本文采用有限体积法对圆形四立柱涡激运动进行数值模拟。圆形四立柱涡激运动系统简化为两自由度的质量-弹簧-阻尼模型，引入雷诺平均应力模型求解不可压缩粘性Navier-Stokes方程,并结合SST k-w湍流模型对低质量比弹性支撑的圆形四立柱涡激运动进行模拟。将四阶Runge-Kutta代码嵌入用户自定义函数UDF(User Defined Function)中求解四立柱的动力响应，采用动网格技术来实现立柱和流场之间的耦合。研究发现，圆形四立柱涡激运动流向和横向振幅随着折合速度的增大而先增大后减小，并出现幅值跳跃现象，跳跃点在折合速度9.0处。横向振幅最大值出现在折合速度为8.0时，大小为1.99D，远大于流向振幅最大值0.26D。圆形四立柱流向运动平衡位置随折合速度增大并非一直增大，在折合速度9.0时突然下降随后增大。圆形四立柱涡激运动出现了明显的频率锁定现象，锁定区间为5.0-8.0。当系统走过锁定系统后，流向幅值和流向幅值迅速减小。最后本文对不同折合速度下圆形四立柱运动轨迹和尾涡脱落模式进行讨论分析。
Abstract
In this paper, the finite volume method is used to simulate vortex-induced motion of four circular columns. The vortex-induced motion system of four circular columns is simplified into spring-mass-damping model. Reynolds-Averaged Navier-Stokes solver combined with the SST (Shear-Stress Transport) k-ω turbulence model for the Navier-Stokes equation has been used to simulate the vortex induced motion at low mass ratio. Fourth order Runge-Kutta method was manually written into the User Defined Functions to solve the dynamic response of four circular columns, and then dynamic mesh technology was adopted to resolve the coupling fluid structure interaction. It is found that the amplitude of the four circular columns first increase and then decrease with the increase of reduced velocity, ‘jump’ phenomenon is observed in the amplitude curve at the reduced velocity of 9.0. The transverse maximum amplitude appeared at reduced velocity of 8.0, the value is 1.99D, which is much larger than the stream-wise maximum amplitude, 0.26D. In-line balance position of square column didn’t always increase with the increase of reduced velocity, it suddenly decreases at the reduced velocity of 9.0 and then increase. Frequency lock-in phenomenon is found on the study of four circular columns vortex-induced motion, the lock-in region is at the reduced velocity of 5.0-8.0. When the vortex-induced system passed the lock-in region, stream-wise and transverse amplitude suddenly decrease. Finally, the trajectory and vortex shedding pattern of four circular columns at different velocities are discussed.
关键词
圆形四立柱 /
涡激运动 /
频率锁定 /
动网格
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Key words
four circular columns /
vortex-induced motion /
frequency lock in /
dynamic mesh
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