层流条件下并列三圆柱涡激振动响应与尾流形态
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摘要
应用基于嵌入式压强-力迭代的高精度浸入边界法研究等间距并列三圆柱涡激振动。其中,雷诺数Re=100,间距比T/D=2.0～5.0,圆柱质量比m*=2.0,折合流速Ur=2.0～10.0,忽略振动系统的阻尼且三圆柱仅横向振动。研究发现,圆柱的振动响应随折合流速的增加呈现初始响应分支和下端响应分支两种模式;振幅响应出现不连续现象,且随着间距比的增加,该不连续现象对应的折合流速增加;尾流模式与间距比和折合流速密切相关。共发现六种尾流形态,分别为窄宽窄尾流、不规律尾流、反相同步尾流、调制尾流、同相同步尾流和偏斜尾流。总结并绘制了尾流形态在参数空间[Ur,T/D]内的分区图。
Flow-induced vibrations(FIVs)of three side-by-side cylinders are numerically investigated using a highly accurate immersed boundary method(IBM)utilizing the built-in pressure-force iterations.The Reynolds nubmer is Re=100.The center-to-center spacing ratio T/Dis set as 2.0,2.5,3.0,4.0,5.0,respectively.The mass ratio is m*=2.0 and the reduced velocity is in the range of Ur=2.0～10.0,the damping ratio is zero.The vibration of the cylinders is allowed only in the cross-flow direction.It was found that the response of the cylinders experiences two vibration modes,i.e.the initial and the lower branches,with the increasing reduced velocity.A discontinuity is observed in the response.With the increase of spacing ratio,its corresponding reduced velocity increases.The near-wake patterns significantly depend on T/Dand Ur.Six near-wake patterns are observed,i.e.,the narrow-wide-narrow pattern,the irregular pattern,the anti-phase-synchronized pattern,the modulated pattern,the in-phasesynchronized pattern and the biased gap-flow pattern.A partition map of the near-wake patterns in the parameter space[Ur,T/D]is given.
Flow-induced vibrations(FIVs)of three side-by-side cylinders are numerically investigated using a highly accurate immersed boundary method(IBM)utilizing the built-in pressure-force iterations.The Reynolds nubmer is Re=100.The center-to-center spacing ratio T/Dis set as 2.0,2.5,3.0,4.0,5.0,respectively.The mass ratio is m*=2.0 and the reduced velocity is in the range of Ur=2.0～10.0,the damping ratio is zero.The vibration of the cylinders is allowed only in the cross-flow direction.It was found that the response of the cylinders experiences two vibration modes,i.e.the initial and the lower branches,with the increasing reduced velocity.A discontinuity is observed in the response.With the increase of spacing ratio,its corresponding reduced velocity increases.The near-wake patterns significantly depend on T/Dand Ur.Six near-wake patterns are observed,i.e.,the narrow-wide-narrow pattern,the irregular pattern,the anti-phase-synchronized pattern,the modulated pattern,the in-phasesynchronized pattern and the biased gap-flow pattern.A partition map of the near-wake patterns in the parameter space[Ur,T/D]is given.
引文
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[13]陈威霖,及春宁.单圆柱涡激振动中的振幅不连续和相位切换现象研究[J].水动力学研究与进展A辑,2016,31(4):441-448.(CHEN Wei-lin,JI Chun-ning.Vibration amplitude discontinuity and phase jump of vortex-induced vibration of an isolated circular cylinder[J].Chinese Journal of Hydrodynamics,2016,31(4):441-448.(in Chinese)).
[14]Zhou Y.Vortical structures behind three side-by-side cylinders[J].Experiments in Fluids,2003,34(1):68-76.
[15]Harichandan A B,Roy A.Numerical investigation of low Reynolds number flow past two and three circular cylinders using unstructured grid CFR scheme[J].International Journal of Heat and Fluid Flow,2010,31(2):154-171.
[16]Kang S.Numerical study on laminar flow over three side-by-side cylinders[J].KSME International Journal,2004,18(10):1869-1879.
[17]Han Z,Zhou D,Tu J H.Laminar flow patterns around three side-by-side arranged circular cylinders using semi-implicit three-step Taylor-characteristicbased-split(3-TCBS)algorithm[J].Engineering Applications of Computational Fluid Mechanics,2013,7(1):1-12.
[18]Ji C N,Munjiza A,Williams J J R.A novel iterative direct-forcing immersed boundary method and its finite volume applications[J].Journal of Computational Physics,2012,231(4):1797-1821.
