Numerical Model of Turbulent Flow over Sand Dune
Publication: Journal of Hydraulic Engineering
Volume 122, Issue 1
Abstract
A two-dimensional numerical model, based on solution of the Reynolds-averaged Navier-Stokes equations and the k -ω turbulence model, which takes into account sand-grain roughness, is developed to describe the flow in a fixed dune-bed channel. The model predicts the velocity and turbulence fields, as well as the pressure and friction distributions along the dune. The details of the flow in the separation eddy are calculated. The model predictions are in general agreement with existing detailed experimental data in a rectangular channel with two-dimensional dunes of typical but regular shape. The calculated pressure and friction distributions enable determination of the resistance components of the channel without further empiricism. However, compared to a well-known and representative semiempirical engineering formula for the prediction of resistance of natural dune-bed channels, the two-dimensional numerical model predicts significantly different contributions of friction and pressure to the total resistance, and a much larger total resistance. The numerical model is general enough to be used for channels with different bed topography. Its extension to model the flow in ice-covered channels is in a companion paper.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Chen, H. C., and Patel, V. C.(1987). “Laminar flow at the trailing edge of a flat plate.”AIAA J., 25(7), 920–928.
2.
Engelund, F.(1966). “Hydraulic resistance of alluvial streams.”J. Hydr. Engrg., ASCE, 92(2), 315–327.
3.
Engelund, F.(1967). “Hydraulic resistance of alluvial streams.”J. Hydr. Engrg., ASCE, 93(4), 287–296.
4.
Engelund, F.(1970). “Instability of erodible beds.”J. Fluid Mech., 42(2), 225–244.
5.
Fredsøe, J.(1974). “On the development of dunes in erodible channels.”J. Fluid Mech., 64(4), 1–16.
6.
Fredsøe, J. (1982). “Shape and dimensions of ripples and dunes.”J. Hydr. Div., ASCE, Vol. 108(8), 932–947.
7.
Haque, M. I., and Mahmood, K. (1983). “Analytical determination of form friction factor.”J. Hydr. Engrg., ASCE, Vol. 109(4), 590–610.
8.
Johns, B., Soulsby, R. L., and Xing, J.(1993). “A comparison of numerical model experiments of free surface flow over topography with flume and field observations.”J. Hydr. Res., 31(2), 215–228.
9.
Kennedy, J. F.(1963). “The mechanics of dunes and antidunes in erodible-bed channels.”J. Fluid Mech., 16(4), 521–544.
10.
Kennedy, J. F. (1969). “The formation of sediment ripples, dunes, and antidunes.”Annu. Rev. of Fluid Mech., Vol. 1, Annual Reviewers Inc., Palo Alto, Calif. 147–167.
11.
Knight, D. D. (1982). “Applications of curvilinear coordinate generation techniques to the computation of internal flows.”Numerical grid generation, J. F. Thompson, ed., Elsevier Science Publishing Co., Inc., Amsterdam, The Netherlands, 357–384.
12.
Kobayashi, N., and Madsen, O. S. (1985). “Formation of ripples in erodible channels.”J. Geophys. Res., 90(C4), 7332-7340.
13.
McLean, S. R., and Smith, J. D.(1986). “A model for flow over two-dimensional bed forms.”J. Hydr. Engrg., ASCE, 112(4), 300–317.
14.
Mendoza, C. (1986). “Refined modeling of shallow, turbulent flow over dunes,” PhD Thesis, Colorado State Univ., Fort Collins, Colo.
15.
Mendoza, C., and Shen, H. W.(1990). “Investigation of turbulent flow over dunes.”J. Hydr. Engrg., ASCE, 116(4), 459–477.
16.
Michelassi, V. (1989). “Testing of turbulence models with an artificial compressibility solution method.”Rep. SFB 210/T/49, Univ. of Karlsruhe, Germany.
17.
Mierlo, M. C. L. M., and de Ruiter, J. C. C. (1988). “Turbulence measurements above artificial dunes.”Rep. Q789, Delft Hydr. Lab., Delft, The Netherlands.
18.
Nelson, J. M., and Smith, J. D. (1989). “Mechanics of flow over ripples and dunes.”J. Geophys. Res., 94(C6), 8146–8162.
19.
Patel, V. C., Chon, J. T., and Yoon, J. Y.(1991). “Turbulent flow in a channel with a wavy wall.”J. Fluids Engrg., 113(4), 579–586.
20.
Patel, V. C., and Yoon, J. Y.(1995). “Application of turbulence models to separated flow over rough surfaces.”J. Fluids Engrg., 117(2), 234–241.
21.
Peric, M., Ruger, M., and Scheuerer, G. (1988). “Calculation of the two-dimensional turbulent flow over a sand dune model.”Rep. No. SRR-TN-88-O2, Univ. of Erlangen, Germany.
22.
Richards, K. J. (1980). “The formation of ripples and dunes on erodible bed.”J. Fluid Mech., Vol. 99, 597–618.
23.
Smith, J. D.(1970). “Stability of a sand bed subjected to a shear flow of low Froude number.”J. Geophys. Res., 75(30), 5928–5940.
24.
Sumer, B. M., and Bakioglu, M. (1984). “On the formation of ripples on an erodible bed.”J. Fluid Mech., Vol. 144, 177–190.
25.
Wilcox, D. C. (1993). Turbulence modeling of CFD, DCW Industries, La Canada, Calif.
26.
Yoon, J. Y., and Patel, V. C. (1993). “A numerical model of flow in channels with sand-dune beds and ice covers.”IIHR Rep. No. 362, Univ. of Iowa, Iowa City, Iowa.
27.
Yoon, J. Y., Patel, V. C., and Ettema, R.(1995). “Numerical model of flow in ice-covered channels.”J. Hydr. Engrg., ASCE, 122(1), 19–26.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 122 • Issue 1 • January 1996
Pages: 10 - 18
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Jan 1, 1996
Published in print: Jan 1996
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.