﻿ 便携式波浪测量浮标总体设计及随浪特性分析
 舰船科学技术  2018, Vol. 40 Issue (12): 68-71 PDF

1. 武汉第二船舶设计研究所，湖北 武汉 430064;
2. 华中科技大学，湖北 武汉 430074

General design of portable wave measurement buoy and analysis of wave characteristics
CHEN Xiao-zou1, WAN Yu-xiang2
1. Wuhan Second Ship Design and Research Institute, Wuhan 430064, China;
2. Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: In this paper, a portable wave measurement buoy is designed. The time-domain and frequency-domain responses of the buoy in regular and irregular waves are calculated based on the potential flow theory. The wave height test compensation coefficients and wave cycle test compensation coefficients are obtained. The wave following characteristic of the buoy was analyzed.
Key words: wave buoy     wave parameter     portability     wave following characteristic
0 引　言

1 浮标总体设计及参数

 图 1 浮标外形（单位：mm） Fig. 1 Buoy shape

 图 2 浮标总布置图 Fig. 2 General layout of buoys

2 随浪特性研究 2.1 理论方法 2.1.1 控制方程

 ${\nabla ^2}\varphi = 0\left( {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over V} = \nabla \varphi } \right)\text{，}$ (1)

 $\left( {\nabla \varphi - \overset{\rightharpoonup}V_S} \right) \cdot {\overset{\rightharpoonup}{n}} = 0\text{，}$ (2)

 $\frac{{D\left( {z - \zeta } \right)}}{{Dt}} = 0\;i.e.\frac{{\partial \left( {z - \zeta } \right)}}{{\partial t}} + \nabla \varphi \cdot \nabla \left( {z - \zeta } \right) = 0\text{，}$ (3)

 $\frac{{\partial \varphi }}{{\partial t}} + \frac{p}{\rho } + \frac{1}{2}\nabla \varphi \cdot \nabla \varphi +{\mathcal{g}} \zeta = const\text{，}$ (4)

 $\frac{{\partial \varphi }}{{\partial z}} - \frac{{{\omega ^2}}}{{\mathcal{g}}}\varphi = 0\text{，}$ (5)

 $\nabla \varphi = 0\text{，}({\text{深水}})\text{，}$ (6)
 $\frac{{\partial \varphi }}{{\partial z}} = 0\text{，}({\text{浅水}})\text{。}$ (7)

 ${{F}} = \rho {\ddot X\left( {1 + {C_\alpha }} \right)} \varOmega+ 0.5\rho {C_d}V\left| V \right|D \text{。}$ (8)

 ${{P}} = - \rho \frac{{\partial \varphi }}{{\partial t}}\text{。}$ (9)

 $\begin{split}F_{strc}^2 = - \mathop \oint \limits_{WL}^{} 0.5\rho g\zeta _r^2\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} {\rm d}l + \mathop \int\!\!\!\int \limits_{{S_0}}^{} 0.5\rho {\left| {\nabla \varphi } \right|^2}\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} {\rm d}S+\\ \mathop \int\!\!\!\int \nolimits_{{S_0}}^{} \rho \left( {X \cdot \nabla \frac{{\partial \varphi }}{{\partial t}}} \right)\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} {\rm d}S + {M_s} \cdot R \cdot {\ddot X _g}\text{，}\end{split}$ (10)

 $\left[ { - {\omega ^2}\left( {{M_s} + {M_a}\left( \omega \right)} \right) - i\omega C\left( \omega \right) + K} \right]X\left( \omega \right) = F\left( \omega \right)\text{。}$ (11)

 ${X_{j + 1}} = {X_j} + {{ K}^{ - 1}}\left( {{X_j}} \right){ F}\left( {{X_j}} \right)\text{。}$ (12)

 ${M_\zeta }\ddot X\left( t \right) = F\left( t \right)\text{。}$ (13)

2.1.2 计算网格

 图 3 网格分布图 Fig. 3 Grid distribution map
2.2 计算结果及分析 2.2.1 不同圆频率波浪中的垂荡运动的频域响应

 图 4 垂荡频响图 Fig. 4 Heave frequency response
 ${\rm{Z'}} = \frac{Z}{h}\text{。}$ (14)

 $\left( {1.013 - 1} \right) \div 1 = 0.013 < 2\% \text{。}$
2.2.2 不同圆频率波浪中垂荡运动的时域响应

 ${\rm{T'}} = \frac{T}{{{T_B}}}\text{。}$ (15)

 图 5 无因次化运动周期图 Fig. 5 Dimensionless periodic diagram of motion
2.2.3 4级海况中浮标的运动响应

 图 6 四级海况中垂荡的时域响应 Fig. 6 Time domain response of heave in four-level sea conditions

 ${\rm{S}}\left( w \right) = \frac{{\frac{1}{2}\xi _{an}^2}}{{\Delta w}}\left( {{m^2}.s} \right)\text{。}$ (16)

 图 7 运动频域响应和波浪谱对比图 Fig. 7 Motion frequency domain response and wave spectrum comparisons

3 结　语