基于傅汝德-克雷洛夫力非线性法的规则波浪中船舶运动数学模型

张腾; 任俊生; 梅天龙

doi:10.19818/j.cnki.1671-1637.2020.02.007

基于傅汝德-克雷洛夫力非线性法的规则波浪中船舶运动数学模型

doi: 10.19818/j.cnki.1671-1637.2020.02.007

1.
大连海事大学航海学院, 辽宁大连 116026
2.
上海交通大学船舶海洋与建筑工程学院, 上海 200240

基金项目:

国家高技术研究发展计划项目 2015AA016404

国家自然科学基金项目 51779029

中央高校基本科研业务费专项资金项目 313204330

详细信息

作者简介:
张腾(1991-), 男, 山西大同人, 大连海事大学工学博士, 从事船舶水动力与适航性研究

中图分类号: U666.158
计量
- 文章访问数: 1417
- HTML全文浏览量: 274
- PDF下载量: 398
- 被引次数: 0
出版历程
- 收稿日期: 2019-08-01
- 刊出日期: 2020-04-25

Mathematical model of ship motions in regular waves based on Froude-Krylov force nonlinear method

1.
Navigation College, Dalian Maritime University, Dalian 116026, Liaoning, China
2.
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, Chin

Funds:

National High-tech Research and Development Program of China 2015AA016404

National Natural Science Foundation of China 51779029

Special Foundation for Basic Scientific Research of Central Colleges of China 313204330

More Information

Author Bio:
ZHANGTeng(1991-), male, PhD, E-mail: 13342284962@163.com

Article Text (Baidu Translation)

摘要

摘要: 为准确预报规则波浪中船舶的运动, 提出基于四叉树划分的自适应网格法, 以生成船舶瞬时湿表面, 在船舶瞬时湿表面上计算傅汝德-克雷洛夫(F-K)力与静恢复力; 对于与波面相交的面元, 由于F-K力在波面处剧烈波动, 采用四叉树划分法进一步细分面元; 基于线性理论, 采用瞬时自由面格林函数在船舶平均湿表面上计算扰动力; 为避免瞬时自由面格林函数在自由液面处剧烈波动产生严重数值误差, 舍去扰动势所满足边界积分方程中的水线项, 并对迎浪前进速度为傅汝德数0.2的WigleyⅠ型船舶进行数值计算。计算结果表明: 对低于瞬时波面以下的船体部分, F-K力非线性法所需面元数更少, 为细网格法的1/4~1/8;除不规则频率外, 舍去与未舍去水线项所得水动力系数与试验值的相对误差分别小于33.4%、54.8%, 因此, 舍去水线项所得水动力系数更接近试验结果; 当入射波波幅为0.018 m, 波长与船长比为1.25时, 采用F-K力非线性法与线性法所得纵摇幅值响应因子的计算结果分别比试验值低3.2%、17.0%, 波长与船长比为2.00时, 采用F-K力非线性法与线性法所得纵摇幅值响应因子的计算结果分别比试验值低6.7%、13.5%, 可见, 采用F-K力非线性法能够准确地仿真规则波浪中船舶的运动。
- 船舶工程 /
- 航海模拟器 /
- 傅汝德-克雷洛夫力 /
- 四叉树 /
- 瞬时湿表面 /
- 瞬时自由面格林函数 /
- 水线项
Abstract: To accurately predict the ship motions in regular waves, the adaptive mesh method based on the quad-tree division was proposed to generate the instantaneous wet hull surface. The Froude-Krylov(F-K) force and hydrostatic restoring force were calculated on the instantaneous wet hull surface. For the F-K force fluctuating violently at the wave profile, the quad-tree division method was adopted to further divide the panels interacted with the wave profile. Based on the linear theory, the perturbation forces were calculated on the mean wet hull surface by using the instantaneous free surface Green function. To avoid the serious numerical error caused by the violent fluctuation of instantaneous free surface Green function near the free liquid surface, the waterline integral term of boundary integral equation satisfied by the perturbation potential was excluded. The numerical computation was carried out for the Wigley Ⅰ hull with a forward speed against waves at a Froude number of 0.2. Calculation result shows that for the hull under the instantaneous wave profile, the quantity of panel required by the F-K force nonlinear method is less, being 1/4-1/8 of the fine mesh method. Except for irregular frequencies, the relative errors of hydrodynamic coefficients obtained by the methods with and without waterline term are less than 33.4% and 54.8%, respectively, comparing with the experimental result. Therefore, the hydrodynamic coefficient computational result obtained with the waterline term is closer to the experimental result. When the incident wave amplitude is 0.018 m, and the ratio of wave length to ship length is 1.25, the pitch response amplitude operators obtained by the F-K force nonlinear method and the linear method are 3.2% and 17.0%, respectively, lower than the experimental value. When the ratio of wave length to ship length is 2.00, the pitch response amplitude operators obtained by the F-K force nonlinear method and the linear method are 6.7% and 13.5%, respectively, lower than the experimental value. Thus, the F-K force nonlinear method can accurately simulate the ship motions in regular waves.
- ship engineering /
- maritime simulator /
- Froude-Krylov force /
- quad-tree /
- instantaneous wet surface /
- instantaneous free surface Green function /
- waterline term

