep. No. KRM-R-002, Tehran, Iran.
26.
Sankaranarayanan, S., and Rao, H. S. (1966). “Finite element analysis of free surface flow through gates.” Int. J. Numer. Methods in Fluids, 22, 375–392.
27.
Southwell, R., and Vaisey, G. (1946). “Relaxation methods applied to engineering problems. XII. Fluid motions characterized by free streamlines.” Philosophical Trans. Royal Soc., London, A240, 117–161.
28.
Vanden-Broek, J. M. (1997). “Numerical calculations of the free surface flow under a sluice gate.” J. Fluid Mech., Cambridge, U.K., 330, 339–347.
Information & Authors
Information
Published In
History
Received: Mar 22, 1999
Published online: May 1, 2000
Published in print: May 2000
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.