Ocean Systems Engineering

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Second-order wave radiation by multiple cylinders in time domain through the finite element method

  • Wang, C.Z. (Department of Mechanical Engineering, National University of Singapore) ;
  • Mitra, S. (Department of Mechanical Engineering, National University of Singapore) ;
  • Khoo, B.C. (Department of Mechanical Engineering, National University of Singapore)
  • Received : 2011.11.11
  • Accepted : 2011.12.09
  • Published : 2011.12.25
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Abstract

A time domain finite element based method is employed to analyze wave radiation by multiple cylinders. The nonlinear free surface and body surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a finite element method (FEM). The matrix equation of the FEM is solved through an iteration and the initial solution is obtained from the result at the previous time step. The three-dimensional (3D) mesh required is generated based on a two-dimensional (2D) hybrid mesh on a horizontal plane and its extension in the vertical direction. The hybrid mesh is generated by combining an unstructured grid away from cylinders and two structured grids near the cylinder and the artificial boundary, respectively. The fluid velocity on the free surface and the cylinder surface are calculated by using a differential method. Results for various configurations including two-cylinder and four-cylinder cases are provided to show the mutual influence due to cylinders on the first and second waves and forces.

Keywords

References

  1. Bai, W. and Eatock Taylor, R. (2006), "Higher-order boundary element simulation of fully nonlinear wave radiation by oscillating vertical cylinders", Appl. Ocean Res., 28(4), 247-265. https://doi.org/10.1016/j.apor.2006.12.001
  2. Chau, F.P. and Eatock Taylor, R. (1992), "Second-order wave diffraction by a vertical cylinder", J. Fluid Mech., 240, 571-599. https://doi.org/10.1017/S0022112092000211
  3. Chung, T.J. (2002), Computational Fluid Dynamics, Cambridge University Press.
  4. Goren, O. (1996), "On the second-order wave radiation of an oscillating vertical circular in finite-depth water", J. Ship Res., 40(3), 224-234.
  5. Hecht, F. (1998), "BAMG: Bidimensional anisotropic mesh generator", Website: http://www-rocq1.inria.fr/gamma/cdrom/www/bamg/eng.htm.
  6. Isaacson, M., Ng, J.Y.T. and Cheung, K.F. (1993), "Second-order wave radiation of three-Dimensional bodies by time-domain method", Int. J. Offshore Polar., 3(4), 264-272.
  7. Li, Y. (1995), Simulation of 3D nonlinear wave-structure interaction in a numerical wave basin, Ph.D. Thesis, Tech. Univ. of Nova Scotia Halifax.
  8. Lighthill, M.J. (1979), "Waves and hydrodynamic loading", Proceedings of the 2nd International Conference on the Behaviour of Offshore Structures, London.
  9. Malenica, S., Eatock Taylor, R. and Huang, J.B. (1999), "Second order water wave diffraction by an array of vertical cylinders", J. Fluid Mech., 390, 349-373. https://doi.org/10.1017/S0022112099005273
  10. Molin, B. (1979), "Second order diffraction loads upon three-dimension bodies", Appl. Ocean Res., 1, 197-202. https://doi.org/10.1016/0141-1187(79)90027-0
  11. Nakos, D.E., Kring, D., Sclavounos, P.D. (1993), "Rankine panel methods for transient free surface flows", Proceedings of the 6th International Conference on Numerical Ship Hydrodynamics, Iowa.
  12. Ohkusu, M. (1969), "On the heaving motion of two circular cylinders on the surface of a fluid", Reports of Research Institute for Applied Mechanics, 17(58), 167-185.
  13. Wang, C.Z. and Wu, G.X. (2007), "Time domain analysis of second order wave diffraction by an array of vertical cylinders", J. Fluids Struct., 23(4), 605-631. https://doi.org/10.1016/j.jfluidstructs.2006.10.008
  14. Wang, C.Z., Wu, G.X., Drake, K.R. (2007), "Interactions between fully nonlinear water wave and non-wall-sided structures", Ocean Eng, 34(8-9), 1182-1196. https://doi.org/10.1016/j.oceaneng.2006.07.005
  15. Williams, A.N. and Abul Azm, A.G. (1989), "Hydrodynamic interactions in floating cylinder array-II. Wave radiation", Ocean Eng, 16, 217-263. https://doi.org/10.1016/0029-8018(89)90019-X