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低雷诺数下串列布置双圆柱涡激振动特性研究

涂佳黄 黄林茜 何永康 吕海宇 梁经群

涂佳黄, 黄林茜, 何永康, 吕海宇, 梁经群. 低雷诺数下串列布置双圆柱涡激振动特性研究. 力学学报, 2022, 54(1): 68-82 doi: 10.6052/0459-1879-21-381
引用本文: 涂佳黄, 黄林茜, 何永康, 吕海宇, 梁经群. 低雷诺数下串列布置双圆柱涡激振动特性研究. 力学学报, 2022, 54(1): 68-82 doi: 10.6052/0459-1879-21-381
Tu Jiahuang, Huang Linxi, He Yongkang, Lü Haiyu, Liang Jingqun. Study on the vortex-induced vibration characteristics of two tandem cylinders at low Reynolds number. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 68-82 doi: 10.6052/0459-1879-21-381
Citation: Tu Jiahuang, Huang Linxi, He Yongkang, Lü Haiyu, Liang Jingqun. Study on the vortex-induced vibration characteristics of two tandem cylinders at low Reynolds number. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 68-82 doi: 10.6052/0459-1879-21-381

低雷诺数下串列布置双圆柱涡激振动特性研究

doi: 10.6052/0459-1879-21-381
基金项目: 国家自然科学基金(51434002, 11602214), 湖南省自然科学基金(2020JJ4568, 2021JJ50027)和大学生创新创业训练计划(S202010530021)资助项目
详细信息
    作者简介:

    涂佳黄, 副教授, 主要从事结构与流体相互作用方面的研究. E-mail: tujiahuang1982@163.com

  • 中图分类号: O357.1

STUDY ON THE VORTEX-INDUCED VIBRATION CHARACTERISTICS OF TWO TANDEM CYLINDERS AT LOW REYNOLDS NUMBER

  • 摘要: 基于四步半隐式特征线分裂算子有限元方法, 对串列布置双圆柱双自由度涡激振动问题进行了数值模拟计算, 并分析了间距比、剪切率、频率比以及折减速度4个参数对圆柱结构动力响应的影响. 研究发现: 不同固有频率比与剪切率对下游圆柱振动幅值影响较大, 然而对上游圆柱振动幅值影响较小. 上游圆柱在两个自由度方向达到最大值的折减速度不同, 然而下游圆柱基本同步. 上游圆柱共振区的范围明显宽于下游圆柱, 同时上游圆柱较下游圆柱会更早进入与退出共振区间. 另一方面, 双圆柱主要在锁定区间完成相位的转变, 随频率比增大能量从流体传递到柱体的速度会减慢, 导致圆柱体结构完成从同相到反相的转变速度会减慢. 剪切来流工况下, 当间距比大于3.5时, 升力与位移相位差会出现“平台期”. 当间距比超过临界值时, 随着折减速度的增大, 流体力功率谱密度曲线出现的杂频会增多, 导致出现能量“反哺”现象. 最后, 在均匀来流工况下, 升阻力功率谱密度曲线中主频率值呈两倍关系, 然而随着剪切率的增加, 流体力功率谱密度曲线会基本重合.

     

  • 图  1  计算模型与边界条件

    Figure  1.  The computational model and boundary conditions

    2  不同频率比与剪切率工况下, 串列双圆柱双自由度最大振幅随折减速度的变化(L/D = 2.5)

    2.  The variation of the maximum vibrating amplitude of tandem double cylinders with reduced velocity under different frequency ratios and shear rates in two degrees of freedom (L/D = 2.5)

    图  2  不同频率比与剪切率工况下, 串列双圆柱双自由度最大振幅随折减速度的变化(L/D = 2.5) (续)

    Figure  2.  The variation of the maximum vibrating amplitude of tandem double cylinders with reduced velocity under different frequency ratios and shear rates in two degrees of freedom (L/D = 2.5) (continued)

    图  3  k = 0.0与Ur = 7时, 不同频率比下流场无量纲时均压力图

    Figure  3.  Dimensionless time-averaged pressure diagram of flow field at different frequency ratios at k = 0.0 and Ur = 7

    图  4  不同频率比与剪切率工况下, 串列双圆柱双自由度最大振幅随折减速度的变化(L/D = 3.5)

    Figure  4.  The variation of the maximum vibrating amplitude of tandem double cylinders with reduced velocity under different frequency ratios and shear rates in two degrees of freedom (L/D = 3.5)

    图  5  不同频率比工况下, 流场无量纲时均流场压力图(k = 0.05)

    Figure  5.  Dimensionless time-averaged pressure diagram of flow field at different frequency ratios (k = 0.05)

    图  6  不同频率比与剪切率工况下, 串列双圆柱双自由度最大振幅随折减速度的变化(L/D = 5.5)

