上游圆柱固定条件下串列三圆柱涡激振动响应和尾流特性
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摘要
应用基于嵌入式迭代浸入边界法对雷诺数Re=100下串列三圆柱涡激振动进行了数值模拟,其中上游圆柱固定不动,中游和下游圆柱仅作横向振动。三圆柱间距相同,间距比L~*= 1.2、2.0和5.0,折合流速U_r=3.0-25.0,质量比m~*=2.0。研究发现,各间距比下,串列三圆柱存在强烈的相互作用,中游和下游圆柱的振幅明显大于单圆柱涡激振动的情况。随着L~*的增大,圆柱振幅整体上减小,除个别工况外,下游圆柱的振幅均大于中游圆柱的情况。当间距比较小(L~*=1.2、2.0)时,St数随折合流速的增加而缓慢减小;当间距比较大(L~*=5.0)时,St数几乎不再随折合流速变化,固定在St=0.15上。对尾流的研究发现,当振幅较小时,上游圆柱的剪切层将三圆柱包裹在一起,尾流与绕流时相似,表现为经典的卡门涡街;当振幅较大时,上游圆柱的旋涡/剪切层撞击/重附着于下游圆柱上,圆柱之间存在强烈的相互作用,尾流表现为并排的两列旋涡。
Vortex-induced vibration(VIV) of three tandem cylinders at Re =100 is numerically investigated using the immersed boundary method based on the built-in iterations, where the upstream cylinder is fixed and the middle and downstream cylinders are free to vibrate transversely. The distances between two adjacent cylinders are identical and the center-to-center spacing ratios are set to as L~*=1.2, 2.0 and 5.0. The reduced velocity is in the range of 3.0-25.0 and the mass ratio is2.0. Results show that strong interactions present between three cylinders, and vibration amplitudes of the middle and downstream cylinders are significantly higher than that in the VIV of an isolated cylinder. Generally, the vibration amplitude decreases with the spacing ratio and except at several reduced velocities, the downstream cylinder has a larger amplitude than the middle one. The Strouhal numbers decrease slowly with the reduced velocity at spacing ratios of 1.2 and 2.0 and levels out at St=0.15 at the spacing ratio of 5.0. When the vibration amplitude is small, the shear layers of the upstream cylinder enclose all three cylinders, making the vortex shedding similar to the stationary case and showing a typical Karman vortex street in the wake. When the vibrate amplitude is large, the vortices/shear-layers of the upstream cylinder will impinge/reattach onto the downstream cylinder, presenting strong interferences between cylinders. The wake is characterized by a two-parallel-row vortex street.
Vortex-induced vibration(VIV) of three tandem cylinders at Re =100 is numerically investigated using the immersed boundary method based on the built-in iterations, where the upstream cylinder is fixed and the middle and downstream cylinders are free to vibrate transversely. The distances between two adjacent cylinders are identical and the center-to-center spacing ratios are set to as L~*=1.2, 2.0 and 5.0. The reduced velocity is in the range of 3.0-25.0 and the mass ratio is2.0. Results show that strong interactions present between three cylinders, and vibration amplitudes of the middle and downstream cylinders are significantly higher than that in the VIV of an isolated cylinder. Generally, the vibration amplitude decreases with the spacing ratio and except at several reduced velocities, the downstream cylinder has a larger amplitude than the middle one. The Strouhal numbers decrease slowly with the reduced velocity at spacing ratios of 1.2 and 2.0 and levels out at St=0.15 at the spacing ratio of 5.0. When the vibration amplitude is small, the shear layers of the upstream cylinder enclose all three cylinders, making the vortex shedding similar to the stationary case and showing a typical Karman vortex street in the wake. When the vibrate amplitude is large, the vortices/shear-layers of the upstream cylinder will impinge/reattach onto the downstream cylinder, presenting strong interferences between cylinders. The wake is characterized by a two-parallel-row vortex street.
引文
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[15]YU K R,éTIENNE S,SCOLAN Y M,et al.Flowinduced vibrations of in-line cylinder arrangements at low Reynolds numbers[J].Journal of Fluids and Structures,2016,60:37-61.
[16]杨立红.低雷诺数下串列多圆柱流致振动的数值模拟及其机理研究[D].天津大学,天津,中国:2013.YANG Li-hong.Numerical investigation on flowinduced vibration of multiple circular cylinders in tandem arrangement at a low Reynolds number[D].School of Civil Engineering,Tianjin University,Tianjin,China,2013.
[17]CHEN W,JI C,WILLIAMS J,et al.Vortex-induced vibrations of three tandem cylinders in laminar crossflow:Vibration response and galloping mechanism[J].Journal of Fluids&Structures,2018,78:215-238.
[18]及春宁,刘爽,杨立红,等.基于嵌入式迭代的高精度浸入边界法[J].天津大学学报,2014,47(5):377-382.JI Chun-ning,LIU Shuang,YANG Li-hong,et al.An accurate immersed boundary method based on built-in iterations[J].Journal of Tianjin University,2014,47(5):377-382.
