﻿ 二维弹性平板绕流锁定发生机理研究
 舰船科学技术  2016, Vol. 38 Issue (11): 28-33 PDF

Mechanism research of lock-in on two-dimensional flow around elastic plate
JIA Wen-chao, CHEN Mei-xia, YANG Dan
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: Vortex-induced vibration of a cantilever plate is investigated numerically based on two-way fluid-structure interaction, which is achieved through the exchange of force and displacement data between the fluid and the structure field. In this work, vortex-induced vibration of a cantilever plate at different Reynolds number is simulated, simultaneously successfully captures the lock-in phenomena, and the mechanism was studied. The results suggest that when the vortex shedding frequency is close to the natural frequency of the structure, the surface pressure distribution is consistent with the structure modal, vortex intensity reaches a certain level, the lock-in phenomenon will occur.
Key words: lock-in     two-way fluid-structure interaction     vorticity induced vibration
0 引言

B.S. Carmo等[4]对不同来流速度下弹簧-圆柱系统振动特性进行了数值模拟，将得到的频率锁定区间划分为初始区域和稳定区域，在锁定区间内结构响应并未保持恒定，在初始区域内结构振级急剧上升达到峰值；而在稳定区域，振级逐渐下降。

1 双向流固耦合计算方法 1.1 初始流场控制方程

 $\left\{ \begin{array}{l} u = \bar u + u'\text{，}\\ v = \bar v + v'\text{，}\\ w = \bar w + w'\text{，}\\ p = \bar p + p'\text{。} \end{array} \right.$ (1)

 $\left\{\!\!\!\! \begin{array}{l} \displaystyle\frac{{\partial {u_i}}}{{\partial {x_i}}} = 0\text{，}\\[10pt] \rho\displaystyle \frac{{\partial {u_i}}}{{\partial t}} \!\!+\! \rho \frac{\partial }{{\partial {x_j}}}({u_i}{u_j}) \!=\! \! -\! \frac{{\partial p}}{{\partial {x_i}}} \!\!+\!\! \frac{\partial }{{\partial {x_j}}}(\mu \frac{{\partial {u_i}}}{{\partial {x_j}}} \!\!-\! \rho \overline {{{u'}_i}{{u'}_j}} ) \!+\! {S_i}\text{。} \end{array} \right.$ (2)

1.2 悬臂板振动控制方程

 $\begin{array}{l} {\boldsymbol{M}}\ddot w(x,y,z,t) + {\boldsymbol{C}}\dot w(x,y,z,t) + \\ \quad \quad {\boldsymbol{K}}w(x,y,z,t) = F(x,y,z,t)\text{。} \end{array}$ (3)

1.3 双向流固耦合数据交换

 图 1 悬臂板双向流固耦合求解流程图 Fig. 1 Flow char of two-way fluid-structure interaction algorithm
2 数值计算模型 2.1 流场CFD模型及结构有限元模型

 图 2 悬臂板有限元模型 Fig. 2 Finite element model of plate

 图 3 全局流场网格 Fig. 3 Fluid domain

 图 4 近壁面网格 Fig. 4 Boundary layer
2.2 边界条件

2.3 数值求解方法

3 弹性平板振动特性分析

 图 5 不同雷诺数下2种算法得到自由端总响应的对比 Fig. 5 Bending vibration amplitude of the free edge with different Reynolds number

 图 6 刚性及弹性平板的涡脱落频率随雷诺数的变化规律的对比 Fig. 6 Vortex shedding frequency of the rigid and elastic plate at different Reynolds number

 图 7 某固定翼型绕流位移响应 Fig. 7 Vortex-induced vibration amplitude of a hydrofoil
4 锁定形成条件研究 4.1 频率条件

4.2 脉动压力分布条件

 图 8 静水中平板第2，3阶模态云图 Fig. 8 The second and third order modes of the cantilever plate under water

 图 9 平板上下表面压力幅值分布 Fig. 9 The pressure distribution along the upper surface and the lower surface

 图 10 平板法向脉动压力合力时域分布 Fig. 10 Normal pressure in time domain

4.3 随边形状及尾涡强度条件

 图 11 翼型形状及尾流场测点分布 Fig. 11 Geometrical model and location of the measurement point in the wake

 图 12 不同随边厚度模型对应涡强度的对比 Fig. 12 Vorticity magnitude of the foil with different thickness

 图 13 随边表面一点压力时间历程的对比 Fig. 13 The history of the pressure on the trailing edges with different thickness

 图 14 不同随边厚度模型对应涡脱落涡量云图 Fig. 14 Vortex arrangement along the wake of the trailing edges with different thickness
5 结语

1）当悬臂平板尾部涡发放频率与静水中平板的固有频率相一致的时候，尾部漩涡的周期性发放将会诱导平板产生极大的振动响应。

2）涡与结构发生“锁定”现象，表现为结构位移响应峰值区域加宽，这是由于在共振频率附近区域，结构表面脉动压力幅值大小完全按结构模态分布，使得结构共振区域加宽。

3）结构和流场同时满足频率、压力分布和随边形状几个条件时，流-固之间将产生强耦合作用，结构振幅达到最大，流场涡脱落频率出现锁定现象，在此锁定区内，涡脱落频率保持不变，结构振幅也保持在一个很高的水平。而在其他固有频率处，虽能发生涡激共振，但振级大大低于锁定时的振级，此时流-固之间的耦合相对较弱。

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