﻿ 散货船三维时域波浪载荷计算研究
 舰船科学技术  2016, Vol. 38 Issue (8): 18-22 PDF

Study of the three-dimensional time-domain wave loads of a bulk carrier
YANG Jun, HU Jia-jun, WANG Xue-liang, ZHANG Fan, FENG Qian-dong
China Ship Scientific Research Center, Wuxi 214082, China
Abstract: When the three-dimensional potential flow theory is used to predict the motions and wave loads for ships, two different Green functions are available: transient Green function and Rankine source. Mixed-source method, which combines the transient Green function with the Rankine source, has the benefits of both. In this paper, the three-dimensional time-domain mixed-source method is studied. To verify this theory, motions and loads of a bulk carrier are calculated in time domain. The results are transformed from time domain into frequency domain. Finally, the RAOs of the vertical motions and loads of the bulk carrier under a constant forward speed case are compared with those of WASIM and experiment measurements. A good agreement between the results of the mixed-source method and WASIM is found. When the length of incoming wave is short, the results of mixed-source method and WASIM coincide well with observed values, however, they become greater than measured values when the length of incoming wave becomes large. Evaluations of these two methods agree better with experiment results in following sea cases compared to head sea cases.
Key words: bulk carrier     three-dimensional wave loads     mixed-source method     time domain
0 引言

1 三维时域混合源法理论简介

 ${\Phi _I}(x,y,z,t) = {\Phi _w}(x,y,z,t) + {\Phi _d}(x,y,z,t).$ (1)

 $\left\{ \begin{array}{l} {\nabla ^2}{\Phi _t} = 0\;\;\left( {在外域中} \right),\\ \frac{{{\partial ^2}{\Phi _t}}}{{\partial {t^2}}} + \frac{{\partial \Phi }}{{\partial z}} = 0\;\;\left( {在自由面上} \right),\\ \nabla {\Phi _t} \to 0\;\;\left( {在无穷远处} \right)\\ {\Phi _t} = \frac{{\partial {\Phi _t}}}{{\partial z}} = 0\;\;\left( {t = 0} \right) \end{array} \right.$ (4)

 $2\pi {\Phi _t}(P) + \iint_{SII} {\left[{{\Phi _t}(Q)\frac{{\partial G}}{{\partial n}} - \frac{{\partial {\Phi _t}(Q)}}{{\partial n}}G} \right]}dS = 0.$ (5)

 $\begin{gathered} {G^0} = \frac{1}{r} - \frac{1}{{r'}},r = \left| {PQ} \right|,r' = \left| {PQ'} \right|,P = (x,y,z),\hfill \\ Q = (\xi ,\eta ,\zeta ),Q{\text{'}} = (\xi ,\eta ,- \zeta ),\hfill \\ \end{gathered}$ (6)
 ${G^f} = 2\mathop \smallint \nolimits_0^\infty [1 - \cos (\sqrt {gk} (t - \tau ))]{e^{k(z + \zeta )}}{J_0}(kR){\text{d}}k$ (7)
 $\begin{gathered} P \ne Q,t \geqslant \tau ,\hfill \\ R = \sqrt {{{(x - \xi )}^2} + {{(y - \eta )}^2}} . \hfill \\ \end{gathered}$ (8)

 $2\pi \pi {\Phi _d}(P) + \iint_m {({\Phi _d}(Q)\frac{{\partial {G^0}}}{{\partial n}} - \frac{{\partial {\Phi _d}(Q)}}{{\partial n}}{G^0})dS = M(P,t),}$ (9)

$M({\text{P,t}})$是记忆部分：

 $\begin{gathered} M(P,t) = \mathop \smallint \nolimits_0^t {\text{d}}\tau \left\{ {\smallint \int\limits_{{S_m}} {({\Phi _t}\frac{{{\partial ^2}{G^f}}}{{\partial n\partial \tau }}} } \right. - \frac{{\partial {\Phi _t}}}{{\partial n}}\frac{{\partial {G^f}}}{{\partial \tau }}){\text{d}}S + \hfill \\ \quad \quad \quad \quad {\kern 1pt} \,\frac{1}{{\text{g}}}\int_{\Gamma m} {({\Phi _t}\frac{{{\partial ^2}{G^f}}}{{\partial {\tau ^2}}} - \frac{{\partial {\Phi _t}}}{{\partial \tau }}\;\frac{{\partial {G^f}}}{{\partial \tau }})} \left. {{V_N}dL} \right\}. \hfill \\ \end{gathered}$ (10)

 $\left\{ \begin{gathered} {\Phi _d} = {\Phi _t}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \hfill \\ \frac{{\partial {\Phi _d}}}{{\partial n}} = \frac{{\partial {\Phi _t}}}{{\partial n}},\left( {在控制面上} \right). \hfill \\ \end{gathered} \right.$ (11)

 $\left\{ \begin{gathered} \frac{{D\zeta }}{{Dt}} = \frac{{\partial {\Phi _d}}}{{\partial z}} + U \cdot \nabla \zeta {\text{,}} \hfill \\ \frac{{D{\Phi _d}}}{{Dt}} = - g\zeta + U \cdot \nabla {\Phi _d}. \hfill \\ \end{gathered} \right.$ (12)

