Abstract:To clarify the effects of mass ratio and the vibration conditions of the upstream cylinder (a fixed or a vibrated upstream cylinder) on vortex-induced vibration of two tandem circular cylinders, numerical simulations were carried out at a Reynolds number of 100 with an intermediate pitch ratio of P/D = 4, where P is the distance between the centers of two cylinders and D is the diameter of the cylinder. The effects of the mass ratio (m* = 2, 10 and 20) and the vibration conditions of the upstream cylinder on vibration characteristics and flow patterns of two tandem circular cylinders were analyzed as well as their mechanisms. Results show that the vibration amplitudes of the downstream cylinders decrease with the increase of mass ratio. Compared with a fixed upstream cylinder, a vibrated upstream cylinder would induce a larger transverse vibration amplitude of the downstream cylinder of the same mass ratio. For a vibrated upstream cylinder, apparent “lock-in” regions are observed for both cylinders at three mass ratios. Note that a “soft lock-in” phenomenon arises for both cylinders at the mass ratio of 2. For a fixed upstream cylinder, the “lock-in” region is not detected. Three identical wake flow modes, i.e., “2S” mode, irregular mode and parallel vortex street mode, are observed in the wake region of two tandem cylinders for all three mass ratios. Two flow generation mechanisms, namely, vortex impingement and vortex fusion, arise in the wake of two tandem cylinders for two types of upstream cylinders.
杜晓庆1,唐晨馨1,赵燕2,吴葛菲1,杨骁1. 两类串列圆柱涡激振动的质量比效应[J]. 振动与冲击, 2022, 41(6): 160-168.
DU Xiaoqing1,TANG Chenxin1,ZHAO Yan2,WU Gefei1,YANG Xiao1. Effects of mass ratio on the vortex-induced vibration of two types of tandem circular cylinders. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(6): 160-168.
[1] Takeguchi M, Fukunaga S. Aerodynamic stabilization for wake-induced vibration in parallel hanger ropes of the Akashi Kaikyo Bridge[J]. Wind Engineering, 2012, 37(4): 300-306.
[2] He Xu-hui, Cai Chang, Wang Zi-jian, et al. Experimental verification of the effectiveness of elastic cross-ties in suppressing wake-induced vibrations of staggered stay cables[J]. Engineering Structures, 2018, 167:151-165.
[3] Main J A, Jones N P. A comparison of full-scale measurements of stay cable vibration[C]. Structure Congress 2000: Advanced Technology in Structural Engineering. Reston: ASCE, 2000: 1-8.
[4] 祝志文, 陈魏, 李健朋等. 多塔斜拉桥加劲索涡激振动实测与时域解析模态分解[J]. 中国公路学报, 2019, 32(10): 247-256.
ZHU Zhi-wen, CHEN Wen, LI Jian-peng, et al. Field observation of vortex-induced vibration of stiffening cables in a multi-tower cable-stayed bridge with application of analytical mode decomposition[J]. China Journal of Highway and Transport, 2019, 32(10): 247-256.
[5] Khalak A, Williamson C H K. Dynamics of a hydroelastic cylinder with very low mass and damping[J]. Journal of Fluids and Structures, 1996, 10(5): 455-472.
[6] Govardhan R, Williamson C H K. Modes of vortex formation and frequency response of a freely vibrating cylinder[J]. Journal of Fluid Mechanics, 2000, 420: 85-130.
[7] Jauvtis N, Williamson C H K. The effect of two degrees of freedom on vortex-induced vibration at low mass and damping[J]. Journal of Fluid Mechanics, 2004, 509: 23-62.
[8] Morse T L, Williamson C H K. The effect of Reynolds number on the critical mass phenomenon in vortex-induced vibration[J]. Physics of Fluids, 2009, 21(4): 045105.
[9] Khalak A, Williamson C H K. Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping[J]. Journal of fluids and Structures, 1999, 13(7-8): 813-851.
[10] 谷家扬, 杨琛, 朱新耀, 等. 质量比对圆柱涡激特性的影响研究[J]. 振动与冲击,2016,35(4):134-140.
GU Jia-yang, YANG Chen, ZHU Xin-yao, et al. Influences of mass ratio on vortex induced vibration characteristics of a circular cylinder[J]. Journal of Vibration and Shock, 2016, 35(4): 134-140.
[11] 陈正寿,赵宗文,张国辉,等. 质量比对刚性圆柱体涡激振动影响的研究[J]. 振动与冲击, 2017, 11: 038.
CHEN Zheng-shou, ZHAO Zong-wen, ZHANG Guo-hui, et al. Effects of mass ratio on vortex-induced vibration of a rigid cylinder[J]. Journal of Vibration and Shock, 2017, 11: 038.
[12] Mittal S, Kumar V. Finite element study of vortex-induced crossflow and in-line oscillations of a circular cylinder at low Reynolds numbers[J]. International Journal for Numerical Methods in Fluids, 1999, 31(7): 1087-1120.
[13] Sanaati B, Kato N. A study on the proximity interference and synchronization between two side-by-side flexible cylinders[J]. Ocean Engineering, 2014, 85: 65-79.
[14] Assi G R S, Bearman, Meneghini J R. On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism[J]. Journal of Fluid Mechanics, 2010, 661: 365.
[15] Assi G R. Wake-induced vibration of tandem and staggered cylinders with two degrees of freedom[J]. Journal of Fluids and Structures, 2014, 50, 340-357.
