GALLOPING IN VORTEX-INDUCED VIBRATION OF THREE TANDEM CYLINDERS AT LOW REYNOLDS NUMBERS AND ITS INFLUENCING FACTORS
ChenWeilin, JiChunning*,, XuDong State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China 中图分类号:P751,TV131.2 文献标识码:A
关键词:涡激振动;串列三圆柱;弛振;质量比;雷诺数 Abstract Vortex-induced vibrations of three tandem cylinders at the spacing ratio of 1.2 and the Reynolds number of 100 shows that when the reduced velocity is larger than a critical value, the galloping is observed where the amplitudes of three cylinders increase with the reduced velocity. Three factors, including shift of equilibrium position, low vibration frequency and timing between vortex shedding and motion of cylinders, determine the appearance of galloping. Further investigations show that the galloping occurs at a range with lower mass ratio no more than 2.0 and Reynolds number no more than 100. When the mass ratio is large, the equilibrium position is unchanged and the displacements are irregular, which leads to the variation of timing between vortex shedding and motion of cylinders. When Re is large, the shift of the most upstream cylinder is zero and no more accommodate cylinders’ vibration, which makes the vibration irregular and change of timing between vortex shedding and motion of cylinders.
Keywords:vortex-induced vibration;three tandem cylinders;galloping;mass ratio;Reynolds number -->0 PDF (10472KB)元数据多维度评价相关文章收藏文章 本文引用格式导出EndNoteRisBibtex收藏本文--> 陈威霖, 及春宁, 许栋. 低雷诺数下串列三圆柱涡激振动中的弛振现象及其影响因素 <sup>^1)</sup>[J]. 力学学报, 2018, 50(4): 766-775 https://doi.org/10.6052/0459-1879-18-057 ChenWeilin, JiChunning, XuDong. GALLOPING IN VORTEX-INDUCED VIBRATION OF THREE TANDEM CYLINDERS AT LOW REYNOLDS NUMBERS AND ITS INFLUENCING FACTORS[J]. Acta Mechanica Sinica, 2018, 50(4): 766-775 https://doi.org/10.6052/0459-1879-18-057 弛振现象一直是工程实际中一个值得关注的现象. 例如, 桥梁工程中的悬索桥, 由于其自身质量小、频率低、阻尼小, 在风的作用下极易发生大幅振动, 塔科马悬索桥的破坏就是一个典型的例子[1]. 此外, 工业中常见的热交换器管阵也容易发生弛振, 造成热交换器的疲劳破坏. 由于热交换管的直径较小, 且热媒多为密度较小的水蒸气, 其雷诺数较低. 因此, 对低雷诺数弛振现象的研究将具有非常重要的意义. 弛振现象最早发现于非圆形结构物的涡激振动中, 随着来流流速的增大, 结构的振幅持续增大. Den Hartog[2]基于对被冰包裹电缆的研究发现弛振一般伴随着低频的出现. Parkinson和Smith[3] 建立了一个准稳态的理论, 用来预测弛振下方柱的振幅. 该理论成功地预测了较大和较小阻尼下空气中方柱的弛振现象. Nemes 等[4]通过水槽实验研究发现, 当攻角为 时, 振动的方柱表现为弛振, 角度设置如图1(a)所示. Zhao 等[5]发现, 三倍振动频率的升力成分对方柱弛振的出现有重要的影响. 目前的研究表明, 方柱的弛振现象仅在较高的雷诺数下出现. Barrero-Gril 等[6] 发现当Re < 159时, 振动的方柱不会出现弛振. Zhao 等[7] 对不同攻角( )下弹性支撑方柱的数值模拟发现, 当 时, 弛振没有出现. 此外, 对弹性支撑三角柱实验研究发现, 当雷诺数较高时, 振动的三角柱在某些攻角下表现为弛振现象[8,9]. Wang 等[10]对不同攻角( ) 下振动三角柱的数值模拟研究表明, 当 和 时, 攻角设置如图1(b)所示, 三角柱表现为弛振现象, 振幅随着折合流速的增大而增强. 显示原图|下载原图ZIP|生成PPT 图1方柱和三角柱的攻角(). -->Fig.1The attack angle of the square and triangular cylinder -->
