Parametric Rolling Prediction Of Ships In Head Seas With Added Resistance Taken Into Account

When a ship sails in the seas, in case the roll frequency of the ship is equal to or near to half of the encounter frequency, this roll motion could be most significant, and is called as parametric rolling. Parametric rolling is one of the three typical dangerous phenomena-pure stability loss, parametric rolling, and broaching to-that could result in capsizing or cargo damage. Parametric rolling is a nonlinear phenomena induced by time-varying restoring arm.In 1998, a post-Panamax C11 class containership suffered heavy parametric rolling in the North Pacific Ocean. The maximum roll angle reached about 40°in head seas, with the loss of 400 containers and damage to almost as many others. Parametric rolling in longitudinal waves has attracted practical attention as a most dangerous phenomenon for large containerships. Similar incident of head-sea parametric rolling was reported for a PCTC in the Azores Islands waters. These serious accidents triggered off a review of the Intact Stability Code (IS Code) of the IMO, and it has been discussed to set performance-based criteria as an alternative to the existing prescribed criteria. The new performance-based criteria are requested to cover three major capsizing scenarios including parametric rolling as one of roll restoring variation problems. In this stage, a prediction method for parametric rolling with quantitative accuracy is required. The 24th (2005) and 25th (2008) ITTC's Specialist Committee on Stability in Waves also makes parametric rolling prediction as one of main tasks. Therefore, it is urgency to develop an exact method to predict parametric rolling.Because parametric rolling is roll motion induced by time-varying restoring arm, the estimation of roll restoring variation is essential for parametric rolling prediction. Similar principle to calculate restoring arm in clam water is used to calculate restoring variation in waves with the constraint of volume remaining constant and the constraint of trim balance. That is to say, the balance between ship weight and buoyancy and the balance of trim are used to determine the simultaneous relative position of the ship to waves. This method can be used to study the rule of restoring variation in waves, however, the roll motion is coupled with heave and pitch motions in waves, especially in head seas, so for improving the estimation precision of parametric rolling in head seas, heave and pitch motions should be used to determine the simultaneous relative position of the ship to waves.For improving the estimation precision of roll restoring variation, firstly, heave and pitch motions obtained by a strip theory applied to an upright hull is used to determine the simultaneous relative position of the ship to waves in time domain, that is to say, the nonlinear Froude-Krylov component of roll restoring variation is calculated by integrating wave pressure up to wave surface with heave and pitch motion obtained by a strip theory applied to an upright hull; secondly, the dynamic effect which consists of radiation and diffraction components is taken into account.Surge motion also affects the simultaneous relative position of the ship to waves in the time domain, and surge motion could modulate periodic restoring variation so that the parametric rolling to some extent could be deteriorated. Base on the study of parametric rolling pediction cosidering heave and pith motions, surge motion and added resistance are also taken into account to predict parametric rolling in head regular seas. In case of following waves, the encounter frequency is much lower than the natural frequencies of heave and pitch so that coupling with heave and pitch is not significant. In addition, added resistance in following waves is generally small. In case of head waves, however, prediction of parametric rolling is not so easy because coupling with heave and pitch are significant and added resistance cannot be ignored. In this thesis, not only effect of dynamic heave and pitch motions on parametric rolling is investigated, but effect of added resistance on parametric rolling is also further investigated. The author attempts to develop a numerical prediction method for parametric roll in head seas in which both the restoring variation and the Kochin function for added resistance are calculated with a strip theory.In the field of seakeeping, many attempts for validating calculation methods of added resistance were reported focusing on the comparison in the case of short wavelength. This is because energy consumption of larger ships depends on such short wavelength cases. Among them, Kashiwagi executed a systematic validation study of his Enhanced Unified theory (EUT) using a modified Wigley model. The author calculated added resistance with different methods of source distribution for the modified Wigley model, and compared the calculated results with Kashiwagi's experiment data and EUT results. Based on the comparison, it can be concluded that Maruo and Ishii's method is the most appropriate for the purpose of prediction of parametric rolling in regular head seas.In the other hand, in order to find out the inner relation between the parametric rolling and added resistance in regular head seas, the effect of parametric rolling on the added resistance in regular head seas should be studied. Added resistance in waves is mainly caused by energy dissipation when a ship generates radiation waves by oscillations and diffraction waves by an incident wave on the ship hull. Maruo obtained an exact formula for added resistance in waves, within linear potential theory, based on the principle of momentum and energy conservation in 1963. In linear ship dynamics the frequency of ship oscillations is equal to encounter frequency, and no roll, sway and yaw motions occur in longitudinal waves. All calculation methods of added resistance so far do not include wave radiations due to parametric rolling in head seas, and the effect of parametric rolling on added resistance cannot be discussed. Here based on Maruo'theory, the authors attempt to theoretically obtain a new formula for added resistance in regular head seas with parametric rolling taken into account, and then to compare its numerical calculation with free running experiment when parametric rolling occurs in head seas.The method of parametric rolling predictionin head regular seas is entended to predict parametric rolling in head long-crest irregular seas. Base on the study of parametric rolling pediction cosidering heave and pith motions, surge motion and added resistance are also taken into account to predict parametric rolling in head long-creast irregular seas. Three methods of calculating added resistance in irregular head seas were investigated and then Pinkster's method which considers the time-varying added resistance in irregular head seas is extended for further investigations in this thesis. As validated for the case of parametric rolling, the added resistance in each harmonic wave is calculated by Maruo's formula, in which the source distribution is estimated with the Maruo and Ishii's method. The "practical non-ergodicity" of parametric roll in irregular head seas is investigated by the model experiment at zero forward speed and the simulation, and the effect of added resistance in irregular head seas is investigated by the simulation.