HTML全文

图 1 流域和坐标系定义

Figure 1. Definitions of fluid domain and coordinate system

下载: 全尺寸图片幻灯片

图 2 面元与瞬时波面的相对位置

Figure 2. Relative positions between panel and instantaneous wave profile

下载: 全尺寸图片幻灯片

图 3 面元的四叉树划分

Figure 3. Panel subdivision by quad-tree

下载: 全尺寸图片幻灯片

图 4 面元受力计算流程

Figure 4. Calculation process of forces acting on panel

下载: 全尺寸图片幻灯片

图 5 Wigley Ⅰ型船舶面元分布

Figure 5. Panel distribution of Wigley Ⅰ hull

下载: 全尺寸图片幻灯片

图 6 Wigley Ⅰ型船舶量纲一垂荡附加质量

Figure 6. Non-dimensional heave added masses of Wigley Ⅰ hull

下载: 全尺寸图片幻灯片

图 7 Wigley Ⅰ型船舶量纲一垂荡阻尼系数

Figure 7. Non-dimensional heave damping coefficients of Wigley Ⅰ hull

下载: 全尺寸图片幻灯片

图 8 Wigley Ⅰ型船舶量纲一纵摇附加质量

Figure 8. Non-dimensional pitch added masses of Wigley Ⅰ hull

下载: 全尺寸图片幻灯片

图 9 Wigley Ⅰ型船舶量纲一纵摇阻尼系数

Figure 9. Non-dimensional pitch damping coefficients of Wigley Ⅰ hull

下载: 全尺寸图片幻灯片

图 10 采用方案1时瞬时入射波波面下的船体面元划分

Figure 10. Panel division of hull under instantaneous incident wave profile when using scheme 1

下载: 全尺寸图片幻灯片

图 11 采用方案2时瞬时入射波波面下的船体面元划分

Figure 11. Panel division of hull under instantaneous incident wave profile when using scheme 2

