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The effect of gravity and cavitation on a hydrofoil near the free surface

  • ODD M. FALTINSEN (a1) and YURIY A. SEMENOV (a1)

Abstract

A nonlinear analysis has been made to determine the effects of the free surface and transverse gravity field on the steady cavity flow past a shaped hydrofoil beneath the free surface. A closed cavity wake model has been proposed, and a method for the determination of an analytical function from its modulus and argument on the region boundary has been employed to derive the complex flow potential in a parameter plane. The boundary-value problem is reduced to a system of integral and integro-differential equations in the velocity modulus along the free boundaries and the velocity angle along the hydrofoil surface, both written as a function of parametric variables. The system of equations is solved through a numerical procedure, which is validated in the cases of a cavitating flat plate and non-cavitating shaped hydrofoils by comparison with data available in the literature. The results are presented in a wide range of Froude numbers and depths of submergence in terms of the cavity and free-surface shapes and force coefficients. The influences of the free surface and gravity on the aforementioned quantities are discussed. The limiting cavity size corresponding to zero cavitation number in the presence of gravity is found for various initial flow parameters.

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Acosta, A. J. 1973 Hydrofoils and hydrofoil craft. Annu. Rev. Fluid Mech. 5, 161184.
Arakeri, V. 1975 Viscous effects on the position of cavitation separation from smooth bodies. J. Fluid Mech. 68, 779799.
Bernicker, R. P. 1966 A linearized two-dimensional theory for high-speed hydrofoils near the free surface. J. Ship Res. 10, 2548.
Chapman, S. J. & Vanden-Broeck, J.-M. 2006 Exponential asymptotics and gravity waves. J. Fluid Mech. 567, 299326.
Dagan, G. 1971 Free-surface gravity flow past a submerged cylinder. J. Fluid Mech. 49, 179192.
Dawson, T. E. 1959 An experimental investigation of a fully cavitating two-dimensional flat plate hydrofoil near a free surface. PhD thesis, California Institute of Technology, Pasadena.
Dias, F. & Vanden-Broeck, J.-M. 2003 On the internal fronts. J. Fluid Mech. 479, 145154.
Dias, F. & Vanden-Broeck, J.-M. 2004 Trapped waves between submerged obstacles. J. Fluid Mech. 509, 93102.
Duncan, J. 1983 The breaking and non-breaking wave resistance of a two-dimensional hydrofoil. J. Fluid Mech. 126, 507520.
Faltinsen, O. M. 2005 Hydrodynamics of High-Speed Marine Vehicles. Cambridge University Press.
Furuya, O. 1975 Nonlinear calculation of arbitrary shaped supercavitating hydrofoils near a free surface. J. Fluid Mech. 68, 2140.
Giesing, J. P. & Smith, A. M. O. 1967 Potential flow about two-dimensional hydrofoils. J. Fluid Mech. 28, 113129.
Gurevich, M. I. 1965 Theory of Jets in Ideal Fluids. Academic.
Havelock, T. H. 1926 The method of images in some problems of surface waves. Proc. R. Soc. Lond. A 115, 268280.
Helmholtz, H. 1868 Ueber discontinuirliche Flussigkeitsbewegungen. Monasber. Berlin Akad. pp. 215–228.
Hough, G. R. & Moran, J. P. 1969 Froude number effects on two-dimensional hydrofoils. J. Ship Res. 13, 5360.
Johnson, V. E. Jr, 1961 Theoretical and experimental investigation of supercavitating hydrofoils operating near the free water surface. NASA TRR-93.
Keldysh, M. V. & Lavrentiev, M. A. 1935 On the motion of a wing under the surface of a heavy fluid. TsAGI, Moscow; translation in Science Translation Service, STS-75, Cambridge, MA, 1949.
King, A. C. & Bloor, M. I. G. 1989 A semi-inverse method for free-surface flow over a submerged body. J. Mech. Appl. Maths. 42, 183202.
Kirchoff, G. 1869 Zur Theorie freier Flussigkeitsstrahlen. J. reine u. angew. Math. 70, 289298.
Kochin, N. E. 1937 On the wave resistance and lift of bodies submerged in a fluid. TsAGI, Moscow; translation in SNAME Technical and Research Bulletin, 1951, pp. 1–8.
Landrini, M., Lugni, C. & Bertram, V. 1999 Numerical simulation of the unsteady flow past a hydrofoil. Ship Technol. Res. 46, 14.
Larock, B. E. & Street, R. L. 1967 a A nonlinear solution for a fully cavitating hydrofoil beneath a free surface. J. Ship Res. 11, 131139.
Larock, B. E. & Street, R. L. 1967 b A non-linear theory for a full cavitating hydrofoil in a transverse gravity field. J. Fluid Mech. 29, 317336.
Parkin, B. R. 1957 A note on the cavity flow past a hydrofoil in a liquid with gravity. Engineering Division, California Institute of Technology, Pasadena, Rep. 47-9.
Salvesen, N. 1969 On higher-order wave theory for submerged two-dimensional bodies. J. Fluid Mech. 38, 415432.
Schwartz, L. W. 1974 Computer extension and analytic continuation of Stokes' expansion for gravity waves. J. Fluid Mech. 62, 553578.
Semenov, Yu. A. & Cummings, L. J. 2006 Free boundary Darcy flows with surface tension: analytical and numerical study. Euro. J. Appl. Math. 17, 607631.
Semenov, Yu. A. & Iafrati, A. 2006 On the nonlinear water entry problem of asymmetric wedges. J. Fluid Mech. 547, 231256.
Smith, F. T. 1986 Steady and unsteady boundary-layer separation. Annu. Rev. Fluid Mech. 18, 197220.
Tuck, E. O. 1965 The effect of non-linearity at the free surface on the flow past a submerged cylinder. J. Fluid Mech. 22, 401414.
Tulin, M. P. 1964 The shape of cavities in supercavitating flows. XI IUTAM Congress Paper, Munich, Germany.
Tulin, M. P. & Burkart, M. P. 1955 Linearized theory for flows about lifting foils at zero cavitation number. David W. Taylor Model Basin, Navy Dept. Rep. C-638.
Vanden-Broeck, J.-M. 2004 Nonlinear capillary free-surface flows. J. Engng. Maths. 50, 415426.
Wilmot, P. 1987 On the motion of a small two-dimensional body submerged beneath surface waves. J. Fluid Mech. 176, 465481.
Wu, T. Y. 1962 A wake model for free-streamline flow theory. J. Fluid Mech. 13, 161181.
Zhukovskii, N. E. 1890 Modification of Kirchoff's method for determination of a fluid motion in two directions at a fixed velocity given on the unknown streamline. Math. Coll. 15, 121278.
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The effect of gravity and cavitation on a hydrofoil near the free surface

  • ODD M. FALTINSEN (a1) and YURIY A. SEMENOV (a1)

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