舰船科学技术  2017, Vol. 39 Issue (2): 12-18 PDF

A study on direct assessment method of dead ship failure mode of the second generation intact stability
WANG Xin-yu, MAO Xiao-fei, OU Shan, WU Ming-hao
Wuhan University of Technology Department of Designing and Building for The Naval Architectureand Ocean Engineering, Wuhan 430063, China
Abstract: International maritime organization (IMO) is developing the second generation of the intact stability regulations, three levels of criteria will be proposed for each stability failure mode. The first and second levels of vulnerability criteria for dead ship mode have now been completed, but the third level vulnerability criteria, direct assessment, has not yet been formed. Direct-assessment method is the important content of the second generation intact stability currently. Based on the draft of the second level of vulnerability criteria of the dead ship mode-proposed on first meeting of the IMO sub-committee on ship design and construction (SDC1), using the mathematical model with one degree of freedom, the simulation programs of ship rolling in the beam wind and wave under extreme conditions are developed to calculate the ship-capsizing probability, the simulation results are compared with the model tests of the standard ship model CEHIPAR2792 to validate and evaluate the reliability of the numerical methods. Meanwhile, the references for the direct assessment method for this failure mode are provided to develop the method.
Key words: the second generation intact stability     dead ship failure mode     numerical simulation     direct assessment     model test     Monte Carlo simulation
0 引 言

IMO 目前正在制定船舶第二代完整稳性衡准相关草案，瘫船稳性薄弱性衡准是 5 个薄弱性衡准中的重要组成。瘫船稳性第 1 层和第 2 层薄弱性衡准草案是由意大利和日本在 SDC1 会议上提出并得到通过的[1]

Kubo 等[3]讨论了横风横浪联合作用下瘫船横摇运动数值模拟方案，提供了单自由度直接模拟方法。该方案模型相对简单，可以大幅缩短计算时间，经过试验验证具有一定的参考性。

1 单自由度横摇运动模型

 $I_{xx}'\ddot \theta + N(\dot \theta ) + D(\theta ) = M\text{，}$ (1)

 $T = 2\pi \sqrt {\frac{{I_{xx}'}}{{\Delta \cdot GM}}} \text{，}$ (2)

 $N(\dot \theta ) = {N_1}\dot \theta + {N_3}{\dot \theta ^3}\text{，}$ (3)

 $D(\theta ) = \Delta \cdot \sum\limits_{i = 1}^n {{C_i}{\theta ^{2i - 1}}}\text{，}$ (4)

 $I_{xx}'\ddot \theta + {N_1}\dot \theta + {N_3}{\dot \theta ^3} + \Delta \cdot \sum\limits_{i = 1}^n {{C_i}{\theta ^{2i - 1}}} = M\text{。}$ (5)
1.1 回复力矩项

 图 1 货物移动导致的横倾使GZ 改变 Fig. 1 Cargo shift changes theGZ

 $\begin{array}{l} \varphi + \alpha = 90^\circ\text{，} \\[5pt] \alpha + \beta + \theta = 90^\circ \text{，}\end{array}$

 $\beta = \varphi - \theta \text{，}$ (6)

 ${G_2}{Z_2} = G{Z_\theta } = {G_1}{Z_1} - GZ(\theta ) \times \cos (\beta ) \text{。}$ (7)

 图 2 不同固有横倾状态下的GZ 曲线 Fig. 2 GZ with different cargo shift

 $GZ(\theta ) = \sum\limits_{i = 1}^8 {{C_i}{\theta ^{2i - 1}}} \text{，}$ (8)
 图 3 初始状态正浮时的GZ 曲线拟合 Fig. 3 Fitting ofGZ

1.2 能量法求解衰减系数

 $N(\dot \theta ) = {N_1}\dot \theta + {N_3}{\dot \theta ^3}\text{，}$ (9)

 $E(t) = \frac{1}{2}{\dot \theta ^2} + \int_0^t {D(\theta )} \dot \theta {\rm d}t \text{。}$ (10)

 $E({t_{i + 1}}) - E({t_i}) = - \int_{{t_i}}^{{t_{i + 1}}} {N(\dot \theta )} \dot \theta {\rm d}t \text{，}$ (11)

 $\begin{split} \!\!\!\!\!\!Q({t_i}) = E({t_{i + 1}}) - E({t_i}) = \frac{1}{2}(\dot \theta _{i + 1}^2 - \dot \theta _i^2) + \int_{{t_i}}^{{t_{i + 1}}} {D(\theta )} \dot \theta {\rm d}t \text{，}\end{split}$ (12)

