Iterative Solution for Ideal Fluid Jets
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 8
Abstract
Free jets are important flow phenomena from outflow structures of dams and reservoirs. The basic case of jet flow originates from a free overfall with upstream critical flow conditions and a fully ventilated nappe. In this paper, a two-dimensional potential flow model has been developed. Semiinverse mapping of the Laplace equation has been employed in conjunction with an analytical solution of the Boussinesq equations to initiate iterations for locating the free streamlines under atmospheric pressure. A systematic iteration method is proposed using the squaring technique for solving the Laplacian field, a computation of the free streamlines using the curvilinear formulation of velocity at boundary streamlines in the energy equation, and an iteration of the position of the terminal jet section versus the brink section conditions. The model permits a convergent numerical solution, which was verified against experimental data, thereby indicating that the proposed ideal fluid flow model can be applied to predict the shape of free jets by simple computations.
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References
Boadway, J. D. (1976). “Transformation of elliptic partial differential equations for solving two-dimensional boundary value problems in fluid flow.” Int. J. Num. Meth. Eng., 10(3), 527–533.
Bose, S. K., and Dey, S. (2007). “Curvilinear flow profiles based on Reynolds averaging.” J. Hydraul. Eng., 133(9), 1074–1079.
D’Alpaos, L. (1986). “Effeti scala nei moti di efflusso fortemente accelerate (Scale effects in highly-accelerated outflows).” 20th Italian Congress of Hydraulics and Hydraulic Structures, Padova, 15–23 (in Italian).
Guo, Y. K. (2005). “Numerical modeling of free overfall.” J. Hydraul. Eng., 131(2), 134–138.
Hager, W. H. (1983). “Hydraulics of the plane free overfall.” J. Hydraul. Eng., 109(12), 1683–1697.
Jaeger, C. (1948). “Hauteur d’eau a l’extrémité d’un long déversoir [Flow depth at extremity of a long weir].” La Houille Blanche, 3(6), 518–523 (in French).
Khan, A. A., and Steffler, P. M. (1996). “Modeling overfalls using vertically averaged and moment equations.” J. Hydraul. Eng., 122(7), 397–402.
Marchi, E. (1993). “On the free overfall.” J. Hydraul. Res., 31(6), 777–790.
Markland, E. (1965). “Calculation of flow at a free overfall by relaxation methods.” ICE Proc., 31(1), 71–78.
Matthew, G. D. (1991). “Higher order, one-dimensional equations of potential flow in open channels.” ICE Proc., 91(2), 187–201.
Matthew, G. D. (1995). “Discussion to ‘A potential flow solution for the free overfall.’” ICE Proc., 112(1), 81–85.
Montes, J. S. (1992). “A potential flow solution for the free overfall.” ICE Proc., 96(6), 259–266.
Montes, J. S. (1994a). “On the free overfall.” J. Hydraul. Res., 32(5), 792–796.
Montes, J. S. (1994b). “Potential flow solution to the 2D transition from mild to steep slope.” J. Hydraul. Eng., 120(5), 601–621.
Montes, J. S. (1995). “Closure to ‘A potential flow solution for the free overfall.’” ICE Proc., 112(1), 85–87.
Montes, J. S. (1998). Hydraulics of open channel flow, ASCE, Reston, VA.
Ramamurthy, A. S., Qu, J., and Vo, D. (2005). “Volume of fluid model for an open channel flow problem.” Can. J. Civ. Eng., 32(5), 996–1001.
Rouse, H. (1932). “The distribution of hydraulic energy in weir flow in relation to spillway design.” M.S. thesis, Massachusetts Institute of Technology, Boston.
Rouse, H. (1938). Fluid mechanics for hydraulic engineers, McGraw-Hill, New York.
Southwell, R. V., and Vaisey, G. (1946). “Relaxation methods applied to engineering problems. XII. Fluid motions characterized by ‘free’ stream-lines.” Phil. Trans. Roy. Soc. London A, 240(815), 117–161.
Thom, A., and Apelt, C. (1961). Field computations in engineering and physics, Van Nostrand, London.
Vallentine, H. R. (1969). Applied hydrodynamics, Butterworths, London.
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Published In
Journal of Hydraulic Engineering
Volume 139 • Issue 8 • August 2013
Pages: 905 - 910
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Aug 12, 2012
Accepted: Jan 29, 2013
Published online: Jul 15, 2013
Published in print: Aug 1, 2013
Discussion open until: Dec 15, 2013
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