基于有限差分法刚性圆柱体涡激振动响应特性数值研究
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摘要
基于尾流振子模型对刚性圆柱体涡激振动响应特性进行数值研究.建立圆柱体结构振子及尾流振子之间的耦合方程,基于二阶精度中心差分格式对耦合模型先离散后迭代进行求解.对不同质量比及不同阻尼比圆柱体涡激振动响应的无量纲位移、无量纲升力、频率比及锁定区间等参数进行分析.结果表明数值方法可以很好地模拟刚性圆柱体的涡激振动响应特性.随着质量比的增加,锁定开始点逐渐延后,锁定结束点逐渐提前,锁定区间宽度逐渐变窄.
Numerical study based on a wake oscillator model is conducted to determine response performance of vortex-induced vibration(VIV) on a rigid cylinder. A coupled model of structural oscillator of a rigid cylinder and wake oscillator is established, and then the model is discretized and solved based on a standard central finite difference method of the second order. VIV response characteristics including dimensionless displacement, dimensionless lift, and frequency ratio and lock-in region varied with mass ratios and damping ratios are compared. It can be found that the numerical method simulates response performances of vortex-induced vibration on a rigid cylinder very well. As dimensionless mass ratio increases, onset of lock-in region occurs later, lock-out point occurs earlier, and so the lock-in region becomes smaller.
Numerical study based on a wake oscillator model is conducted to determine response performance of vortex-induced vibration(VIV) on a rigid cylinder. A coupled model of structural oscillator of a rigid cylinder and wake oscillator is established, and then the model is discretized and solved based on a standard central finite difference method of the second order. VIV response characteristics including dimensionless displacement, dimensionless lift, and frequency ratio and lock-in region varied with mass ratios and damping ratios are compared. It can be found that the numerical method simulates response performances of vortex-induced vibration on a rigid cylinder very well. As dimensionless mass ratio increases, onset of lock-in region occurs later, lock-out point occurs earlier, and so the lock-in region becomes smaller.
引文
[1] 邓枫, 伍贻兆, 刘学强. 用DNS数值模拟分离绕流中的旋涡运动 [J]. 计算物理, 2008, 25(6): 683-688.
[2] 谢志刚, 许春晓, 崔桂香, 等. 方柱绕流大涡模拟 [J]. 计算物理, 2007, 24(2): 171-180.
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[4] 刘松, 符松. 纵向受迫振荡圆柱绕流问题的数值模拟 [J]. 计算物理, 2001, 18(2): 157-162.
[5] 张永波, 郭海燕, 孟凡顺, 等. 基于小波变换的顶张力立管涡激振动规律实验研究 [J]. 振动与冲击, 2011, 30(2): 149-154.
[6] 康庄, 贾鲁生. 圆柱体双自由度涡激振动轨迹的模型试验 [J]. 力学学报, 2012, 44(6): 970-979.
[7] CHEN W L, ZHANG Q Q, LI H, et al. An experimental investigation on vortex induced vibration of a flexible inclined cable under a shear flow [J]. Journal of Fluids and Structures, 2015, 54: 297-311.
[8] 唐友刚, 樊娟娟, 张杰, 等. 高雷诺数下圆柱顺流向和横流向涡激振动分析 [J]. 振动与冲击, 2013, 32(13):88-92.
[9] ZHANG H, FAN C F, 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: 30-44.
[10] ZHAO M, CHENG L, AN H W, Lu L. Three-dimensional numerical simulation of vortex-induced vibration of a elastically mounted rigid circular cylinder in steady current [J]. Journal of Fluids and Structures, 2014, 50: 292-311.
[11] 高云, 王盟浩, 宗智, 等. 高雷诺数时分离盘长度对圆柱绕流特性的影响 [J] 上海交通大学学报, 2017, 51(4): 504-512.
[12] 陈伟民, 张立武, 李敏. 采用改进尾流振子模型的柔性海洋立管的涡激振动响应分析 [J]. 工程力学, 2010, 27(5):240-246.
[13] 郑中钦, 陈伟民. 结构与尾流非线性耦合涡激振动预测模型 [J]. 海洋工程, 2012, 30(4):37-54.
[14] GROUTHIER C, MICHELIN S, BOURGUET R, et al. On the efficiency of energy harvesting using vortex-induced vibrations of cables [J]. Journal of Fluids and Structures, 2014, 49:427-440.
[15] XU K, GE Y, ZHANG D. Wake oscillator model for assessment of vortex-induced vibration of flexible structures under wind action [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2015, 136:192-200.