    Figure  6.  The variation of the maximum vibrating amplitude of tandem double cylinders with reduced velocity under different frequency ratios and shear rates in two degrees of freedom (L/D = 5.5)

    7  r = 1.5, k = 0.1时不同折减速度下的同一时刻流场瞬时涡量图

    7.  Instantaneous vorticity diagram of flow field at the same time at r = 1.5 and k = 0.1

    图  7  r = 1.5, k = 0.1时不同折减速度下的同一时刻流场瞬时涡量图 (续)

    Figure  7.  Instantaneous vorticity diagram of flow field at the same time at r = 1.5 and k = 0.1 (continued)

    图  8  在不同剪切率与频率比下, 串列双圆柱升力与横流向位移相位差变化图(L/D = 2.5)

    Figure  8.  Diagram of phase difference between lift and transverse displacement of double cylinders in series at different shear rate and frequency ratio (L/D = 2.5)

    图  9  Ur = 6, 8, 10时, 上游圆柱升力与横流向位移时程曲线图 (k = 0.0, r = 2.0)

    Figure  9.  The time history curve of lift force and transverse displacement of upstream cylinder at Ur = 6, 8 and 10 (k = 0.0, r = 2.0)

    图  10  在不同剪切率与频率比下, 串列双圆柱升力与横流向位移相位差变化图(L/D = 3.5)

    Figure  10.  Diagram of phase difference between lift and transverse displacement of double cylinders in series at different shear rate and frequency ratio (L/D = 3.5)

    图  11  在不同频率比工况下, 下游圆柱升力与横流向位移时程曲线图(k = 0.1, Ur = 8)

    Figure  11.  The time history curve of lift force and transverse displacement of downstream cylinder at Ur = 6, 8 and 10 (k = 0.1, Ur = 8)

    图  12  在不同剪切率与频率比下, 串列双圆柱升力与横流向位移相位差变化图(L/D = 5.5)

    Figure  12.  Diagram of phase difference between lift and transverse displacement of double cylinders in series at different shear rate and frequency ratio (L/D = 5.5)

    图  13  Ur = 14时, 串列双圆柱升力与横流向位移时程曲线图(k = 0.1, r = 1.0)

    Figure  13.  The time history curve of lift force and transverse displacement of upstream cylinder and downstream cylinder at Ur = 14 (k = 0.1, r = 1.0)

    图  14  不同间距比工况下, 下游圆柱升力系数功率谱密度(红线)与阻力系数功率谱密度(黑线) (k = 0.0, r = 1.5)

    Figure  14.  The power spectral density of lift coefficient (red) and drag coefficient (black) of downstream cylinder under different spacing ratios (k = 0.0, r = 1.5)

    图  15  不同间距比工况下, 下游圆柱升力系数功率谱密度(红线)与阻力系数功率谱密度(黑线) (k = 0.1, r = 1.5)

    Figure  15.  The power spectral density of lift coefficient (red) and drag coefficient (black) of downstream cylinder under different spacing ratios (k = 0.1, r = 1.5)

    16  Ur = 7与Ur = 8工况下串列双圆柱的能量曲线(L/D = 3.5, k = 0.1, r = 1.5)

    16.  Energy curve of tandem double cylinders under the of Ur = 7 and Ur = 8 cases (L/D = 3.5, k = 0.1, r = 1.5)

    图  16  Ur = 7与Ur = 8工况下串列双圆柱的能量曲线(L/D = 3.5, k = 0.1, r = 1.5) (续)

    Figure  16.  Energy curve of tandem double cylinders under the of Ur = 7 and Ur = 8 cases (L/D = 3.5, k = 0.1, r = 1.5) (continued)

    表  1  网格独立性验证: 串列布置双圆柱流致振动计算结果(L/D = 2.5, r = 1.0, k = 0.0, Ur = 6.0)

    Table  1.   Grid independence test: the results for the two tandem circular cylinders at L/D = 2.5, r = 1.0, k = 0.0, Ur = 6.0

    GridGrid nodes distributed
    on the cylinder
    No. of elementsNo. of nodesXmax/DVariation of Xmax/DYmax/DVariation of Ymax/D
    GI16022952115620.0145(UC), 0.0063(DC)4.63%, 6.25%0.6276(UC), 0.4480(DC)4.76%, 4.96%
    GII20050239254690.01505(UC), 0.0067(DC)0.33%, 0.00%0.6586(UC), 0.4714(DC)0.06%, 0.00%
    GIII25080214401940.0151(UC), 0.0067(DC)0.6590(UC), 0.4714(DC)
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  • 收稿日期:  2021-08-06
  • 录用日期:  2021-10-16
  • 网络出版日期:  2021-10-17
  • 刊出日期:  2022-01-05

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