Mathematical model of ship motion in regular wave based on three-dimensional time-domain Green function method
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摘要: 在小时间区域采用级数展开法, 在大时间区域采用渐进展开法, 在大、小时间过渡区域采用精细积分法, 对三维时域Green函数进行数值计算; 采用线性叠加原理求解船舶辐射与绕射问题, 构造出船舶在规则波浪中的运动数学模型, 并采用数值方法计算WigleyⅠ型船舶和S60型船舶以Froude数为0.2迎波浪航行时的水动力系数、波浪激励力与运动时间历程。计算结果表明: 由于不规则频率的影响, 当量纲一频率为1.7时, WigleyⅠ型船舶的垂荡附加质量计算结果比试验结果小44%, 当量纲一频率为2.5时, S60型船舶的纵摇阻尼系数计算结果比试验结果小43%;随着入射波频率的增加, WigleyⅠ型船舶和S60型船舶的水动力系数和波浪激励力的大部分计算结果与试验结果的相对误差小于30%, 且二者的变化趋势一致; 对于WigleyⅠ型船舶, 当波长与船长比为1.25时, 采用三维时域方法计算的垂荡幅值响应因子和纵摇幅值响应因子分别比试验值小11.3%和4.8%, 采用三维频域方法计算的垂荡幅值响应因子比试验值大48.4%, 纵摇幅值响应因子比试验值小48.4%, 当波长与船长比为1.50时, 采用三维时域方法计算的垂荡幅值响应因子和纵摇幅值响应因子分别比试验值小3.0%和11.3%, 采用三维频域方法计算的垂荡幅值响应因子比试验值大9.8%, 纵摇幅值响应因子比试验值小23.6%。可见, 采用三维时域方法能准确地仿真船舶在波浪中的运动时间历程。Abstract: The series expansion method was adopted in the short time interval region, the asymptotic expansion method was adopted in the long time interval region, and the precise integration method was adopted in the transitional region between the short and long time interval regions to numerically calculate the three-dimensional time-domain Green function. The radiation and diffraction problems of ship were solved by the linear superposition principle. The ship motion mathematical model in regular wave was formulated. The hydrodynamic coefficients, wave exciting forces and motion time histories of a Wigley Ⅰ hull and a S60 hull were calculated by the numerical method when they sail on the wave with a Froude number of 0.2. Calculation result shows that due to the influence of irregular frequencies, when the dimensionless frequency is 1.7, the numerical result of heave added mass of Wigley Ⅰ hull is 44% smaller than the test result. When the dimensionless frequency is 2.5, the numerical result of pitch damping coefficient of S60 hull is 43% smaller than the test result. As the incident wave frequency increases, for a Wigley Ⅰ hull and a S60 hull, the relative errors of hydrodynamic coefficients and wave exciting forces between most of the numerical results and the test results are less than 30%, and the two have a same variation trend. For a Wigley Ⅰ hull, when the ratio of wave length to ship length is 1.25, the heave response amplitude operator and the pitch response amplitude operator calculated by the three-dimensional time-domain method are 11.3% and 4.8% smaller than the test values, respectively, the heave response amplitude operator calculated by the three-dimensional frequency-domain method is 48.4% larger than the test value, and the pitch response amplitude operator is 48.4% smaller than the test value. When the ratio of wave length to ship length is 1.50, the heave response amplitude operator and the pitch response amplitude operator calculated by the three-dimensional time-domain method are 3.0% and 11.3% smaller than the test values, respectively, the heave response amplitude operator calculated by the three-dimensional frequency-domain method is 9.8% larger than the test value, and the pitch response amplitude operator is 23.6% smaller than the test value. Thus, the three-dimensional time-domain method can accurately simulate the time history of ship motion in wave.