下载: 全尺寸图片幻灯片

图 12 λ/L为1.25时的量纲一垂荡F-K力时历

Figure 12. Time histories of non-dimensional heave F-K force when λ/L is 1.25

下载: 全尺寸图片幻灯片

图 13 λ/L为1.25时的量纲一纵摇F-K力时历

Figure 13. Time histories of non-dimensional pitch F-K force when λ/L is 1.25

下载: 全尺寸图片幻灯片

图 14 λ/L为2.00时的量纲一垂荡F-K力时历

Figure 14. Time histories of non-dimensional heave F-K force when λ/L is 2.00

下载: 全尺寸图片幻灯片

图 15 λ/L为2.00时的量纲一纵摇F-K力时历

Figure 15. Time histories of non-dimensional pitch F-K force when λ/L is 2.00

下载: 全尺寸图片幻灯片

图 16 λ/L为1.25时量纲一垂荡运动时历

Figure 16. Time histories of non-dimensional heave motion when λ/L is 1.25

下载: 全尺寸图片幻灯片

图 17 λ/L为1.25时量纲一纵摇运动时历

Figure 17. Time histories of non-dimensional pitch motion when λ/L is 1.25

下载: 全尺寸图片幻灯片

图 18 λ/L为2. 00时量纲一垂荡运动时历

Figure 18. Time histories of non-dimensional heave motion when λ/L is 2.00

下载: 全尺寸图片幻灯片

图 19 λ/L为2. 00时量纲一纵摇运动时历

Figure 19. Time histories of non-dimensional pitch motion when λ/L is 2.00

下载: 全尺寸图片幻灯片

图 20 垂荡幅值响应因子

Figure 20. Heave response amplitude operators

下载: 全尺寸图片幻灯片

图 21 纵摇幅值响应因子

Figure 21. Pitch response amplitude operators

下载: 全尺寸图片幻灯片

表 1 Wigley Ⅰ型船舶参数

Table 1. Parameters of Wigley Ⅰ hull

参数	船长L/m	船宽/m	吃水/m	排水体积/m³	纵摇惯性半径	重心与基线距离/m	方形系数
数值	3	0.3	0.187 5	0.094 6	0.25L	0.17	0.56

下载: 导出CSV

表 2 采用方案1对F-K压力在面元上的积分结果

Table 2. F-K pressures integration results on panels by scheme 1 N

面元划分次数	面元A	面元B	面元C	面元D
1	-0.433 70	-0.332 26	-0.239 42	0.000 00
2	-0.422 23	-0.351 28	-0.336 21	0.490 38
3	-0.397 04	-0.382 73	-0.328 53	0.235 59
4	-0.397 44	-0.389 72	-0.333 55	0.235 59
5	-0.397 44	-0.389 72	-0.333 55	0.235 59

下载: 导出CSV

表 3 采用不同方案对F-K压力在面元上积分的结果

Table 3. F-K pressures integration results on panels adopting different schemes N

方案编号	a	b	c	d
1	0.599 12	0.479 36	0.471 82	0.483 95
2	0.599 12	0.479 36	0.471 82	0.483 95
3	0.599 12	0.479 36	0.471 82	0.483 95

下载: 导出CSV

参考文献(31)

