平面剪切来流作用下串列布置三圆柱流致运动特性研究
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摘要
基于四步半隐式特征线分裂算子有限元方法,对Re=100时,剪切来流作用下串列三圆柱体双自由度流致振动问题进行了数值计算.首先,与现有文献结果进行对比验证该方法的正确性.然后,着重分析剪切率、固有频率比和折减速度三个关键参数对串列三圆柱体结构流致动力响应及流场特性的影响.数值计算结果表明:剪切率、固有频率比与折减速度对结构振幅和运动轨迹的影响较大.随剪切率的增大,上游圆柱最大振幅的变化与单圆柱工况类似.中下游圆柱最大振幅会增大且会出现双向共振现象,同时,发生共振响应区域会扩大.随固有频率比的增大,上游圆柱顺流向锁定区间范围会减小,而中下游圆柱双向锁定区间会扩大.另一方面,均匀来流作用下,结构运动轨迹以"8"字形和不规则形状为主.随剪切率的增大,锁定区间内运动轨迹会由"8"字形转变为"雨滴"形.在大剪切率与高固有频率比工况下,中游圆柱体结构运动轨迹会出现"双雨滴"形状.最后,通过对流场特性的分析,揭示了剪切来流作用下串列三圆柱结构流致运动响应的内在机理.
Flow-induced motions of three elastically mounted circular cylinders subjected to the planar shear flow in tandem arrangement at Re = 100 were numerically investigated by using semi-implicit characteristics-based split(CBS)finite element algorithm. Firstly, the results are compared with the existing data in the literature to verify the accurateness of the method. Then, the influence of some key parameters, such as shear ratio(k), natural frequency ratio(r) and reduced velocity(U_r) on the characteristics of flow-induced dynamic responses and flow field of three circular cylinders with tandem arrangement was analyzed. The numerical results show that the shear ratio, natural frequency ratio and reduced velocity play an important role in the amplitude and trajectory of motion. The change of maximum amplitude of the upstream cylinder is similar to that of an isolated cylinder case with the increasing of k. The maximum amplitudes of the midstream and downstream cylinders increase, and the dual resonance is observed. Meanwhile, the increasing of k causes the extension of the resonance region. With the increasing of r, the lock-in region of the upstream cylinder reduces in the in-line direction. However, for the midstream and downstream ones, the dual-lock-in region broadens. On the other hand,the prominent X-Y trajectories of three circular cylinder resemble figure-eight shape and irregular one in the uniform flow. With the change of k, the motion orbit transforms from figure-eight to the raindrop shape in the lock-in region. In the larger shear ratio and higher natural frequency ratio case, the dual-raindrop is observed in the X-Y vibrating trajectory of the midstream cylinder. Finally, the flow-induced motion mechanism of three tandem circular cylinders exposed to planar shear flow is revealed according to the analysis of the characteristic of the flow field.
Flow-induced motions of three elastically mounted circular cylinders subjected to the planar shear flow in tandem arrangement at Re = 100 were numerically investigated by using semi-implicit characteristics-based split(CBS)finite element algorithm. Firstly, the results are compared with the existing data in the literature to verify the accurateness of the method. Then, the influence of some key parameters, such as shear ratio(k), natural frequency ratio(r) and reduced velocity(U_r) on the characteristics of flow-induced dynamic responses and flow field of three circular cylinders with tandem arrangement was analyzed. The numerical results show that the shear ratio, natural frequency ratio and reduced velocity play an important role in the amplitude and trajectory of motion. The change of maximum amplitude of the upstream cylinder is similar to that of an isolated cylinder case with the increasing of k. The maximum amplitudes of the midstream and downstream cylinders increase, and the dual resonance is observed. Meanwhile, the increasing of k causes the extension of the resonance region. With the increasing of r, the lock-in region of the upstream cylinder reduces in the in-line direction. However, for the midstream and downstream ones, the dual-lock-in region broadens. On the other hand,the prominent X-Y trajectories of three circular cylinder resemble figure-eight shape and irregular one in the uniform flow. With the change of k, the motion orbit transforms from figure-eight to the raindrop shape in the lock-in region. In the larger shear ratio and higher natural frequency ratio case, the dual-raindrop is observed in the X-Y vibrating trajectory of the midstream cylinder. Finally, the flow-induced motion mechanism of three tandem circular cylinders exposed to planar shear flow is revealed according to the analysis of the characteristic of the flow field.
