Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-12-01T03:54:25.282Z Has data issue: false hasContentIssue false
  • English
  • Français

Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth

Published online by Cambridge University Press:  14 August 2014

Bo T. Paulsen ,
H. Bredmose ,
H. B. Bingham  and
N. G. Jacobsen
Bo T. Paulsen*
Affiliation:
Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark Deltares, Rotterdamseweg 185, 2629HD Delft, The Netherlands
H. Bredmose
Affiliation:
Department of Wind Energy, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
H. B. Bingham
Affiliation:
Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
N. G. Jacobsen
Affiliation:
Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark Deltares, Rotterdamseweg 185, 2629HD Delft, The Netherlands
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Forcing by steep regular water waves on a vertical circular cylinder at finite depth was investigated numerically by solving the two-phase incompressible Navier–Stokes equations. Consistently with potential flow theory, boundary layer effects were neglected at the sea bed and at the cylinder surface, but the strong nonlinear motion of the free surface was included. The numerical model was verified and validated by grid convergence and by comparison to relevant experimental measurements. First-order convergence towards an analytical solution was demonstrated and an excellent agreement with the experimental data was found. Time-domain computations of the normalized inline force history on the cylinder were analysed as a function of dimensionless wave height, water depth and wavelength. Here the dependence on depth was weak, while an increase in wavelength or wave height both lead to the formation of secondary load cycles. Special attention was paid to this secondary load cycle and the flow features that cause it. By visual observation and a simplified analytical model it was shown that the secondary load cycle was caused by the strong nonlinear motion of the free surface which drives a return flow at the back of the cylinder following the passage of the wave crest. The numerical computations were further analysed in the frequency domain. For a representative example, the secondary load cycle was found to be associated with frequencies above the fifth- and sixth-harmonic force component. For the third-harmonic force, a good agreement with the perturbation theories of Faltinsen, Newman & Vinje (J. Fluid Mech., vol. 289, 1995, pp. 179–198) and Malenica & Molin (J. Fluid Mech., vol. 302, 1995, pp. 203–229) was found. It was shown that the third-harmonic forces were estimated well by a Morison force formulation in deep water but start to deviate at decreasing depth.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave breaking Waves/Free-surface Flows: Wave-structure interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , pp. 1 - 34
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bai, W. & Eatock-Taylor, R. 2007 Numerical simulation of fully nonlinear regular and focused wave diffraction around a vertical cylinder using domain decomposition. Appl. Ocean Res. 29 (1–2), 55–71.CrossRefGoogle Scholar
Berberović, E., van Hinsberg, N., Jakirlić, S., Roisman, I. & Tropea, C. 2009 Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution. Phys. Rev. E 79, 036306.Google Scholar
Bredmose, H., Mariegaard, J., Paulsen, B. T., Jensen, B., Schløer, S., Larsen, T. J., Kim, T. & Hansen, A. M.2013 The wave loads project. Final report for the ForskEL 10495 Wave Loads project. DTU Wind Energy Report E-0045.Google Scholar
Chaplin, J. R., Rainey, R. C. T. & Yemm, R. W. 1997 Ringing of a vertical cylinder in waves. J. Fluid Mech. 350, 119–147.Google Scholar
Engsig-Karup, A. P., Bingham, H. B. & Lindberg, O. 2009 An efficient flexible-order model for 3D nonlinear water waves. J. Comput. Phys. 228 (6), 2100–2118.Google Scholar
Faltinsen, O. M., Newman, J. N. & Vinje, T. 1995 Nonlinear wave loads on a slender vertical cylinder. J. Fluid Mech. 289, 179–198.Google Scholar
Fenton, J. D. 1988 The numerical solution of steady water wave problems. Comput. Geosci. 14 (3), 357–368.Google Scholar
Fenton, J. D. 1990 Nonlinear wave theories. In Ocean Engineering (ed. Mehaute, Le. & Hanes, D. M.), vol. 9, pp. 1–18. Wiley.Google Scholar
Ferrant, P. 1995 Nonlinear wave loads and runup upon a surface piercing cylinder. In International Workshop for Water Waves and Floating Bodies (IWWWFB), Department of Engineering Science, University of Oxford, Oxford (ed. Eatock Taylor, R.).Google Scholar
Ferrant, P.1999 Fully nonlinear interactions of long-crested wavepackets with a three-dimensional body. In Twenty-Second Symposium on Naval Hydrodynamics, pp. 405–415.Google Scholar
