绕圆柱湍流场发展及立管涡激振动的研究
|
摘要
随着世界对石油需求量的逐年增加,石油短缺的矛盾越来越突出,为缓解该矛盾,人类逐渐从陆地钻井发展到海上钻井,并逐年加大了深海石油勘探、开发的力度。作为深海油气用开发系统结构的重要组成部分,海洋立管以其全新的形式、动态的特性以及高技术特点变得格外引人注目。海流、波浪及平台的运动不断作用于立管之上,尤其是当涡脱落频率接近立管的固有频率时,会引起立管的共振,发生所谓的“锁定”现象,严重时甚至会引起立管的疲劳损坏,缩短立管的使用寿命,因此在立管的设计过程中首先要考虑涡激振动的影响。
本文的研究内容包括三大部分：一是绕圆柱湍流场计算尺度效应的研究及湍流场发展变化的研究；二是弹性支撑刚性圆柱体涡激振动的数值计算；三是立管在真实海洋环境下的非线性涡激动力响应研究。
本文通过阐述我国海洋石油开采能力与世界先进水平的差距以及涡激振动对立管设计的重要性,论证了本文选题的理论意义和工程意义。分别从实验流体力学方法(EFD)、计算流体力学方法(CFD)和半经验方法(SEM)总结和归纳了涡激振动的研究进展,指出了当前涡激振动研究领域存在的一些亟待解决的问题。同时系统地阐述了涡激振动的机理、详细归纳了涡激振动的相关参数,并概述了求解湍流运动和流固耦合问题的数值方法。
对雷诺数103～107范围内圆柱体的绕流场进行了大量细致的数值计算。应用雷诺平均纳维尔——斯托克斯方程(RANS),通过方程分析得到了有关湍动能和湍流耗散率这两个表征湍流脉动特性的相似数,用以衡量湍流计算的尺度效应,并给出相似数随雷诺数变化的规律。结果表明,在主流方向的尾流中心线上当Re≥3×106时,湍动能和湍流耗散率随着雷诺数的变化趋于平稳。而后研究了四种计算尺度下的湍流场及其发展变化(包括流向平均速度场、涡量场、湍流动能和湍流耗散率),并比较了不同计算尺度下圆柱湍流场的特征。最后,对Re≥3×106这一雷诺数范围的湍流场特征进行了详细的研究,给出湍流脉动量在下游的发展变化规律。
采用雷诺平均纳维尔——斯托克斯方程(RANS),结合RNG k-ε和SST k-ω这两种不同的湍流模型,研究了低质量比弹性支撑刚性圆柱体的自激振动问题。从频率响应、振幅响应、对升力的谱分析、三个响应分支的水动力性能、尾涡模式和计算效率等方面比较了两种湍流模型的模拟效果,结果表明SST k-ω湍流模型在整体上优于RNG k-ε湍流模型。并对振动圆柱体的三个响应分支(初始分支、上端分支和下端分支)的湍流场(包括壁面压力系数、壁面切应力系数、流向平均速度、流向速度脉动值、横向速度脉动值和雷诺应力的分布)及其发展变化进行了研究,与同等雷诺数下固定圆柱体的湍流场进行了对比。
建立了真实海洋环境下立管三维非线性涡激动力响应控制方程。采用Morison方程求解顺流力；Facchinetti改进的尾流振子模型求解横向升力,考虑了附加质量系数的变化：轴向力的计算考虑平台的升沉运动。在计算分析中考虑的非线性主要包括大变形引起的几何非线性、流体动力非线性和流固耦合非线性。在边界条件的处理上,综合考虑了波浪、海流、平台运动(升沉和纵荡运动)的影响,并且上下边界的处理考虑了转动刚度的影响。采用更新的拉格朗日方法(Updated Lagrangian Method)解决大变形引起的几何非线性问题,采用Newton-Raphson迭代法求解非线性方程组。在此基础上讨论了三维空间立管的非线性涡激动力响应的影响因素。同时,研究了高雷诺数剪切流条件立管的多模态涡激振动响应,讨论了剪切参数对立管涡激动力响应的影响,并比较了均匀来流和剪切流条件下不同的响应特征。
In the oil and gas industry where the hydrocarbon drilling exploration and floating production activities move progressively towards deepwater areas with depths greater than1000meter or beyond, vortex induced vibration (VIV) of such key structures as drilling/production risers have become the subject of increasingly intense research investigation. In China, the key of ocean exploitation has turned into the South China Sea. Riser is the necessary device to connect the floater with oil well. Nevertheless, the prediction of deepwater riser VIV is very challenging owing to the fact that the incident flows are practically non-uniform and the associated fluid-structure interaction phenomena are highly complex. These result in a nonlinear coupled system which depends on several physical and mechanical parameters. Large amplitude oscillations occur when the vortex shedding and the structural vibration frequencies coincide, a condition referred to as 'lock-in'. The lock-in condition can occur over a range of oncoming flow velocities and the vortex shedding frequency can be driven relatively far from the Strouhal frequency which leads to increase in hydrodynamic loading and reduction in service life due to fatigue.
