﻿ 弧型布局浮式防波堤波浪载荷特性分析
 舰船科学技术  2022, Vol. 44 Issue (15): 92-99    DOI: 10.3404/j.issn.1672-7649.2022.15.019 PDF

Wave load analysis of floating breakwater with arc-shaped layout
MAO Xiang-qian, GUO Jian-ting, JI Chun-yan, BIAN Xiang-qian
School of Nowal Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212100, China
Abstract: Compared with the linear arrangement, the non-linear floating breakwater has a better shielding effect on multiple wave directions, but the wave load characteristics are also more complicated. This paper proposes an arc-shaped floating breakwater layout plan. Based on the three-dimensional potential flow theory, the wave load characteristics of the arc-shaped floating breakwater are analyzed, the first-order wave force and the second-order wave force of different wave downwards are calculated, and the typical section loads are given. Compared with the linear layout of the floating breakwater, the results show that the use of the arc layout can effectively reduce the first-order wave force and the second-order wave force on the floating breakwater structure, and make the section loads of the structure consistent under different waves.
Key words: floating breakwater     wave load     arc layout     section load
0 引　言

1 基本理论 1.1 三维势流理论

 ${\nabla ^2}\phi (x,y,z) = 0 z \leqslant 0 ,$ (1)

 $\phi (x,y,z,t) = {\phi _I}(x,y,z,t) + {\phi _d}(x,y,z,t) + {\phi _R}(x,y,z,t)。$ (2)

 $\frac{{\partial \phi }}{{\partial n}} = V, \quad 在物面上 ，$ (3)
 $\frac{{\partial \phi }}{{\partial t}} = g\frac{{\partial \phi }}{{\partial z}},\quad z = 0 ，$ (4)
 $\frac{{\partial \phi }}{{\partial n}} = 0 ,\quad z = - \infty，$ (5)
 $\mathop {\lim }\limits_{x \to \pm \infty } \left( {\frac{{\partial \phi }}{{\partial y}} + ik\phi } \right) = 0, \quad z = 0 。$ (6)

1.2 浮式防波堤波浪载荷计算方法

 ${F_i}^{wave(1)}(t) = \int_{ - \infty }^t {{h_i}(t - \tau )} \eta (\tau ){\rm{d}}\tau ，$ (7)

 $\left\{ \begin{gathered} {f_{\omega i}}(\omega ) = \int_{ - \infty }^\infty {{h_i}(t){e^{ - i\omega t}}{\rm{d}}t} ，\\ {h_i}(t) = \frac{1}{{2 \text{π} }}\int_{ - \infty }^\infty {{f_{\omega i}}(\omega ){e^{ - i\omega t}}{\rm{d}}t} 。\\ \end{gathered} \right.$ (8)

 $g({\tau _1},{\tau _2}) = {\left( {\frac{1}{{2 \text{π} }}} \right)^2}\int_{ - \infty }^\infty {\int_{ - \infty }^\infty {G_i^{(2)}({\omega _1},{\omega _2}){e^{\left( {i{\omega _1}{t_1} - i{\omega _2}{t_2}} \right)}}{\rm{d}}{\omega _1}{\omega _2}} }，$ (9)
 $G_i^{(2)}({\omega _1},{\omega _2}) = P({\omega _1},{\omega _2}) + iQ({\omega _1},{\omega _2})。$ (10)

 ${F_i}^{wave(2)}(t) = \int_{ - \infty }^\infty {\int_{ - \infty }^\infty {{g_i}({\tau _1},{\tau _2})\zeta \left( {t - {\tau _1}} \right)\zeta \left( {t - {\tau _2}} \right)d{\tau _1}{\tau _2}} }。$ (11)
1.3 剖面载荷计算方法

 $\left[ {\bar M} \right] = \int_{{x_a}}^x {\left[ {\bar m} \right]{\rm{d}}x} 。$ (12)

 $\left\{ Q \right\} = \left\{ \begin{gathered} N \\ S{F_y} \\ S{F_z} \\ TM \\ B{M_y} \\ B{M_z} \\ \end{gathered} \right\} = - \iint\limits_{{S_x}} {p\left( {x,y,z} \right)\left\{ {{n_j}} \right\}}{\rm{d}}s - {\omega ^2}\left[ {\bar M} \right]\left\{ \eta \right\}。$ (13)

2 弧型布局浮式防波堤波浪载荷特性数值算例 2.1 弧型总布置形式及主体参数

 图 1 弧型布局总布置示意图 Fig. 1 Schematic diagram of the arc layout

2.2 设计海况条件

2.3 波浪力计算结果及分析 2.3.1 一阶波浪力

 图 2 弧型布局在不同浪向下的一阶波浪力 Fig. 2 F-K+diffraction force of arc layout in different waves
2.3.2 二阶波浪力

 图 3 弧型布局在不同浪向下的二阶波浪力 Fig. 3 Second order wave force of arc layout in different waves
2.4 关键剖面载荷计算结果及分析

 图 4 弧型布局在不同浪向下的剖面载荷 Fig. 4 Section loads of arc layout in different waves
3 不同布局形式下浮式防波堤波浪载荷对比分析 3.1 用于对比的直线型总布置设计

 图 5 直线1型总布置示意图 Fig. 5 Schematic diagram of the linear I layout
3.2 波浪力对比分析 3.2.1 一阶波浪力对比分析

 图 6 横浪工况下3种布局浮式防波堤一阶波浪力 Fig. 6 F-K+diffraction force of three layouts in transverse waves

 图 7 斜浪工况下3种布局浮式防波堤一阶波浪力 Fig. 7 F-K+diffraction force of three layouts in oblique waves
3.2.2 二阶波浪力对比分析

 图 8 横浪工况下3种布局浮式防波堤二阶波浪力 Fig. 8 Second order wave force of three layouts in transverse waves

 图 9 斜浪工况下3种布局浮式防波堤二阶波浪力 Fig. 9 Second order wave force of three layouts in oblique waves
3.3 关键剖面载荷对比分析

 图 10 直线型布局在不同浪向下的剖面载荷 Fig. 10 Section loads of linear layout in different waves
4 结　语

1）在横浪工况下，除横摇和纵摇方向外，弧型布局在其余4个方向上的一阶波浪力和力矩上均明显小于直线型布局，且直线2型布局在首摇方向上的峰值是弧型的15.9倍。在纵荡、垂荡、纵摇和首摇方向上，直线1型的二阶波浪力或力矩显著大于弧型布局，且直线1型在首摇方向上的峰值约是弧型布局的42倍。采用弧型布局能够显著降低结构在横浪下的一阶与二阶波浪力。

2）在斜浪工况下，除横摇方向外，弧型布局在其余5个方向上的一阶波浪力和力矩上与2种直线型布局总体相差不大。在横荡、垂荡及纵摇方向上，直线1型的二阶波浪力或力矩较大，在波浪频率为1.4～1.5 rad/s时达到最大值。

3）弧型布局能够显著降低位于两端的模块在斜浪下的剖面载荷，位于中间的模块在斜浪下的剖面载荷约是横浪工况下的1.2～4.2倍，而直线型布局在斜浪下的剖面载荷显著大于横浪工况，斜浪下的垂向弯矩达到了横浪工况下的8.9倍。采用弧形布局能够降低结构剖面载荷受浪向角的影响。

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