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A new modelling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section

Published online by Cambridge University Press:  26 April 2006

Akihiro Kubota ,
Hiroharu Kato  and
Hajime Yamaguchi
Akihiro Kubota
Affiliation:
Department of Naval Architecture and Ocean Engineering. Faculty of Engineering, The University of Tokyo, 7–3-1 Hongo, Bunkyo-ku, Tokyo 113. Japan
Hiroharu Kato
Affiliation:
Department of Naval Architecture and Ocean Engineering. Faculty of Engineering, The University of Tokyo, 7–3-1 Hongo, Bunkyo-ku, Tokyo 113. Japan
Hajime Yamaguchi
Affiliation:
Department of Naval Architecture and Ocean Engineering. Faculty of Engineering, The University of Tokyo, 7–3-1 Hongo, Bunkyo-ku, Tokyo 113. Japan
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Abstract

A new cavity model that can explain the interaction between viscous effects including vortices and cavitation bubbles is presented in this study. This model, which is named a bubble two-phase flow (BTF) model, treats the inside and outside of a cavity as one continuum by regarding the cavity as a compressible viscous fluid whose density changes greatly. Navier–Stokes equations including cavitation bubble clusters are solved in finite-difference form by a time-marching scheme, where the growth and collapse of a bubble cluster is given by a modified Rayleigh's equation. Computation was made on a two-dimensional flow field around a hydrofoil NACA0015 at angles of attack of 8° and 20°. The Reynolds number was 3 × 105. The experiments were also performed at the same Reynolds number for comparison. The computed results by the BTF cavity model can express the feature of cloud-type cavitation shed from the trailing edge of the attached cavities when the angle of attack is 8°. It shows the mechanism of cavitation cloud generation and large-scale vortices. The boundary layer separates at the cavity leading edge. Then it rolls up and produces the cavitation cloud. In other words, the instability of the shear layer may produce the cavitation cloud. When the angle of attack is 20°, the flow was fully separated from the leading edge of the hydrofoil and vortex cavitation occurs in the separated region. The BTF cavity model can also express the generation of such vortex cavitation and the effect of cavitation nuclei in the uniform flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992 , pp. 59 - 96
Copyright
© 1992 Cambridge University Press