引文
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2 Williamson C,Govardhan R.Vortex-induced vibrations.Annual Review of Fluid Mechanics,2004,36(1):413-455
3 Gabbai R,Benaroya H.An overview of modeling and experiments of vortex-induced vibration of circular cylinders.Journal of Sound and Vibration,2005,282(3):575-616
4 Wu X,Ge F,Hong Y.A review of recent studies on vortex-induced vibrations of long slender cylinders.Journal of Fluids and Structures,2012,28(1):292-308
5 Bathe K,Ledezma G.Benchmark problems for incompressible fluid flows with structural interactions.Computers and Structures,2007,85(11-14):628-644
6 Sun X,Zhang J,Ren X.Characteristic-based split(CBS)finite element method for incompressible viscous flow with moving boundaries.Engineering Applications of Computational Fluid Mechanics,2012,6(3):461-474
7何涛.基于ALE有限元法的流固耦合强耦合数值模拟.力学学报,2018,49(2):1549-1561(He Tao.A partitioned strong coupling algorithm for fluid-structure interaction using arbitrary lagrangianeulerian finite element formulation.Chinese Journal of Theoretical and Applied Mechanics,2018,49(2):1549-1561(in Chinese))
8 Behara S,Ravikanth B,Chandra V.Vortex-induced vibrations of three staggered circular cylinders at low Reynolds numbers.Physics of Fluids,2017,29(8):083606
9 Prasanth T,Mittal S.Vortex-induced vibration of two circular cylinders at low Reynolds number.Journal of Fluids and Structures,2009,25(4):731-741
10段松长,赵西增,叶洲腾等.错列角度对双圆柱涡激振动影响的数值模拟研究.力学学报,2018,50(2):244-253(Duan Songchang,Zhao Xizeng,Ye Zhouteng et al.Numerical study of staggered angle on the vortex-induced vibration of two cylinders.Chinese Journal of Theoretical and Applied Mechanics,2018,50(2):244-253(in Chinese))
11 Wang X,So R,Xie W,et al.Free-stream turbulence effects on vortex-induced vibration of two side-by-side elastic cylinders.Journal of Fluids and Structures,2008,24:664-679
12 Cui Z,Zhao M,Teng B.Vortex-induced vibration of two elastically coupled cylinders in side-by-side arrangement.Journal of Fluids and Structures,2014,44(2):270-291
13 Papaioannou G,Yue D,Triantafyllou M,et al.On the effect of spacing on the vortex-induced vibrations of two tandem cylinders.Journal of Fluids and Structures,2008,24(6):833-854
14李朋,郭海燕,李效民等.干涉对海洋立管涡激振动影响实验研究.船舶力学,2015,19(10):1227-1234(Li Peng,Guo Haiyan,Li Xiaoming et al.Experimental investigation of vortex-induced vibration of marine risers with interference.Journal of Ship Mechanics,2015,19(10):1227-1234(in Chinese))
15 Prasanth T,Mittal S.Flow-induced oscillation of two circular cylinders in tandem arrangement at low Re.Journal of Fluids and Structures,2009,25(6):1029-1048
16 Mysa R,Law Y,Jaiman R.Interaction dynamics of upstream vortex with vibrating tandem circular cylinder at subcritical Reynolds number.Journal of Fluids and Structures,2017,75:27-44
17 Yu K,′Etienne S,Scolan Y,et al.Flow-induced vibrations of in-line cylinder arrangements at low Reynolds numbers.Journal of Fluids and Structures,2016,60:37-61
18 Mahmoud S,Atef M.Flow-induced vibration of three unevenly spaced in-line cylinder in cross-flow.Journal of Fluids and Structures,2018,76:367-383
19 Chen W,Ji C,Williams J,et al.Vortex-induced vibrations of three tandem cylinders in laminar cross-flow:Vibration response and galloping mechanism.Journal of Fluids and Structures,2018,78:215-238
20罗竹梅,张立翔.耦合四圆柱涡激振动的力特性及水动能获取分析.振动与冲击,2015,34(17):25-29(Luo Zhumei,Zhang Lixiang.Force characteristics and hydrokinetic energy harvesting for VIVof four coupling-linked cylinders.Journal of vibration and shock,2015,34(17):25-29(in Chinese))
21 Han Z,Zhou D,He T,et al.Flow-induced vibrations of four circular cylinders with square arrangement at low Reynolds numbers.Ocean Engineering,2015,96:21-33
22 Lin J,Jiang R,Chen Z,et al.Poiseuille flow-induced vibrations of two cylinders in tandem.Journal of Fluids and Structures,2013,40(7):70-85
