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细长柔性悬臂管道涡激振动响应特性数值研究

NUMERICAL STUDY ON RESPONSE CHARACTERISTICS OF VORTEX-INDUCED VIBRATION OF A LONG, FLEXIBLE CANTILEVERED PIPE

  • 摘要: 基于尾流振子模型, 对末端带有集中质量块的柔性悬臂管道涡激振动响应特性进行了数值研究, 研究过程中考虑了3种不同的流剖面: 线性剪切、指数剪切以及真实阶梯流剖面. 首先建立了柔性悬臂管道结构振子和尾流振子之间的耦合模型; 紧接着基于二阶精度中心差分格式对耦合模型先离散后迭代进行求解; 最后系统地分析了3种流剖面下结构的振动位移、振动频率等响应特性. 数值计算结果表明: 针对带末端集中质量块的悬臂式管道结构, 3种不同流剖面作用下, 沿整个管道轴线方向上, 结构振动均呈现出多频响应特征, 结构振动主导模态阶数非常接近, 结构振动呈现出驻波和行波相互混合的特征, 且结构振动行波传播方向总是从流速较大的上端区域到流速较小的下端区域. 尽管存在一定共性, 不同流剖面下柔性悬臂管道涡激振动响应特性仍存在一些差异, 线性剪切以及指数剪切流剖面下柔性悬臂管道涡激振动位移响应最大值均出现在管道末端, 而真实阶梯流剖面下结构振动位移响应最大值并不出现在结构末端; 线性剪切流剖面下悬臂管道涡激振动频率能量分布较为集中, 呈“簇状峰”模式振动, 结构振动呈准周期特征; 而指数剪切和真实阶梯流剖面下悬臂管道涡激振动频率能量分布非常分散, 呈宽带分布, 结构振动表现出混乱特征.

     

    Abstract: The vortex-induced vibration (VIV) response characteristics of a flexible cantilevered pipe with a concentrated mass block at the free end are numerically investigated based on the wake oscillator model under three typical flow profiles: linear shear flow, exponential shear flow, and real stepped flow. First, a coupling model is developed between the structural oscillator of the flexible cantilevered pipe and the wake oscillator. Then, the coupling model is discretized using a second-order central difference scheme and solved through iterative methods. Finally, the vibration displacement, dominant vibration frequency, and other response features of the structure are systematically analyzed under the influence of the three flow profiles. Numerical results show that, for the cantilevered pipe with a tip mass, the VIV responses along the pipe axis under all three flow conditions exhibit multi-frequency characteristics. The dominant modal orders of vibration are very close for different flow profiles. The structural vibration patterns feature a combination of standing and traveling waves, with the traveling waves consistently propagating from the upper region with higher flow velocity toward the lower region with slower flow velocity, indicating a common propagation trend. Despite these similarities, notable differences in VIV responses are observed among the three flow profiles. Under linear shear flow and exponential shear flow, the maximum vibration displacement of the pipe appears at the free end. However, under the real stepped flow profile, the maximum displacement occurs at a lower or middle section of the pipe. Moreover, the VIV frequency energy distribution under linear shear flow is more concentrated, forming a “clustered peak” spectrum and showing quasi-periodic vibration characteristics. In contrast, under exponential shear flow and real stepped flow, the frequency energy distribution becomes more dispersed, presenting a broadband spectrum and a more chaotic vibration behavior.

     

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