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References

Abbott, I. H. & von Doenhoff, A. E. 1958 Theory of Wing Sections. Dover.
D'Agostino, L. & Brennen, C. E. 1989 Linearized dynamics of spherical bubble clouds. J. Fluid Mech. 199, 155–176.Google Scholar
Alexander, A. J. 1974 Hydrofoil oscillation induced by cavitation. Conf. on Cavitation, Edinburgh, IME, Herriot—Watt University, 27–35.
Chahine, G. L. & Lie, H. L. 1985 A singular-perturbation theory of the growth of a bubble cluster in a superheated liquid. J. Fluid Mech. 156, 257–279.Google Scholar
Efros, D. 1946 Hydrodynamics theory of two-dimensional flow with cavitation. Dokl. Akad. Nauk. SSSR 51, 267–270.Google Scholar
Franc, J. P. & Michel, J. M. 1985 Attached cavitation and the boundary layer: experimental investigation and numerical treatment. J. Fluid Mech. 154, 63–90.Google Scholar
Furness, R. A. & Hutton, S. P. 1975 Experimental and technical studies of two-dimensional fixed-type cavities. Trans. ASME I: J. Fluids Engng 97, 515–522.Google Scholar
Furuya, O. 1975 Three-dimensional theory on supercavitating hydrofoils near a free surface. J. Fluid Mech. 71, 339–359.Google Scholar
Furuya, O. 1980 Non-linear theory for partially cavitating cascade flows. IAHR 10th Symp., Tokyo, pp. 221–241.Google Scholar
Gates, E. M. 1977 The influence of freestream turbulence, freestream nuclei population and a drag-reduction polymer on cavitation inception on two axisymmetric bodies. PhD Thesis, California Institute of Technology.
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182.Google Scholar
Helmholtz, H. 1868 On discontinuous movements of fluids. Phil. Mag. 36 (4), 337–346.Google Scholar
Hess, J. L. & Smith, A. M. O. 1967 Calculation of potential flow about arbitrary bodies. Progress in Aeronautical Science, vol. 8. Pergamon.
Van Houten, R. J. 1982 The numerical prediction of unsteady sheet cavitation on high aspect ratio hydrofoils. 14th Symp. on Naval Hydrodyn. University of Michigan, Session V, pp. 109–158.Google Scholar
Hutton, S. P. 1986 Studies of cavitation erosion and its relation to cavitating flow patterns. Proc. Intl Symp. on Cavitation, Sendai, Japan, vol. 1, pp. 21–29.Google Scholar
Inoue, S., Kato, H. & Yamaguchi, H. 1986 The effect of a slat on boundary layer characteristics and cavitation of the main foil. Naval Arch. Ocean Engng, 24, 27–38.Google Scholar
Izumida, Y., Tamiya, S., Kato, H. & Yamaguchi, H. 1980 The relationship between characteristics of partial cavitation and flow separation. Proc. 10th IAHR Symp., Tokyo, pp. 169–181.Google Scholar
Johnsson, C. A. 1969 Cavitation inception on head forms, further tests. Proc. 12th Intl Towing Tank Conf., Rome, 381–392.Google Scholar
Joussellin, F., Delannoy, Y., Sauvage-Boutar, E. & Goirand, B. 1991 Experimental investigation on unsteady attached cavities. Cavitation '91, ASME, FED-116, pp. 61–66.Google Scholar
Kato, H. 1985 On the structure of cavity — new insight into the cavity flow: a summary of the keynote speech. Intl Symp. Jets and Cavities, ASME, FED-31, pp. 13–19.Google Scholar
Kato, H., Yamaguchi, H. & Kubota, A. 1987 Laser Doppler velocimeter measurements in cavitation tunnel. Proc. 18th ITTC, Kobe, vol. 2, pp. 433–437.Google Scholar
Kawamura, T. & Kuwahara, K. 1984 Computation of high Reynolds number flow around a circular cylinder with surface roughness. AIAA papr 84–0341.Google Scholar
Kermeen, R. W. 1956 Water tunnel test of NACA 4412 and Walchner profile 7 hydrofoil in non-cavitating and cavitating flows. Hydrodynamic Laboratory, California Institute of Technology, Pasadena, California, Rep. no. 47–5.
Kirchhoff, G. 1869 Zur Theorie Freier Flussigkeitsstrahlen. J. reine angew. Math. 70, 289–298.Google Scholar
Kiya, M. & Sasaki, K. 1985 Structure of large-scale vortices and unsteady reverse flow in the reattaching zone of a turbulent separation bubble. J. Fluid Mech. 154, 463–491.Google Scholar
Knapp, R. T., Daily, J. W. & Hammit, F. G. 1970 Cavitation. McGraw-Hill.
Kodama, Y. 1988 Three-dimensional grid generation around a ship hull using the geometrical method. J. Soc. Naval Arch. Japan 164, 1–8.Google Scholar
Kodama, Y., Take, N., Tamiya, S. & Kato, H. 1981 The effect of nuclei on the inception of bubble and sheet cavitation on axisymmetric bodies. Trans. ASME I: J. Fluids Engng 103, 557–563.Google Scholar
Kreisel, G. 1946 Cavitation with finite cavitation numbers. Admiralty Res. Lab. Rep. no. R1/H/36, p. 289.Google Scholar