This study contains three parts:the first one is investigation of scale effect for turbulence flow around a circular cylinder and development of turbulence flow around circular cylinder; the second one is numerical pridiction of vortex induced vibration of elastically supported rigid circular cylinder with low mass damping in a fluid flow and the last one is vortex induced dynamic response of marine riser under true ocean environment.
The structures of this thesis are listed as follows:
By analysis the state of art of VIV, the engineering sense of present study is proofed. Conclusions are made of current research status from the aspects of experimental fluid dynamics, computational fluid dynamics and empirical method. The basic theory of VIV and associated parameters are introduced.
Numerical computation of flow parameters around a two-dimensional circular cylinder within Reynolds numbers range from103to107is accomplished. Velocity field, vorticity field, the fluctuation of turbulence flow and its development downstreams are discussed and comparisons of characteristics of turbulence flow at different scales are also made. In order to investigate the scale effect of turbulent flow around a circular cylinder, two items of simlarity criterion based on turbulent kinetic and turbulent dissipation rate which are associated with the fluctuation characteristics of turbulence wake are deduced by the equation analysis of Reynolds-Averaged Navier-Stokes equations (RANS). The result indicates that the fluctuations of turbulence flow along the center line in the wake of circular cylinder can never be changed with the increasing Reynolds numbers when Re≥3×106. Then characteristics of turbulence field when Re≥3×106are discussed specially and laws of fluctuations of turbulence downstreams are given.
RNG k-ε and SST k-co turbulence models are adopted to predict transverse vortex induced vibration of elastically supported rigid cylinder with low mass damping in a fluid flow. By comparing the peak amplitude, response frequency and hydrodynamic coefficients as well as wake modes of three different response branches at two different turbulence models, analysis of differences between two turbulence models are presented. Results indicate there exisit significant differences between two turbulence models, and SST k-co model is better than RNG k-ε model on the whole. By comparing turbulence fields and developments of three different response branches with static cylinder at coequal Reynolds number, some differences are observed. Pressure coefficient on the wall, shear stress coefficient on the wall, mean streamwise velocity, streamwise velocity fluctuation, cross-flow velocity fluctuation and Reynolds shear stress of three branches are different from each other and from those of static cylinder.
An investigation on the nonlinear dynamic response and vortex-induced vibration of marine riser subjected to waves and currents is performed. Three dimensional governing equations which considered nonlinearities including the geometrical nonlinearities, fluid dynamic and fluid-structure coupling nonlinearities are given. The in-line force is solved by Morison equation under combined waves, currents and platform movement while cross-flow force is solved by wake oscillator model which considered variation of added mass coefficient. The nonlinear governing equations are solved by Updated Lagrangian method(UL) and Newton-Raphson interation method in time domain. The influence of basic parameters on the dynamic response and vortex-induced vibration of marine riser were investigated. This research provides a basic foundation for practical design and theoretical analysis of marine riser. Since the vortex shedding frequency varies with flow velocity, a depth varying flow past a flexible cylinder will result in multi-frequency excitation. Depending on the range of velocity covered by the flow profile, many vibration modes of the structure can be excited. Understanding the vibration mechanisms of the structure in those cases is not a simple task. Based on this model, multi-mode excitation of riser pipeline in linear sheared flow, the effect of shear parameter on vortex induced vibration and dynamic response of riser pipeline are discussed, and the different responses in uniform and linearly sheared currents are compared. The results indicate that shear parameter has a significant effect on vortex induced vibration and dynamic response of riser pipeline. The multi-mode response of riser pipeline in linearly sheared flow differs from that in uniform current.
