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A numerical simulation method for the flow around floating bodies in regular waves using a three-dimensional rectilinear grid system

  • Received : 2015.04.09
  • Accepted : 2016.03.03
  • Published : 2016.05.31

Abstract

The motion of a floating body and the free surface flow are the most important design considerations for ships and offshore platforms. In the present research, a numerical method is developed to simulate the motion of a floating body and the free surface using a fixed rectilinear grid system. The governing equations are the continuity equation and Naviere-Stokes equations. The boundary of a moving body is defined by the interaction points of the body surface and the centerline of a grid. To simulate the free surface the Modified Marker-Density method is implemented. Ships advancing in regular waves, the interaction of waves by a fixed circular cylinder array and the response amplitude operators of an offshore platform are simulated and the results are compared with published research data to check the applicability. The numerical method developed in this research gives results good enough for application to the initial design stage.

Keywords

References

  1. Basting, C., Kuzmin, D., 2013. A minimization-based finite element formulation for interface-preserving level set reinitialization. Computing 95 (1), 13-25. https://doi.org/10.1007/s00607-012-0259-z
  2. Davidson, L., 2011. An Introduction to Turbulence Models. Chalmers University of Technology, Sweden.
  3. Ferziger, J.H., Peric, M., 2002. Computational Methods for Fluid Dynamics. Springer.
  4. Guo, B.J., Steen, S., Deng, G.B., 2012. Seakeeping prediction of KVLCC2 in head waves with RANS. Appl. Ocean Res. 35, 56-67. https://doi.org/10.1016/j.apor.2011.12.003
  5. Harlow, F.H.,Welch, J.E., 1965. Numerical calculation of time-dependent viscous incompressible flow of fluids with free-surface. Phys. Fluids 8, 2182-2189. https://doi.org/10.1063/1.1761178
  6. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundary. J. Comput. Phys. 39, 201-225. https://doi.org/10.1016/0021-9991(81)90145-5
  7. Hu, C., Kashiwagi, M., 2009. Two-dimensional numerical simulation and experiment on strongly nonlinear wave-body interaction. J. Mar. Sci. Technol. 14, 200-213. https://doi.org/10.1007/s00773-008-0031-4
  8. Journee, J.M.J., Massie, W.W., 2001. Offshore Hydromechanics. Delft university of Technology First Edition.
  9. Kashiwagi, M., Nakagawa, D., Yamamoto, K., 2012. Analysis of unsteady waves and added resistance using CIP-based cartesian grid method. In: Proceedings of 2nd International Conference on Violent Flows, pp. 238-245. Nantes, France.
  10. Kawamura, T., Kuwahara, K., 1984. Computation of high Reynolds number flow around a circular cylinder with surface roughness. In: Proceedings of the AIAA Paper 84-0340.
  11. Kim, C.H., 2008. Nonlinear Waves and Offshore Structures. World Scientific.
  12. Kim, W.J., Van, S.H., Kim, D.H., 2001. Measurement of flows around modern commercial ship models. Exp. Fluids 31, 567-578. https://doi.org/10.1007/s003480100332
  13. Lee, J., Kim, J., Choi, H., Yang, K.S., 2011. Sources of spurious force oscillations from an immersed boundary method for moving-body problems. J. Comput. Phys. 230, 2677-2695. https://doi.org/10.1016/j.jcp.2011.01.004
  14. Lee, Y.G., Jeong, K.L., Kim, N.C., 2012. The marker-density method in cartesian grids applied to nonlinear ship. Comput. Fluids 63, 57-69. https://doi.org/10.1016/j.compfluid.2012.04.003
  15. Lee, Y.G., Jeong, K.L., Kim, N.C., 2013. A numerical simulation method for free surface flows near a two-dimensional moving body in fixed rectangular grid system. Ocean Eng. 59, 285-295. https://doi.org/10.1016/j.oceaneng.2012.12.001
