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Propulsion of a foil moving in water waves.

Published online by Cambridge University Press:  21 April 2006

John Grue ,
Asbjørn Mo  and
Enok Palm
John Grue
Affiliation:
Department of Mechanics, University of Oslo, Norway
Asbjørn Mo
Affiliation:
Department of Mechanics, University of Oslo, Norway
Enok Palm
Affiliation:
Department of Mechanics, University of Oslo, Norway
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Abstract

Propulsion of a foil moving in the water close to a free surface is examined. The foil moves with a forward speed U and is subjected to heaving and pitching motions in calm water, head waves or following waves. The model is two-dimensional and all equations are linearized. The fluid is assumed to be inviscid and the motion irrotational, except for the vortex wake. The fluid layer is infinitely deep.

The problem is solved by applying a vortex distribution along the centreline of the foil and the wake. The local vortex strength is found by solving a singular integral equation of the first kind, which appropriately is transformed to a non-singular Fredholm equation of the second kind. The vortex wake, the forward thrust upon the foil and the power supplied to maintain the motion of the foil are investigated. The scattered free surface waves are computed. For moderate values of Uσ/g (U is forward speed of the foil, σ is frequency of oscillation, g is acceleration due to gravity) it is found that the free surface strongly influences the vortex wake and the forces upon the foil. When the foil is moving in incoming waves it is found that a relatively large amount of the wave energy may be extracted for propulsion. As an application of the theory the propulsion of ships by a foil propeller is examined. The theory is compared with experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 186 , January 1988 , pp. 393 - 417
Copyright
© 1988 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.
Faltinsen, O. M., Liapis, N., Minsaas, K. J. & Skjørdal, S. O. 1980 Prediction of resistance and propulsion of a ship in a seaway. 13th Symp. on Naval Hydrodyn. The Shipbuilding Association of Japan.
Grue, J. & Palm, E. 1985 Wave radiation and diffraction from a submerged body in a uniform current. J. Fluid Mech. 151, 257.Google Scholar
Haskind, M. D. 1954 On wave motion of a heavy fluid. Prikl. Math. Mech. 18, 15.Google Scholar
Isshiki, H. 1982 A theory of wave devouring propulsion (1st report). Thrust generation by a linear Wells Turbine. J. Soc. Nav. Arch. Japan 151, 54.Google Scholar
Isshiki, H. & Murakami, M. 1983 A theory of wave devouring propulsion (3rd report). An experimental verification of thrust generation by a passive-type hydrofoil propulsor. J. Soc. Nav. Arch. Japan 154, 125.Google Scholar
Isshiki, H., Murakami, M. & Terao, Y. 1984 Utilization of wave energy into propulsion of ships - wave devouring propulsion. 15th Symp. on Naval Hydrodyn. National Academy Press, Washington, D.C.
Jakobsen, E. 1981 The foil propeller, wave power for propulsion. 2nd Intl Symp. on Wave and Tidal Energy. BHRA Fluid Engineering, 363.
Von Kármán, Th. & Burgers, J. M. 1934 Aerodynamic Theory. A General Review of Progress, ed. W. F. Durand. California Institute of Technology 1943.
Lighthill, J. 1970 Aquatic animal propulsion of high hydrodynamical efficiency. J. Fluid Mech. 44, 265.Google Scholar
Mo, A. & Palm, E. 1987 On radiated and scattered waves from a submerged elliptic cylinder in a uniform current. J. Ship Res. 31, 23.Google Scholar
Newman, J. N. 1977 Marine Hydrodynamics. MIT Press.
Newman, J. N. 1978 The theory of ship motions. Adv. Appl. Mech. 18, 221.Google Scholar
Wachnik, Z. C. & Zarnik, E. E. 1965 Ship motion prediction in realistic short-crested seas. Soc. Nav. Arch. and Marine Engnrs Trans. 73, 100.Google Scholar
Watson, G. N. 1922 A Treatise on the Theory of Bessel Functions. Cambridge University Press.
Wu, T. Y. 1961 Swimming of a waving plate. J. Fluid Mech. 10, 321.Google Scholar
Wu, T. Y. 1971a Hydromechanics of swimming propulsion. Part 1. Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid. J. Fluid Mech. 46, 337.Google Scholar
Wu, T. Y. 1971b Hydromechanics of swimming propulsion. Part 2. Some optimum shape problems. J. Fluid Mech. 46, 521.Google Scholar
Wu, T. Y. 1972 Extraction of flow energy by a wing oscillating in waves. J. Ship Res. 16, 66.Google Scholar