船舶迎浪中考虑波浪增阻影响的参数横摇预报
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摘要
航行在波浪中的船舶,当横摇频率等于或接近遭遇频率的一半时,横摇运动最明显,这种横摇运动被称为参数横摇。参数横摇是船舶在波浪中三种典型倾覆现象——纯稳性丧失,参数横摇,横甩——之一,是波浪中船舶复原力变化引起的非线性现象。
1998年,巴拿马型C11集装箱船APL CHINA号在北太平洋海域迎浪时遭遇严重参数横摇,横摇角甚至达40°,损失400个集装箱,其他货物几乎全部受到损坏。经过这次事故,参数横摇引起船舶界的重视,参数横摇是大型集装箱船在纵浪中最危险的现象之一。其后一艘汽车卡车专运船在北大西洋亚舒尔群岛也遭遇严重的迎浪参数横摇。这些严重的参数横摇事故促使人们要对国际海事组织(IMO)的完整稳性规范(Intact Stability Code (IS code))进行重新评估,研究制定基于性能的衡准代替现有的描述性衡准,这个新的基于性能的衡准中就包括三种典型倾覆现象之一的参数横摇。在现阶段,需要一个具有定量精确性的参数横摇预报方法。第24(2004)届和25(2008)届ITTC之波浪稳性委员会也把参数横摇预报研究作为其一个主要任务。因此,急需开发一个准确的方法来预报参数横摇。
参数横摇是时变的复原力力臂导致的横摇运动,评估复原力变化是参数横摇预报的关键。一般采用和静水中复原力臂计算相似的原理来计算波浪中复原力臂,把排水量不变和纵倾平衡作为约束条件。也就是说船—波瞬时相对位置是由船舶重力—浮力平衡和纵倾力矩平衡来决定的。这种方法可以用来研究波浪中船舶复原力变化规律,然而在波浪中船舶横摇运动还伴随着垂荡和纵摇运动,尤其是在迎浪中更为明显。因此,在预报迎浪参数横摇时应该考虑用垂荡和纵摇运动确定船—波瞬时相对位置,以提高迎浪参数横摇预报精度。
为提高参数横摇预报精度,首先,基于切片理论,求解出船舶无横倾时在波浪中时间序列垂荡和纵摇运动,用垂荡纵摇运动确定船—波瞬时相对位置,也就是说横摇复原力的Froude-Krylov部分是通过对波浪压力沿船长湿表面积分得到的,船长瞬时湿表面由无横倾时的垂荡纵摇运动确定的船—波瞬时相对位置确定。其次,考虑了由作用在横倾船舶上的辐射力和绕射力组成的动态复原力的影响。
纵荡运动也影响时域内船—波瞬时相度位置,纵荡运动可能会调节复原力变化周期,这会在一定程度上影响参数横摇。在考虑垂荡、纵摇的基础上,进一步考虑了纵荡和波浪增阻对迎浪规则波中参数横摇数值预报的影响。随浪中,遭遇频率远低于垂荡和纵摇的固有频率,因此和垂荡纵摇的耦合不是很明显,另外随浪中波浪增阻通常很小但迎浪中,参数横摇预报很复杂,这是因为和垂荡纵摇的耦合很明显,同时波浪增阻不能忽视。本论文中,不仅研究了垂荡纵摇运动对参数横摇的影响,也进一步研究了波浪增阻对参数横摇的影响。本文尝试开发一个预报迎浪参数横摇的数值方法,在这个方法中复原力变化和波浪增阻的Kochin函数的计算都基于切片理论。
在耐波性领域,目前有许多对波浪增阻计算方法的验证,主要集中在短波长情况,这是因为大型船的能量消耗依赖于这种短波长情况。其中之一,Kashiwagi等采用一艘modified Wigley船型对其计算波浪增阻的Enhanced Unified theory (EUT)方法的有效性作了一系列系统研究。本文采用了相同的Wigley船型,在计算波浪增阻时采用了不同的源密度分布函数,并和Kashiwagi的试验结果以及他的EUT计算结果进行了比较。通过比较,确认Maruo & Ishii的方法更适合迎浪规则波中参数横摇预报。
另一方面,为找出迎浪规则波中参数横摇和波浪增阻的内在联系,应该研究参数横摇对波浪增阻的影响。波浪增阻主要是由船舶运动产生的辐射势以及入射波碰到船体后产生的绕射势导致的能量损耗造成的。Maruo公式在线性势流理论框架里作为完整的理论被广泛接受,其公式推导是基于动量和能量守恒定律。在线性船舶动力学里,船舶摇动频率等于遭遇频率,纵浪中没有横摇、横荡和艏摇运动发生。目前为止所有的波浪增阻计算方法都没有考虑迎浪参数横摇导致的辐射势,没有讨论参数横摇对波浪增阻的影响。基于Maruo波浪增阻理论,从理论上推导出迎浪规则波中考虑参数横摇时的波浪增阻新公式。同时把数值计算结果和发生迎浪参数横摇的自由航模试验做一比较。
把规则波中参数横摇预报方法拓展到不规则波中,在考虑垂荡、纵摇的基础上,进一步考虑了纵荡和波浪增阻对迎浪长峰不规则波中参数横摇数值预报的影响。本文研究了三种计算迎浪不规则波中波浪增阻的方法,然后把考虑了迎浪不规则波中时变波浪增阻的Pinkster方法进一步延伸作了研究。前面已经确认每个谐波中的波浪增阻计算采用Maruo公式,其源密度分布函数采用Maruo & Ishii的方法。通过零航速的模型试验和数值模拟研究了迎浪不规则波中参数横摇的“实际非各态历经(practical non-ergodicity) "的特点,同时通过数值模拟研究了迎浪不规则波中波浪增阻对参数横摇的影响。
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.
