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A numerical nonlinear analysis of two-dimensional ventilating entry of surface-piercing hydrofoils with effects of gravity

Published online by Cambridge University Press:  30 June 2010

VIMAL VINAYAN  and
SPYROS A. KINNAS
VIMAL VINAYAN*
Affiliation:
Ocean Engineering Group, Department of Civil, Architectural and Environmental Engineering, University of Texas at Austin, Austin, TX 78712, USA
SPYROS A. KINNAS
Affiliation:
Ocean Engineering Group, Department of Civil, Architectural and Environmental Engineering, University of Texas at Austin, Austin, TX 78712, USA
*
†Email address for correspondence: vvinayan@mail.utexas.edu
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Abstract

The presence of the free surface adds an element of difficulty to the development of numerical and theoretical methods for the performance prediction of surface-piercing hydrofoils. Existing methods of analysis for two-dimensional surface-piercing hydrofoils or blade sections of a surface-piercing propeller solve either a linear problem, assuming a thin section and ventilated surface along with linear free-surface boundary conditions, or a nonlinear problem in a self-similar setting. Both these approaches cannot be used when the effects of gravity are important, which is the case when a craft is operating at low speeds. A two-dimensional boundary-element-method-based numerical scheme is presented here that overcomes these drawbacks by solving the fully ventilated flow past a surface-piercing hydrofoil of finite dimensions and includes the whole gamut of nonlinear free-surface interactions. The unique aspect of the numerical scheme is that fully nonlinear boundary conditions are applied on the free surface which allows for the accurate modelling of the jet generated on the wetted boundary and the ventilated surface formed on the suction side as a result of the passage of the hydrofoil through the free surface. Moreover, the effects of gravity can be considered to take into account the influence of the Froude number. Ventilated-surface shapes predicted by the present scheme are compared with existing experimental results and are shown to be in good agreement.

JFM classification

Mathematical Foundations: Computational methods
Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 383 - 408
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes, and Cavities. Academic.Google Scholar
Chekin, B. S. 1989 The entry of a wedge into an incompressible fluid. J. Appl. Math. Mech. 53 (3), 300–307.CrossRefGoogle Scholar
Cox, B. D. 1971 Hydrofoil theory for vertical water entry. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
Dobrovol'skaya, Z. N. 1969 On some problems of similarity flow of fluid with a free surface. J. Fluid Mech. 36 (4), 805–829.CrossRefGoogle Scholar
Dussan, V. E. B. 1976 On the difference between a bounding surface and a material surface. J. Fluid Mech. 75 (4), 609–623.CrossRefGoogle Scholar
Faltinsen, O. M. 2005 Hydrodynamics of High-Speed Marine Vehicles. Cambridge University Press.Google Scholar
Faltinsen, O. M. & Semenov, Y. A. 2008 Nonlinear problem of flat-plate entry into an incompressible liquid. J. Fluid Mech. 611, 151–173.CrossRefGoogle Scholar
Gilbarg, D. 1960 Jets and cavities. Handbuch Phys. 9, 311–445.Google Scholar
Kihara, H. 2006 A computing method for the flow-analysis around a prismatic planing-hull. In Proceedings of the 5th International Conference on High-Performance Marine Vehicles, Australia (ed. Sahoo, P. K.), pp. 262–272.Google Scholar
Kinnas, S. A. & Fine, N. E. 1993 A numerical nonlinear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils. J. Fluid Mech. 254 (1), 151–181.CrossRefGoogle Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water. I. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
Olofsson, N. 1996 Force and flow characteristics of a partially submerged propeller. PhD thesis, Department of Naval Architecture and Ocean Engineering, Division of Hydromechanics, Chalmers University of Technology, Gothenburg, Sweden.Google Scholar
Panton, R. L. 1984 Incompressible Flow. John Wiley.Google Scholar
Savineau, C. M. & Kinnas, S. A. 1995 A numerical formulation applicable to surface piercing hydrofoils and propellers. In 24th American Towing Tank Conference (ed. Johnson, P.). Texas A&M University.Google Scholar
Shiba, H. 1953 Air-drawing of marine propellers. Tech. Rep. 9. Transportation Technical Research Institute, Tokyo, Japan.Google Scholar
Sun, H. & Faltinsen, O. M. 2007 The influence of gravity on the performance of planing vessels in calm water. J. Engng Math. 58 (1), 91–107.CrossRefGoogle Scholar
Terent'ev, A. G. 1979 Inclined entry of a thin body with ventilated cavity into an ideal imponderable liquid. Fluid Dyn. 14 (3), 377–385.CrossRefGoogle Scholar
Vinayan, V. 2009 A boundary element method for the strongly nonlinear analysis of ventilating water-entry and wave-body interaction problems. UT-OE Rep. 09-2. PhD thesis, Ocean Engineering Group, Department of Civil Engineering, Architectural and Environmental Engineering, University of Texas at Austin, Austin, TX.Google Scholar
Vinayan, V. & Kinnas, S. A. 2008 Numerical modeling of surface piercing hydrofoils and propellers. In Proceedings of the 27th Symposium on Naval Hydrodynamics, Seoul, Korea. Office of Naval Research.Google Scholar
Wang, D. P. 1977 Water entry and exit of a fully ventilated foil. J. Ship Res. 21 (1), 44–68.CrossRefGoogle Scholar
Wang, D. P. 1979 Oblique water entry and exit of a fully ventilated foil. J. Ship Res. 23 (1), 43–54.CrossRefGoogle Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. Handbuch Phys. 9 (3), 446–778.Google Scholar
Wu, T. Y. T. 1955 A free streamline theory for two-dimensional fully cavitated hydrofoils. Tech. Rep. 21–17. California Institute of Technology, Pasadena, CA.Google Scholar
Yim, B. 1969 An application of linearized theory to water entry and water exit problems. Part 2. With ventilation. Rep. 3171. NSRDC, Washington, DC.Google Scholar
Yim, B. 1971 Investigation of gravity and ventilation effects in water entry of thin foils. In Proceedings of the IUTAM Symposium on Nonsteady Flows of Water with High Velocities (ed. Sedov, L. I. & Stepanov, G. Yu.), pp. 471–489. Nauka.Google Scholar
Yim, B. 1974 Linear theory on water entry and exit problems of a ventilating thin wedge. J. Ship Res. 18 (1), 1–11.CrossRefGoogle Scholar
Young, Y. L. 2002 Numerical modeling of supercavitating and surface-piercing propellers. UT-OE Rep. 02-1. PhD thesis, Ocean Engineering Group, Department of Civil, Architectural and Environmental Engineering, University of Texas at Austin, Austin, TX.Google Scholar
Young, Y. L. & Kinnas, S. A. 2003 Numerical modeling of supercavitating propeller flows. J. Ship Res. 47 (1), 48–62.CrossRefGoogle Scholar
Zhao, R. & Faltinsen, O. 1993 Water entry of two-dimensional bodies. J. Fluid Mech. 246, 593–612.CrossRefGoogle Scholar
Zhao, R., Faltinsen, O. M. & Aarsnes, J. 1996 Water entry of arbitrary two-dimensional sections with and without flow separation. In Proceedings of the 21st Symposium on Naval Hydrodynamics, pp. 408–423. National Academy Press.Google Scholar