[16] Wang H, Yang W, Nguyen K D, et al. Wake-induced vibrations of an elastically mounted cylinder located downstream of a stationary larger cylinder at low Reynolds numbers[J]. Journal of Fluids and Structures, 2014, 50, 479-496.
[17] Mysa R C., Kaboudian A., Jaiman R K. On the origin of wake-induced vibration in two tandem circular cylinders at low Reynolds number[J]. Journal of Fluids and Structures, 2016, 61, 76-98.
[18] Geraci G., de Tullio M D, Iaccarino G. Stochastic analysis of vortex-induced vibrations of two oscillating cylinders in the proximity-wake interference region[C]. Annual research briefs, Stanford, CA: Stanford University, Center for Turbulence Research, 2015, 197-210.
[19] Borazjani I., Sotiropoulos F. Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity–wake interference region[J]. Journal of fluid mechanics,2009, 621, 321.
[20] 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.
[21] 王凯鹏, 赵西增, 段松长.不同运动自由度组合串列双圆柱涡激振动数值模拟[J]. 海洋工程, 2018, 36(05): 12-21.
WANG Kai-peng, ZHAO Xi-zeng, DUAN Song-chang. Numerical simulation of two tandem cylinders undergoing vortex-induced vibrations with various motion freedom combinations[J]. The Ocean Engineering, 2018, 36(05): 12-21.
[22] Vandiver J K, Jong J Y. The relationship between in-line and cross-flow vortex-induced vibration of cylinders[J]. Journal of Fluids and Structures, 1987, 1(4): 381-399.
[23] 郭晓玲, 唐国强, 刘名名, 等. 低雷诺数下串列双圆柱流致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.
[24] Brika D, Laneville A. Vortex-induced oscillations of two flexible circular cylinders coupled mechanically[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1997, 69: 293-302.
[25] 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: A辑, 2018, 33(1): 58-65.
ZOU Lin, WANG Hua-ao, WANG Miao, et al. Numerical simulation on vortex-induced vibration response of two cylinders in tandem arrangements[J]. Journal of Hydrodynamics, 2018, 33(1): 58-65.
[26] Papaioannou G V, Yue D K P, Triantafyllou M S, et al. On the effect of spacing on the vortex-induced vibrations of two tandem cylinders[J]. Journal of Fluids and Structures, 2008, 24(6): 833-854.
[27] 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.
[28] Sumner D. Two circular cylinders in cross-flow: A review.[J]. Journal of Fluids and Structures, 2010, 26(6): 849-899.
[29] Huhe-Aode T. Visual studies of wake structure behind two cylinders in tandem arrangement[J]. Rep. Res. Inst. Appl. Mech. Kyushu Univ., 1985, 32(99): 1-20.
[30] Li J, Chambarel A, Donneaud M, et al. Numerical study of laminar flow past one and two circular cylinders[J]. Computers and Fluids, 1991, 19(2): 155-170.
[31] Sharman B, Lien F S, Davidson L, et al. Numerical predictions of low Reynolds number flows over two tandem circular cylinders[J]. International Journal for Numerical Methods in Fluids, 2005, 47(5): 423-447.
[32] Tofa M M, Maimun A, Ahmed Y M, et al. Numerical Study of the Flow-Induced Vibration of Two Equal-Diameter Cylinders in Tandem With Varying the Mass Ratio[C]. ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014: V002T08A010-V002T08A010.
[33] Jiang R J, Lin J Z. Poiseuille flow-induced vibrations of two tandem circular cylinders with different mass ratios[J]. Physics of Fluids, 2016, 28(6): 064105.
[34] 杨骁, 赵燕, 杜晓庆等. 双圆柱尾流致涡激振动的质量比效应及其机理[J]. 振动工程学报, 2020, 33(01): 24-34.
YANG Xiao, ZHAO Yan, DU Xiao-qing, et al. Effects of mass ratio on wake-induced vibration of two tandem circular cylinders and its mechanism[J]. Journal of Vibration Engineering, 2020, 33(01): 24-34.
[35] Ravi C M, Abouzar K, Rajeev K J. On the origin of wake induced vibration in tandem circular cylinders at low Reynolds number. Journal of Fluids and Structures, 2016, 61: 76-98.
[36] Mysa R C, Law Y Z, Jaiman R K. Interaction dynamics of upstream vortex with vibrating tandem circular cylinder at subcritical Reynolds number[J]. Journal of Fluids and Structures, 2017, 75:27-44.
[37] Prasanth, T.K., Mittal, S. Vortex-induced vibration of two circular cylinders at low Reynolds number[J]. Journal of Fluids and Structures, 2009, 25(4), 731-741.
[38] Chung M H. On characteristics of two-degree-of-freedom vortex induced vibration of two low-mass circular cylinders in proximity at low Reynolds number[J]. International Journal of Heat and Fluid Flow, 2017, 65: 220-245.
[39] 杜晓庆, 邱涛, 赵燕. 低雷诺数串列双方柱流致振动质量比效应的数值研究[J]. 力学学报, 2019, 51(6):1740-1751.
DU Xiao-qing, QIU Tao, ZHAO Yan, Numerical simulation of wake-induced vortex vibration on two tandem square cylinders[J]. Theoretical and Applied Mechanics, 2019, 51(6):1740-1751.