正三角形排列三圆柱绕流与涡致振动数值模拟

Numerical simulation of vortex-induced vibration of three cylinders subjected to a cross flow in equilateral arrangement

基于有限体积法求解二维粘性不可压缩N-S方程,对低雷诺数下正三角形排列等直径三圆柱的绕流与涡致振动进行数值模拟。圆柱振动简化为两自由度的质量-弹簧-阻尼模型,圆柱的动力响应通过Newmark-β方法求解。间距比在1.5~6.0之间变化,重点研究各圆柱的气动力和响应及相关的频率特性、尾流流动模式随间距比的变化。研究结果表明：三圆柱发生振荡时的气动力要远大于绕流结果,当间距比在3.5~4.0之间气动干扰最为强烈。当间距比大于3.0时,下游圆柱的横向和流向位移相位差出现周期性切换,导致升力系数均值出现波动,并且下游圆柱的质心运动轨迹为斜向上和斜向下椭圆形的叠加。三圆柱的最大横向位移幅值均能达到0.9D,下游圆柱的最大流向振幅达到1.1D,这说明组成多圆柱振荡系统单柱的横向位移远大于孤立圆柱发生涡激共振的最大位移,并且下游圆柱的流向振荡不可忽视。

A numerical simulation the vortex-induced vibration of three equal diameter cylinders subjected to cross flow in equilateral arrangement is presented in this paper at low Reynolds number.The 2-D Navier-Stokes equations are solved by a finite volume method with an industrial CFD code in which a Newmark-β procedure has been implemented in order to obtain the cylinder response.The motion of every single cylinder,which is free to oscillate in two degrees-of-freedom,is modeled by a mass-spring-damping system.The aerodynamic forces,response,related frequency characteristic and flow pattern for each cylinder are mainly studied with spacing ratio changing from 1.5 to 6.0.The results indicate that the aerodynamic forces are larger than the results of flow around static cylinders and the aerodynamic interference is most intensive when the space ratio is in the range of 3.5~4.0.The phase difference between the transverse and streamwise displacements appears a periodic switch,which induces the fluctuation of mean value of lift coefficient and makes that the trajectory of the mass centre of the downstream cylinder is the superimposition of an oblique upside ellipse and an oblique downside ellipse when the space ratio is larger than 3.0.The maximum transverse amplitude of three cylinders can reach to 0.9D and the streamwise oscillation of downstream cylinder could be as large as 1.1D.It is indicated that the transverse oscillation amplitude of three cylinders significantly increased compared with the flow-induced vibration of an elastic cylinder and the streamwise oscillation of downstream cylinder is unneglectable for vortex-induced vibration of multi-cylinder system.