1998年,巴拿马型C11集装箱船APL CHINA号在北太平洋海域迎浪时遭遇严重参数横摇,横摇角甚至达40°,损失400个集装箱,其他货物几乎全部受到损坏。经过这次事故,参数横摇引起船舶界的重视,参数横摇是大型集装箱船在纵浪中最危险的现象之一。其后一艘汽车卡车专运船在北大西洋亚舒尔群岛也遭遇严重的迎浪参数横摇。这些严重的参数横摇事故促使人们要对国际海事组织(IMO)的完整稳性规范(Intact Stability Code (IS code))进行重新评估,研究制定基于性能的衡准代替现有的描述性衡准,这个新的基于性能的衡准中就包括三种典型倾覆现象之一的参数横摇。在现阶段,需要一个具有定量精确性的参数横摇预报方法。第24(2004)届和25(2008)届ITTC之波浪稳性委员会也把参数横摇预报研究作为其一个主要任务。因此,急需开发一个准确的方法来预报参数横摇。
参数横摇是时变的复原力力臂导致的横摇运动,评估复原力变化是参数横摇预报的关键。一般采用和静水中复原力臂计算相似的原理来计算波浪中复原力臂,把排水量不变和纵倾平衡作为约束条件。也就是说船—波瞬时相对位置是由船舶重力—浮力平衡和纵倾力矩平衡来决定的。这种方法可以用来研究波浪中船舶复原力变化规律,然而在波浪中船舶横摇运动还伴随着垂荡和纵摇运动,尤其是在迎浪中更为明显。因此,在预报迎浪参数横摇时应该考虑用垂荡和纵摇运动确定船—波瞬时相对位置,以提高迎浪参数横摇预报精度。
为提高参数横摇预报精度,首先,基于切片理论,求解出船舶无横倾时在波浪中时间序列垂荡和纵摇运动,用垂荡纵摇运动确定船—波瞬时相对位置,也就是说横摇复原力的Froude-Krylov部分是通过对波浪压力沿船长湿表面积分得到的,船长瞬时湿表面由无横倾时的垂荡纵摇运动确定的船—波瞬时相对位置确定。其次,考虑了由作用在横倾船舶上的辐射力和绕射力组成的动态复原力的影响。
纵荡运动也影响时域内船—波瞬时相度位置,纵荡运动可能会调节复原力变化周期,这会在一定程度上影响参数横摇。在考虑垂荡、纵摇的基础上,进一步考虑了纵荡和波浪增阻对迎浪规则波中参数横摇数值预报的影响。随浪中,遭遇频率远低于垂荡和纵摇的固有频率,因此和垂荡纵摇的耦合不是很明显,另外随浪中波浪增阻通常很小但迎浪中,参数横摇预报很复杂,这是因为和垂荡纵摇的耦合很明显,同时波浪增阻不能忽视。本论文中,不仅研究了垂荡纵摇运动对参数横摇的影响,也进一步研究了波浪增阻对参数横摇的影响。本文尝试开发一个预报迎浪参数横摇的数值方法,在这个方法中复原力变化和波浪增阻的Kochin函数的计算都基于切片理论。
在耐波性领域,目前有许多对波浪增阻计算方法的验证,主要集中在短波长情况,这是因为大型船的能量消耗依赖于这种短波长情况。其中之一,Kashiwagi等采用一艘modified Wigley船型对其计算波浪增阻的Enhanced Unified theory (EUT)方法的有效性作了一系列系统研究。本文采用了相同的Wigley船型,在计算波浪增阻时采用了不同的源密度分布函数,并和Kashiwagi的试验结果以及他的EUT计算结果进行了比较。通过比较,确认Maruo & Ishii的方法更适合迎浪规则波中参数横摇预报。
另一方面,为找出迎浪规则波中参数横摇和波浪增阻的内在联系,应该研究参数横摇对波浪增阻的影响。波浪增阻主要是由船舶运动产生的辐射势以及入射波碰到船体后产生的绕射势导致的能量损耗造成的。Maruo公式在线性势流理论框架里作为完整的理论被广泛接受,其公式推导是基于动量和能量守恒定律。在线性船舶动力学里,船舶摇动频率等于遭遇频率,纵浪中没有横摇、横荡和艏摇运动发生。目前为止所有的波浪增阻计算方法都没有考虑迎浪参数横摇导致的辐射势,没有讨论参数横摇对波浪增阻的影响。基于Maruo波浪增阻理论,从理论上推导出迎浪规则波中考虑参数横摇时的波浪增阻新公式。同时把数值计算结果和发生迎浪参数横摇的自由航模试验做一比较。
把规则波中参数横摇预报方法拓展到不规则波中,在考虑垂荡、纵摇的基础上,进一步考虑了纵荡和波浪增阻对迎浪长峰不规则波中参数横摇数值预报的影响。本文研究了三种计算迎浪不规则波中波浪增阻的方法,然后把考虑了迎浪不规则波中时变波浪增阻的Pinkster方法进一步延伸作了研究。前面已经确认每个谐波中的波浪增阻计算采用Maruo公式,其源密度分布函数采用Maruo & Ishii的方法。通过零航速的模型试验和数值模拟研究了迎浪不规则波中参数横摇的“实际非各态历经(practical non-ergodicity) "的特点,同时通过数值模拟研究了迎浪不规则波中波浪增阻对参数横摇的影响。
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.
引文
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[24]Neves M A S and Rodriguez C. A Non-Linear Mathematical Model of Higher Order for Strong Parametric Resonance of the Roll Motion of Ship in Waves [J]. Marine Systems and Ocean Technology,2005,1(2):69-81.