本文的研究内容包括三大部分：一是绕圆柱湍流场计算尺度效应的研究及湍流场发展变化的研究；二是弹性支撑刚性圆柱体涡激振动的数值计算；三是立管在真实海洋环境下的非线性涡激动力响应研究。
本文通过阐述我国海洋石油开采能力与世界先进水平的差距以及涡激振动对立管设计的重要性,论证了本文选题的理论意义和工程意义。分别从实验流体力学方法(EFD)、计算流体力学方法(CFD)和半经验方法(SEM)总结和归纳了涡激振动的研究进展,指出了当前涡激振动研究领域存在的一些亟待解决的问题。同时系统地阐述了涡激振动的机理、详细归纳了涡激振动的相关参数,并概述了求解湍流运动和流固耦合问题的数值方法。
对雷诺数103～107范围内圆柱体的绕流场进行了大量细致的数值计算。应用雷诺平均纳维尔——斯托克斯方程(RANS),通过方程分析得到了有关湍动能和湍流耗散率这两个表征湍流脉动特性的相似数,用以衡量湍流计算的尺度效应,并给出相似数随雷诺数变化的规律。结果表明,在主流方向的尾流中心线上当Re≥3×106时,湍动能和湍流耗散率随着雷诺数的变化趋于平稳。而后研究了四种计算尺度下的湍流场及其发展变化(包括流向平均速度场、涡量场、湍流动能和湍流耗散率),并比较了不同计算尺度下圆柱湍流场的特征。最后,对Re≥3×106这一雷诺数范围的湍流场特征进行了详细的研究,给出湍流脉动量在下游的发展变化规律。
采用雷诺平均纳维尔——斯托克斯方程(RANS),结合RNG k-ε和SST k-ω这两种不同的湍流模型,研究了低质量比弹性支撑刚性圆柱体的自激振动问题。从频率响应、振幅响应、对升力的谱分析、三个响应分支的水动力性能、尾涡模式和计算效率等方面比较了两种湍流模型的模拟效果,结果表明SST k-ω湍流模型在整体上优于RNG k-ε湍流模型。并对振动圆柱体的三个响应分支(初始分支、上端分支和下端分支)的湍流场(包括壁面压力系数、壁面切应力系数、流向平均速度、流向速度脉动值、横向速度脉动值和雷诺应力的分布)及其发展变化进行了研究,与同等雷诺数下固定圆柱体的湍流场进行了对比。
建立了真实海洋环境下立管三维非线性涡激动力响应控制方程。采用Morison方程求解顺流力；Facchinetti改进的尾流振子模型求解横向升力,考虑了附加质量系数的变化：轴向力的计算考虑平台的升沉运动。在计算分析中考虑的非线性主要包括大变形引起的几何非线性、流体动力非线性和流固耦合非线性。在边界条件的处理上,综合考虑了波浪、海流、平台运动(升沉和纵荡运动)的影响,并且上下边界的处理考虑了转动刚度的影响。采用更新的拉格朗日方法(Updated Lagrangian Method)解决大变形引起的几何非线性问题,采用Newton-Raphson迭代法求解非线性方程组。在此基础上讨论了三维空间立管的非线性涡激动力响应的影响因素。同时,研究了高雷诺数剪切流条件立管的多模态涡激振动响应,讨论了剪切参数对立管涡激动力响应的影响,并比较了均匀来流和剪切流条件下不同的响应特征。
In the oil and gas industry where the hydrocarbon drilling exploration and floating production activities move progressively towards deepwater areas with depths greater than1000meter or beyond, vortex induced vibration (VIV) of such key structures as drilling/production risers have become the subject of increasingly intense research investigation. In China, the key of ocean exploitation has turned into the South China Sea. Riser is the necessary device to connect the floater with oil well. Nevertheless, the prediction of deepwater riser VIV is very challenging owing to the fact that the incident flows are practically non-uniform and the associated fluid-structure interaction phenomena are highly complex. These result in a nonlinear coupled system which depends on several physical and mechanical parameters. Large amplitude oscillations occur when the vortex shedding and the structural vibration frequencies coincide, a condition referred to as 'lock-in'. The lock-in condition can occur over a range of oncoming flow velocities and the vortex shedding frequency can be driven relatively far from the Strouhal frequency which leads to increase in hydrodynamic loading and reduction in service life due to fatigue.
This study contains three parts:the first one is investigation of scale effect for turbulence flow around a circular cylinder and development of turbulence flow around circular cylinder; the second one is numerical pridiction of vortex induced vibration of elastically supported rigid circular cylinder with low mass damping in a fluid flow and the last one is vortex induced dynamic response of marine riser under true ocean environment.
The structures of this thesis are listed as follows:
By analysis the state of art of VIV, the engineering sense of present study is proofed. Conclusions are made of current research status from the aspects of experimental fluid dynamics, computational fluid dynamics and empirical method. The basic theory of VIV and associated parameters are introduced.
