Kinetic Theory for Particles in Dilute and Dense Solid-Liquid Flows
Publication: Journal of Hydraulic Engineering
Volume 126, Issue 12
Abstract
This paper presents a kinetic theory for modeling the vertical profile of particle concentration in dilute and dense solid-liquid flow conditions. The kinetic theory properly describes the mechanism of suspended sediment transport over a wider range of conditions and gives more detailed microscopic information than previous theories. Experimental data have been measured using laser Doppler anemometry. The results are in agreement with measurements by Wang and Qian in 1989, Michalik in 1973, and Segré and Silberberg in 1962. The present work makes a special contribution in predicting the particle concentration distribution in a dense liquid-particle flow with reasonable accuracy.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bagnold, R. A. ( 1954). “Experiments on a gravity-free dispersion of large solid spheres in Newtonian fluid under shear.” Proc., Royal Soc., London, A225, 49–63.
2.
Barenblatt, G. N. ( 1956). The sediment movement in turbulent flow, Water Conservancy Press, Beijing, 61.
3.
Chapman, S., and Cowling, T. G. ( 1970). The mathematical theory of non-uniform gases, 3rd Ed., Cambridge University Press, Cambridge, England.
4.
Chen, C. L. (1988a). “Generalized viscoplastic modeling of debris flow.”J. Hydr. Engrg., ASCE, 114(3), 237–258.
5.
Chen, C. L. (1988b). “General solutions for viscoplastic debris flow.”J. Hydr. Engrg., ASCE, 114(3), 259–282.
6.
Chen, C. L. (1996). “Granular-flow rheology: Role of shear-rate number in transition regime.”J. Engrg. Mech., ASCE, 122(5), 469–480.
7.
Chen, C. L. (1998). “Rheological equations in asymptotic regimes of granular flow.”J. Engrg. Mech., ASCE, 124(3), 301–310.
8.
Chien, N. ( 1988). Hyper-concentrated flow, Tsinghua University Press, Beijung.
9.
Chien, N., and Wan, Z. H. ( 1986). Sediment transport mechanics, Science Press, Beijing.
10.
Crowe, C. T. ( 1991). “The state-of-the-art in the development of numerical models for dispersed phase flows.” Proc., Int. Symp. on Multi-phase Flow, Vol. 3, 49–60.
11.
Culick, F. ( 1964). “Boltzmann equation to a problem of two-phase flow.” Phys. Fluids, 7, 1898–1904.
12.
Drew, D. A. ( 1983). “Mathematical modeling of two-phase flows.” Ann. Rev. Fluid Mech., 15, 261–291.
13.
Einstein, H. A., and Chien, N. ( 1955). Effects of heavy sediment concentration near the bed on velocity and sediment distribution, MRD Ser. 8, Univ. of California, Inst. of Engrg. and U.S. Army Engrg. Div., M. River, Corps of Engineers, Omaha, Neb.
14.
Hunt, J. N. ( 1954). “The turbulent transport of suspended sediment in open channels.” Proc., Royal Soc., London, 224(1158), 322–335.
15.
Ishii, M. ( 1975). Thermo-fluid dynamic theory of two-phase flow, Eyrolles, Paris.
16.
Itakura, T., and Kishi, T. (1980). “Open channel flow with suspended sediments.”J. Hydr. Div., ASCE, 106(8), 1325–1343.
17.
Lane, E. W., and Kalinske, A. A. ( 1941). Engineering calculations of suspended sediment.” Trans. Am. Geophys. Union, 22, 56–65.
18.
Laursen, E. M. ( 1982). “A concentration distribution formula from the revised theory of Prandtl mixing length.” Proc., Int. Symp. on River Sedimentation 1, Guanghua Press, Beijing, 237–244.
19.
McTigue, D. F. (1981). “Mixture theory for suspended sediment transport.”J. Hydr. Div., ASCE, 107(6), 659–673.
20.
Marble, F. E. ( 1963). “Dynamics of a gas containing small solid particles.” Proc., 5th AGARD Combustion and Propulsion Colloquium, 175–215.
21.
Marble, F. E. ( 1970). “Dynamics of dusty gases.” Ann. Rev. Fluid Mech., 2, 397–446.
22.
Mendoza, C., and Zhou, D. ( 1955). “A dynamic approach to sediment-laden turbulent flows.” Water Resources Res., 31(12), 3075–3087.
23.
Michalik, A. ( 1973). “Density patterns of the inhomogeneous liquids in the industrial pipeline measured by means of radiometric scanning.” La Houille Blanche, Grenobel, France, 1, 53–59.
24.
Ni, J. R., and Wang, G. Q. (1987). “On the two patterns of vertical distribution of sediment concentration and their formation cause.”J. Hydr. Engrg., 7, 60–68 (in Chinese).