Grue, J. 2002 On four highly nonlinear phenomena in wave theory and marine hydrodynamics. Appl. Ocean Res. 24 (5), 261–274.CrossRefGoogle Scholar
Grue, J. & Huseby, M. 2002 Higher-harmonic wave forces and ringing of vertical cylinders. Appl. Ocean Res. 24 (4), 203–214.Google Scholar
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225.Google Scholar
Huseby, M. & Grue, J. 2000 An experimental investigation of higher-harmonic wave forces on a vertical cylinder. J. Fluid Mech. 414, 75–103.Google Scholar
Jacobsen, N. G., Fuhrman, D. R. & Fredsø, J. 2012 A wave generation toolbox for the open-source CFD library: openfoam® . Intl J. Numer. Meth. Fluids 70 (9), 1073–1088.CrossRefGoogle Scholar
Jefferys, E. R. & Rainey, R. C. T. 1994 Slender body models of TLP and GBS ringing. In Seventh International Conference on the Behaviour of Offshore Structures (ed. Chryssostomidis, C.). Pergamon.Google Scholar
Jefferys, R. 1993 A slender body model of ringing. In International Workshop for Water Waves and Floating Bodies, IWWWFB, Institute for Marine Dynamics, St John’s, Newfoundland, Canada (ed. Pawlowski, J.).Google Scholar
Johannessen, T. B. 2011 Nonlinear superposition methods applied to continuous ocean wave spectra. Trans. ASME: J. Offshore Mech. Arctic Engng 134, 011302.Google Scholar
Krokstad, J. R. & Solaas, F.2000 Study of nonlinear local flow. In International Offshore and Polar Engineering Conference, Seattle, vol. 3.Google Scholar
Krokstad, J. R. & Stansberg, C. T. 1995 Ringing load models verified against experiments. In OMAE 1995, 14th International Conference on Offshore Mechanics and Arctic Engineering, 18–22 June 1995, Copenhagen, Denmark, vol. I, pp. 223–233. ASME.Google Scholar
Krokstad, J. R., Stansberg, C. T., Nestegaard, A. & Marthinsen, T. 1998 A new non-slender ringing load approach verified against experiments. Trans. ASME: J. Offshore Mech. Arctic Engng 120, 20–29.Google Scholar
Langen, I., Skjåstad, O. & Haver, S. 1998 Measured and predicted dynamic behaviour of an offshore gravity platform. Appl. Ocean Res. 20, 15–26.Google Scholar
Lighthill, J. 1986 Fundamentals concerning wave loading on offshore structures. J. Fluid Mech. 173, 667–681.Google Scholar
Liu, Y., Xue, M. & Yue, D. K. P. 2001 Computations of fully nonlinear three-dimensional wave–wave and wave–body interactions. Part 2. Nonlinear waves and forces on a body. J. Fluid Mech. 438, 41–66.CrossRefGoogle Scholar
Madsen, P. A. & Sørensen, O. R. 1993 Bound waves and triad interactions shallow water in shallow water. J. Ocean Engng 20 (4), 359–388.Google Scholar
Malenica, Š. & Molin, B. 1995 Third-harmonic wave diffraction by a vertical cylinder. J. Fluid Mech. 302, 203–229.Google Scholar
Manners, W. & Rainey, R. C. T. 1992 Hydrodynamic forces on fixed submerged cylinders. Proc. R. Soc. Lond. A 436, 13–32.Google Scholar
Morison, J. R., O’Brien, M. P., Johnson, J. W. & Schaaf, S. A. 1950 The forces exerted by surface waves on piles. J. Petrol. Tech. 2 (5), 149–154.CrossRefGoogle Scholar
Natvig, B. J. & Teigen, P. 1993 Review of hydrodynamic challenges in TLP design. Intl Offshore Polar Engng Conf. 3 (4), 243–249.Google Scholar
Newman, J. N.1994 Nonlinear scattering of long waves by a vertical cylinder. In Symposium in Honour of Professor Enok Palm, Oslo.Google Scholar
Nielsen, A. W., Schlutter, F., Sørensen, J. V. T. & Bredmose, H.2012 Wave loads on a monopile in 3D waves. In International Conference on Ocean, Offshore and Arctic Engineering, pp. 1–10.Google Scholar
Paulsen, B. T., Bredmose, H. & Bingham, H. B. 2014 An efficient domain decomposition strategy for wave loads on surface piercing circular cylinders. Coast. Engng 86, 57–76.CrossRefGoogle Scholar
Rainey, R. C. T. 1995 Slender-body expressions for the wave load on offshore structures. Proc. R. Soc. Lond. A 450, 391–416.Google Scholar
Rainey, R. C. T. 2007 Weak or strong nonlinearity: the vital issue. J. Engng Maths 58, 229–249.Google Scholar
Rainey, R. C. T. & Chaplin, J. R. 2003 Wave breaking and cavitation around a vertical cylinder: experiments and linear theory. In International Workshop for Water Waves and Floating Bodies (ed. Clement, A. H. & Ferrant, P.), pp. 1–6. Ecole Centrale de Nantes.Google Scholar
Schäffer, H. a. & Steenberg, C. M. 2003 Second-order wavemaker theory for multidirectional waves. Ocean Engng 30 (10), 1203–1231.CrossRefGoogle Scholar
Sumer, B. M. & Fredsø, J. 2006 Hydrodynamics Around Cylindrical Structures. World Scientific.Google Scholar
Williams, J. M. 1981 Limiting gravity waves in water of finite depth. Phil. Trans. R. Soc. Lond. A 302 (1466), 139–188.Google Scholar