[2]及春宁,李非凡,陈威霖,等.圆柱涡激振动研究进展与展望[J].海洋技术学报,2015,34(1):106-118.(JI Chun-ning,LI Fei-fan,CHEN Wei-lin,et al.Progress and prospect of the study on vortex-induced vibration of circular cylinders[J].Journal of Ocean Technology,2015,34(1):106-118.(in Chinese))
[3]徐枫,欧进萍.低雷诺数下弹性圆柱体涡激振动及影响参数分析[J].计算力学学报,2009,26(5):613-619.(XU Feng,OU Jin-ping.Analysis of vortexinduced vibration of an elastic cylinder and influence parameters at low Reynolds number[J].Chinese Journal of Computational Mechanics,2009,26(5):613-619.(in Chinese))
[4] Williamson C H K,Roshko A.Vortex formation in the wake of an oscillating cylinder[J].Journal of Fluids and Structures,1988,2(4):355-381.
[5] Ji C N,Xiao Z,Wang Y Z,et al.Numerical investigation on vortex-induced vibration of an elastically mounted circular cylinder at low Reynolds number using the fictitious domain method[J].International Journal of Computational Fluid Dynamics,2011,25(4):207-221.
[6] Alam M M,Zhou Y.Intrinsic features of flow around two side-by-side square cylinders[J].Physics of Fluids,2013,25(8):085106.
[7] Supradeepan K,Roy A.Characterisation and analysis of flow over two side by side cylinders for different gaps at low Reynolds number:A numerical approach[J].Physics of Fluids,2014,26(6):063602.
[8] Chen W L,Ji C N,Xu W H,et al.Responses and wake patterns of two side-by-side elastically supported circular cylinders in uniform laminar cross-flow[J].Journal of Fluids and Structure,2015,55:218-236.
[9] Xu Y,Liu Y,Xia Y,et al.Lattice-Boltzmann simulation of two-dimensional flow over two vibrating sideby-side circular cylinders[J].Physical Review E,Statistical Nonlinear&Soft Matter Physics,2008,78(4):046314.
[10]Bao Y,Zhou D,Tu J H,et al.Flow characteristics of two in-phase oscillating cylinders in side-by-side arrange-ment[J].Computers&Fluids,2013,71:124-145.
[11]及春宁,陈威霖,黄继露,等.串列双圆柱流致振动的数值模拟及其耦合机制[J].力学学报,2014,46(6):862-870.(JI Chun-ning,CHEN Wei-lin,HUANG Jilu,et al.Numerical investigation on flow-induced vibration of two cylinders in tandem arrangements and its coupling mechanisms[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(6):862-870.(in Chinese))
[12]陈威霖,及春宁,徐万海.并列双圆柱流致振动的不对称振动和对称性迟滞研究[J].力学学报,2015,47(5):731-739.(CHEN Wei-lin,JI Chun-ning,XU Wan-hai.Numerical investigation on the asymmetric vibration and symmetry hysteresis of flow-induced vibration of two side-by-side cylinders[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(5):731-739.(in Chinese))
[13]陈威霖,及春宁.单圆柱涡激振动中的振幅不连续和相位切换现象研究[J].水动力学研究与进展A辑,2016,31(4):441-448.(CHEN Wei-lin,JI Chun-ning.Vibration amplitude discontinuity and phase jump of vortex-induced vibration of an isolated circular cylinder[J].Chinese Journal of Hydrodynamics,2016,31(4):441-448.(in Chinese)).
[14]Zhou Y.Vortical structures behind three side-by-side cylinders[J].Experiments in Fluids,2003,34(1):68-76.
[15]Harichandan A B,Roy A.Numerical investigation of low Reynolds number flow past two and three circular cylinders using unstructured grid CFR scheme[J].International Journal of Heat and Fluid Flow,2010,31(2):154-171.
[16]Kang S.Numerical study on laminar flow over three side-by-side cylinders[J].KSME International Journal,2004,18(10):1869-1879.
[17]Han Z,Zhou D,Tu J H.Laminar flow patterns around three side-by-side arranged circular cylinders using semi-implicit three-step Taylor-characteristicbased-split(3-TCBS)algorithm[J].Engineering Applications of Computational Fluid Mechanics,2013,7(1):1-12.
[18]Ji C N,Munjiza A,Williams J J R.A novel iterative direct-forcing immersed boundary method and its finite volume applications[J].Journal of Computational Physics,2012,231(4):1797-1821.