Strip Integral Method Applied to Settling Tanks
Publication: Journal of Hydraulic Engineering
Volume 110, Issue 1
Abstract
The nonstratified steady flow hydrodynamics of rectangular sedimentation tanks is simulated using a combination of the strip integral and finite element methods. The strip integral method is generally a forward marching scheme in which the partial differential equations of continuity and momentum are reduced to a set of ordinary differential equations in terms of certain preselected parameters. These parameters, along with a set of shape functions, describe the velocity distribution. In this study three shape functions are chosen, corresponding to the boundary layer, the potential core, and the free mixing and recirculation zone. The shape functions were: (1) Power law in the boundary layer; (2) uniform velocity in the potential core; and (3) Gaussian distribution in the free mixing zone. The shape functions are chosen to allow recirculation above the mixing zone. A modified mixing length approach is used to introduce the effect of recirculation into the solution. A Runge‐Kutta method is used to integrate the set of ordinary differential equations; a finite element solution is used in the withdrawal zone. The numerical results compare favorably with experimental velocity distributions obtained by laser anemometry and with available field data. The convective and mixing characteristics of the flow can be obtained from this model and used with a transport model to determine the removal efficiency of the tank.
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References
1.
Camp, T. R., “Sedimentation and the Design of Settling Tanks,” ASCE, Transactions, Vol. III, 1946, pp. 895–936.
2.
Clements, M. S., “Velocity Variation in Rectangular Sedimentation Tanks,” Proceedings, Institution Civil Engineers, 1966, pp. 171–200.
3.
Desai, C. S., and Abel, J. F., Introduction to the Finite Element Method, Van Nostrand Reinhold Co., Princeton, N.Y., 1972.
4.
Dobbins, W. E., “Effect of Turbulence on Sedimentation,” ASCE, Transactions, Paper No. 2218, Vol. 109, 1944.
5.
Imam, E. H., “Numerical Modelling of Rectangular Clarifiers,” thesis presented to the University of Windsor, at Windsor, Ontario, in 1981, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
6.
Larock, B. E., and Schamber, D. R., “Finite Element Computation of Turbulent Flows,” Third International Conference in Finite Element in Water Resources, 1980, pp. 4.31–4.47.
7.
Larsen, P., “On the Hydraulics of Rectangular Settling Basins—Experimental and Theoretical Studies,” Report No. 1001, Department of Water Resources Engineering, Lund, Sweden, 1977.
8.
Launder, B. E., and Spalding, D. B., “Lectures in Mathematical Models of Turbulence,” Academic Press, London and New York, 1972.
9.
McCorquodale, J. A., “Hydraulic Study of the Circular Settling Tanks at the West Windsor Pollution Control Plant,” report submitted to Lafontaine, Cowie, Buratto and Associates, Ltd., Consulting Engineers, Windsor, Ontario, 1976.
10.
McCorquodale, J. A., Abdel‐Gawad, S. M., and Imam, E. H., “Modeling Sedimentation Basins,” International Conference on Computation Methods and Experimental Measurements, Washington, D.C., July, 1982.
11.
McCorquodale, J. A., and Khalifa, A., “Internal Flow in Hydraulic Jump,” Proceedings, Journal of the Hydraulics Division, ASCE, Vol. 109, No. 5, May, 1983, pp. 684–701.
12.
Moses, Hal L., “A Strip‐Integral Method for Predicting the Behavior of the Turbulent Boundary Layer,” Proceedings, Computation of Turbulent Boundary Layers, 1968, AFOSR‐IFP‐Stanford Conference, pp. 76–82.
13.
Narayanan, R., “Theoretical Analysis of Flow Past Leaf Gate,” Journal of the Hydraulics Division, ASCE, No. HY6, June, 1972, pp. 992–1011.
14.
Narayanan, R., “Wall Jet Analogy to Hydraulic Jump,” Journal of the Hydraulics Division, ASCE, Vol. 101, No. HY3, Proc. Paper 11172, Mar., 1975, pp. 347–359.
15.
Rajaratnam, N., “Submerged Hydraulic Jump,” Journal of the Hydraulics Division, ASCE, Vol. 91, No. HY4, Proc. Paper 4403, July, 1965, pp. 71–96.
16.
Rajaratnam, N., Turbulent Jets, Elsevier Scientific Co., New York, N.Y., 1976.
17.
Reynolds, A. J., Turbulent Flows in Engineering, John Wiley & Sons, New York, N.Y., 1974.
18.
Rouse, N., Siao, T. T., and Rajaratnam, R., “Turbulence Characteristics of the Hydraulic Jump,” Journal of the Hydraulics Division, ASCE, Vol. 84, No. HY1, Proc. Paper 1528, Feb., 1958, pp. 1528‐1–1528‐30.
19.
Rodi, W., “Turbulence Models and Their Application in Hydraulics—A Stateof‐the‐Art Review,” International Association of Hydraulics Research, June, 1980.
20.
Schamber, D. R., and Larock, B. E., “A Finite Element Model of Turbulent Flow in Primary Sedimentation Basins,” Proceedings, Finite Element in Water Resources, FE2, London, England, July, 1978, pp. 3.3–3.21.
21.
Schamber, D. R., and Larock, B. E., “Numerical Analysis of Flow in Sedimentation Basins,” Journal of the Hydraulics Division, ASCE, Vol. 107, No. HY5, May, 1981, pp. 575–591.
22.
Schlichting, H., Boundary Layer Theory, McGraw‐Hill Book Co., Inc., New York, N.Y., 1968.
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Copyright © 1984 ASCE.
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Published online: Jan 1, 1984
Published in print: Jan 1984
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