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Impact of a rising stream on a horizontal plate of finite extent

Published online by Cambridge University Press:  12 February 2009

P. CHRISTODOULIDES  and
F. DIAS
P. CHRISTODOULIDES
Affiliation:
Faculty of Engineering and Technology, Cyprus University of Technology, Limassol, Cyprus
F. DIAS*
Affiliation:
CMLA, ENS Cachan and CNRS, UniverSud, 61 avenue du President Wilson, F-94235 Cachan Cedex, France
*
†Email address for correspondence: dias@cmla.ens-cachan.fr
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Abstract

The steady flow of a stream emerging from a nozzle, hitting a horizontal plate and falling under gravity is considered. Depending on the length of the plate L and the Froude number F, the plate can either divert the stream or lead to its detachment. First, the problem is reformulated using conformal mappings. The resulting problem is then solved by a collocation Galerkin method; a particular form is assumed for the solution, and certain coefficients in that representation are then found numerically by satisfying Bernoulli's equation on the free surfaces at certain discrete points. The resulting equations are solved by Newton's method, yielding various configurations of the solution based on the values of F and L. The lift exerted on the plate is computed and discussed. If the plate is long enough, physically meaningful solutions are found to exist only for values of F greater than or equal to a certain critical value F0, which is to be determined. Results are presented, both for F > F0 where the detachment is horizontal and for F = F0 where the detachment point is a stagnation point at a 120° corner. Related asymmetric flows where the rising stream is inclined are also studied.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 621 , 25 February 2009 , pp. 243 - 258
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Clanet, C. 1998 On large-amplitude pulsating fountains. J. Fluid Mech. 366, 333–350.CrossRefGoogle Scholar
Cooker, M. J. & Peregrine, D. H. 1995 Pressure-impulse theory for liquid impact problems. J. Fluid Mech. 297, 193–214.CrossRefGoogle Scholar
Dias, F. & Christodoulides, P. 1991 Ideal jets falling under gravity. Phys. Fluids A 3 (7), 1711–1717.CrossRefGoogle Scholar
Dias, F., Dutykh, D. & Ghidaglia, J.-M. 2008 A two-fluid model for violent aerated flows, preprint.Google Scholar
Dias, F., Keller, J. & Vanden-Broeck, J.-M. 1988 Flows over rectangular weirs. Phys. Fluids 31, 2071–2076.CrossRefGoogle Scholar
Dias, F. & Tuck, E. O. 1991 Weir flows and waterfalls. J. Fluid Mech. 230, 525–539.CrossRefGoogle Scholar
Dias, F. & Vanden-Broeck, J.-M. 1990 Flows emerging from a nozzle and falling under gravity. J. Fluid Mech. 213, 465–477.CrossRefGoogle Scholar
Dias, F. & Vanden-Broeck, J.-M. 1993 Nonlinear bow flows with spray. J. Fluid Mech. 255, 91–102.CrossRefGoogle Scholar
Goh, K. H. M. & Tuck, E. O. 1985 Thick waterfalls from horizontal slots. J. Engng Math. 19, 341–349.CrossRefGoogle Scholar
Hureau, J., Brunon, E. & Legallais, P. H. 1996 Ideal free streamline flow over a curved obstacle. J. Comput. Appl. Math. 72, 193–214.CrossRefGoogle Scholar
Milne-Thomson, L. M. 1996 Theoretical Hydrodynamics (5th ed.). Dover Publications.Google Scholar
Peng, W. & Parker, D. F. 1997 An ideal fluid jet impinging on an uneven wall. J. Fluid Mech. 333, 231–255.CrossRefGoogle Scholar
Raad, P. E., Chen, S. & Johnson, D. B. 1995 The introduction of micro cells to treat pressure in free surface fluid flow problems. J. Fluid Engng Trans. ASME 117, 683–690.CrossRefGoogle Scholar
Tuck, E. O. 1987 Efflux from a slit in a vertical wall. J. Fluid Mech. 176, 253–264.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. 1993 Two-dimensional jet aimed vertically upwards. J. Austral. Math. Soc. Ser. B 34, 393–400.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1982 Jets rising and falling under gravity. J. Fluid Mech. 124, 335–345.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1986 Pouring flows. Phys. Fluids 29, 3958–3961.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1987 Weir flows. J. Fluid Mech. 176, 283–293.CrossRefGoogle Scholar
Wiryanto, L. H. & Tuck, E. O. 2000 An open-channel flow meeting a barrier and forming one or two jets. J. Austral. Math. Soc. Ser. B 41, 458–472.CrossRefGoogle Scholar