[19]JI C,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.
[20]ZDRAVKOVICH M M.Review of flow interference between two circular cylinders in various arrangements[J].Journal of Fluids Engineering,1977,99(4):618-633.
[21]SUMNER D.Two circular cylinders in cross-flow:Areview[J].Journal of Fluids and Structures,2010,26(6):849-899.
[22]CHEN W,JI C,XU W,et al.Response and wake patterns of two side-by-side elastically supported circular cylinders in uniform laminar cross-flow[J].Journal of Fluids and Structures,2015,55:218-236.
[23]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,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.
[2]WILLIAMSON C H K,GOVARDHAN R.Vortexinduced vibrations[J].Annual Review of Fluid Mechanics,2004,36:413-455.
[3]SARPKAYA T.A critical review of the intrinsic nature of vortex-induced vibrations[J].Journal of Fluids and Structures,2004,19(4):389-447.
[4]BEARMAN P W.Circular cylinder wakes and vortexinduced vibrations[J].Journal of Fluids and Structures,2011,27(5):648-658.
[5]MITTAL S,KUMAR V.Flow-induced oscillations of two cylinders in tandem and staggered arrangements[J].Journal of Fluids and Structures,2001,15(5):717-736.
[6]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.
[7]PAPAIOANNOU G V,YUE D K P,TRIANTAFYLLOUM S,et al.On the effect of spacing on the vortexinduced vibrations of two tandem cylinders[J].Journal of Fluids and Structures,2008,24(6):833-854.
[8]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 Xiao-ling,TANG Guo-qiang,LIU Ming-ming,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.
[9]BRIKA D,LANEVILLE A.The flow interaction between a stationary cylinder and a downstream flexible cylinder[J].Journal of Fluids and Structures,1999,13(5):579-606.
[10]CARMO B S,SHERWIN S J,BEARMAN P W,et al.Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number[J].Journal of Fluids and Structures,2011,27(4):503-522.
[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 Ji-lu,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.
[12]KIM S,ALAM M M,SAKAMOTO H,et al.Flowinduced vibrations of two circular cylinders in tandem arrangement.Part 1:Characteristics of vibration[J].Journal of Wind Engineering and Industrial Aerodynamics,2009,97(5):304-311.
[13]邹琳,王华奥,汪秒,等.串列双圆柱涡激振动响应的数值模拟[J].水动力学研究与进展,2018,33(1):58-65.ZHOU Lin,WANG Hua-ao,WANG Miao,et al.Numerical simulation on vortex-induced vibration response of two cylinders in tandem arrangements[J].Chinese Journal of Hydrodynamics,2018,33(1):58-65.
[14]张大可,赵西增,胡子俊,等.低雷诺数下串列双圆柱涡激振动的数值模拟[J].哈尔滨工程大学学报,2018,39(2):247-253.ZHANG Da-ke,ZHAO Xi-zeng,HU Zi-jun,et al.Numerical study of flow-induced vibration of tandem circular cylinders at low Reynolds number[J].Journal of Harbin Engineering University,2018,39(2):247-253.
[15]YU K R,éTIENNE S,SCOLAN Y M,et al.Flowinduced vibrations of in-line cylinder arrangements at low Reynolds numbers[J].Journal of Fluids and Structures,2016,60:37-61.
[16]杨立红.低雷诺数下串列多圆柱流致振动的数值模拟及其机理研究[D].天津大学,天津,中国:2013.YANG Li-hong.Numerical investigation on flowinduced vibration of multiple circular cylinders in tandem arrangement at a low Reynolds number[D].School of Civil Engineering,Tianjin University,Tianjin,China,2013.
[17]CHEN W,JI C,WILLIAMS J,et al.Vortex-induced vibrations of three tandem cylinders in laminar crossflow:Vibration response and galloping mechanism[J].Journal of Fluids&Structures,2018,78:215-238.
[18]及春宁,刘爽,杨立红,等.基于嵌入式迭代的高精度浸入边界法[J].天津大学学报,2014,47(5):377-382.JI Chun-ning,LIU Shuang,YANG Li-hong,et al.An accurate immersed boundary method based on built-in iterations[J].Journal of Tianjin University,2014,47(5):377-382.
[19]JI C,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.
[20]ZDRAVKOVICH M M.Review of flow interference between two circular cylinders in various arrangements[J].Journal of Fluids Engineering,1977,99(4):618-633.
[21]SUMNER D.Two circular cylinders in cross-flow:Areview[J].Journal of Fluids and Structures,2010,26(6):849-899.
[22]CHEN W,JI C,XU W,et al.Response and wake patterns of two side-by-side elastically supported circular cylinders in uniform laminar cross-flow[J].Journal of Fluids and Structures,2015,55:218-236.
[23]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,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.