Numerical computation of flow parameters around a two-dimensional circular cylinder within Reynolds numbers range from103to107is accomplished. Velocity field, vorticity field, the fluctuation of turbulence flow and its development downstreams are discussed and comparisons of characteristics of turbulence flow at different scales are also made. In order to investigate the scale effect of turbulent flow around a circular cylinder, two items of simlarity criterion based on turbulent kinetic and turbulent dissipation rate which are associated with the fluctuation characteristics of turbulence wake are deduced by the equation analysis of Reynolds-Averaged Navier-Stokes equations (RANS). The result indicates that the fluctuations of turbulence flow along the center line in the wake of circular cylinder can never be changed with the increasing Reynolds numbers when Re≥3×106. Then characteristics of turbulence field when Re≥3×106are discussed specially and laws of fluctuations of turbulence downstreams are given.
RNG k-ε and SST k-co turbulence models are adopted to predict transverse vortex induced vibration of elastically supported rigid cylinder with low mass damping in a fluid flow. By comparing the peak amplitude, response frequency and hydrodynamic coefficients as well as wake modes of three different response branches at two different turbulence models, analysis of differences between two turbulence models are presented. Results indicate there exisit significant differences between two turbulence models, and SST k-co model is better than RNG k-ε model on the whole. By comparing turbulence fields and developments of three different response branches with static cylinder at coequal Reynolds number, some differences are observed. Pressure coefficient on the wall, shear stress coefficient on the wall, mean streamwise velocity, streamwise velocity fluctuation, cross-flow velocity fluctuation and Reynolds shear stress of three branches are different from each other and from those of static cylinder.
An investigation on the nonlinear dynamic response and vortex-induced vibration of marine riser subjected to waves and currents is performed. Three dimensional governing equations which considered nonlinearities including the geometrical nonlinearities, fluid dynamic and fluid-structure coupling nonlinearities are given. The in-line force is solved by Morison equation under combined waves, currents and platform movement while cross-flow force is solved by wake oscillator model which considered variation of added mass coefficient. The nonlinear governing equations are solved by Updated Lagrangian method(UL) and Newton-Raphson interation method in time domain. The influence of basic parameters on the dynamic response and vortex-induced vibration of marine riser were investigated. This research provides a basic foundation for practical design and theoretical analysis of marine riser. Since the vortex shedding frequency varies with flow velocity, a depth varying flow past a flexible cylinder will result in multi-frequency excitation. Depending on the range of velocity covered by the flow profile, many vibration modes of the structure can be excited. Understanding the vibration mechanisms of the structure in those cases is not a simple task. Based on this model, multi-mode excitation of riser pipeline in linear sheared flow, the effect of shear parameter on vortex induced vibration and dynamic response of riser pipeline are discussed, and the different responses in uniform and linearly sheared currents are compared. The results indicate that shear parameter has a significant effect on vortex induced vibration and dynamic response of riser pipeline. The multi-mode response of riser pipeline in linearly sheared flow differs from that in uniform current.
引文
[1]缪国平.挠性部件力学导论[M].上海交通大学出版社,1995.
[2]康庄.深海工程中的立管系统研究,http://www. deepwatercenter. com.
[3]黄维平,李华军.深水开发的新型立管系统——钢悬链线立管(SCR)[J].中国海洋大学学报,2006,36(5)：775-780.
[3]杨明华.海洋油气管道工程[M].天津大学出版社,1994.
[5]Y. Bai. Pipelines and risers [M]. Elsevier,2001.
[6]聂武.海洋工程结构动力分析[M].哈尔滨工程大学出版社,2002.
[7]C. Norberg. Fluctuating lift on a circular cylinder:Review and new measurements [J]. Journal of Fluids and Structures,2003,17(1):57-96.
[8]孔珑.工程流体力学[M].中国电力出版社,2007.
[9]R. D. Blevins. Flow-induced vibration [M]. Van Nostrand Reinhold,1990.
[10]R. N. Govardhan, C. H. K. Williamson. Defining the'modified griffin plot'in vortex-induced vibration:Revealing the effect of Reynolds number using controlled damping [J]. Journal of Fluid Mechanics,2006,561:147-180.
[11]J. T. Klamo, A. Leonard, A. Roshko. On the maximum amplitude for a freely vibrating cylinder in cross-flow [J]. Journal of Fluids and Structures,2005,21(4):429-434.