表1给出了串列三圆柱绕流下各圆柱阻力均值与Harimi和Saghafian[30]结果的对比, 其中最大差别仅为6.7%, 从而验证本文数值方法和程序的正确性. 更多的验证算例包括单圆柱涡激振动、并列双圆柱绕流、串列双圆柱绕流和涡激振动等参见文献 [24,26-29]. Table 1 表1 表1串列三圆柱绕流的阻力均值, 其中和 Table 1The mean drag coefficients of flow past three tandem circular cylinders at and
选取 和 研究雷诺数对串列三圆柱涡激振动中弛振现象的影响, 此时质量比为 和间距比为 . 由于研究的雷诺数范围内, 串列三圆柱的振动规律, 因此用圆柱振动的最大幅值( ) 表示圆柱的振动响应. 如图9(a)所示, 当 时, 串列三圆柱的振动在 以后急剧增强并在达到峰值之后缓慢减弱, 之后三圆柱的振动在某个折合流速以后随着折合流速的增大而持续增强. 因此, 可以认为此时串列三圆柱涡激振动中出现了弛振现象. 与 时的工况相比, 此时圆柱的振幅要更大一些, 随着折合流速增大而增大的幅度也要稍大一些. 表3 给出了折合流速 和 时串列三圆柱最大振幅的对比结果, 可以发现, 雷诺数 下串列三圆柱的振幅增大可以持续到 时; 雷诺数 时串列三圆柱的振幅要明显大于雷诺数 下的情况. 显示原图|下载原图ZIP|生成PPT 图9不同雷诺数下串列三圆柱响应随折合流速变化的情况. -->Fig.9Variations of the vibration of three cylinders with at different -->
Table 3 表3 表3不同雷诺数和折合流速下串列三圆柱的最大振幅 Table 3The maximum amplitudes of three cylinders at different Reynolds numbers and reduced velocities
*80
40
0.87
1.33
1.35
80
0.98
1.48
1.50
*100
40
0.80
1.25
1.27
80
0.84
1.28
1.28
新窗口打开 当 时, 串列三圆柱的振幅从 以后开始增大, 均在 时达到最大值, 此后, 振幅随折合流速增大而减小. 如图9(b) 所示, 三圆柱的振幅均在 以后又开始增大并在 出现一个峰值. 当 以后三圆柱的振幅均几乎不再发生变化. 虽然三圆柱的振幅可以维持在较大的值上, 但是由于振幅不再随折合流速的增大而增大, 因此, 弛振现象不再出现. 为进一步解释尾流弛振现象出现在低雷诺数 ( 为80和100) 而没有出现在 下串列三圆柱涡激振动中的原因, 对该现象出现决定性因素展开如下讨论. 如图10所示, 各雷诺数下, 串列三圆柱的平衡位置均发生偏移. 随着雷诺数的增大, 平衡位置偏移出现更小的折合流速下. 对比 和 下平衡位置的偏移可以发现, 圆柱2和3 的平衡位置偏向同一个方向, 而圆柱1会偏向另一个方向. 当 时, 圆柱1和2在 时偏向同一个方向, 而圆柱3偏向另一个方向. 当 以后, 圆柱1 的平衡位置逐渐恢复到初始位置 ( ) 上. 当 时, 圆柱1 的平衡位置不再发生偏移, 而圆柱2 和3的平衡位置偏向了同一个方向, 且此时圆柱3 的平衡位置偏移要明显大于圆柱2的情况. 因此, 可以这么认为, 此时圆柱1不再具有调和圆柱2 和3 振动响应的作用了. 显示原图|下载原图ZIP|生成PPT 图10不同雷诺数下三圆柱平衡位置偏移随折合流速变化的情况. -->Fig.10Variations of the shift of the equilibrium position with at different Reynolds numbers -->
如图11所示, 各雷诺数下, 串列三圆柱的非常接近. 当时, 串列三圆柱在时进入锁定区间, 而当取80和100时, 三圆柱在时进入锁定区间, 之后, 随着折合流速的增大, 下降. 在锁定区间以后的折合流速范围内, 不同雷诺数下的均非常接近. 显示原图|下载原图ZIP|生成PPT 图11不同雷诺数下串列三圆柱的随折合流速变化情况. -->Fig.11Variations of the Strouhal number of three cylinders with at different Reynolds numbers -->
如图12所示, 当和时, 串列三圆柱的振动不规律, 此时串列三圆柱之间的相互作用不稳定. 图13给出了时串列三圆柱后的尾流情况, 尾涡不规律, 旋涡脱落与圆柱运动的时机不固定, 弛振现象不再出现. 显示原图|下载原图ZIP|生成PPT 图12当和时, 串列三圆柱响应的历时曲线. -->Fig.12Time histories of the displacements of three cylinders at and -->
显示原图|下载原图ZIP|生成PPT 图13当和时, 串列三圆柱后的涡量场. -->Fig.13Vorticity contour around three cylinders at and -->
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