Journal of Ship and Ocean Technology

The Society of Naval Architects of Korea (대한조선학회)
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A Numerical Method for a High-Speed Ship with a Transom Stern

  • Kyoung Jo-Hyun (Korea Research Institute of Ships & Ocean Engineering) ;
  • Bai Kwang-June (Department of Naval Architecture and Ocean Engineering, Seoul National University)
  • Published : 2004.09.01
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Abstract

A numerical method is developed for computing the free surface flows around a transom stern of a ship at a high Froude number. At high speed, the flow may be detached from the flat transom stern. In the limit of the high Froude number, the problem becomes a planning problem. In the present study, we make the finite-element computations for a transom stern flows around a wedge-shaped floating ship. The numerical method is based on the Hamilton's principle. The problem is formulated as an initial value problem with nonlinear free surface conditions. In the numerical procedures, the domain was discretized into a set of finite elements and the numerical quadrature was used for the functional equation. The time integrations of the nonlinear free surface condition are made iteratively at each time step. A set of large algebraic equations is solved by GMRES(Generalized Minimal RESidual, Saad and Schultz 1986) method which is proven very efficient. The computed results are compared with previous numerical results obtained by others.

Keywords

References

  1. Bai, KJ. 1977. A localized finite-element method for steady three-dimensional freesurface flow problems. Proc.2nd Int. Conf. on Num. Ship Hydrodynam., Berkeley, 78-87
  2. Bai, K.J., J.W. Kim and Y.H. Kim. 1989. Numerical computations for a nonlinear free surface flow problem. Proc.5th Int. Conf. on Num. Ship Hydrodynam., Hiroshima, 403-419
  3. Bai, K.J., J.W. Kim and H.K. Lee. 1994. A localized finite element method for nonlinear free-surface wave problems. Proc. 19th Symposium on Naval Hydrodynamics, Hague, Washington, D.C., 113-139
  4. Bai, K.J. and J.W. Kim. 1995. A finite-element method for free-surface flow problems. J. Theoretical and Applied Mechanics, 1, 1, 1-26
  5. Bai, KJ., J.H. Kyoung. and J.W. Kim. 2002. Numerical computations for a nonlinear free surface problem in a shallow water. The 21st International Conference Offshore Mechanics and Artie Engineering, OMAE2002-28463, Oslo, Norway, 23-28
  6. Cheng, B.H. 1989. Computations of 3D transom stem flows. Proc. 5th Int. Conf. on Num. Ship Hydrodynam., Hiroshima, 581
  7. Coleman, R.M. and H.J. Haussling. 1981. Nonlinear waves behind an accelerated transom stem. Proc. of the Third International Conf. on Nurnnerical Ship Hydrodynamics, Paris, France, 111
  8. Dagan,G. and M.P. Tulin. 1972. Two dimensional free-surface gravity flow past blunt bodies. J. Fluid. Mech., 51, 529
  9. Dawson, C.W. 1977. A practical computer method for solving ship wave problems, Proc. of the Second International Conf. on Numerical Ship Hydrodynamics, Univ. of Califonia, Berkeley, CA, 30
  10. Doctors, L.J. and A.H. Day. 2001. Steady-state hydrodynamics of high-speed vessels with a transom stem. 23th Symposium on Naval Hydrodynamics
  11. Eca, L. and M. Hoekstra. 1997. Numerical calculations of ship stem flows at full-scale Reynolds number. 21st symposium on Naval Hydrodynamics
  12. Haussling, H.J. 1980. Two-dimensional linear and nonlinear stem waves. 1 Fluid Mech., 97,759
  13. Kyoung, J.H., J.W. Kim and K.J. Bai. 2003. A finite element method for a nonlinear sloshing problem. The 22nd International Conference Offshore Mechanics and Artie Engineering, OMAE2003-37306, Mexico, Cancun, 8-13
  14. Loguet-Higgins, M.S. and E.D. Cokelet. 1976. The deformation of steep surface waves on water. I. A Numerical Method of Computation, Proc. R. Soc. London Ser., A350, 1
  15. Luke, J.C. 1967. A variational principle for a fluid with a free surface. J. Fluid. Mech., 27, 395
  16. Miles, J.W. 1977. On Hamiton's principle for surface waves. J. Fluid. Mech., 83, 395
  17. Reed, A.M., J.G. Telste and C. Scragg. 1981. Analysis of transom stem flows. 18th Symposium on Naval Hydrodynamics, Washington D.C, 207
  18. Saad, Y. and M.H. Schultz. 1986. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7, 856-869
  19. Telste, J.G. and A.M. Reed. 1993. Calculation of transom stem flows. Proc. 6th International Conference on Numerical Ship Hydrodynamics, Iowa, USA, 79
  20. Tulin, M.P and C.C. Hsu. 1986. Theory of high-speed displacement ships witt: transomstems. J. Ship Research, 30, 3, 186-193
  21. Val Eseltine, R.T. and H.J. Haussling. 1981. Flow about transom stems, Proc. of the Third International Conf. on Numerical Ship Hydrodynamics, Paris, France, 121
  22. Vanden-Broeck, J.M. 1980. Nonlinear stem waves. J. Fluid Mech., 96, 603
  23. Vanden-Broeck, J.M., L.W. Schwartz and E.O. Tuck. 1978, Divergent low Froude number series expansions of nonlinear free-surface flow problem. Proc. Roy. Soc. London, A.361, 207
  24. Vanden-Broeck, J.M. and E.O. Tuck. 1977. Computation of near-bow or stem flows, using series expansion in the Froude number. Proc. Of the Second International Conf. on Numerical Ship Hydrodynamics, University of Califonia, Berkeley, CA, 371
  25. Zakharov, V.E. 1968. Stability of periodic waves of finite amplitude on the free surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190