[12]K. Raghavan, M. M. Bernitsas. Experimental investigation of Reynolds number effect on vortex induced vibration of rigid circular cylinder on elastic supports [J]. Ocean Engineering,2011,38(5-6):719-731.
[13]黄智勇.柔性立管涡激振动时域响应分析[D].上海交通大学,2008.
[14]P. W. Bearman. Vortex shedding from oscillating bluff bodies [J]. Annual Review of Fluid Mechanics,1984,16(1):195-222.
[15]C. H. K. Williamson, R. Govardhan. Vortex-induced vibrations [J]. Annual Review of Fluid Mechanics,2004,36:413-455.
[16]P. W. Bearman. Circular cylinder wakes and vortex-induced vibrations [J]. Journal of Fluids and Structures,2011,27(5-6):648-658.
[17]T. Sarpkaya. A critical review of the intrinsic nature of vortex-induced vibrations [J]. Journal of Fluids and Structures,2004,19(4):389-447.
[18]X. Wu, F. Ge, Y. Hong. A review of recent studies on vortex-induced vibrations of long slender cylinders [J]. Journal of Fluids and Structures,2012,28:292-308.
[19]R. D. Gabbai, H. Benaroya.An overview of modeling and experiments of vortex-induced vibration of circular cylinders [J]. Journal of Sound and Vibration,2005,282(3-5): 575-616.
[20]C. H. K. Williamson, R. Govardhan. A brief review of recent results in vortex-induced vibrations [J].Journal of Wind Engineering and Industrial Aerodynamics,2008,96(6-7): 713-735.
[21]C. M. Larsen, K. H. Halse. Comparison of models for vortex induced vibrations of slender marine structures [J]. Marine Structure,1997,10:413-441.
[22]G. Parkinson. Phenomena and modelling of flow-induced vibrations of bluff bodies [J]. Progress in Aerospace Sciences,1989,26(2):169-224.
[23]M. A. Tognarelli, S. T. Slocum, W. R. Frank. VIV response of a long flexible cylinder in uniform and linearly sheared currents [C]. Offshore Technology Conference. Houston, Texas.2004.
[24]A. D. Trim, H. Braaten, H. Lie. Experimental investigation of vortex-induced vibration of long marine risers [J]. Journal of Fluids and Structures,2005,21(3):335-361.
[25]J. R. Chaplin, P. W. Bearman. Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current [J]. Journal of Fluids and Structures, 2005,21(1):3-24.
[26]H. Lie, K. E. Kaasen. Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow [J]. Journal of Fluids and Structures,2006,22(4): 557-575.
[27]F. J. Huera-Huarte, P. W. Bearman. Wake structures and vortex-induced vibrations of a long flexible cylinder—part 1:Dynamic response [J]. Journal of Fluids and Structures,2009,25(6):969-990.
[28]F. J. Huera-Huarte, P. W. Bearman. Wake structures and vortex-induced vibrations of a long flexible cylinder—part 2:Drag coefficients and vortex modes [J]. Journal of Fluids and Structures,2009,25(6):991-1006.
[29]H. Marcollo, H. Chaurasia, J. K. Vandiver. Phenomena observed in VIV bare riser field tests [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering,2007,989-995.
[30]J. K. Vandiver, V. Jaiswal, S. B. Swithenbank. Fatigue damage from high mode number vortex-induced vibration [C]. Proceedings of the 25th International Conference on Offshore Mechanics and Arctic Engineering,2006,1-9.
[31]J. K. Vandiver, H. Marcollo, S. Swithenbank. High mode number vortex-induced vibration field experiments [C]. Offshore Technology Conference. Houston, Texas.2005.
[32]J. Xu, M. He, N. Bose. Vortex modes and vortex-induced vibration of a long, flexible riser [J]. Ocean Engineering,2009,36(6-7):456-467.
[33]J. K. Vandiver, V. Jaiswal, V. Jhingran. Insights on vortex-induced, traveling waves on long risers [J]. Journal of Fluids and Structures,2009,25(4):641-653.
[34]S. Pasto. Vortex-induced vibrations of a circular cylinder in laminar and turbulent flows [J]. Journal of Fluids and Structures,2008,24(7):977-993.
[35]Z. J. Ding, S. Balasubramanian, R. T. Lokken. Lift and Damping Characteristics of Bare and Straked Cylinders at Riser Scale Reynolds Numbers [C]. Offshore Technology Conference. Houston, Texas.2004.