  16. Lin, P., 2006. A fixed-grid model for simulation of a moving body in free surface flows. Comput. Fluids 36 (3), 549-561. https://doi.org/10.1016/j.compfluid.2006.03.004
  17. Malenica, S., Eatock Taylor, R., Huang, J.B., 1999. Second-Order Water Wave diffraction by an array of vertical cylinder. J. Fluid Mech 390, 349-373. https://doi.org/10.1017/S0022112099005273
  18. Mittal, R., Iaccarino, G., 2005. Immersed boundary methods. Ann. Rev. Fluid Mech. 37, 239-261. https://doi.org/10.1146/annurev.fluid.37.061903.175743
  19. Noh, W.F., Woodward, P., 1982. SLIC (simple line interface calculation). In: van Dooren, A.I., Zandberger, P.J. (Eds.), Lecture Notes in Physics, vol. 59, pp. 273-285.
  20. Ohl, C.O.G., Eatock Taylor, R., Taylor, P.H., Borthwick, A.G.L., 2001. Water wave diffraction by a cylinder array. Part 1. Regular waves. J. FluidMech. 442, 1-32.
  21. Osher, S., Sethian, J.A., 1988. Fronts propagating with curvature-dependent speed: Algorithms based on HamiltoneJacobi formulations. J. Comput. Phys. 79, 12-49. https://doi.org/10.1016/0021-9991(88)90002-2
  22. Park, I.R., Van, S.H., Kim, J., Kang, K.J., 2003. Level-set simulation of viscous free surface flow around a commercial hull form. In: Proceedings of the 5th Asian Computational Fluid Dynamics, Busan, Korea.
  23. Park, J.C., Kim, M.H., Miyata, H., 1999. Fully non-linear free-surface simulations by a 3d viscous numerical wave tank. Int. J. Numer. Meth. Fluids 29, 685-703. https://doi.org/10.1002/(SICI)1097-0363(19990330)29:6<685::AID-FLD807>3.0.CO;2-D
  24. Roberson, Crowe, 1997. Engineering Fluid Mechanics, sixth ed. Wiley.
  25. Sadat-Hosseini, H., Wu, P.C., Carrica, P.M., Kim, H., Toda, Y., Stern, F., 2013. CFD verification and validation of added resistance and motions of KVLCC2 with fixed and free surge in short and long head waves. Ocean Eng. 59, 240-273. https://doi.org/10.1016/j.oceaneng.2012.12.016
  26. Seo, J.H., Mittal, R., 2011. A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. J. Comput. Phys. 230, 7347-7363. https://doi.org/10.1016/j.jcp.2011.06.003
  27. Seo, M.G., Lee, J.H., Park, D.M., Yang, K.K., Kim, K.H., Kim, Y., 2013. Analysis of added resistance: comparative study on different methodologies. In: Proceedings of OMA-2013, OMAE 2013-10228, Nantes, France.
  28. Simonsen, C.D., Otzen, J.F., Joncquez, S., Stern, F., 2013. EFD and CFD for KCS heaving and pitching in regular head waves. J. Mar. Sci. Technol. http://dx.doi.org/10.1007/s00773-013-0219-0.
  29. Smagorinsky, J., 1963. General circulation experiments with the primitive equations. I. the basic experiment. Mon. Weather Rev. 91, 99-164. https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
  30. Van, S.H., Kim, W.J., Kim, D.H., Yim, G.T., Lee, C.J., Eom, J.Y., 1997. Measurement of flows around a 3600TEU container ship model. In: Proceedings of the Annual Autumn Meeting, SNAK, Seoul, pp. 300-304.
  31. Yang, J., Stern, F., 2009. Sharp interface immersed-boundary/level-set method for wave-body interactions. J. Comput. Phys. 228 (17), 6590-6616. https://doi.org/10.1016/j.jcp.2009.05.047
  32. Yang, K.K., Lee, J.H., Nam, B.W., Kim, Y., 2013a. Analysis of added resistance using a Cartesian-grid-based computational method. J. Soc. Nav. Archit. Korea 50 (2), 79-87. https://doi.org/10.3744/SNAK.2013.50.2.79
  33. Yang, K.K., Nam, B.W., Lee, J.H., Kim, Y., 2013b. Numerical analysis of large-amplitude ship motions using FV-based Cartesian grid method. Int J Offshore Polar Eng. 23 (3), 186-196.
  34. Yokoi, K., 2007. Efficient implementation of THINC scheme: a simple and practical smoothed VOF algorithm. J. Comput. Phys. 226, 1985-2002. https://doi.org/10.1016/j.jcp.2007.06.020
  35. Youngs, D.L., 1982. Time-dependent multi-material flow with large fluid distortion. In: Morton, K.W., Baines, M.J. (Eds.), Numerical Methods for Fluid Dynamics, vol. 24. Academic Press, New York, pp. 273-285.

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