 $Q({t_i}) = {N_1}\int_{{t_i}}^{{t_{i + 1}}} {{{\dot \theta }^2}{\rm d}t} + {N_3}\int_{{t_i}}^{{t_{i + 1}}} {{{\dot \theta }^3}\dot \theta {\rm d}t} \text{。}$ (13)

 ${u_{i1}} = \int_{{t_i}}^{{t_{i + 1}}} {{{\dot \theta }^2}{\rm d}t} ,\;\;\;\;\;{u_{i{\rm{2}}}} = \int_{{t_i}}^{{t_{i + 1}}} {{{\dot \theta }^3}\dot \theta {\rm d}t} \text{，}$ (14)

 $Q({t_i}) = {N_1}{u_{i1}} + {N_3}{u_{i{\rm{2}}}} \text{，}$ (15)

 $\left[ {\begin{array}{*{20}{c}} {{u_{i1}}} & {{u_{i{\rm{2}}}}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{N_1}}\\ {{N_3}} \end{array}} \right] ={ Q} \text{。}$ (16)

 $\begin{array}{l} {N_1} = 0.278\text{，}\\[5pt] {N_3} = 1.74\text{。} \end{array}$ (17)

 图 4 模拟自由衰减与实验值对比 Fig. 4 Comparison of numerical and experimental free decay

2 波浪力矩的计算 2.1 波浪条件

 $I_{xx}'\ddot \theta + {B_1}\dot \theta + {B_3}{\dot \theta ^3} + \Delta GZ(\theta ) = M$ (18)

 $\ddot \theta + {b_1}\dot \theta + {b_3}{\dot \theta ^3} + \frac{\Delta }{{I_{xx}'}}\sum\limits_{i = 1}^8 {{C_i}{\theta ^{2i - 1}}} = m(t)\text{，}$ (19)

 $\left\{ \begin{array}{l} \dot x(t) = y(t)\text{，}\\ \dot y(t) = - {b_1}x(t) + {b_3}{x^3}(t) + \frac{\Delta }{{I_{xx}'}}\sum\limits_{i = 1}^8 {{C_i}{\theta ^{2i - 1}}} + m(t) \end{array} \right.\text{。}$ (20)

 $M(t) = \Delta GM \cdot {K_\phi }\Theta (t) \text{。}$ (21)

 $M(t) = \Delta GM \cdot {K_\phi }\sum\limits_{i = 1}^{{N_W}} {\frac{{{h_i}}}{{{\lambda _i}}}} s{\rm in}({\omega _i}t + {\varepsilon _i}) \text{。}$ (22)

 $M(t) = \Delta GM \cdot {K_\phi }\sum\limits_{i = 1}^{{N_W}} {\omega _i^2\sqrt {2{S_{wave}}({\omega _i})\delta \omega } } s{\rm in}({\omega _i}t + {\varepsilon _i})\text{，}$ (23)

ITTC 双参数谱：

 ${S_{wave}}({\omega _i}) = 173{\rm{ }}\frac{{H_{1/3}^2}}{{{T^4}\omega _i^5}}{\rm exp}(\frac{{ - 691}}{{{T^4}\omega _i^4}})\text{。}$ (24)

 图 5 试验采用的 ITTC 谱 Fig. 5 ITTC spectrum used in tests
2.2 有效波倾系数K

 ${\alpha _m} = {K_\phi }\alpha = {K_\phi }{\alpha _0}\sin \omega t = {\alpha _{{m_0}}}\sin \omega t\text{。}$ (25)

 图 6 简化的有效波倾系数 Fig. 6 Simplified effective wave slope coefficient
3 风倾力矩的计算

 $\begin{array}{l} \frac{{{M_{wind}}(t)}}{{(1 - \sin \phi )}} = 0.5 \times {\rho _{air}}{C_m}U_W^2{A_L}{H_C} +\\ {\rho _{air}}{C_m}U_W{A_L}{H_C}\chi (\omega )U(t)\text{。} \end{array}$ (26)

 图 7 横风作用示意图 Fig. 7 Diagram of the transversal wind
 $\begin{array}{l} U(t) = \sum\limits_{i = 1}^{{N_W}} {{b_i}\sin ({\omega _{wi}}t + {\varepsilon _i})}\text{，} \\[5pt] {b_i} = \sqrt {2{S_{wind}}({\omega _{wi}})\delta \omega } \text{，}\\[5pt] {S_{wind}}({\omega _{wi}}) = 4K\frac{{U_W^2}}{\omega }\frac{{X_D^2}}{{{{(1 + X_D^2)}^{4/3}}}}\text{，}\\[5pt] \chi ({\omega _w}) = \frac{1}{{1 + {{\left( {\frac{{{\omega _w}\sqrt {{A_L}} }}{{\pi {U_W}}}} \right)}^{4/3}}}}\text{。} \end{array}$ (27)