[36]J. K. Vandiver, A. Marcollo. High mode number VIV experiments [C]. IUTAM Symposium on Integrated Modeling of Fully Coupled Fluid Structure Interactions Using Analysis, Computations and Experiments. Springer Netherlands.2003:211-231.
[37]E. Huse, F. G. Nielsen, T. Soreide. Coupling between in-line and transverse VIV response [C]. Proceedings of the 21th International Conference on Offshore Mechanics and Arctic Engineering,2002,835-847.
[38]D. W. Allen, D. L.Henning. Prototype vortex-induced vibration tests for production risers [C]. Offshore Technology Conference. Houston, Texas.2001.
[39]K. Vikestad. Multi-frequency response of a cylinder subjected to vortex shedding and support motions [D]. Norwegian University of Science and Technology,1998.
[40]E. Huse, G. Kleiven, F.G.Nielsen. Large scale model testing of deep sea risers [C]. Offshore Technology Conference. Houston, Texas.1998.
[41]唐国强,吕林,滕斌.大长细比柔性杆件涡激振动实验[J].海洋工程,2011,1：18-25.
[42]黄维平,曹静,张恩勇,唐世振.大柔性圆柱体两自由度涡激振动试验研究[J].力学学报,2011,43(2)：436-440.
[43]郭海燕,董文乙,娄敏.海中输流立管涡激振动试验研究及疲劳寿命分析[J].中国海洋大学学报(自然科学版),2008,162(3)：503-507.
[44]E. Guilmineau, P. Queutey. Numerical simulation of vortex-induced vibration of a circular cylinder with low mass-damping in a turbulent flow [J]. Journal of Fluids and Structures,2004,19(4):449-466.
[45]J. B. V. Wanderley, G. H. B. Souza, S. H. Sphaier. Vortex-induced vibration of an elastically mounted circular cylinder using an upwind TVD two-dimensional numerical scheme [J]. Ocean Engineering,2008,35(14-15):1533-1544.
[46]Z. Y. Pan, W. C. Cui, Q. M. Miao. Numerical simulation of vortex-induced vibration of a circular cylinder at low mass-damping using rans code [J]. Journal of Fluids and Structures,2007,23(1):23-37.
[47]J. B. V. Wanderley, S. H. Sphaier, C. Levi. A numerical investigation of vortex induced vibration on an elastically mounted rigid cylinder [C]. Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering,2008,703-711.
[48]P. Bhattacharjee, K. K. Nielsen, G. Stewart. Numerical simulation of pipeline VIV for steady and unsteady flow [C].Proceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering,2009,843-851.
[49]A. Sanchis, G. Salevik, J. Grue. Two-degree-of-freedom vortex-induced vibrations of a spring-mounted rigid cylinder with low mass ratio [J]. Journal of Fluids and Structures,2008,24(6):907-919.
[50]Z. S. Chen, W. J, Kim, D. Y. Yu. Numerical simulation of a large-scale riser with vortex-induced vibration [C]. Proceedings of the 8th ISOPE Pacific/Asia Offshore Mechanics Symposium.2008,121-128.
[51]J. B. V. Wanderley, G. H. B. Souza, C. Levi.Two-dimensional numerical simulation of vortex induced vibration of a circular cylinder [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering,2007,623-632.
[52]J. P. Pontaza, H. C. Chen. Three-dimensional numerical simulations of circular cylinders undergoing two degree-of-freedom vortex-induced vibrations [J]. Journal of Offshore Mechanics and Arctic Engineering,2007,129(3):158-164.
[53]A. Placzek, J. F. Sigrist, A. Hamdouni. Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number:Forced and free oscillations [J]. Computers & Fluids,2009,38(1):80-100.
[54]K. Huang, H. C. Chen, C. R. Chen. Riser VIV analysis by a CFD approach [C].17th International Offshore and Offshore and Polar Engineering Conference Proceedings, 2007,2723-2729.
[55]Y. Constantinides, H. Owen, J. Oakley. CFD high L/D riser modeling study [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering,2007,715-722.
[56]J. B. V. Wanderley, G. H. B. Souza, C. Levi.Numerical simulation of vortex induced vibration using the k-epsilon model [C]. Proceedings of the 25th International Conference on Offshore Mechanics and Arctic Engineering,2006,607-614.
[57]J. R. Meneghini, F. Saltara, R. D. A. Fregonesi. Numerical simulations of VIV on long flexible cylinders immersed in complex flow fields [J]. European Journal of Mechanics-B/Fluids,2004,23(1):51-63.
[58]H. Al-Jamal, C. Dalton. Vortex induced vibrations using large eddy simulation at a moderate Reynolds number [J]. Journal of Fluids and Structures,2004,19(1):73-92.
