Prandtl's Mixing Length Concept Modified for Equilibrium Sediment-Laden Flows
Publication: Journal of Hydraulic Engineering
Volume 124, Issue 8
Abstract
The Prandtl-von Karman mixing length concept for clear-water flows is generalized for sediment-laden flows. The new model is applied for the analysis of dilute equilibrium sediment-laden flows down an inclined flat bed composed of mobile suspendable sediment particles. The derivation and the features of the modified formulation are discussed in detail. The model incorporates the effect of density stratification and accounts for the presence of a solid phase in the flow. Computational results are compared with experimental data. The model successfully explains the observed characteristics of these flows.
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References
1.
Allen, J. R. L. (1985). Principles of physical sedimentology. George Allen & Unwin, London.
2.
ASCE Task Committee on Turbulence Models in Hydraulic Computations.(1988). “Turbulence modeling of surface water flow and transport: Parts I–IV.”J. Hydr. Engrg., ASCE, 114, 970–1073.
3.
Bagnold, R. A. (1966). “An approach to the sediment transport problem from general physics.”Profl. Paper No. 422-I, U.S. Geological Survey, Menlo Park, Ca.
4.
Barenblatt, G. I. (1953). “On the motion of suspended particles in a turbulent stream.”Prikl. Matem. Mekh., 17, 261–273 (in Russian).
5.
Barenblatt, G. I. (1955). “Concerning the motion of suspended particles in turbulent flow occupying a half-space or flat open channel of finite depth.”Prikl. Matem. Mekh., 19, 61–88 (in Russian).
6.
Coleman, N. L.(1969). “A new examination of sediment suspension in open channel.”J. Hydr. Res., 7, 67–82.
7.
Coleman, N. L.(1981). “Velocity profiles with suspended sediment.”J. Hydr. Res., 19(3), 211–229.
8.
Drew, D. A. (1975). “Turbulent sediment transport over flat bottom using momentum balance.”J. Appl. Mech., Trans., ASME, 97 E, 38–44.
9.
Drew, D. A.(1983). “Mathematical modeling of two-phase flow.”Annu. Rev. of Fluid Mech., 15, 261–291.
10.
Einstein, H. A., and Chien, N. (1955). “Effects of heavy sediment concentration near the bed on velocity and sediment distribution.”MRD Sediment Ser. Rep. No. 8, Univ. of California, Inst. of Engrg. Res., Berkeley, Calif.
11.
Elata, C., and Ippen, A. T. (1961). “The dynamics of open channel flow with suspensions of neutrally buoyant particles.”Tech. Rep. No. 45, Hydrodyn. Lab., MIT, Cambridge, Mass.
12.
Garcia, M. (1989). “Depositing and eroding sediment-driven flows: Turbidity currents,” PhD thesis, Saint Anthony Falls Hydr. Lab., Univ. of Minnesota.
13.
Garcia, M., and Parker, G.(1991). “Entrainment of bed sediment into suspension.”J. Hydr. Engrg., ASCE, 117(4), 414–435.
14.
Henderson, F. M. (1966). Open channel flow. Macmillan Publishing Co., Inc., New York, N.Y.
15.
Hino, M.(1963). “Turbulent flow with suspended particles.”Proc., ASCE, Reston, Va., 89(4), 161–178.
16.
Hinze, J. O.(1961). “Momentum and mechanical-energy balance equations for a flowing homogeneous suspension with slip between the two phases.”Appl. Sci. Res. Ser. A, 11, 795–821.
17.
Itakura, T., and Kishi, T.(1980). “Open channel flow with suspended sediments.”Proc., ASCE, Reston, Va., 106(8), 1325–1343.
18.
Jobson, H. E., and Sayre, W. W.(1979). “Predicting concentration in open channels.”J. Hydr. Div., ASCE, 96(10), 1983–1996.
19.
Lau, Y. L.(1983). “Suspended sediment effect on flow resistance.”J. Hydr. Engrg., ASCE, 109(5), 757–763.
20.
Laursen, E. M. (1980). “A sediment concentration distribution based on a revised Prandtl mixing length theory.”Int. Symp. on River Sedimentation, Wiley-Interscience, New York, N.Y., 237–244.
21.
Liggett, J. A. (1994). Fluid mechanics. McGraw-Hill Book Co., Inc., New York, N.Y.
