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Prediction of Parametric Rolling in Irregular Head Waves

  • Hirotada Hashimoto
  • Naoya Umeda
Chapter
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 119)

Abstract

For providing a benchmark data for numerical codes for parametric roll prediction, a model experiment of a post-Panamax C11 class containership whose hull form is slightly modified from its original but opened for public was conducted and significant parametric rolling in irregular head waves was recorded. A 3DOF (degrees of freedom) numerical model based on the nonlinear strip theory is developed. The numerical code for time domain simulations is developed for the prediction of large amplitude of parametric roll both in regular and irregular head waves. Comparisons between the model experiment and the numerical simulations show good agreement under the consideration of dispersion due to practical non-ergodicity. By utilizing the developed numerical model, it was demonstrated that small height of the bilge keels is a major reason why significant parametric roll could happen for a C11 class post-Panamax containership in 1998.

Nomenclature

\(a_{ij}\)

Added mass/added moment of inertia

\(b_{1} , b_{2}\)

Linear and quadratic coefficients of roll damping

\(b_{ij}\)

Wave-making damping coefficient

\(F_{i}^{DF}\)

Diffraction force

\(F_{i}^{FK + B}\)

Froude-Krylov force and buoyancy

\(F_{n}\)

Froude number

g

Gravity

H

Wave height

Ixx

Roll moment of inertia

Iyy

Pitch moment of inertia

m

Ship mass

t

Time

\(\xi_{G}\)

Longitudinal position of centre of gravity

\(\phi\)

Roll angle

\(\lambda\)

Wave length

\(\theta\)

Pitch angle

\(\omega\)

Angular frequency

\(\zeta\)

Heave displacement

Notes

Acknowledgements

This work was supported by a Grant-in Aid for Scientific Research of the Japan Society for Promotion of Science (No. 20760558 & 21360427). The authors express their sincere gratitude to the ITTC (International Towing Tank), as well as MARIN, for providing geometric data of the modified C11 class containership for works on the development of the second generation intact stability criteria. The authors thank also Messrs. Yu Sanya and Yasuhiro Sogawa for their great contribution to this work.

References

  1. Belenky, V. L., (2004), On Risk Evaluation at Extreme Seas, Proceedings of the 7th International Ship Stability Workshop, pp. 188–202, Shanghai.Google Scholar
  2. Belenky, V. L., Degtyarev, A. B., Boukhanovsky, A. V., (1998), Probabilistic Qualities of Nonlinear Stochastic Rolling, Ocean Engineering, Vol. 25, pp. 1–25.Google Scholar
  3. Bulian, G., Francescutto, A., Umeda, N. and Hashimoto, H., (2008), Qualitative and Quantitative Characteristics of Parametric Ship Rolling in Random Waves in the Light of Physical Model Experiments, Ocean Engineering, Vol. 35, pp. 1661–1675.CrossRefGoogle Scholar
  4. France, W. N., Levadou, M., Treakle, T. W. et al., (2003), An Investigation of Head-Sea Parametric Roll and Its Influence on Container Lashing System, Marine Technology, 40(1), pp. 1–19.Google Scholar
  5. Hashimoto, H. and Umeda, N., (2012), Validation of a Numerical Simulation Model for Parametric Rolling Prediction Using a PCTC, Proceedings of the 11th International conference on Stability of Ships and Ocean Vehicles, Athens, Vol. 1, pp. 109–118.Google Scholar
  6. Hashimoto, H., Umeda, N. and Matsuda, A., (2011), Experimental Study on Parametric Roll of a Post-Panamax Containership in Short-Crested Irregular Waves, Contemporary Ideas on Ship Stability and Capsizing in Waves (Belenky, V.L., de Kat, J.O., Spyrou, K. and Umeda, N. eds.), Springer, pp. 267–276.Google Scholar
  7. Hua, J., Palmquist, M. and Lindgren, G., (2006), An Analysis of the Parametric Roll Events Measured Onboard the PCTC AIDA, Proceedings of the 9th International conference on Stability of Ships and Ocean Vehicles, Rio de Janeiro, Vol. 1, pp. 109–118.Google Scholar
  8. Levadou, M. and van’t Veer, R., (2006), Parametric Roll and Ship Design, Proceedings of the 9th International Conference on Stability of Ships and Ocean Vehicles Rio-de-Janeiro, Vol. 1, pp. 191–206.Google Scholar
  9. Munif, A., Ikeda, Y., Fujiwara, T. and Katayama, T., (2011), Parametric Roll Resonance of a Large Passenger Ship in Dead Ship Condition in All Heading Angles, Contemporary Ideas on Ship Stability and Capsizing in Waves (Belenky, V.L., de Kat, J.O., Spyrou, K. and Umeda, N. eds.), Springer, pp. 331–345.Google Scholar
  10. Neves, M. A. S., Pérez, N. A., Osvaldo, M. L. and Rodríguez, C. A., (2011), An Investigation of Head-Sea Parametric Rolling for Two Fishing Vessels, Contemporary Ideas on Ship Stability and Capsizing in Waves (Belenky, V.L., de Kat, J.O., Spyrou, K. and Umeda, N. eds.), Springer, pp. 231–252.Google Scholar
  11. Reed, A. M., (2011), 26th ITTC Parametric Roll Benchmark Study, Proceedings of the 12th International Ship Stability Workshop, Washington D.C., pp. 195–204.Google Scholar
  12. Salvesen, N., Tuck E. O. and Faltinsen, O., (1970), Ship Motions and Sea Load, TSNAME, Vol. 78.Google Scholar
  13. Spanos, D.A. and Papanikolaou, A., (2009), Benchmark Study on Numerical Simulation Methods for the Prediction of Parametric Roll of Ships in Waves, Proceedings of the 10th International Conference on Stability of Ships and Ocean Vehicles, St. Petersburg, pp. 1–9.Google Scholar
  14. Thompson, J. M. T. and Stewart, H. B., (2002), Nonlinear Dynamics and Chaos, second edition, John Wiley & Sons. Led (Chichester), pp. 191–192.Google Scholar
  15. Umeda, N., Hashimoto, H., Tsukamoto, I. and Sogawa, Y., (2011), Estimation of Parametric Resonance in Random Waves, Parametric Resonance in Dynamical Systems (Fossen, T. and Nijmeijer, H. eds.), Springer, pp. 45–62.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Naval Architecture and Ocean Engineering, Graduate School of EngineeringOsaka UniversitySuita, OsakaJapan

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