Simulation of Curved Open Channel Flows by 3D Hydrodynamic Model
Publication: Journal of Hydraulic Engineering
Volume 124, Issue 7
Abstract
A mathematical model of three-dimensional (3D) free surface flows has been applied to simulate the curved channel flows and mass transport. In the horizontal plane, a channel-fitted curvilinear coordinate system is used, whereas in the vertical plane, the σ-transformation is adopted to track the free surface and variable bed topography. To reduce the numerical diffusion, the second-order upwind scheme of Roe is incorporated to discretize the convection terms. The standard k-ε model has been modified to take account of some anisotropic effects appearing in shallow curved channels, i.e., streamline curvature and the damping effects of free surface and solid walls. The governing equations are solved in a collocated grid system by a fractional three-step implicit algorithm. Two test cases from curved flumes have been studied: (1) A 270° channel bend with a sloped outer bank; and (2) a meandering channel with mass transport. The results are compared with the available data, which shows generally good agreement.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Chang, H. H. (1992). Fluvial processes in river engineering. Krieger Publishing Co., Malabar, Fla.
2.
Chang, Y. C. (1971). “Lateral mixing in meandering channels,” PhD thesis, Univ. of Iowa, Iowa City, Iowa.
3.
Cheng, G. C., and Farokhi, S.(1992). “On turbulent flows dominated by curvature effects.”J. Fluid Engrg., ASME, 114(1), 52–57.
4.
Cokljat, D., and Younis, B. A.(1995). “Second-order closure study of open-channel flows.”J. Hydr. Engrg., ASCE, 121(2), 94–105.
5.
Demuren, A. O.(1991). “Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section.”AIAA J., 29(4), 531–537.
6.
Demuren, A. O.(1993). “A numerical model for flow in meandering channels with natural bed topography.”Water Resour. Res., 29(4), 1269–1277.
7.
Demuren, A. O., and Rodi, W.(1986). “Calculation of flow and pollutant dispersion in meandering channels.”J. Fluid Mech., 172(11), 65–92.
8.
De Vriend, H. J.(1981). “Velocity redistribution in curved rectangle channels.”J. Fluid Mech., 107(6), 423–439.
9.
Dou, G. (1986). “General laws of turbulent flows.”Proc., 3rd Int. Symp. on River Sedimentation, 47–57.
10.
Fisher, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H. (1979). Mixing in inlands and coastal waters. Academic Press, New York, N.Y.
11.
Galmes, J. M., and Lakshminarayana, B.(1984). “Turbulence modeling for three-dimensional shear flows over curved rotating bodies.”AIAA J., 22(10), 1420–1428.
12.
Hicks, F. E. (1985). “Shear and velocity near a sloped bank in a curved channel,” MS thesis, Univ. of Alberta, Edmonton, Alta., Canada.
13.
Hicks, F. E., Jin, Y. C., and Steffler, P. M.(1990). “Flow near sloped bank in curved channel.”J. Hydr. Engrg., ASCE, 116(1), 55–70.
14.
Johannesson, H., and Parker, G.(1989). “Velocity redistribution in meandering rivers.”J. Hydr. Engrg., ASCE, 115(8), 1019–1039.
15.
Krishnappan, B. G., and Lau, Y. L.(1977). “Transverse mixing in meandering channels with varying bottom topography.”J. Hydr. Res., 15(4), 351–369.
16.
Launder, B. E., Priddin, C. H., and Sharma, B. I.(1977). “The calculation of turbulent boundary layers on spinning and curved surface.”J. Fluid Engrg., ASME, 99(1), 231–239.
17.
Launder, B. E., and Spalding, D. B. (1972). Lectures in mathematical models of turbulence. Academic Press, London, England.
18.
Launder, B. E., and Spalding, D. B.(1974). “The numerical computation of turbulent flows.”Comp. Methods Appl. Meth. and Engrg., 3, 269–289.
19.
