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Three-dimensional theory on supercavitating hydrofoils near a free surface

Published online by Cambridge University Press:  29 March 2006

Okitsugu Furuya
Okitsugu Furuya
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology Present Address: Tetra Tech, Inc., Pasadena, California 91107, U.S.A.
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Abstract

Supercavitating hydrofoils of large aspect ratio operating near a free surface are investigated, assuming an inviscid and irrotational flow with the effects of gravity and surface tension neglected. The flow near the foil, treated as two-dimensional, is solved by a nonlinear free-streamline theory, then a three-dimensional ‘downwash’ correction is made using Prandtl's lifting-line theory. The strength of the lifting-line vortex is determined by information from the two-dimensional solution through a matching procedure, in which the inverse of aspect ratio is used as a small parameter for asymptotic expansions. The analysis incorporates a free-surface reference level to determine the submergence depth of the foil. The present method can be applied to any type of foil having an arbitrary planform or profile shape, including a rounded leading edge, a twist and even a small dihedral angle, within the assumption of large aspect ratio. Numerical computations made on rectangular flat-plate hydrofoils show excellent agreement of results with existing experimental data, even for large angles of attack and relatively low aspect ratios. The pressure distributions, shapes of the cavity and free surface are also calculated as a function of spanwise position.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 2 , 23 September 1975 , pp. 339 - 359
Copyright
© 1975 Cambridge University Press

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References

Acosta, A. J. 1968 Two models for cavity flow, a theoretical summary and application. J. Basic Engng, Trans. A.S.M.E. D 90, 634.Google Scholar
Acosta, A. J. 1973 Hydrofoils and hydrofoil craft. Ann. Rev. Fluid Mech. 5, 161–184.Google Scholar
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Blaisdel.
Furuya, O. 1975 Nonlinear calculation of arbitrarily shaped supercavitating hydrofoils near a free surface. J. Fluid Mech. 68, 21–40.Google Scholar
Glauert, H. 1948 The Elements of Aerofoil and Airscrew Theory. Cambridge University Press.
Green, A. E. 1936 Note on the sliding of a plate on the surface of a stream. Proc. Camb. Phil. Soc. 32, 248–252.Google Scholar
Johnson, V. E. 1957 Theoretical and experimental investigation of arbitrary aspect ratio, supercavitating hydrofoils operating near the free surface. N.A.C.A., R.M., LS 7116.
Larock, B. & Street, R. 1987 Nonlinear solution for a fully cavitating hydrofoil beneath a free surface. J. Ship Res. 11, 131–140.Google Scholar
Leehey, P. 1971 Supercavitating hydrofoil of finite span. IUTAM Symp., Leningrad, pp. 277–299.
Nishiyama, T. 1970 Lifting line theory of supercavitating hydrofoil of finite span. Z. angew. Math. Mech. 50, 645–653.Google Scholar
Nishiyama, T. & Miyamoto, M. 1969 Lifting-surface method for calculating the hydro-dynamic characteristics of supercavitating hydrofoil operating near the free water surface. Tohoku University, Tech. Rep. 34, 2, 123–139.Google Scholar
Schiebe, F. R. & Wetzel, J. M. 1961 Ventilated cavities on submerged three-dimensional hydrofoils. St Anthony Falls Hydraulic Lab., University of Minneapolis, Tech. Paper, B 36
Shen, Y. T. & Ogilvie, T. F. 1972 Nonlinear hydrodynamic theory for finite-span planing surface. J. Ship Res. 16, 3–21Google Scholar
Tulin, M. P. 1964 Supercavitating flows: small perturbation theory. J. Ship Res. 7, 16–37Google Scholar
Van Dyke, M. 1964a Perturbation Methods in Fluid Mechanics. Academic
Van Dyke, M. 1964b Lifting-line theory as a singular perturbation problem. J. Appl. Math. Mech. 28, 90–101Google Scholar
Widnall, S. E. 1966 Unsteady loads on supercavitating hydrofoils of finite span. J. Ship Res. 10, 107–118Google Scholar
Wu, T. Y. 1959 A note on the linear and nonlinear theories for fully cavitated hydrofoils. Hydrodynamic Lab., Calif. Inst. of Tech., Rep. no. 21–22