Vortex-induced vibration of cylinder under sub-critical Reynolds number
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摘要:
目的 为了实现亚临界雷诺数下圆柱涡激振动振幅响应的准确预报，利用数值模拟方法研究强迫振动时圆柱的升力系数与振幅比（Cl-A/D）之间的关系。 方法 基于Realizable k-ε 湍流模型，采用有限体积法对圆柱的强迫振动进行二维数值模拟，计算得到激振频率比fe/fn=1附近范围内不同振幅比下的升力系数曲线。选取圆柱振动速度最大时对应的升力系数，建立Cl-A/D关系曲线。 结果 结果表明，Cl-A/D拟合曲线总体变化趋势与涡激振动预报程序SHEAR7的结果吻合良好。同时，各激振频率比fe/fn下的零升力系数点均位于振幅比A/D=0.8附近，且结构尾涡脱落模式在A/D=0.8附近发生了转变，由“P+S”模式转变到“2P”模式（P 表示一对旋转方向相反的旋涡脱落，S 表示单个旋涡脱落）。在圆柱涡激振动实验中，发现涡激振动出现“锁定”时的最大振幅在0.8D附近。 结论 亚临界雷诺数下强迫振动圆柱Cl-A/D关系曲线升力系数为零时对应的振幅比与圆柱在涡激振动中的最大响应振幅比基本保持一致，且圆柱尾涡脱落模式在此振幅比下发生了转变。 Abstract:Objective In order to achieve the accurate prediction of the amplitude response of a vortex-induced vibrating cylinder under the sub-critical Reynolds number, a method for establishing a Cl-A/D (lift coefficient-amplitude ratio)model of the forced vibration of the cylinder by numerical simulation is proposed. Methods Based on the Realizable k-ε model, a two-dimensional numerical simulation of the forced vibration of a cylinder is carried out using the finite volume method. The calculated lift coefficient curves under different amplitude ratios A/D in the range of excitation frequency ratio fe/fn=1 are obtained. The lift coefficient corresponding to the maximum vibration velocity of the cylinder is then selected to establish the Cl-A/D model. Results The results show that the overall trend of the Cl-A/D fitting curve is in good agreement with the predicted results of SHEAR7. At the same time, it is found that the "zero lift coefficient" points under each excitation frequency ratio fe/fn are all located near the amplitude ratio A/D=0.8, and the wake shedding mode changes around A/D=0.8 from "P+S" to "2P" (P represents a pair of vortex shedding with opposite rotation directions, and S represents a single vortex shedding). In the vortex-induced vibration experiment of a single cylinder, the maximum amplitude when "lock-in" occurs is around 0.8D. Conclusions The amplitude ratio corresponding to the "zero lift coefficient" of the Cl-A/D model of forced vibrating cylinder under sub-critical Reynolds number is consistent with the maximum response amplitude ratio of the cylinder under vortex-induced vibration, and the shedding mode of the wake vortex changes under this amplitude ratio. -
Key words:
- vortex-induced vibration /
- forced oscillation /
- vortex shedding mode /
- amplitude ratio /
- frequency ratio
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图 3 Re=20 000固定圆柱升力系数能量谱密度
Figure 3. Energy spectral density of lift coefficient of fixed cylinder with Re=20 000
图 5 单周期内振动速度及升力系数变化曲线
Figure 5. Oscillating speed and lift coefficient varies within a single period
图 7 各激振频率下升力系数拟合曲线
Figure 7. Fitting curves of lift coefficient at each excitation frequency
图 8 各工况下Cl随振幅比A/D变化曲线
Figure 8. Variation of lift coefficient with A/D under all conditions
图 9 圆柱涡激振动实验装置
Figure 9. Experimental device setup of cylindrical vortex-induced vibration
图 10 圆柱振幅比及自激振动频率比随约化速度变化图
Figure 10. Changes in the amplitude ratio and self-induced vibration frequency ratio of the cylinder at different reduced speeds
图 11 各频率比下涡量随振幅比变化图
Figure 11. Variation of vorticity with amplitude ratio at various frequency ratios
表 1 无量纲频率比及振幅比范围
Table 1. Non-dimensional frequency ratio and amplitude ratio
A/D fe/fn 0.3~1.2 0.83，0.91，1.00，1.11，1.25，1.42 
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