Skip to main content
SpringerLink
Log in

Fully nonlinear modeling of radiated waves generated by floating flared structures

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The nonlinear radiated waves generated by a structure in forced motion, are simulated numerically based on the potential theory. A fully nonlinear numerical model is developed by using a higher-order boundary element method (HOBEM). In this model, the instantaneous body position and the transient free surface are updated at each time step. A Lagrangian technique is employed as the time marching scheme on the free surface. The mesh regridding and interpolation methods are adopted to deal with the possible numerical instability. Several auxiliary functions are proposed to calculate the wave loads indirectly, instead of directly predicting the temporal derivative of the velocity potential. Numerical experiments are carried out to simulate the heave motions of a submerged sphere in infinite water depth, the heave and pitch motions of a truncated flared cylinder in finite depth. The results are verified against the published numerical results to ensure the effectiveness of the proposed model. Moreover, a series of higher harmonic waves and force components are obtained by the Fourier transformation to investigate the nonlinear effect of oscillation frequency. The difference among fully nonlinear, body-nonlinear and linear results is analyzed. It is found that the nonlinearity due to free surface and body surface has significant influences on the numerical results of the radiated waves and forces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Eatock Taylor, R., Hung, S.M.: Second order diffraction forces on a vertical cylinder in regular waves. Appl. Ocean Res. 9, 19–30 (1987)

    Article  Google Scholar 

  2. Abul-Azm, A.G., Williams, A.N.: Second-order diffraction loads on truncated cylinders. J. Waterway, Port, Coastal & Ocean Eng. 114, 436–454 (1988)

    Article  Google Scholar 

  3. Kim, Y., Kring, D.C., Sclavounos, P.D.: Linear and nonlinear interactions of surface waves with bodies by a three-dimensional Rankine panel method. Appl. Ocean Res. 19, 235–249 (1997)

    Article  Google Scholar 

  4. Bai, W., Teng, B.: Second-order wave diffraction around 3-D bodies by a time-domain method. China Ocean Eng. 15, 73–85 (2001)

    Google Scholar 

  5. Goren, O.: On the second-order wave radiation of an oscillating vertical circular in finite-depth water. J. Ship Res. 40, 224–234 (1996)

    Google Scholar 

  6. Isaacson, M., Ng, J.Y.T.: Second-order wave radiation of threedimensional bodies by time-domain method. Int. J. Offshore Polar Eng. 3, 264–272 (1993)

    Google Scholar 

  7. Teng, B., Bai, W., Dong, G.H.: Simulation of second-order radiation of 3D bodies in time domain by a B-spline method. In: Proc. of 12th International Offshore and Polar Engineering Conference, Kitakyushu, Japan, 487–493 (2002)

    Google Scholar 

  8. Wu, G.X.: Hydrodynamic forces on a submerged circular cylinder undergoing large-amplitude motion. J. Fluid Mech. 254, 41–58 (1993)

    Article  MATH  Google Scholar 

  9. Wu, G.X.: Hydrodynamic forces on a submerged sphere undergoing large amplitude motion. J. Ship Res. 38, 272–277 (1994).

    Google Scholar 

  10. Zhu, D.X., Katory.: A time-domain prediction method of ship motions. Ocean Eng. 25, 781–791 (1998)

    Article  Google Scholar 

  11. Koo, W.C, Kim, M.H.: Numerical simulation of nonlinear wave and force generated by a wedge-shape wave maker. Ocean Eng. 33, 983–1006 (2006)

    Article  Google Scholar 

  12. Ferrant, P.: A coupled time and frequency approach for nonlinear radiation. In: Proc. of 18th Symposium on Naval Hydro, Ann Arbor, Michigan, 67–83 (1991)

    Google Scholar 

  13. Qiu, W., Peng, H.: Numerical solution of body-exact problem in the time domain with a panel-free method. In: Proc. of 22nd IWWWFB, Plitvice, Croatia (2007)

    Google Scholar 

  14. Longuet-Higgins, M.S., Cokelet, C.D.: The deformation of steep surface waves on water: I. A numerical method of computation. Proc. R Soc. Lond. A. 350, 1–26 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ma, Q.W., Wu, G.X., Eatock Taylor, R.: Finite element simulation of fully non-linear interaction between vertical cylinders and steep waves—Part 1: Methodology and numerical procedure. Int J. Numer. Meth. Fluids 36, 265–285 (2001)

    Article  MATH  Google Scholar 

  16. Ma, Q.W., Wu, G.X., Eatock Taylor, R.: Finite element simulation of fully non-linear interaction between vertical cylinders and steep waves—Part 2: Numerical results and validation. Int J. Numer. Meth. Fluids 36, 287–308 (2001)

    Article  Google Scholar 

  17. Hu, P.X., Wu, G.X., Ma, Q.W.: Numerical simulation of nonlinear wave radiation by a moving vertical cylinder. Ocean Eng. 29, 1733–1750 (2002)

