Numerical Simulation of Hydraulic Jump
Publication: Journal of Hydraulic Engineering
Volume 117, Issue 9
Abstract
Boussinesq equations describing one‐dimensional unsteady, rapidly varied flows are integrated numerically to simulate both the sub‐ and supercritical flows and the formation of a hydraulic jump in a rectangular channel having a small bottom slope. For this purpose the MacCormack (second‐order accurate in space and time) and two‐four (second‐order accurate in time and fourth‐order in space) explicit finite‐difference schemes are used to solve the governing equations subject to specified end conditions until a steady state is reached. The inclusion of initial and boundary conditions is discussed, and the importance of the Boussinesq terms is investigated. Complete test results for a range of Froude numbers are presented that may be used by other researchers for the verification of mathematicalmodels. A comparison of the computed and measured results shows that the agreement between them is satisfactory for the fourth‐order finite‐difference scheme although the second‐order scheme does not accurately predict the location of the jump. These simulations show that the Boussinesq terms have little effect in determining the location of the hydraulic jump.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abbott, M. B. (1979). Computational hydraulics; elements of the free surface flow. Pitman Publishing Limited, London, England.
2.
Abbott, M. B., Marshall, G., and Rodenhius, G. S. (1969). “Amplitude‐dissipative and phase‐dissipative scheme for hydraulic jump simulation.” 13th Congress IAHR, (Int. Assoc. of Hydr. Res.). Tokyo, Japan, Vol. 1, 313–329.
3.
Abbott, M. B., McCowan, A., and Warren, I. R. (1983). “Improved simulations of wave propagation.” IAHR, 7, (Sep.), 78–81.
4.
Anderson D. A., Tannehill, J. D., and Pletcher, R. H. (1984). Computational fluid mechanics and heat transfer. McGraw‐Hill Book Co., Inc., New York, N.Y.
5.
ASCE Task Force. (1964). “Energy dissipators for spillways and outlet works.” J. Hydr. Div., ASCE, 90(1), 121–147.
6.
Bakhmeteff, B. A., and Matzke, A. E. (1936). “The hydraulic jump in terms of dynamic similarity.” Trans. ASCE, Vol. 101, 630–680.
7.
Basco, D. R. (1983). “Introduction to rapidly‐varied unsteady, free‐surface flow computation.” USGS, Water Resour. Invest. Report No. 83‐4284. U.S. Geological Service, Reston, Va.
8.
Belanger, J. B. (1828). Essai sur la solution numeric de quelques problems relatifs an mouvement permenent des causcourantes (in French), Paris, France.
9.
Bidone, G. (1819). “Observations sur le hauteur du ressaut hydraulique en 1818.” Report (in French), Royal Academy of Sciences, Turin, Italy.
10.
Bradley, J. N., and Peterka, A. J. (1957). “Hydraulic design of stilling basins.” J. Hydr. Div. ASCE, 83(5), 1401–1406.
11.
Chaudhry, M. H. (1987). Applied hydraulic transients, 2nd Ed., Van Nostrand Reinhold Company, New York, N.Y.
12.
Chaudhry, M. H., and Hussaini, M. Y. (1985). “Second‐order explicit methods for transient flow analysis.” J. Fluids Engrg., 107, (Dec), 523–529.
13.
Chow, V. T. (1959). Open channel hydraulics. McGraw‐Hill Book Co., Inc., New York, N.Y.
14.
Fennema, R. J. and Chaudhry, M. H. (1986). “Explicit numerical schemes for unsteady free‐surface flows with shocks.” Water Resour. Res., 22(13), 1923–1930.
15.
Garg, S. P., and Sharma, H. R. (1971). “Efficiency of hydraulic jump,” J. Hydr. Div., ASCE, 97(3), 409–420.
16.
Gharangik, A. M. (1988). “Numerical Simulation of Hydraulic Jump,” thesis presented to Washington State University, at Pullman, Wash., in partial fulfillment of the requirements for the degree of Master of Science.
17.
Gottlieb, D. and Turkel, E. (1976). “Dissipative two‐four methods for time‐dependent problems.” Mathematics of computation, 30(136), 703–723.
18.
Hager, W. H., and Wanoschek, R. (1987). “Hydraulic jump in triangular channel.” J. Hydr. Res., ASCE, 25(5) 549–564
19.
Jameson, A., Schmidt, W., and Turkel, E. (1981). “Numerical solutions of the Euler equations by finite volume methods using Runge‐Kutta time‐stepping schemes.” AIAA 14th Fluid and Plasma Dynamics Conf.: AIAA 81‐1259, American Institute of Aeronautics and Astronautics, Palo Alto, Calif.
20.
Katopodes, N. D. (1984). “A dissipative Galerkin scheme for open‐channel flow.” J. Hydr. Engrg., ASCE, 110(4), 450–466.
21.
Lai, C. (1986). “Numerical modeling of unsteady open‐channel flow.” Advances in Hydrosci., Vol. 14, 161–331.
22.
Leutheusser, H. J., and Kartha, V. (1972). “Effects of inflow conditions on hydraulic jump.” J. Hydr. Engrg. Div., ASCE, 98(8), 1367–1385
23.
Liggett, J. A., and Cunge, J. (1975). “Numerical methods of solution of unsteady flow equations.” Unsteady open channel flow, K. Mahmood, and V. Yevjevich, eds., Water Resources Publications, Fort Collins, Col.
24.
MacCormack, R. W. (1969). “The effect of viscosity in hypervelocity impact cra‐tering.” Paper 69‐354, American Institute of Aeronautics and Astronautics, Cincinnati, Ohio.
25.
McCorquodale, J. A., and Khalifa, A. (1983). “Internal flow in hydraulic jumps.” J. Hydr. Engrg., ASCE, 109(5), 684–701.
26.
McCowan, A. D. (1987). “The range of application of Boussinesq type numerical short wave models.” IAHR XXII Congress, Int. Assoc. of Hydro. Res., 378–384.
27.
MacCowan, A. D. (1985). “Equation systems for modeling dispersive flow in shallow water,” XXI IAHR Congress, Int. Assoc. of Hydro. Res., Melbourne, Australia, Vol. 2, 50–57.
28.
Rajaratnam, N. (1968). “Profile of the hydraulic jump.” J. Hydr. Div., ASCE, 94(3), 663–673.
29.
Rajaratnam, N. (1967). “Hydraulic jump.” Advances in Hydrosci., Academic Press, Vol. 4, 198–280.
30.
Rouse, H., Siao, T. T., and Nagaratnam, S. (1959). “Turbulence characteristics of the hydraulic jump.” Trans., ASCE, 926–966.
31.
Safranez, K. (1929). “Researches relating to the hydraulic jump” (English translation by D. P. Barnes), Bureau of Reclamation Files, Nos. 37 and 38, Bureau of Reclamation, Denver, Colo.
32.
Sarma, K. V. N., and Newnham, D. A. (1973). “Surface profiles of hydraulic jump for Froude number less than four.” Water Resour, London, England, 25, (April), 139–142.
33.
Silvester, R. (1964). “Hydraulic jump in all shapes of horizontal channels.” J. Hydr. Div., ASCE, 90(1), 23–55.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 117 • Issue 9 • September 1991
Pages: 1195 - 1211
Copyright
Copyright © 1991 ASCE.
History
Published online: Sep 1, 1991
Published in print: Sep 1991
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.