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
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- 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

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

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图 1 流域和坐标系定义

Figure 1. Definitions of fluid domain and coordinate system

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图 2 面元与瞬时波面的相对位置

Figure 2. Relative positions between panel and instantaneous wave profile

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图 3 面元的四叉树划分

Figure 3. Panel subdivision by quad-tree

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图 4 面元受力计算流程

Figure 4. Calculation process of forces acting on panel

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图 5 Wigley Ⅰ型船舶面元分布

Figure 5. Panel distribution of Wigley Ⅰ hull

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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图 20 垂荡幅值响应因子

Figure 20. Heave response amplitude operators

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图 21 纵摇幅值响应因子

Figure 21. Pitch response amplitude operators

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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

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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

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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

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