    Article  Google Scholar 

  18. Wu, G.X., Hu, Z.Z.: Simulation of nonlinear interactions between waves and floating bodies through a finite-element-based numerical tank. Proc. R. Soc. Lond. A 460, 2797–2817 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang, C.Z., Wu, G.X.: An unstructured mesh based finite element simulations of wave interactions with non-wall-sided bodies. J. Fluids Struct. 22, 441–461 (2006)

    Article  Google Scholar 

  20. Wang, C.Z., Wu, G.X., Drake, K.R.: Interactions between fully nonlinear water waves and non-wall-sided 3D structures. Ocean Eng. 34, 1182–1196 (2007)

    Article  Google Scholar 

  21. Xue, M., Xu, H., Liu, Y., et al.: Computations of fully nonlinear three dimensional wave-wave and wave-body interactions. Part 1. Dynamics of steep three-dimensional waves. J. Fluid Mech. 438, 11–39 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  22. Xue, M., Xu, H., Liu, Y., et al.: 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, 41–46 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  23. Bai, W., Eatock Taylor, R.: Higher-order boundary element simulation of fully nonlinear wave radiation by oscillating ver tical cylinders. Appl. Ocean Res. 28, 247–265 (2006)

    Article  Google Scholar 

  24. Bai, W., Eatock Taylor, R.: Numerical simulation of fully nonlinear regular and focused wave diffraction around a vertical cylinder using domain decomposition. Appl. Ocean Res. 29, 55–71 (2007)

    Article  Google Scholar 

  25. Bai, W., Eatock Taylor, R.: Fully nonlinear simulation of wave interaction with fixed and floating flaRes. structures. Ocean Eng. 36, 223–236 (2009).

    Article  Google Scholar 

  26. Bai, W., Feng, X., Eatick Taylor, R., et al.: Fully nonlinear analysis of near-trapping phenomenon around an array of cylinders. Appl. Ocean Res. 44, 71–81 (2014)

    Article  Google Scholar 

  27. Ning, D.Z., Zhou, B.Z., Teng, B., et al.: Numerical simulation of nonlinear regular and focused waves generated by a piston wave maker. In: Proc. of the 5th international conference on Asian and Pacific Coasts, Singapore (2009)

    Google Scholar 

  28. Zhou, B.Z., Teng. B, Ning, D.Z., et al.: Fully Nonlinear Wave Diffraction by a velocity potential division method. In: Proc. of the 22nd International Offshore and Polar Engineering Conference, Rhodes, Greece (2012)

    Google Scholar 

  29. Liu, Y.Z., Miao, G.P.: Theory of Ship Motions in Waves. Shanghai Jiao Tong University Press, Shanghai (1987) (in Chinese)

    Google Scholar 

  30. Ning, D.Z., Zhou, B.Z., Teng, B.: Numerical simulation of nonlinear wave generation by a piston wave maker in a steptype wave flume. Advances in Eng. Res. 2 (2011)

  31. Wu, G.X.: Transient motion of a floating body in steep water waves. In: Proc. of 11th IWWWFB, Hamburg, Germany (1996)

    Google Scholar 

  32. Wu, G.X., Eatock Taylor, R.: The coupled finite element and boundary element analysis of nonlinear interactions between waves and bodies. Ocean Eng. 30, 387–400 (2003)

    Article  Google Scholar 

  33. Kashiwagi, M.: Non-linear simulations of wave-induced motions of a floating body by means of the mixed Eulerian-Lagrangian method. In: Proc. Inst. Mech. Engrs. C, 214, 841–855 (2000)

    Article  Google Scholar 

  34. Grilli, S.T., Guyenne, P., Dias, F.A.: Fully non-linear model for three-dimensional overturning waves over an arbitrary bottom. Int. J. Numer. Meth. Fluids 35, 829–867 (2001)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Ship Building Engineering, Harbin Engineering University, 150001, Harbin, China

    Bin-Zhen Zhou

  2. State Kay Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, 116023, Dalian, China

    Bin-Zhen Zhou, De-Zhi Ning & Bin Teng

  3. School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith, 2751, NSW, Australia

    Ming Zhao

Authors
  1. Bin-Zhen Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. De-Zhi Ning
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Teng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ming Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Teng.

Additional information

The project was supported by the National Natural Science Foundation of China (51222902, 51221961, and 51379032), the Program for New Century Excellent Talents in University (NCET-13-0076), The Fundamental Research Fund for the Central University (HEUCF140103), The Open Fund of State Key Laboratory of Coastal and Offshore Engineering (LP1407), and the Lloyd’s Register Foundation (LRF) through the Joint Centre Involving University College London, Shanghai Jiaotong University and Harbin Engineering University.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, BZ., Ning, DZ., Teng, B. et al. Fully nonlinear modeling of radiated waves generated by floating flared structures. Acta Mech Sin 30, 667–680 (2014). https://doi.org/10.1007/s10409-014-0045-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-014-0045-6

Keywords

Search

Navigation