Leschziner, A., and Rodi, W.(1979). “Calculation of strongly curved open channel flow.”J. Hydr. Div., ASCE, 105(10), 1297–1314.
20.
Leschziner, A., and Rodi, W.(1981). “Calculation of annular and twin parallel jets using various discretisation schemes and turbulence-model variations.”J. Fluids Engrg., ASME, 103(2), 352–360.
21.
Majumdar, M.(1988). “Role of underrelaxation in momentum interpolation for calculation of flow with non-staggered grids.”Numer. Heat Transfer, 13(1), 125–132.
22.
Naot, D., and Rodi, W.(1982). “Numerical simulation of secondary currents in a channel flow.”J. Hydr. Div., ASCE, 108(8), 948–968.
23.
Odgaard, A. J.(1986). “Meander flow model. I: Development.”J. Hydr. Engrg., ASCE, 112(12), 1117–1136.
24.
Patankar, S. V. (1980). Numerical heat transfer and fluid flow. Hemisphere Publishing Corp., Bristol, Pa.
25.
Rodi, W. (1984). Turbulence models and their application in hydraulics—A state of art review, 2nd Ed., Int. Assoc. for Hydr. Res., Delft, The Netherlands.
26.
Roe, P. L.(1981). “Approximate Riemann solvers, parameter vectors, and different schemes.”J. Comp. Phys., 43(2), 357–372.
27.
Shimizu, Y., Yamaguchi, Y., and Itakura, T.(1990). “Three-dimensional computation of flow and bed deformation.”J. Hydr. Engrg., ASCE, 116(9), 1090–1107.
28.
Steffler, P. M. (1984). “Turbulent flow in a curved rectangular channel,” PhD thesis, Univ. of Alberta, Edmonton, Alta., Canada.
29.
Stelling, G., and Van Kester, J. A. Th. M.(1994). “On the approximation of horizontal gradients in SIGMA co-ordinates for bathymetry with steep bottom slopes.”Int. J. Numer. Methods in Fluids, 18(10), 915–935.
30.
Tamamidis, P., and Assanis, D. N.(1993). “Evaluation of various high-order-accuracy schemes with and without flux limiters.”Int. J. Numer. Methods Fluids, 16(10), 931–948.
31.
Van Doormaal, J. P., and Raithby, G. D.(1984). “Enhancements of the SIMPLE method for predicting incompressible fluid flows.”Numer. Heat Transfer, 7(2), 147–163.
32.
Yanenko, N. N. (1971). The method of fractional steps. Springer-Verlag KG, Berlin, Germany.
33.
Ye, J. (1992). “Improvement of wall function in turbulence modelling.”Proc., 5th Asian Congr. of Fluid Mech.
34.
Ye, J., and Dou, G. (1990). “The investigation of the k-ε-s turbulence model.”Proc., 4th Int. Symp. on Refined Flow Modeling and Turbulent Measurement, 77–84.
35.
Ye, J., and McCorquodale, J. A. (1996). “A 3D free surface hydrodynamic modelling with curvilinear coordinate collocated grid arrangement.”Rep. No. 1996-01, Great Lakes Inst. for Envir. Res., Univ. of Windsor, Canada.
36.
Ye, J., and McCorquodale, J. A.(1997a). “Depth-averaged hydrodynamic model in curvilinear collocated grid.”J. Hydr. Engrg., ASCE, 123(5), 380–388.
37.
Ye, J., and McCorquodale, J. A.(1997b). “Three dimensional, numerical modelling of mass transport in curved channels,”Can. J. Civ. Engrg., CSCE, 24, 471–479.
38.
Yen, B. C. (1965). “Characteristics of subcritical flow in a meandering channel.”Rep., Inst. of Hydr. Res., Univ. of Iowa, Iowa City, Iowa.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 124 • Issue 7 • July 1998
Pages: 687 - 698
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Jul 1, 1998
Published in print: Jul 1998
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.