Kubota, A., Kato, H. & Yamaguchi, H. 1988 A new numerical simulation method of cavitating flow caused by large-scale vortices. Theoret. Appl. Mech., Tokyo 36, 93–100.Google Scholar
Kubota, A., Kato, H., Yamaguchi, H. & Maeda, M. 1989a Unsteady strcuture measurement of cloud cavitation on a foil section using conditional sampling technique. Trans. ASME I: J. Fluids Engng 111, 204–210.Google Scholar
Kubota, A., Kato, H. & Yamaguchi, H. 1989b Finite difference analysis of unsteady cavitation on a two-dimensional hydrofoil. 5th Intl Conf. Numerical Ship Hydrodyn., Hiroshima, pp. 472–487.Google Scholar
Lamb, H. 1932 Hydrodynamics. Dover. 112 pp.
Lemonnier, H. & Rowe, A. 1988 Another approach in modelling cavitating flows. J. Fluid Mech. 195, 557–580.Google Scholar
Maeda, M., Yamaguchi, H. & Kato, H. 1991 Laser holography measurement of bubble population in cavitation cloud on a foil section. Cavitation '91. ASME. FED-116, pp. 67–75.Google Scholar
Mehta, U. B. & Lavan, Z. 1975 Starting vortex, separation bubbles and stall: a numerical study of laminar unsteady flow around an airfoil. J. Fluid Mech. 67, 227–256.Google Scholar
Mørch, K. A. 1981 Cavity cluster dynamics and cavitation erosion. Cavitation and Polyphase Flow Forum — 1981, pp. 1–10.
Nishiyama, T. & Miyamoto, M. 1969 Lifting-surface method for calculating the hydrodynamic characteristics of supercavitating hydrofoil operating near the free water surface. Tech. Rep. Tohoku University 34, 123–139.Google Scholar
Riabouchinsky, D. 1920 On steady fluid motion with free surface. Proc. Lond. Math. Soc. 2, 19, 206.Google Scholar
Roache, P. J. 1976 Computational Fluid Dynamics. Albuquerque: Hermosa.
Shen, Y. T. & Peterson, F. B. 1978 Unsteady cavitation on an unsteady hydrofoil. 12th Symp. Naval Hydrodyn., Washington DC, pp. 470–493.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations — I. The basic experiment. Mon. Weather Rev. 91, 99–164.Google Scholar
Soetrisno, M., Eberhardt, S., Riley, J. J. & McMurtry, P. 1988 A study of inviscid, supersonic mixing layers using a second-order TVD scheme. Proc. of AIAA/ASME/SIAM/APS 1st Natl Fluid Dyn. Congress, Cincinnati, Ohio, pp. 1087–1094.
Tamura, K., Kato, H., Yamaguchi, H., Komura, T., Maeda, M. & Miyanaga, M. 1985 Measurement of bubble nuclei by a scattered light technique. Laser Doppler Velocimetry and Hot Wire/Film Anemometry, Association for the Study of Flow Measurement, pp. 281–294.
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A, 138, 41–48.Google Scholar
Thompson, J. F., Warsi, Z. U. A. & Mastin, C. W. 1985 Numerical Grid Generation—Foundations and Applications. Elsevier Science Publishing.
Tulin, M. P. 1955 Supercavitating flow past foils and struts. Proc. NPL Symp. Cavitation Hydrodyn. paper no. 16, pp. 1–19.Google Scholar
Tulin, M. P. 1964 Supercavitating flows—small perturbation theory. J. Ship Res. 7 (3), 16–37.Google Scholar
Tulin, T. P. & Hsu, C. C. 1980 New applications of cavity flow theory. 13th Symp. Naval Hydrodyn., Tokyo, Shipbuilding Research Association of Japan, pp. 107–131.
Wade, R. B. & Acosta, A. J. 1966 Experimental observation on the flow past a plano-convex hydrofoil. Trans. ASME I: J. Fluids Engng 88, 273–283.Google Scholar
Van Wijngaarden, L. 1964 On the collective collapse of a large number of gas bubbles in water. Proc. 11th Intl Cong. Appl. Mech. pp. 854–861. Springer.Google Scholar
Van Wijngaarden, L. 1968 On the equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33, 465–474.Google Scholar
Wu, T. Y. 1962 A wake model for free-stream flow theory. Part 1. Fully and partially developed wake flows and cavity flows past an oblique flat plate. J. Fluid Mech. 13, pp. 161–181.Google Scholar
Yamaguchi, H. & Kato, H. 1982 A study on a supercavitating hydrofoil with rounded nose. Naval Arch. Ocean Engng, 20, 51–60.Google Scholar
Yamaguchi, H. & Kato, H. 1983 On application of nonlinear cavity flow theory to thick foil sections. Conf. on Cavitation, Edinburgh, IME, pp. 167–174.Google Scholar
Yamaguchi, H., Oshima, A., Kato, H., Komura, T. & Maeda, M. 1985 Measurement of the flow field downstream of a sheet type cavity. Laser Doppler Velocimetry and Hot Wire/Film Anemometry, Association for the Study of Flow Measurement, pp. 29–38.
Yamaguchi, H., Kato, H., Sugatani, A., Kamijo, A., Honda, T. & Maeda, M. 1988 Development of marine propellers with better cavitation performance — 3rd report: pressure distribution to stabilize cavitation. J. Soc. Naval Arch. Japan 164, 28–42.Google Scholar