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图 6 Wigley Ⅰ型船舶量纲一垂荡阻尼系数
Figure 6. Dimensionless heave damping coefficients of Wigley Ⅰ hull
图 8 Wigley Ⅰ型船舶量纲一纵摇阻尼系数
Figure 8. Dimensionless pitch damping coefficients of Wigley Ⅰ hull
图 13 Wigley Ⅰ型船舶量纲一垂荡波浪力幅值
Figure 13. Dimensionless heave wave exciting force amplitudes of Wigley Ⅰ hull
图 14 Wigley Ⅰ型船舶量纲一纵摇波浪力幅值
Figure 14. Dimensionless pitch wave exciting force amplitudes of Wigley Ⅰ hull
图 15 S60型船舶量纲一垂荡波浪力幅值
Figure 15. Dimensionless heave wave exciting force amplitudes of S60 hull
图 16 S60型船舶量纲一纵摇波浪力幅值
Figure 16. Dimensionless pitch wave exciting force amplitudes of S60 hull
图 17 λ/L为1.25时Wigley Ⅰ型船舶量纲一垂荡运动时间历程
Figure 17. Dimensionless heave motion time histories of Wigley Ⅰ hull when λ/L is 1.25
图 18 λ/L为1.25时Wigley Ⅰ型船舶量纲一纵摇运动时间历程
Figure 18. Dimensionless pitch motion time histories of Wigley Ⅰ hull when λ/L is 1.25
图 19 λ/L为1.50时Wigley Ⅰ型船舶量纲一垂荡运动时间历程
Figure 19. Dimensionless heave motion time histories of Wigley Ⅰ hull when λ/L is 1.50
图 20 λ/L为1.50时Wigley Ⅰ型船舶量纲一纵摇运动时间历程
Figure 20. Dimensionless pitch motion time histories of Wigley Ⅰ hull when λ/L is 1.50
图 21 λ/L为2.0时Wigley Ⅰ型船舶量纲一垂荡运动时间历程
Figure 21. Dimensionless heave motion time histories of Wigley Ⅰ hull when λ/L is 2.0
图 22 λ/L为2.0时Wigley Ⅰ型船舶量纲一纵摇运动时间历程
Figure 22. Dimensionless pitch motion time histories of Wigley Ⅰ hull when λ/L is 2.0
表 1 不同方法计算所得f (0, β) 的相对误差
Table 1. Relative errors of f (0, β) calculated by different methods
计算方法 β取值不同时各方法计算结果与解析解的相对误差 2.53 6.26 9.15 12.48 4阶Runge-Kutta法 3.0×10-5 2.9×10-2 -2.5×10-2 6.8×10-3 精细积分法 1.3×10-16 4.7×10-14 6.3×10-15 -5.1×10-14 
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表 2 Wigley Ⅰ型船舶与S60型船舶的参数
Table 2. Parameters of Wigley Ⅰand S60 hulls
船型 船长L/m 船宽/m 吃水/m 排水量/m3 纵摇惯性半径 重心距离基线距离/m 方形系数 Wigley Ⅰ 3 0.3 0.187 5 0.094 6 0.25L 0.17 0.56 S60 140 20 8 15 680 0.25L 8 0.70
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[1] 金一丞, 尹勇. 公约、技术与航海模拟器的发展[J]. 中国航海, 2010, 33 (1): 1-6. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGHH201001002.htmJIN Yi-cheng, YIN Yong. Maritime simulators: convention and technology[J]. Navigation of China, 2010, 33 (1): 1-6. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGHH201001002.htm [2] 钱小斌, 尹勇, 张秀凤, 等. 海上不规则波浪扰动对船舶运动的影响[J]. 交通运输工程学报, 2016, 16 (3): 116-124. doi: 10.3969/j.issn.1671-1637.2016.03.014QIAN Xiao-bin, YIN Yong, ZHANG Xiu-feng, et al. Influence of irregular disturbance of sea wave on ship motions[J]. Journal of Traffic and Transportation Engineering, 2016, 16 (3): 116-124. (in Chinese). doi: 10.3969/j.issn.1671-1637.2016.03.014 [3] 侯圣贤. 迎浪航行时船舶垂荡纵摇运动建模与仿真[D]. 大连: 大连海事大学, 2015.HOU Sheng-xian. Simulation on ship heave and pitch motions in head seas[D]. Dalian: Dalian Maritime University, 2015. (in Chinese). [4] SALVENSEN N, TUCK E O, FALTINSEN O. Ship motions and sea loads[J]. Transactions Society of Naval Architects and Marine Engineers, 1970, 78: 250-287. [5] 洪亮, 朱仁传, 缪国平, 等. 三维频域有航速格林函数的数值计算与分析[J]. 