[25]Brunswig J and Pereira R. Validation of Parametric Roll Motion Predictions for a Modern Containership Design. Proceedings of the 9th International Conference on Stability of Ships and Ocean Vehicles,2006[C]:157-168.
[26]Spanos D and Papanikolaou A. Numerical Simulation of Parametric Roll in Head Seas. Proceedings of the 9th International Conference on Stability of Ships and Ocean Vehicles, 2006[C]:169-180.
[27]Roberts J B. Effect of Parametric Excitation of Nonlinear Rolling Motion in Random Seas[J].Journal of Ship Research,1982,26:246-253.
[28]Bulian G, Francescutto A and Lugni C. On the Nonlinear Modeling of Parametric Rolling in Regular and Irregular Waves. Proceedings of the 8th International Stability of Ships and Ocean Vehicles,2003[C]:305-323.
[29]Levadou M and van't Veer R. Parametric Roll and Ship Design.Proceedings of the 9th International Conference on Stability of Ships and Ocean Vehicles,2006[C]:191-206.
[30]Bulian G, Francescutto A. On the Effect of Stochastic Variations of Restoring Moment in Long-crested Irregular Longitudinal Sea. Proceedings of the 9th International Stability of Ships and Ocean Vehicles,2006[C]:131-146.
[31]Themelis N and Spyrou K J. Probabilistic Assessment of Resonant Instability. Proceedings of the 9th International Stability of Ships and Ocean Vehicles,2006[C]:37-48.
[32]Belenky V, Yu H C and Weems K. Numerical Procedures and Practical Experience of Assessment of Parametric Roll of Container Carriers. Proceedings of the 9th International Conference on Stability of Ships and Ocean Vehicles,2006[C]:119-130.
[33]Paulling J R. Transverse Stability of Tuna Clippers. Fishing Boat of the World, edited by J.O.Traung, Fishing News Limited,1960,2:489-495.
[34]Nechaev Y. Modelling of Ship Stability in Waves.Sudostroenie Publishing,1989.(in Russian).
[35]Boroday I K. Ship Stability in Waves:On the Problem of Righting Moment Estimations for Ships in Oblique Waves. Proceedings of the 4th International Conference on Stability of Ships and Ocean Vehicles,1990[C]:441-451.
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[39]林焰,邢殿录,纪卓尚,杨栖.船舶随浪运动稳性仿真计算[J].海洋工程,1994.03：30-41.
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