 $p = - \rho (\frac{{\partial \Phi }}{{\partial t}} + gz{\text{ + }}\frac{{{{\left| {\nabla \Phi } \right|}^2}}}{2}){\text{.}}$ (13)
 $\left\{ \begin{gathered} F = \iint\limits_S {np{\text{d}}S}{\text{, }} \hfill \\ {M_G} = \iint\limits_S {(r \times n)p{\text{d}}S}. \hfill \\ \end{gathered} \right.$ (14)
 $\left\{ \begin{gathered} \frac{{{\text{d}}(MV)}}{{{\text{d}}t}} = F,\hfill \\ \frac{{{\text{d}}(I\omega + Mr \times V)}}{{{\text{d}}t}} = {M_G},\hfill \\ \end{gathered} \right.$ (15)

2 算例分析 2.1 船舶主尺度

 图 1 散货船网格示意图 Fig. 1 Grids on the surface of the bulk carrier
2.2 时域分析

 图 2 垂荡时域曲线 Fig. 2 The time history of heave

 图 3 纵摇时域曲线 Fig. 3 The time history of pitch

 图 4 船中垂向弯矩时域曲线 Fig. 4 The time history of vertical bending moment at midship

2.3 频域分析

 图 5 垂荡RAO Fig. 5 The RAO of heave

1）在随浪和顶浪海况下，l/L较小时（比如小于1.5），混合源结果和WASIM结果、模型试验符合地较好，l/L较大时，理论计算与试验结果之间有差别。总的来说，随浪工况理论计算结果与试验值符合地更好；波长船长比较大时顶浪工况2种理论计算结果和试验值相差较大。

 图 6 纵摇RAO Fig. 6 The RAO of pitch

 图 7 船中垂向弯矩RAO Fig. 7 The RAO of the vertical bending moment at midship

2）运动和载荷的RAO比较都显示出了这样规律：波长较短时，数值计算结果与模型试验结果值较接近，波长较长时，则差别较大。原因可能是混合源法和WASIM都需要对一定范围的自由面进行网格划分，而且自由面的尺寸不能太小，当波长增大后，自由面的范围没有相应进行调整，这需要进一步的研究。

3 结语

1）混合源法的计算结果和WASIM结果大体一致，均与试验结果相符，验证了该方法的可行性，可用于实际船舶载荷预报。

2）该方法在波长船长比小于1.2时与试验值很好地吻合，当波长较大时，则预报结果与试验值有一定差别；随浪计算结果比顶浪更贴近试验值。

 [1] ﻿LIN W M, ZHANG S, WEEMS K, et al. A mixed-source formulation for nonlinear ship-motion and wave-load simulations[C]//Proceedings of the 7th International Conference on Numerical Ship Hydrodynamics. Nantes, France: NSH, 1999: 131-122. [2] ZHANG S G, LIN W M, WEEMS K. A hybrid boundary-element method for non-wall-sided bodies with or without forward speed[C]//Proceedings of the 13th International Workshop on Water Waves and Floating Bodies. Alphen aan den Rijn, Netherlands: IWWWFB, 1998: 178-182. [3] LIU S K, PAPANIKOLAOU A. A time-domain hybrid method for calculating hydrodynamic forces on ships in waves[C]//Proceedings of the 13th Congress of International Maritime Association of Mediterranean. Istanbul, Turkey: IMAM, 2009. [4] 唐恺, 朱仁传, 缪国平, 等. 应用混合格林函数法计算波浪中浮体运动及离散参数取值的算例分析[J]. 中国造船 , 2015, 56 (1) :102–113. TANG Kai, ZHU Ren-chuan, MIAO Guo-ping, et al. Analysis of motions of floating body in waves by hybrid Green function method and discretization of parameters[J]. Shipbuilding of China , 2015, 56 (1) :102–113. [5] 唐恺, 朱仁传, 缪国平, 等.基于混合格林函数法的波浪中船舶时域运动计算[C]//2013年船舶水动力学学术会议论文集.西安:中国造船工程学会, 2013: 353-364. TANG Kai, ZHU Ren-chuan, MIAO Guo-ping, et al. Hybird green function method for time-domain analysis of motions of floating body in waves[C]//Conference on Ship Hydrodynamics. Xi'an: China Shipbuilding Engineering Society, 2013: 353-364. [6] 汪雪良, 胡嘉骏, 顾学康, 等.基于混合源方法的船舶在波浪中的响应预报[C]//2008年船舶水动力学学术会议暨中国船舶学术界进入ITTC30周年纪念会.杭州:中国造船工程学会, 2008: 190-197. WANG Xue-liang, HU Jia-jun, GU Xue-kang, et al. Numerical investigation on response of a ship in waves based on a mixed source formulation[C]//Conference on Ship Hydrodynamics. Hangzhou: China Shipbuilding Engineering Society, 2008: 190-197. [7] 刘应中, 缪国平. 船舶在波浪上的运动理论[M]. 上海: 海洋出版社, 1884 . [8] 丁军, 胡嘉骏. 20.5万吨散货船波激振动和砰击振动模型试验报告[R].中国船舶科学研究中心研究报告, 2013. [9] 丁军, 汪雪良, 田超, 等.大型散货船波激振动和砰击振动模型试验研究[C]//第二十五届全国水动力学研讨会暨第十二届全国水动力学学术会议文集(上册).北京:中国力学学会, 2013: 502-510. DING Jun, WANG Xue-liang, TIAN Chao, et al. Experimental investigations of springing and slamming responses of a large bulk carrier[C]//Proceedings of the 25th National Conference on Hydrodynamics. Beijing: Chinese Society of Theoretical and Applied Mechanics, 2013: 502-510. [10] SESAM. User Manual[Z]. Det Norsake Veritas, 2010.