International Journal of Ocean System Engineering

Korean Society of Ocean Engineers (한국해양공학회)
권호 표지
DOI QR코드

DOI QR Code

Semi-Analytical Methods for Different Problems of Diffraction-Radiation by Vertical Circular Cylinders

  • Received : 2012.03.05
  • Accepted : 2012.05.25
  • Published : 2012.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

As in the other fields of mechanics, analytical methods represent an important analysis tool in marine hydrodynamics. The analytical approach is interesting for different reasons : it gives reference results for numerical codes verification, it gives physical insight into some complicated problems, it can be used as a simplified predesign tool, etc. This approach is of course limited to some simplified geometries (cylinders, spheres, ...), and only the case of one or more cylinders, truncated or not, will be considered here. Presented methods are basically eigenfunction expansions whose complexity depends on the boundary conditions. The hydrodynamic boundary value problem (BVP) is formulated within the usual assumptions of potential flow and is additionally simplified by the perturbation method. By using this approach, the highly nonlinear problem decomposes into its linear part and the higher order (second, third, ...) corrections. Also, periodicity is assumed so that the time dependence can be factorized i.e. the frequency domain formulation is adopted. As far as free surface flows are concerned, only cases without or with small forward speed are sufficiently simple to be solved semi-analytically. The problem of the floating body advancing in waves with arbitrary forward speed is far more complicated. These remarks are also valid for the general numerical methods where the case of arbitrary forward speed, even linearized, is still too difficult from numerical point of view, and "it is fair to say that there exists at present no general practical numerical method for the wave resistance problem" [9], and even less for the general seakeeping problem. We note also that, in the case of bluff bodies like cylinders, the assumptions of the potential flow are justified only if the forward speed is less than the product of wave amplitude with wave frequency.

Keywords

References

  1. Abramowitz M. & Stegun I., Handbook of mathematical functions, Dover, (1970).
  2. Aranha J.A.P., Second order horizontal steady forces and moment on a floating body with small forward speed, J. Fluid Mech., Vol. 313, (1996) pp. 39-54. https://doi.org/10.1017/S002211209600211X
  3. Chau F.P. & Eatock Taylor R., Second order wave diffraction by a vertical cylinder, J. Fluid Mech., Vol.240, (1992) pp. 571-599. https://doi.org/10.1017/S0022112092000211
  4. Chen X.B., Second order high frequency loads on tension leg platform columns, Institut Francais du Petrole, Rep ort No. 38741, (1991).
  5. Chen X.B. & Malenica S., Interaction effects of local steady flow on wave diffraction-radiation at low forward speed, Int. Journal of Offshore and Polar Engg., Vol. 8/2, (1998), pp. 102-109.
  6. Noblesse F. & Chen X.B., Decomposition of free surface effects into wave and near-field components, Ship Technology Res., Vol. 42/4, (1995).
  7. Clark P.J., S.Mal nica & B.Molin, An heuristic approach to wave drift damping, Appl. Ocean Res., Vol.15, (1993).
  8. Emmerhoff O.J. & P.D.Sclavounos, The slow drift motion of arrays of vertical cylinders, J. Fluid Mech., Vol.242, (1992) pp. 31-50. https://doi.org/10.1017/S002211209200226X
  9. Faltinsen O.M., Sea loads on Ships and Offshore Structures, Cambridge University Press (1990).
  10. Garrett C.J.R., Waves forces on a circular dock, J. Fluid Mech. Vol. 46, (1971) pp. 129-139. https://doi.org/10.1017/S0022112071000430
  11. Grue J., Personal communication(1993).
  12. Havelock T.H., Forced surface waves on water, Philosophical Magazine 8, (1929) pp. 304-311. https://doi.org/10.1080/14786440908564889
  13. John F., On the motion of floating bodies II, Comm. Pure Appl. Math, Vol.3, (1950) pp. 45-101. https://doi.org/10.1002/cpa.3160030106
  14. Linton C.M., Evans D.V., The interaction of waves with arrays of vertical circular cylinders, J. Fluid Mech., Vol.215, (1990) pp. 549-569. https://doi.org/10.1017/S0022112090002750
  15. Malenica S. & S. Etienne, A propos des methodes semi-analytiques pour les differents problemes de diffraction-radiation par un cylindre tronque., Proc. of 5ieme Journees de l'Hydro dynamique, Rouen, France (1995).
  16. Malenica S., P.J. Clark & B.Molin, 1994. Wave and current forces on a vertical cylinder free to surge and sway, Appl. Ocean Res., Vol.17. 1995.
  17. Malenica S., Molin B., Third harmonic wave diffraction by a vertical cylinder, J. Fluid Mech., Vol. 302, (1995) pp. 203-229. https://doi.org/10.1017/S0022112095004071
  18. Malenica S., Some aspects of water wave diffraction-radiation at small forward speed, Brodogradnja, Vol. 45, (1997) pp.35-43.
  19. Malenica S., R. Eatock Taylor & J.B. Huang, Semi-analytical solution for second order water wave diffraction by an array of vertical cylinders, Submitted to J. Fluid Mechanics (1998).
  20. Malenica S., Hydroelastic coupling of beam structural model with 3D hydro dynamic model, 2nd Int. Conf. on Hydroelasticity, Fukuoka, Japan (1998).
  21. Matsui T., Yeob L.S. & Kimitoshi S., Hydro dynamic forces on a vertical cylinder incurrent and waves, J. of the Soc. of Naval Arch. of Japan, Vol.170, pp. 277-287 (in Japanese), (1991).
  22. Molin B., Second order hydrodynamics applied to moored structures, Ship Tech. Research, Vol. 41/2 (1994).
  23. Newman J.N., Wave effects on deformable bodies, Applied Ocean Research, Vol. 16, (1994) pp.47-59. https://doi.org/10.1016/0141-1187(94)90013-2
  24. Newman J.N., The second order wave force on a vertical cylinder, J. Fluid Mech. (1996)
  25. Noblesse F. & X.B. Chen, Decomposition of free surface effects into wave and near-field components, Ship Technology Res., Vol. 42/4 (1995).
  26. Nossen J., J. Grue & E. Palm, Wave forces on three-dimensional floating bodies with small forward speed, J. Fluid Mech., Vol.227,(1991) pp. 135-160. https://doi.org/10.1017/S002211209100006X
  27. Senjanovic I., Finite element method in the analysis of ship structures, University Zagreb, Faculty of Mechanical Engg. and Naval Arch (1986).