[16] FACCHINETTI M L, de LANGRE E, BIOLLEY F. Coupling of structure and wake oscillators in vortex-induced vibrations [J]. Journal of Fluids and Structures, 2004, 19:123-40.
[17] NAYFEH A H. Introduction to perturbation techniques [M]. New York:Wiley, 1993.
[18] BALASUBRAMANIAN S, SKOP R A, HAAN F L, et al. Vortex-excited vibrations of uniform pivoted cylinders in uniform and shear flow [J]. Journal of Fluids and Structures, 2000, 14: 65-85.
[19] SARPKAYA T. Fluid forces on oscillating cylinders[J]. ASCE J Waterway, Port, Coastal, Ocean Div, 1978, 104, 275-290.
[20] BLEVINS R D, COUGHRAN C S. Experimental investigation of vortex-induced vibration in one or two dimensions with variable mass, damping and Reynolds number [J]. Journal of Fluid Engineering, Transactions of the ASME, 2009, 131(10): 101202-7.
[2] 谢志刚, 许春晓, 崔桂香, 等. 方柱绕流大涡模拟 [J]. 计算物理, 2007, 24(2): 171-180.
[3] BLEVINS R D. Flow-induced vibration [M]. 2nd ed. Malabar/Florida: Krieger Publishing, Inc, 2001.
[4] 刘松, 符松. 纵向受迫振荡圆柱绕流问题的数值模拟 [J]. 计算物理, 2001, 18(2): 157-162.
[5] 张永波, 郭海燕, 孟凡顺, 等. 基于小波变换的顶张力立管涡激振动规律实验研究 [J]. 振动与冲击, 2011, 30(2): 149-154.
[6] 康庄, 贾鲁生. 圆柱体双自由度涡激振动轨迹的模型试验 [J]. 力学学报, 2012, 44(6): 970-979.
[7] CHEN W L, ZHANG Q Q, LI H, et al. An experimental investigation on vortex induced vibration of a flexible inclined cable under a shear flow [J]. Journal of Fluids and Structures, 2015, 54: 297-311.
[8] 唐友刚, 樊娟娟, 张杰, 等. 高雷诺数下圆柱顺流向和横流向涡激振动分析 [J]. 振动与冲击, 2013, 32(13):88-92.
[9] ZHANG H, FAN C F, 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: 30-44.
[10] ZHAO M, CHENG L, AN H W, Lu L. Three-dimensional numerical simulation of vortex-induced vibration of a elastically mounted rigid circular cylinder in steady current [J]. Journal of Fluids and Structures, 2014, 50: 292-311.
[11] 高云, 王盟浩, 宗智, 等. 高雷诺数时分离盘长度对圆柱绕流特性的影响 [J] 上海交通大学学报, 2017, 51(4): 504-512.
[12] 陈伟民, 张立武, 李敏. 采用改进尾流振子模型的柔性海洋立管的涡激振动响应分析 [J]. 工程力学, 2010, 27(5):240-246.
[13] 郑中钦, 陈伟民. 结构与尾流非线性耦合涡激振动预测模型 [J]. 海洋工程, 2012, 30(4):37-54.
[14] GROUTHIER C, MICHELIN S, BOURGUET R, et al. On the efficiency of energy harvesting using vortex-induced vibrations of cables [J]. Journal of Fluids and Structures, 2014, 49:427-440.
[15] XU K, GE Y, ZHANG D. Wake oscillator model for assessment of vortex-induced vibration of flexible structures under wind action [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2015, 136:192-200.
[16] FACCHINETTI M L, de LANGRE E, BIOLLEY F. Coupling of structure and wake oscillators in vortex-induced vibrations [J]. Journal of Fluids and Structures, 2004, 19:123-40.
[17] NAYFEH A H. Introduction to perturbation techniques [M]. New York:Wiley, 1993.
[18] BALASUBRAMANIAN S, SKOP R A, HAAN F L, et al. Vortex-excited vibrations of uniform pivoted cylinders in uniform and shear flow [J]. Journal of Fluids and Structures, 2000, 14: 65-85.
[19] SARPKAYA T. Fluid forces on oscillating cylinders[J]. ASCE J Waterway, Port, Coastal, Ocean Div, 1978, 104, 275-290.
[20] BLEVINS R D, COUGHRAN C S. Experimental investigation of vortex-induced vibration in one or two dimensions with variable mass, damping and Reynolds number [J]. Journal of Fluid Engineering, Transactions of the ASME, 2009, 131(10): 101202-7.