[59]D. Shiels, A. Leonard, A. Roshko. Flow-induced vibration of a circular cylinder at limiting structural parameters [J]. Journal of Fluids and Structures,2001,15(1): 3-21.
[60]H. M. Blackburn, R. N. Govardhan, C. H. K. Williamson. A complementary numerical and physical investigation of vortex-induced vibration [J]. Journal of Fluids and Structures,2001,15(3-4):481-488.
[61]D. Sampaio. Simulating vortex shedding at high Reynolds numbers [C].10th International Offshore and Offshore and Polar Engineering Conference Proceedings, 2000,461-466.
[62]C. Evangelinos, D. Lucor, G. E. Karniadakis. DNS-derived force distribution on flexible cylinders subject to vortex-induced vibration [J]. Journal of Fluids and Structures,2000,14(3):429-440.
[63]B. C. Ferreira, M. A. Vitola, J. B. V. Wanderley. A numerical investigation of the response of an elastically mounted rigid cylinder with two degrees of freedom [C]. Proceedings of the 29th International Conference on Offshore Mechanics and Arctic Engineering,2010,383-392.
[64]C. T. Yamamoto, J. R. Meneghini, F. Saltara. Numerical simulations of vortex-induced vibration on flexible cylinders [J]. Journal of Fluids and Structures,2004,19(4): 467-489.
[65]Z. Huang, C. M. Larsen. Numerical simulation on vortex-induced vibration of an elastically mounted circular cylinder with two degrees-of-freedom [C]. Proceedings of the 30th International Conference on Offshore Mechanics and Arctic Engineering, 2011,447-455.
[66]J. S. Wang, H. Liu, S. Q. Jiang. Vortex-induced vibration on 2D circular riser using a high resolution numerical scheme [J]. Journal of Hydrodynamics, Ser B,2010,22(5): 954-959.
[67]L.F. N. Soares, J. B. V. Wanderley, M. Vitola. The response of an elastically mounted rigid cylinder subjected to vortex shedding and support motion [C]. Proceedings of the 29th International Conference on Offshore Mechanics and Arctic Engineering,2010, 393-400.
[68]王成官,王嘉松.海洋隔水管涡激振动的三维数值模拟研究[J].水动力学研究与进展,2011,6(4)：437-443.
[69]陶实, 周力,宗智.基于格子Boltzmann方法的圆柱两自由度涡激振动的研究[J].水动力学研究与进展,2013,28(2)：167-175.
[70]艾尚茂,孙丽萍.时间步长对低质量比圆柱涡激振动数值结果的影响[J].船海工程,2011,40：168-171.
[71]潘志远,崔维成,刘应中.低质量—阻尼因子圆柱体的涡激振动预报模型[J].船舶力学,2005,5：115-124.
[72]王成官,王嘉松.不同预紧力时隔水管涡激振动特性三维数值模拟研究[J].中国海上油气,2011,6：415-419.
[73]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,2009,5：613-619.
[74]赵静,吕林,董国海.亚临界雷诺数下圆柱受迫振动的数值研究[J].计算力学学报,2012,1：74-80.
[75]M. L. Facchinetti. Coupling of structure and wake oscillators in vortex-induced vibrations [J]. Journal of Fluids and Structures,2004,19(2):123-140.
[76]M. L Facchinetti, E. de Langre, F. Biolley. Vortex-induced travelling waves along a cable [J]. European Journal of Mechanics-B/Fluids,2004,23(1):199-208.
[77]L. Mathelin, E. de Langre. Vortex-induced vibrations and waves under shear flow with a wake oscillator model [J]. European Journal of Mechanics-B/Fluids,2005,24(4): 478-490.
[78]R. Violette, E. de Langre, J. Szydlowski. Computation of vortex-induced vibrations of long structures using a wake oscillator model:Comparison with DNS and experiments [J]. Computers & Structures,2007,85(11-14):1134-1141.
[79]A. Farshidianfar, N. Dolatabadi. Modified higher-order wake oscillator model for vortex-induced vibration of circular cylinders [J]. Acta Mechanica,2013,1-16.
[80]N. Srinil. Multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures with geometric nonlinearities [J]. Journal of Fluids and Structures,2010,26(7-8):1098-1122.
[81]R. Bourguet, G. E. Karniadakis, M. S. Triantafyllou. Vortex-induced vibrations of a long flexible cylinder in shear flow [J]. Journal of Fluid Mechanics,2011,677: 342-382.
