Discrete Vortex Model of Jet‐Forced Flow in Circular Reservoir
Publication: Journal of Hydraulic Engineering
Volume 114, Issue 3
Abstract
A computer model of two-dimensional steady flow in a confined space is described in this paper. The simplest case of radial jet-forced flow within a circular cylinder with a single inlet and outlet is considered. The first stage in the numerical model consists of mapping the circular flow boundary onto a rectangle by means of a Schwarz-Christoffel transformation. As a result, two opposite sides of the rectangle represent the inlet and outlet. A potential uniform flow solution is then obtained for the flow in the rectangle and hence the cylinder. In the second stage of the flow simulation, discrete vortices are added at the inlet in order to model the inflow shear layers. Velocity components resulting from the discrete vortices and their images in the walls of the cylinder are superimposed on the potential uniform flow solution. The positions of the vorticese are updated using a finite-difference time-stepping scheme. Thus, a qualitative simulation of the complete flow is built up. The results show reasonable agreement with experimental observations.
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References
1.
Ali, K. H. M., Hedges, T. S., and Whittington, R. B. (1978). “A scale model investigation of the circulation in reservoirs,” Proc. Instn. Civ. Engrs., Part 2, 65, Mar., 129–161.
2.
Ali, K. H. M., and Pateman, D. (1981). “Prediction of the circulation in reservoirs,” Proc. Inst. Civ. Engrs., Part 2, 71, 427–461, June.
3.
Barfield, W. D. (1970). “Numerical method for generating orthogonal curvilinear meshes.” J. of Comp. Phys., 5, 23–33.
4.
Baturin, W. W. (1959). Luftengsanlagen fur Industriebauten, Veb Verlag Technik, Berlin, W. Germany (in German).
5.
Borthwick, A. (1986). “Comparison between two finite‐difference schemes for computing the flow around a cylinder,” Int. J. for Numer. Meth. in Fluids, 6, 275–290.
6.
Byrd, P. F., and Friedman, M. D. (1954). Handbook of elliptic integrals for engineers and physicists, Springer.
7.
Chaplin, J. R. (1973). “Computer model of vortex shedding from a cylinder,” Proc. ASCE, 99(1) Proc. Paper 9491, Jan., 155–165.
8.
Dennis, S. C. R. (1974). Proc. 4th. Int. Conf. on Num. Meth. in Fluid Dynamics, Univ. of Colorado, Springer, 146–151, Jun.
9.
Ligget, J. A., and Hadjitheodorou, C. (1969). “Circulation in shallow homogenous lakes,” J. Hydraul. Div., ASCE, 95(2), 609–620.
10.
Mills, R. D. (1977). “Computing internal viscous flow problems for the circle by integral methods,” J. of Fluid‐Mech., 79(2), 609–624.
11.
Milne‐Thomson, L. M. (1968). Theoretical Hydrodynamics, 5th Ed., Macmillan Press, New York, N.Y.
12.
Raudkivi, A. J., and Callender, R. A. (1975). “Advanced fluid mechanics,” Arnold, 1975.
13.
Sarpkaya, T., and Schoaff, R. L. (1979). “Inviscid model of two‐dimensional vortex shedding by a circular cylinder,” Amer. Inst. of Aero. and Astro. J., 17(11), 1193–1200.
14.
Sobey, R. J., and Savage, S. B. (1974). “Jet‐forced circulation in water‐supply reservoirs,” J. Hydraul. Div., ASCE, 100(12), 1809–1828.
15.
Stansby, P. K. (1977). “An inviscid model of vortex shedding from a circular cylinder in steady and oscillatory far flows,” Proc. Inst. Civ. Engrs., Part 2, 63, 865–880.
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Published In
Journal of Hydraulic Engineering
Volume 114 • Issue 3 • March 1988
Pages: 283 - 298
Copyright
Copyright © 1988 ASCE.
History
Published online: Mar 1, 1988
Published in print: Mar 1988
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