23 Jiang R,Lin J.Poiseuille flow-induced vibrations of two tandem circular cylinders with different mass ratios.Physics of Fluids,2016,28(6):413-381
24 Zhao M,Cheng L,An H.Numerical investigation of vortex-induced virbration of circular cylinder in transverse direction in oscillatory flow.Ocean Engineering,2012,41(5):39-52
25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.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.Chinese Journal of Theoretical and Applied Mechanic,2014,46(2):173-182(in Chinese))
26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.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.Journal of Harbin Engineering University,2007,28(12):1301-1306(in Chinese))
27 Zhang H,Fan B,Chen Z,et al.An in-depth study on vortex-induced vibration of a circular cylinder with shear flow.Computers and Fluids,2014,100(100):30-44
28 Tu J,Zhou D,Bao Y,et al.Flow-induced vibration on a circular cylinder in planar shear flow.Computers and Fluids,2014,105(105):138-154
29 Gsell S,Bourguet R,Braza M.Vortex-induced vibrations of a cylinder in planar shear flow.Journal of Fluid Mechanics,2017,825:353-384
30 Tu J,Zhou D,Bao Y,et al.Flow-induced vibrations of two circular cylinders in tandem with shear flow at low Reynolds number.Journal of Fluids and Structures,2015,59:224-251
31及春宁,花阳,许栋等.不同剪切率来流作用下柔性圆柱涡激振动数值模拟.力学学报,2018,50(1):21-31(Ji Chunning,Hua Yang,Xu Dong et al.Numerical simulation of vortex-induced vibration of a flexible cylinder exposed to shear flow at different shear rates.Chinese Journal of Theoretical and Applied Mechanic,2018,50(1):21-31(in Chinese))
32 Masud A,Bhanabhagvanwala M,Khurram R.An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction.Computers and Fluids,2007,36(1):77-91
33 Dahl J,Hover F,Triantafyllou M.Resonant vibrations of bluff bodies cause multivortex shedding and high frequency forces.Physical Review Letters,2007,99:144503
2 Williamson C,Govardhan R.Vortex-induced vibrations.Annual Review of Fluid Mechanics,2004,36(1):413-455
3 Gabbai R,Benaroya H.An overview of modeling and experiments of vortex-induced vibration of circular cylinders.Journal of Sound and Vibration,2005,282(3):575-616
4 Wu X,Ge F,Hong Y.A review of recent studies on vortex-induced vibrations of long slender cylinders.Journal of Fluids and Structures,2012,28(1):292-308
5 Bathe K,Ledezma G.Benchmark problems for incompressible fluid flows with structural interactions.Computers and Structures,2007,85(11-14):628-644
6 Sun X,Zhang J,Ren X.Characteristic-based split(CBS)finite element method for incompressible viscous flow with moving boundaries.Engineering Applications of Computational Fluid Mechanics,2012,6(3):461-474
7何涛.基于ALE有限元法的流固耦合强耦合数值模拟.力学学报,2018,49(2):1549-1561(He Tao.A partitioned strong coupling algorithm for fluid-structure interaction using arbitrary lagrangianeulerian finite element formulation.Chinese Journal of Theoretical and Applied Mechanics,2018,49(2):1549-1561(in Chinese))
8 Behara S,Ravikanth B,Chandra V.Vortex-induced vibrations of three staggered circular cylinders at low Reynolds numbers.Physics of Fluids,2017,29(8):083606
9 Prasanth T,Mittal S.Vortex-induced vibration of two circular cylinders at low Reynolds number.Journal of Fluids and Structures,2009,25(4):731-741
10段松长,赵西增,叶洲腾等.错列角度对双圆柱涡激振动影响的数值模拟研究.力学学报,2018,50(2):244-253(Duan Songchang,Zhao Xizeng,Ye Zhouteng et al.Numerical study of staggered angle on the vortex-induced vibration of two cylinders.Chinese Journal of Theoretical and Applied Mechanics,2018,50(2):244-253(in Chinese))
11 Wang X,So R,Xie W,et al.Free-stream turbulence effects on vortex-induced vibration of two side-by-side elastic cylinders.Journal of Fluids and Structures,2008,24:664-679