 图 8 风速 3 m/s Davenport 风谱 Fig. 8 Davenport wind spectrum

4 计算结果 4.1 初始固定横倾

4.2 规则波模拟及与试验的比较

 $\begin{array}{l} I_{xx}'\ddot \theta + {N_1}\dot \theta + {N_3}{{\dot \theta }^3} + \Delta \cdot \sum\limits_{i = 1}^n {{C_i}{\theta ^{2i - 1}}} =\\ \quad\quad\;\;\, \Delta \cdot GM \cdot {\alpha _{m0}} \cdot \sin (\textit{Ω} t)\text{，} \end{array}$ (28)
 ${\alpha _{m0}} = {K_\phi }{\alpha _0} = {K_\phi }\frac{{2\pi {\zeta _A}}}{\lambda } = {K_\phi }k{\zeta _A}\text{。}$ (29)

 图 9 规则波中模型试验结果与模拟对比 Fig. 9 Comparison of ship motion in regular waves between model tests and numerical results

4.3 不规则波中倾覆概率计算 4.3.1 不规则波数值模拟

 $0.002 = \frac{{\int_0^{{\omega _{\min }}} {S(\omega ){\rm d}\omega } }}{{\int_0^\infty {S(\omega ){\rm d}\omega } }} = \frac{{\int_{{\omega _{\max }}}^\infty {S(\omega ){\rm d}\omega } }}{{\int_0^\infty {S(\omega ){\rm d}\omega } }}\text{，}$ (30)

 $\zeta (t) = \sum\limits_{i = 1}^N {\sqrt {2S({\omega _i})\delta \omega } } {\rm {sin}}({\omega _i}t + {\varepsilon _i})\text{。}$ (31)

 图 10 数值模拟与试验测量波浪时历对比 Fig. 10 Comparison of irregular wave between model tests and numerical result

 图 11 数值模拟与试验测量船舶横摇运动时历对比 Fig. 11 Comparison of ship rolling on the irregular wave between model tests and numerical result

4.3.2 蒙特卡罗模拟

 $Pc = \frac{{Nc}}{N}\text{，}$ (32)

 $P(Nc) = \frac{{N!}}{{Nc!(N - Nc)!}}{p^{Nc}}{(1 - p)^{N - Nc}}\text{，}$ (33)

 $\Delta p = \frac{2}{{\sqrt N }}\sqrt {Pc(1 - Pc)} {z_{\alpha /2}}\text{，}$ (34)

 $Pc - \frac{{\Delta p}}{2} \leqslant p \leqslant Pc + \frac{{\Delta p}}{2}\text{。}$ (35)

4.3.3 倾覆概率计算

 图 12 船舶倾覆概率计算值和试验值对比 Fig. 12 Comparison of capsizing probability between model test and numerical result

5 结 语

1）船舶在不同初始横倾下的静稳性曲线变化明显，需重新计算，本文给出了计算方法。

2）采用能量法计算船舶横摇阻尼系数能够获得良好的结果，采用一次项加三次项多项式模拟 CEHIPAR2792标准模型阻尼力矩的方法结果可靠。

3）不规则波计算中，从模拟计算时历与实验值时历图比较来看，运动幅值的误差在可接受的范围内。这种单自由度直接模拟船舶在不规则风浪中横摇运动是可行的。

4）有效波倾系数的准确取值对波浪载荷计算具有重要影响，本文采用简化模型，并使用了 SDC1/INF.6 中的有效波倾值。在未来的研究中，有条件的情况下应采用试验法测量船舶有效波倾系数，使计算结果准确。

5）当船舶具有货物移动等造成的初始横倾角时，同等海况下的倾覆概率增加。因此在实际航行中，货物绑扎的检查尤为重要，由于绑扎不牢、横摇过大等原因导致货物移动，会使船舶倾覆风险大大增加，

6）单自由度计算未将其他自由度运动（如升沉、横荡、首摇等）考虑在内，相比于实际运动结果，理论预报必然存在误差。在今后的研究中，进行多自由度耦合研究是该失效模式直接评估方法发展的必然趋势。

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