25.
Ni, J. R., and Wang, G. Q. (1991). “Vertical sediment distribution.”J. Hydr. Engrg., ASCE, 117(9), 1184–1194.
26.
Ni, J. R., and Wang, G. Q. (1992). “Closure to `Vertical sediment distribution.' ”J. Hydr. Engrg., ASCE, 118(10), 1460–1461.
27.
Ni, J. R., Wang, G. Q., and Zhang, H. W. ( 1991). Basic theories of solid-liquid two-phase flows and their recent applications, Science Press, Beijing (in Chinese).
28.
Owen, P. R. ( 1969). “Pneumatic transport.” J. Fluid Mech., Cambridge, U.K., 39, 407–432.
29.
Pai, S. I. ( 1971). “Fundamental equations of a mixture of a gas and small spherical solid particles from kinetic theory.” J. Math. Phys. Sci., 8, 1–15.
30.
Pai, S. I. ( 1977). “Two-phase flow.” Vieweg tracts in pure and applied physics, R. Oswatitsch, ed., Vol. 3, Vieweg, Brunswick, Germany.
31.
Repetti, R. V., and Leonard, E. F. ( 1964). “Segre-Silberberg annulus formation: A possible explanation.” Nature, 203, 1346–1348.
32.
Rouse, H. ( 1937). “Modern conceptions of the mechanics of turbulence.” Trans. ASCE, 102, 463–507.
33.
Rubinnow, S. I., and Keller, J. B. ( 1961). “The transverse force on a spinning sphere moving in a viscous fluid.” J. Fluid Mech., Cambridge, U.K., 11, 447–459.
34.
Saffman, P. G. ( 1965). “The lift on a small sphere in a slow shear flow.” J. Fluid Mech., Cambridge, U.K., 22, 385–400.
35.
Saffman, P. G. ( 1968). “Corrigendum.” J. Fluid Mech., Cambridge, U.K., 31, 624.
36.
Segré, G., and Silberberg, A. ( 1962a). “Behavior of macroscopic rigid spheres in Poiseuille flow. Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beam.” J. Fluid Mech., Cambridge, U.K., 14, 115–135.
37.
Segré, G., and Silberberg, A. ( 1962b). “Behavior of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation.” J. Fluid Mech., Cambridge, U.K., 14, 136–157.
38.
Soo, S. ( 1967). Fluid dynamics of multi-phase systems, Blaisdell, Waltham, Mass.
39.
Tanaka, S., and Sugimoto, S. ( 1958). “On the distribution of suspended sediment in experimental flume flow.” Mem. Facu. of Engrg., Kobe University, Kobe, Japan, 61–71.
40.
Tsuji, Y. Morikawa, Y., and Mizinu, O. ( 1985). “Experimental measurement of the Magnus force on a rotating sphere at low Reynolds numbers.” J. Fluids Engrg., 107, 484–488.
41.
Vanoni, V. A. ( 1946). “Transportation of suspended sediment by water.” Trans. ASCE, 111, 67–113.
42.
Velicanov, M. A. ( 1958). Alluvial process, State Publishing House for Physical and Mathematical Literature, Moscow, 395 (in Russian).
43.
Wang, G. Q. ( 1989). “The kinetic theory with experimental studies for solid-liquid two-phase flow and granular flow.” PhD thesis, Tsinghua University, Beijing (in Chinese).
44.
Wang, G. Q., and Ni, J. R. (1990). “Kinetic theory for particle concentration distribution in two-phase flows.”J. Engrg. Mech., ASCE, 116(12), 2738–2748.
45.
Wang, G. Q., and Ni, J. R. ( 1991). “The kinetic theory for dilute solid liquid two-phase flow.” Int. J. Multiphase Flow, 17(2), 273–281.
46.
Woo, H. S., Julien, P. Y., and Richardson, E. V. (1988). “Suspension of large concentrations of sand.”J. Hydr. Engrg., ASCE, 114(8), 888–898.
47.
Wang, X., and Qian, N. (1989). “Turbulence characteristics of sediment-laden flow.”J. Hydr. Engrg., ASCE, 115(6), 781–800.
48.
Yalin, M. S. ( 1972). Mechanics of sediment transport, Pergamon, Oxford, England.
49.
Zagustin, K. (1968). “Sediment distribution in turbulent flow.”J. Hydr. Res., Delft, The Netherlands, 6(2), 163–171.
50.
Zhou, D., and Ni, J. R. ( 1995). “Effects of dynamic interaction on sediment-laden turbulent flows.” J. Geophys. Res., 100(C1), 981–996.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 126 • Issue 12 • December 2000
Pages: 893 - 903
History
Received: May 3, 1999
Published online: Dec 1, 2000
Published in print: Dec 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.