﻿ 水翼涡激振动的数值模拟研究
 舰船科学技术  2016, Vol. 38 Issue (6): 7-13 PDF

1. 上海交通大学 船舶海洋与建筑工程学院, 上海 200240 ;
2. 高新船舶与深海开发装备协同创新中心(船海协创中心), 上海 200240

Research on vortex induced vibration of hydrofoil
LIU Hu-tao1, ZHANG Huai-xin1,2, YAO Hui-lan1
1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China ;
2. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai 200240, China
Abstract: The objective of this research is to investigate the fluid-structure interaction motion of a two-dimensional hydrofoil in viscous flow. Large-eddy simulation method is used to calculate the flow field around hydrofoil, and RungeKutta method is applied to solve equations of rigid body motion. Flow results and motion results exchange data at the hydrofoil wall surface, by compiling a user-defined functions to control rigid body motion and flow field grid update. The influence of the hydrofoil parameters, i.e. attack angle, elastic axis position and flow velocity, on vibration are discussed. Once the velocity increase to a certain value, hydrofoil flutter phenomenon occurred. Also, discussion on time and frequency domain is held to investigate the flutter phenomenon.
Key words: two-dimensional wing flow     fluid Structure Interaction     flutter
0 引言

1 数学模型 1.1 刚体模型

 图 1 两自由度水翼模型 Fig. 1 Two degrees of freedom hydrofoil models

 图 2 水翼计算网格 Fig. 2 Grid of hydrofoil

 $\left[\!\!\! {\begin{array}{*{20}{c}} m\!\! & \!\!{{S_\theta }}\!\!\\ {{S_\theta }} \!\! & \!\! {{I_\theta }}\!\! \end{array}} \!\!\!\right]\left\{ {\begin{array}{*{20}{c}} \!\!{\ddot h}\!\! \\ \!\!{\ddot \theta }\!\! \end{array}} \right\} \!+\!\left[\!\!\! {\begin{array}{*{20}{c}} {{C_h}}\!\! & \!\!0 \\ 0\!\! & \!\!{{C_\theta }} \end{array}}\!\! \right]\left\{ {\begin{array}{*{20}{c}} \!\!{\dot h}\!\!\\ \!\!{\dot \theta }\!\! \end{array}} \right\} \!+ \!\left[\!\!{\begin{array}{*{20}{c}} {{K_h}}\!\! & \!\!0 \\ 0 \!\!& \!\!{{K_\theta }} \end{array}}\!\! \right]\left\{ {\begin{array}{*{20}{c}} \!\!h\!\!\\ \!\!\theta\!\! \end{array}}\! \right\}\!\! =\!\! \left\{\!\!\! {\begin{array}{*{20}{c}} L\\ M \end{array}}\!\!\! \right\}\text{。}$ (1)

 ${{ M}_s} \ddot{ X} + {{ C}_s}\dot { X} + {{ K}_s}{ X} = { F}\text{。}$ (2)

1.2 流体模型

 $\frac{{\partial \rho }}{{\partial t}} + \frac{\partial }{{\partial {x_i}}}(\rho {\bar u_i}) = 0\text{，}$ (3)
 $\frac{\partial }{{\partial {x_i}}}(\rho {\bar u_i}) + \frac{\partial }{{\partial {x_j}}}(\rho {\bar u_i}{\bar u_j}) = \frac{\partial }{{\partial {x_i}}}(\mu \frac{{\partial {{\bar u}_i}}}{{\partial {x_j}}})-\frac{{\partial \bar p}}{{\partial {x_i}}}-\frac{{\partial {\tau _{ij}}}}{{\partial {x_j}}}\text{。}$ (4)

 ${\tau _{ij}}-\frac{1}{3}{\tau _{kk}}{\delta _{ij}} =-2{\mu _t}{\bar S_{ij}}\text{。}$ (5)

 ${\mu _t} = \rho L_s^2\left| {\bar S} \right|\text{。}$ (6)

 图 7 不同来流速度下振动情况对比，α=10°，a = -1 Fig. 7 Hydrofoil vibration under different velocity

 图 8 不同来流速度下纵摇运动相图及频谱 Fig. 8 Motion phase diagram and velocity spectrum in various velocity

 图 9 不同流速下水翼的声学指向性图 Fig. 9 Acoustic directivity chart in various velocity

 图 10 不同流速下特征点声压值对比图 Fig. 10 SPL of feature points in various velocity
3 结论

1）大涡模拟方法能够较好的捕捉高雷诺数、复杂湍流中的细节，模拟出小攻角水翼绕流后完整的涡街现象。

2）水翼振动状态对系统的初始值具有依赖性，在没有扰动的情况下，水翼在 0° 攻角时始终保持微幅振动，攻角越大，振动平衡位置越偏离初始位置，且垂荡运动幅值衰减较明显。

3）航行速度对水翼振动影响较为直观，且随着速度的不断增大，水翼出现颤振现象，即振幅不衰减的自激振动。虽然水中颤振产生的条件比较苛刻，但是随流速增大而产生的振动加剧现象仍不容忽视。

4）流噪声随来流速度增大而增大，其在低频段的数值高于高频段的数值，它能够直观地反应出结构振动对流场的扰动情况。

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