[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.htm JIN 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]	江玉玲, 彭国均. 航海模拟器中船舶数学模型仿真研究[J]. 实验室研究与探索, 2016, 35(3): 24-27, 31. doi: 10.3969/j.issn.1006-7167.2016.03.007 JIANG Yu-ling, PENG Guo-jun. Mathematical model simulation of ship navigation simulator[J]. Research and Exploration in Laboratory, 2016, 35(3): 24-27, 31. (in Chinese). doi: 10.3969/j.issn.1006-7167.2016.03.007
[3]	任俊生, 杨盐生, 杜嘉立. 高速水翼双体船波浪中运动建模与仿真[J]. 大连海事大学学报, 2004, 30(2): 4-7. doi: 10.3969/j.issn.1006-7736.2004.02.002 REN Jun-sheng, YANG Yan-sheng, DU Jia-li. Modeling and simulation of the motions of hydrofoil catamaran in wave[J]. Journal of Dalian Maritime University, 2004, 30(2): 4-7. (in Chinese). doi: 10.3969/j.issn.1006-7736.2004.02.002
[4]	张秀凤, 尹勇, 金一丞. 规则波中船舶运动六自由度数学模型[J]. 交通运输工程学报, 2007, 7(3): 40-43. doi: 10.3321/j.issn:1671-1637.2007.03.009 ZHANG Xiu-feng, YIN Yong, JIN Yi-cheng. Ship motion mathematical model with six degrees of freedom in regular wave[J]. Journal of Traffic and Transportation Engineering, 2007, 7(3): 40-43. (in Chinese). doi: 10.3321/j.issn:1671-1637.2007.03.009
[5]	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, 7(3): 116-124. doi: 10.3969/j.issn.1671-1637.2016.03.014 QIAN 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, 7(3): 116-124. (in Chinese). doi: 10.3969/j.issn.1671-1637.2016.03.014
[6]	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.
[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]	LIAPIS S J. Time-domain analysis of ship motions[D]. Ann Arbor: The University of Michigan, 1986.
[9]	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(2): 1444-1452.
[10]	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
[11]	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. doi: 10.3969/j.issn.1671-7031.2018.01.002 ZHANG 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). doi: 10.3969/j.issn.1671-7031.2018.01.002
[12]	KING B K. Time domain analysis of wave exciting forces on ships and bodies[D]. Ann Arbor: The University of Michigan, 1987.
[13]	FARA F. Time domain hydrodynamic & amp; amp; hydroelastic analysis of floating bodies with forward speed[D]. Glasgow: University of Strathclyde, 2000.
[14]	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.
[15]	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.htm SUN 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
[16]	LIN W M, YUE D. Numerical solution of large amplitude ship motions in the time domain[C]//National Academy Press. 18th ONR Symposium on Naval Hydrodynamics. Washington DC: National Academy Press, 1990: 41-66.
[17]	FONSECA N, GUEDES SOARES C, INCEIK A. Numerical and experimental study of large amplitude motions of two-dimensional bodies in waves[J]. Applied Ocean Research, 1997, 19(1): 35-47. doi: 10.1016/S0141-1187(97)00010-2
[18]	SEN D. Time-domain computation of large amplitude 3D ship motions with forward speed[J]. Ocean Engineering, 2002, 29(8): 973-1002. doi: 10.1016/S0029-8018(01)00041-5
[19]	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.
[20]	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
[21]	SENGUPTA D, DATTR A, SEN D. A simplified approach for computation of nonlinear ship loads and motions using a 3D time-domain panel method[J]. Ocean Engineering, 2016, 117: 99-113. doi: 10.1016/j.oceaneng.2016.03.039
[22]	RODRIGUES J M, SOARES C G. A generalized adaptive mesh pressure integration technique applied to progressive flooding of floating bodies in still water[J]. Ocean Engineering, 2015, 110: 140-151.
[23]	RODRIGUES J M, SOARES C G. Froude-Krylov forces from exact pressure integrations on adaptive panel meshes in a time domain partially nonlinear model for ship motions[J]. Ocean Engineering, 2017, 139: 169-183. doi: 10.1016/j.oceaneng.2017.04.041
[24]	JOURNÉE J M J. Experiments and calculations on four Wigley Hull forms[R]. Delft: Delft University of Technology, 1992.
[25]	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.
[26]	张腾, 任俊生, 张秀凤. 基于三维时域Green函数法的船舶在规则波浪中的运动数学模型[J]. 交通运输工程学报, 2019, 19(2): 110-121. http://transport.chd.edu.cn/article/id/201902011 ZHANG Teng, REN Jun-sheng, ZHANG Xiu-feng. Mathematical model of ship motion in regular wave based on three-dimensional time-domain Green function method[J]. Journal of Traffic and Transportation Engineering, 2019, 19(2): 110-121. (in Chinese). http://transport.chd.edu.cn/article/id/201902011
[27]	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.1671-1637.2018.04.019 ZAN 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
[28]	CHEN Xi, ZHU Ren-chuan, ZHOU Wen-jun, et al. A 3D multi-domain high order boundary element method to evaluate time domain motions and added resistance of ship in waves[J]. Ocean Engineering, 2018, 159: 112-128.
[29]	BLANDEAU F, FRANCOIS M, MALENICA Š, et al. Linear and non-linear wave loads on FPSOs[C]//International Society of Offshore and Polar Engineers. Proceedings of the Ninth International Offshore Polar Engineering Conference. Mountain View: International Society of Offshore and Polar Engineers, 1999: 252-258.
[30]	MAGEE A R, BECK R F. Compendium of ship motion calculations using linear time-domain analysis[R]. Ann Arbor: The University of Michigan, 1988.
[31]	KIM K H, KIM Y. Comparative study on ship hydrodynamics based on Neumann-Kelvin and double-body linearizations in time-domain analysis[J]. International Journal of Offshore and Polar Engineering, 2010, 10(4): 265-274.