12 Cui Z,Zhao M,Teng B.Vortex-induced vibration of two elastically coupled cylinders in side-by-side arrangement.Journal of Fluids and Structures,2014,44(2):270-291
13 Papaioannou G,Yue D,Triantafyllou M,et al.On the effect of spacing on the vortex-induced vibrations of two tandem cylinders.Journal of Fluids and Structures,2008,24(6):833-854
14李朋,郭海燕,李效民等.干涉对海洋立管涡激振动影响实验研究.船舶力学,2015,19(10):1227-1234(Li Peng,Guo Haiyan,Li Xiaoming et al.Experimental investigation of vortex-induced vibration of marine risers with interference.Journal of Ship Mechanics,2015,19(10):1227-1234(in Chinese))
15 Prasanth T,Mittal S.Flow-induced oscillation of two circular cylinders in tandem arrangement at low Re.Journal of Fluids and Structures,2009,25(6):1029-1048
16 Mysa R,Law Y,Jaiman R.Interaction dynamics of upstream vortex with vibrating tandem circular cylinder at subcritical Reynolds number.Journal of Fluids and Structures,2017,75:27-44
17 Yu K,′Etienne S,Scolan Y,et al.Flow-induced vibrations of in-line cylinder arrangements at low Reynolds numbers.Journal of Fluids and Structures,2016,60:37-61
18 Mahmoud S,Atef M.Flow-induced vibration of three unevenly spaced in-line cylinder in cross-flow.Journal of Fluids and Structures,2018,76:367-383
19 Chen W,Ji C,Williams J,et al.Vortex-induced vibrations of three tandem cylinders in laminar cross-flow:Vibration response and galloping mechanism.Journal of Fluids and Structures,2018,78:215-238
20罗竹梅,张立翔.耦合四圆柱涡激振动的力特性及水动能获取分析.振动与冲击,2015,34(17):25-29(Luo Zhumei,Zhang Lixiang.Force characteristics and hydrokinetic energy harvesting for VIVof four coupling-linked cylinders.Journal of vibration and shock,2015,34(17):25-29(in Chinese))
21 Han Z,Zhou D,He T,et al.Flow-induced vibrations of four circular cylinders with square arrangement at low Reynolds numbers.Ocean Engineering,2015,96:21-33
22 Lin J,Jiang R,Chen Z,et al.Poiseuille flow-induced vibrations of two cylinders in tandem.Journal of Fluids and Structures,2013,40(7):70-85
23 Jiang R,Lin J.Poiseuille flow-induced vibrations of two tandem circular cylinders with different mass ratios.Physics of Fluids,2016,28(6):413-381
24 Zhao M,Cheng L,An H.Numerical investigation of vortex-induced virbration of circular cylinder in transverse direction in oscillatory flow.Ocean Engineering,2012,41(5):39-52
25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.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.Chinese Journal of Theoretical and Applied Mechanic,2014,46(2):173-182(in Chinese))
26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.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.Journal of Harbin Engineering University,2007,28(12):1301-1306(in Chinese))
27 Zhang H,Fan B,Chen Z,et al.An in-depth study on vortex-induced vibration of a circular cylinder with shear flow.Computers and Fluids,2014,100(100):30-44
28 Tu J,Zhou D,Bao Y,et al.Flow-induced vibration on a circular cylinder in planar shear flow.Computers and Fluids,2014,105(105):138-154
29 Gsell S,Bourguet R,Braza M.Vortex-induced vibrations of a cylinder in planar shear flow.Journal of Fluid Mechanics,2017,825:353-384
30 Tu J,Zhou D,Bao Y,et al.Flow-induced vibrations of two circular cylinders in tandem with shear flow at low Reynolds number.Journal of Fluids and Structures,2015,59:224-251
31及春宁,花阳,许栋等.不同剪切率来流作用下柔性圆柱涡激振动数值模拟.力学学报,2018,50(1):21-31(Ji Chunning,Hua Yang,Xu Dong et al.Numerical simulation of vortex-induced vibration of a flexible cylinder exposed to shear flow at different shear rates.Chinese Journal of Theoretical and Applied Mechanic,2018,50(1):21-31(in Chinese))
32 Masud A,Bhanabhagvanwala M,Khurram R.An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction.Computers and Fluids,2007,36(1):77-91
33 Dahl J,Hover F,Triantafyllou M.Resonant vibrations of bluff bodies cause multivortex shedding and high frequency forces.Physical Review Letters,2007,99:144503