22.
Lyn, D. A.(1988). “A similarity approach to open-channel sediment laden flows.”J. Fluid Mech., 193, 1–26.
23.
Lyn, D. A.(1989). “Resistance in flat-bed sediment-laden flows.”J. Hydr. Engrg., ASCE, 117(1), 94–112.
24.
McLean, S. R.(1992). “On the calculation of suspended load for noncohesive sediments.”J. Geophys. Res., 97(4), 5759–5770.
25.
Montes, J. S., and Ippen, A. T. (1973). “Interaction of two-dimensional turbulent flow with suspended particles.”Paper No. 164, Rep. Ralph M. Parsons Lab., Water Resour. and Hydrodyn., MIT, Cambridge, Mass.
26.
Nezu, I., Nakagawa, H., and Tominaga, A. (1985). “Secondary currents in a straight channel flow and the relation to its aspect ratio.”Turbulent shear flows 4, L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw, eds., Springer-Verlag New York, Inc., New York, N.Y., 246–260.
27.
Parker, G., and Coleman, N. L.(1986). “Simple model of sediment-laden flows.”J. Hydr. Engrg., ASCE, 112(5), 356–375.
28.
Prandtl, L. (1925). “Uber die ausgebildete turbulenz.”Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM), 5, 136–139 (in German).
29.
Rashidi, M., Hetsroni, G., and Banerjee, S.(1990). “Particle-turbulence interaction in a boundary layer.”Int. J. Multiphase Flow, 16(6), 935–949.
30.
Rodi, W. (1980). “Turbulence models and their applications in hydraulics.”State-of-the-Art Paper, IAHR, Delft, The Netherlands.
31.
Smith, J. D., and McLean, S. R.(1977). “Spatially averaged flow over a wavy surface.”J. Geophys. Res., 82(12), 1735–1746.
32.
Soulsby, R. L., and Wainwright, B. L. S. A.(1987). “Criterion for effect of suspended sediment on near-bottom velocity profiles.”J. Hydr. Res., ASCE, 25(3), 341–355.
33.
Sutton, O. G. (1977). Micrometeorology. R. E. Krieger Publishing Co., Inc., Malabar, Fla.
34.
Taylor, P. A., and Dyer, K. R. (1977). “Theoretical models of flow near the bed and their implications for sediment transport.”The sea, E. D. Goldberg, ed., Vol. 6, Wiley-Interscience, New York, N.Y., 579–601.
35.
Umeyama, M.(1992). “Vertical distribution of suspended sediment in uniform open-channel flow.”J. Hydr. Engrg., ASCE, 118(6), 936–941.
36.
Umeyama, M., and Gerittsen, F.(1992). “Velocity distribution in uniform sediment laden flow.”J. Hydr. Engrg., ASCE, 118(2), 229–245.
37.
Vanoni, V. A.(1946). “Transportation of suspended sediment by water.”Trans., ASCE, Reston, Va., 3, 67–133.
38.
Vanoni, V. A. (1977). Sedimentation engineering. Hydr. Div., ASCE, Reston, Va.
39.
Vanoni, V. A., and Nomicos, G. N.(1960). “Resistance properties of sediment-laden streams.”Trans., ASCE, Reston, Va., 125, 1140–1164.
40.
van Rijn, L. C.(1984). “Sediment transport. II: Suspended load transport.”J. Hydr. Engrg., ASCE, 110(11), 1613–1641.
41.
Villaret, C., and Davies, A. G.(1995). “Modeling sediment-turbulent flow interactions.”Appl. Mech. Rev., 48(9), 601–609.
42.
Villaret, C., and Trowbridge, J. H.(1991). “Effects of stratification by suspended sediments on turbulent shear flows.”J. Geophys. Res., 96(6), 10659–10680.
43.
von Karman, T. (1930). “Mechanische anlichkeit und turbulenz.”Proc., 3rd Int. Congr. of Appl. Mech., Math.-Phys. Klasse, Gottengen, Germany (in German).
44.
Yalin, M. S. (1977). Mechanics of sediment transport. Pergamon Press, New York, N.Y.
Information & Authors
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Published In
Journal of Hydraulic Engineering
Volume 124 • Issue 8 • August 1998
Pages: 803 - 812
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Aug 1, 1998
Published in print: Aug 1998
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