剪切来流作用下串列布置双圆柱流致运动分析
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摘要
基于任意拉格朗日-欧拉方法,将四步半隐式特征线分裂算子有限元与动网格技术相结合,并发展了一种求解流致振动问题的算法。首先,通过求解文献中经典涡激振动算例来验证本文方法的正确性;然后,着重分析了雷诺数Re=160与间距比Lx/D=5.5工况,折减速度与剪切率两个关键参数对串列排布双圆柱两自由度流致运动特性的影响。计算结果表明:随折减速度的增加,上游圆柱振幅变化与单圆柱工况一致;但是,下游圆柱顺流向振幅的变化较为剧烈,且横流向的振幅曲线中会出现两个峰值。随剪切率的增加,双圆柱体两个方向的频率锁定区间会扩大,尤其对顺流向的振幅影响较大。另外,双圆柱体的运动轨迹以‘8’字形与‘O’形为主。最后,分析了剪切来流对双圆柱体之间互扰机制的影响,以及下游圆柱的涡致动力响应特征所发生的变化。
Based on the Arbitrary-Lagrangian-Eulerian(ALE) method, the formulation of four-step semi-implicit characteristic-based split scheme, together with a dynamic mesh technique, is developed to solve the flow-induced vibration problem. Firstly, for the computational code verification, the benchmark vortex-induced vibration problem in the published literatures is examined. And then, the effects of two key parameters, reduced velocity(Ur) and shear ratio(k), on the two-degree-of-freedom flow-induced motion characteristics of two tandem circular cylinders are analyzed in the case of Re=160 and spacing ratio Lx/D=5.5. The results show that the change of the vibration amplitude is similar to that of an isolated cylinder for the upstream cylinder with the increasing of Ur. For the downstream cylinder, however, there is a dramatic change of the in-line vibration amplitude, and two peaks occur at the transverse direction. As k increases, the lock-in region of both cylinders in the in-line and cross-flow direction broadens. Especially, the influence of the shear ratio on the in-line oscillation amplitude is insignificant. Additionally, the prominent motion trajectories of both cylinders are figure-eight and figure-O. Finally, effect of shear flow on the interaction mechanism between circular cylinders and the change of dynamic response characteristics of downstream cylinder are analyzed.
Based on the Arbitrary-Lagrangian-Eulerian(ALE) method, the formulation of four-step semi-implicit characteristic-based split scheme, together with a dynamic mesh technique, is developed to solve the flow-induced vibration problem. Firstly, for the computational code verification, the benchmark vortex-induced vibration problem in the published literatures is examined. And then, the effects of two key parameters, reduced velocity(Ur) and shear ratio(k), on the two-degree-of-freedom flow-induced motion characteristics of two tandem circular cylinders are analyzed in the case of Re=160 and spacing ratio Lx/D=5.5. The results show that the change of the vibration amplitude is similar to that of an isolated cylinder for the upstream cylinder with the increasing of Ur. For the downstream cylinder, however, there is a dramatic change of the in-line vibration amplitude, and two peaks occur at the transverse direction. As k increases, the lock-in region of both cylinders in the in-line and cross-flow direction broadens. Especially, the influence of the shear ratio on the in-line oscillation amplitude is insignificant. Additionally, the prominent motion trajectories of both cylinders are figure-eight and figure-O. Finally, effect of shear flow on the interaction mechanism between circular cylinders and the change of dynamic response characteristics of downstream cylinder are analyzed.
引文
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[8]王俊高,付世晓,许玉旺,等.正弦振荡来流下柔性立管涡激振动发展过程[J].力学学报,2014,46(2):173-182.(WANG Jungao,FU Shixiao,XU Yuwang,et al.VIV developing process of a flexible cylinder under oscillatory flow[J].Chinese journal of theoretical and applied mechanics,2014,46(2):173-182(in Chinese)).
[9]黄智勇,崔维成,黄小平.均匀平面剪切流作用下圆柱体的涡激振动[J].哈尔滨工程大学学报,2007,28(12):1301-1306.(HUANG Zhiyong,CUI Weicheng,HUANG Xiaoping.Vortex-induced vibration of a cylinder in uniform planar shear flow[J].Journal of Harbin engineering university,2014,46(2):173-182(in Chinese)).
[10]TU J H,ZHOU D,BAO Y,et al.Flow-induced vibration on a circular cylinder in planar shear flow[J].Computers and fluids,2014,105(105):138-154.