水动力学研究与进展, 2013, 28 (4): 423-430. https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ201304009.htmHONG Liang, ZHU Ren-chuan, MIAO Guo-ping, et al. Numerical calculation and analysis of 3-D Green's function with forward speed in frequency domain[J]. Chinese Journal of Hydrodynamics, 2013, 28 (4): 423-430. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ201304009.htm [6] 邹元杰, 段文洋, 任慧龙, 等. 船舶在波浪中脉动压力预报的三维方法[J]. 哈尔滨工程大学学报, 2002, 23 (1): 20-25. doi: 10.3969/j.issn.1006-7043.2002.01.005ZOU Yuan-jie, DUAN Wen-yang, REN Hui-long, et al. Three-dimensional method for prediction of oscillating pressure on ship in waves[J]. Journal of Harbin Engineering University, 2002, 23 (1): 20-25. (in Chinese). doi: 10.3969/j.issn.1006-7043.2002.01.005 [7] GUEVEL P, BOUGIS J. Ship-motions with forward speed in infinite depth[J]. International Shipbuilding Progress, 1982, 29: 103-117. doi: 10.3233/ISP-1982-2933202 [8] 周正全, 顾懋祥, 孙伯起, 等. 预报船舶在波浪中航行时相对运动的三维模型[J]. 中国造船, 1992 (2): 1-10. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199202000.htmZHOU Zheng-quan, GU Mao-xiang, SUN Bai-qi, et al. Predictions of relative motions of ships in regular waves[J]. Shipbuilding of China, 1992 (2): 1-10. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199202000.htm [9] LIAPIS S J. Time-domain analysis of ship motions[D]. Ann Arbor: The University of Michigan, 1986. [10] SUN Wei, REN Hui-long, LI Hui, et al. Numerical solution for ship with forward speed based on transient Green function method[J]. Journal of Ship Mechanics, 2014, 18 (12): 1444-1452. [11] KING B K. Time domain analysis of wave exciting forces on ships and bodies[D]. Ann Arbor: The University of Michigan, 1987. [12] KORSMEYER F T, BINGHAM H B. The forward speed diffraction problem[J]. Journal of Ship Research, 1998, 42 (2): 99-112. doi: 10.5957/jsr.1998.42.2.99 [13] SINGH S P, SEN D. A comparative linear and nonlinear ship motion study using 3-D time domain methods[J]. Ocean Engineering, 2007, 34 (13): 1863-1881. doi: 10.1016/j.oceaneng.2006.10.016 [14] SINGH S P, SEN D. A comparative study on 3D wave load and pressure computations for different level of modelling of nonlinearities[J]. Marine Structures, 2007, 20 (1/2): 1-24. [15] DATTA R, RODRIGUES J M, SOARES C G. Study of the motions of fishing vessels by a time domain panel method[J]. Ocean Engineering, 2011, 38 (5/6): 782-792. [16] 孙葳, 任慧龙. 时域格林函数法求解有航速船舶运动问题[J]. 水动力学研究与进展, 2018, 33 (2): 216-222. https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ201802010.htmSUN Wei, REN Hui-long. Ship motions with forward speed by time-domain Green function method[J]. Chinese Journal of Hydrodynamics, 2018, 33 (2): 216-222. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ201802010.htm [17] NEWMAN J N. The approximation of free-surface Green functions[M]//Cambridge University Press. Wave Asymptotic. Cambridge: Cambridge University Press, 1992: 108-135. [18] 黄德波. 时域Green函数及其导数的数值计算[J]. 中国造船, 1992 (1): 16-25. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199204001.htmHUANG De-bo. Approximation of time-domain free surface function and its spatial derivatives[J]. Shipbuilding of China, 1992 (1): 16-25. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC199204001.htm [19] CHUANG J M, QIU W, PENG H. On the evaluation of time-domain Green function[J]. Ocean Engineering, 2007, 34 (7): 962-969. doi: 10.1016/j.oceaneng.2006.05.010 [20] CLEMENT A H. An ordinary differential equation for the Green function of time-domain free-surface hydrodynamics[J]. Journal of Engineering Mathematics, 1998, 33 (2): 201-217. doi: 10.1023/A:1004376504969 [21] BINGHAM H B. A note on the relative efficiency of methods for computing the transient free-surface Green function[J]. Ocean Engineering, 2016, 120: 15-20. doi: 10.1016/j.oceaneng.2016.05.020 [22] DUAN Wen-yang, DAI Yi-shan. New derivation of ordinary differential equations for transient free-surface Green functions[J]. China Ocean Engineering, 2001, 15 (4): 499-507. [23] LI Zhi-fu, REN Hui-long, TONG Xiao-wang, et al. A precise computation method of transient free surface Green function[J]. Ocean Engineering, 2015, 105: 318-326. doi: 10.1016/j.oceaneng.2015.06.048 [24] 钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994, 34 (2): 131-136. https://www.cnki.com.cn/Article/CJFDTOTAL-DLLG199402003.htmZHONG Wan-xie. On precise time-integration method for structural dynamics[J]. Journal of Dalian University of Technology, 1994, 34 (2): 131-136. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DLLG199402003.htm [25] 申亮, 朱仁传, 缪国平, 等. 深水时域格林函数的实用数值计算[J]. 水动力学研究与进展, 2007, 22 (3): 380-386. doi: 10.3969/j.issn.1000-4874.2007.03.017SHEN Liang, ZHU Ren-chuan, MIAO Guo-ping, et al. A practical numerical method for deep water time-domain Green function[J]. Chinese Journal of Hydrodynamics, 2007, 22 (3): 380-386. (in Chinese). doi: 10.3969/j.issn.1000-4874.2007.03.017 [26] 昝英飞, 马悦生, 韩端锋, 等. 基于辨识理论的船舶时域运动快速计算[J]. 交通运输工程学报, 2018, 18 (4): 182-190. doi: 10.3969/j.issn.1671-1637.2018.04.019ZAN Ying-fei, MA Yue-sheng, HAN Duan-feng, et al. Fast computation of vessel time-domain motion based on identification theory[J]. Journal of Traffic and Transportation Engineering, 2018, 18 (4): 182-190. (in Chinese). doi: 10.3969/j.issn.1671-1637.2018.04.019 [27] 张腾, 任俊生, 李志富, 等. 时域格林函数的新实用数值计算方法[J]. 大连海事大学学报, 2018, 44 (1): 1-8. https://www.cnki.com.cn/Article/CJFDTOTAL-DLHS201801001.htmZHANG Teng, REN Jun-sheng, LI Zhi-fu, et al. A new and practical numerical calculation method for time-domain Green function[J]. Journal of Dalian Maritime University, 2018, 44 (1): 1-8. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DLHS201801001.htm [28] HESS J L, SMITH A M O. Calculation of non-lifting potential flow about arbitrary three-dimensional bodies[J]. Journal of Ship Research, 1964, 8 (2): 22-44. [29] MAGEE A R. Large amplitude ship motions in the time domain[D]. Ann Arbor: The University of Michigan, 1991. [30] JOURNÉE J M J. Experiments and calculations on 4 Wigley hull forms in head waves[R]. Delft: Delft University of Technology, 1992. [31] KARA F. Time domain hydrodynamic and hydroelastic analysis of floating bodies with forward speed[D]. Glasgow: University of Strathclyde, 2000. -
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