﻿ 圆柱顺流向涡激振动响应及流体力特征分析
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (12): 1902-1909  DOI: 10.11990/jheu.201706020 0

### 引用本文

XU Wanhai, MA Yexuan, ZHANG Shuhai, et al. Analysis on response and fluid force characteristics of a cylinder subjected to vortex-induced vibration in flow direction[J]. Journal of Harbin Engineering University, 2018, 39(12), 1902-1909. DOI: 10.11990/jheu.201706020.

### 文章历史

1. 天津大学 水利工程仿真与安全国家重点实验室, 天津 300072;
2. 中国电力科学研究院, 北京 100055

Analysis on response and fluid force characteristics of a cylinder subjected to vortex-induced vibration in flow direction
XU Wanhai 1, MA Yexuan 1, ZHANG Shuhai 1, LIU Bin 2
1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin 300072, China;
2. China Electric Power Research Institute, Beijing 100055, China
Abstract: This study investigates the response characteristics and fluid-structure interactions of a flexible cylinder subjected to vortex-induced vibration (VIV) in the flow direction. A model test was conducted, and a modal analysis method was employed to reconstruct the IL response displacement according to the strain information obtained from the model test. A finite element method was used to calculate the IL fluid force, which can be decomposed to obtain the time-varying drag and added mass coefficients by the least square method. The maximum root mean square of the response displacement in the IL direction can reach 0.45D (D is the diameter of the cylinder). In the mode-dominant region, the time-varying drag coefficients decrease with the increase of the response displacements, which reflects the self-limiting feature of the VIV. The added mass coefficients decrease in the mode-dominant region; as a result, the structural response frequency is locked near natural frequency. In addition, the axial distribution of the time-varying drag coefficients are strongly consistent with the response displacement. The phase between the IL displacement and fluid force has a significant influence on the time-varying drag coefficients and added mass coefficients.
Keywords: flexible cylinder    vortex-induced vibration (VIV)    in-line (IL)    total fluid force coefficient    time-varying drag coefficients    added mass coefficients    fluid-structure interaction

1 实验设计

 Download: 图 1 实验装置示意图 Fig. 1 The schematic diagram of the experimental equipment

2 数据处理方法

 ${x_{{\rm{IL}}}} = x + \bar x$ (1)
 Download: 图 2 柔性圆柱均匀来流作用下顺流向位移示意图 Fig. 2 IL displacement of the flexible cylinder in uniform flow

 ${\varepsilon _{{\rm{IL}}}} = \varepsilon + \bar \varepsilon$ (2)

 $x\left( {z,t} \right) = \sum\limits_{n = 1}^S {{w_n}\left( t \right){\varphi _n}\left( z \right)}$ (3)

 ${\varphi _n}\left( z \right) = \sin \frac{{n{\rm{ \mathsf{ π} }}z}}{L}$ (4)

 $\frac{1}{\kappa } = \frac{{x''}}{{{{\left( {1 + {{\left( {x'} \right)}^2}} \right)}^{3/2}}}}$ (5)

 $\frac{\varepsilon }{R} = x''\left( {z,t} \right) = - \sum\limits_{n = 1}^S {{{\left( {\frac{{n{\rm{ \mathsf{ π} }}}}{L}} \right)}^2}{w_n}\left( t \right)\sin \frac{{n{\rm{ \mathsf{ π} }}z}}{L}}$ (6)

3 流体力计算

 ${\rm{EI}}\frac{{{\partial ^4}x}}{{\partial {z^4}}} - T\frac{{{\partial ^2}x}}{{\partial {z^2}}} + c\frac{{\partial x}}{{\partial t}} + m\frac{{{\partial ^2}x}}{{\partial {t^2}}} = {f_x}$ (7)

 $\mathit{\boldsymbol{M\ddot X}} + \mathit{\boldsymbol{C\dot X}} + \mathit{\boldsymbol{KX}} = {\mathit{\boldsymbol{F}}_x}$ (8)

IL位移与流体力之间的相位差ψ

 $\psi = \arctan \left( {\frac{{\rho Dl{U^2}{C_D}\dot x/2\sqrt 2 {{\dot x}_{rms}}}}{{ - \rho {\rm{ \mathsf{ π} }}{D^2}l{C_a}\ddot x/4}}} \right)$ (14)
4 结果分析 4.1 涡激振动响应

 Download: 图 3 顺流向控制模态 Fig. 3 The dominated mode in IL direction

 Download: 图 5 测点处顺流向位移时间历程曲线和频谱图(T=460 N Vr=12.2) Fig. 5 The history and spectra of the IL displacement at measurement points (T=460 N Vr=12.2)
4.2 流体力特征

 Download: 图 6 顺流向流体力合力系数均方根 Fig. 6 RMS of IL total fluid force coefficients

 Download: 图 7 脉动阻力系数随约化速度变化规律 Fig. 7 Vary drag coefficients versus reduced velocity

 ${f_n} = \frac{n}{{2L}}\sqrt {\frac{T}{{{m_s} + {m_a}}} + {{\left( {\frac{{n\pi }}{L}} \right)}^2}\frac{{EI}}{{{m_s} + {m_a}}}}$ (15)

4.3 顺流向流固耦合机制

 Download: 图 10 顺流向位移均方根、流体力系数及相位差的轴向分布 Fig. 10 The axial distribution of IL displacement RMS, fluid force coefficients and phases (T=460 N)

5 结论

1) 模态控制区，IL位移逐渐增大，脉动阻力系数逐步减小，顺流向VIV具有自限制特性。高阶控制模态，响应频率较高，脉动阻力系数显著增大。附加质量系数在模态控制区逐渐减小，结构固有频率增大，使响应频率“锁定”在固有频率附近，体现了顺流向VIV的自激励特性。

2) 脉动阻力系数的轴向分布与IL位移均方根具有高度一致性，取得极值点的位置基本相同。附加质量系数在位移节点处突变，响应频率较高时，附加质量系数在局部区域保持平稳。IL位移与流体力间的相位差与脉动阻力系数和附加质量系数密切相关，是顺流向VIV流固耦合作用中重要参数。

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