[11]ZHANG H,FAN B C,CHEN Z H,et al.An in-depth study on vortex-induced vibration of a circular cylinder with shear flow[J].Computers and fluids,2014,100(100):30-44.
[12]LIN J Z,JIANG R J,CHEN Z L,et al.Poiseuille flow-induced vibrations of two cylinders in tandem[J].Journal of fluids and structures,2013,40(7):70-85.
[13]涂佳黄.剪切来流下钝体结构绕流与涡激振动效应模拟和分析[D].上海:上海交通大学,2014.(TU Jiahuang.Numerical study on flow over bluff bodies and vortex-induced vibrations in planar shear flow[D].Shanghai:Shanghai Jiao Tong University,2014(in Chinese)).
[14]MASUD A,BHANABHAGVANWALA M,KHURRAM R A.An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction[J].Computers and fluids,2007,36(1):77-91.
[2]WU X,GE F,HONG Y.A review of recent studies on vortex-induced vibrations of long slender cylinders[J].Journal of fluids and structures,2012,28(1):292-308.
[3]PRASANTH T K,MITTAL S.Flow-induced oscillation of two circular cylinders in tandem arrangement at low Re[J].Journal of fluids and structures,2009,25(6):1029-1048.
[4]冯志鹏,臧峰刚,张毅雄.两交错排列弹性管的流致振动特性研究[J].应用力学学报,2015,32(1):1-5.(FENG Zhipeng,ZANG Fenggang,ZHANG Yixiong.Investigation of flow induced vibration characteristics in two staggered flexible tubes[J].Chinese journal of applied mechanics,2015,32(1):1-5(in Chinese)).
[5]郭晓玲,唐国强,刘名名,等.低雷诺数下串联双圆柱涡激振动机理的数值研究[J].振动与冲击,2014,33(4):60-69.(GUO Xiaoling,TANG Guoqiang,LIU Mingming,et al.Numerical investigation on vortex-induced vibration of twin tandem circular cylinders under low Reynolds number[J].Journal of vibration and shock,2014,33(4):60-69(in Chinese)).
[6]ANAGNOSTOPOULOS P,ILIADIS G.Numerical study of the flow pattern and the in-line response of a flexible cylinder in an oscillating stream[J].Journal of fluids and structures,1998,12(3):225-258.
[7]ZHAO M,CHENG L,AN H W.Numerical investigation of vortex-induced vibration of a circular cylinder in transverse direction in oscillatory flow[J].Ocean engineering,2012,41(5):39-52.
[8]王俊高,付世晓,许玉旺,等.正弦振荡来流下柔性立管涡激振动发展过程[J].力学学报,2014,46(2):173-182.(WANG Jungao,FU Shixiao,XU Yuwang,et al.VIV developing process of a flexible cylinder under oscillatory flow[J].Chinese journal of theoretical and applied mechanics,2014,46(2):173-182(in Chinese)).
[9]黄智勇,崔维成,黄小平.均匀平面剪切流作用下圆柱体的涡激振动[J].哈尔滨工程大学学报,2007,28(12):1301-1306.(HUANG Zhiyong,CUI Weicheng,HUANG Xiaoping.Vortex-induced vibration of a cylinder in uniform planar shear flow[J].Journal of Harbin engineering university,2014,46(2):173-182(in Chinese)).
[10]TU J H,ZHOU D,BAO Y,et al.Flow-induced vibration on a circular cylinder in planar shear flow[J].Computers and fluids,2014,105(105):138-154.
[11]ZHANG H,FAN B C,CHEN Z H,et al.An in-depth study on vortex-induced vibration of a circular cylinder with shear flow[J].Computers and fluids,2014,100(100):30-44.
[12]LIN J Z,JIANG R J,CHEN Z L,et al.Poiseuille flow-induced vibrations of two cylinders in tandem[J].Journal of fluids and structures,2013,40(7):70-85.
[13]涂佳黄.剪切来流下钝体结构绕流与涡激振动效应模拟和分析[D].上海:上海交通大学,2014.(TU Jiahuang.Numerical study on flow over bluff bodies and vortex-induced vibrations in planar shear flow[D].Shanghai:Shanghai Jiao Tong University,2014(in Chinese)).
[14]MASUD A,BHANABHAGVANWALA M,KHURRAM R A.An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction[J].Computers and fluids,2007,36(1):77-91.