[82]W. Chen, Z. Zheng, M. Li. Effects of varying tension and stiffness on dynamic characteristics and VIV of slender riser [C]. Proceedings of the 30th International Conference on Offshore Mechanics and Arctic Engineering,2011,207-213.
[83]G. F. Rosetti, K. Nishimoto, J. Wilde. Vortex-induced vibrations on flexible cylindrical structures coupled with non-linear oscillators [J]. Proceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering,2009, 217-229.
[84]S. Kaewunruen, J. Chiravatchrade, S. Chucheepsakul. Nonlinear free vibrations of marine risers/pipes transporting fluid [J]. Ocean Engineering,2005,32(3-4):417-440.
[85]A. Farshidianfar, H. Zanganeh. A modified wake oscillator model for vortex-induced vibration of circular cylinders for a wide range of mass-damping ratio [J]. Journal of Fluids and Structures,2010,26(3):430-441.
[86]G. K. Furnes. Flow induced vibrations modeled by coupled non-linear oscillators [C]. 17th International Offshore and Offshore and Polar Engineering Conference Proceedings, 2007,2781-2787.
[87]L. Zhang, W. Chen, Z. Zheng. Controlling parameter for wave types of long flexible cable undergoing vortex-induced vibration [J]. Procedia Engineering,2010,4: 161-170.
[88]W. H. Xu, X. H. Zeng, Y. X. Wu. High aspect ratio (L/D) riser VIV prediction using wake oscillator model [J]. Ocean Engineering,2008,35(17-18):1769-1774.
[89]N. Srinil. Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents [J]. Applied Ocean Research,2011,33(1): 41-53.
[90]F. Ge, W. Lu, L. Wang. Shear flow induced vibrations of long slender cylinders with a wake oscillator model [J]. Acta Mechanica Sinica,2011,27(3):330-338.
[91]R. Bourguet, G. E. Karniadakis, M. S. Triantafyllou. Lock-in of the vortex-induced vibrations of a long tensioned beam in shear flow [J]. Journal of Fluids and Structures, 2011,27(5-6):838-847.
[92]A. Farshidianfar, H. Zanganeh The Lock-in Phenomenon in VIV Using a modified wake oscillator model for both high and low mass-damping ratio [J]. Iranian Journal of Mechanical Engineering,2009,10(2):5-27.
[93]F. Ge, X. Long, L. Wang. Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators [J]. Science China Ser G -Physics, Mechanics & Astronomy,2009,52(7):1086-1093.
[94]R. H. M. Ogink, A. V. Metrikine.A wake oscillator with frequency dependent coupling for the modeling of vortex-induced vibration [J]. Journal of Sound and Vibration,2010, 329(26):5452-5473.
[95]N. Srinil, H. Zanganeh. Modelling of coupled cross-flow/in-line vortex-induced vibrations using double duffing and van der pol oscillators [J]. Ocean Engineering, 2012,53:83-97.
[96]J. Leklong. Dynamic responses of marine risers/pipes transporting fluid subject to top end excitations [C].18th International Offshore and Offshore and Polar Engineering Conference Proceedings,2008,113-120.
[97]李洪春,郭海燕,李效民.基于Matlab的海洋立管涡激振动数值模拟系统研究[J].中国海洋大学学报(自然科学版),2010,1：207-212.
[98]秦伟,康庄,孙丽萍,宋儒鑫.并列双圆柱涡激振动的经验性模型研究[J].海洋工程,2013,31(2)：11-18.
[99]余建星,俞永清,李红涛,吴海欣.海底管跨涡激振动疲劳可靠性研究[J].船舶力学,2005,2：109-114.
[100]郑仲钦,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,2012,43(4)：37-41.
[101]徐万海,杜杰,余建星.非均匀流中立管涡激振动模型预测分析[J].海洋技术,2011,3：94-96.
[102]饶志标,杨建民,付世晓.剪切流下钢悬链线立管涡激振动响应研究[J].振动与冲击,2010.10：4-8.
[103]葛斐,龙旭,王雷,洪友士.长细比圆柱体顺流向与横向耦合涡激振动的研究[J].中国科学(G辑：物理学力学天文学),2009,5：752-759.
[104]黄维平,刘娟,唐世振.考虑流固耦合的大柔性圆柱体涡激振动非线性时域模型[J].振动与冲击,2012,31：140-143.
[105]C. Feng. The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders [D]. University of British Columbia, 1968.
[106]N. Jauvtis, C. H. K. Williamson. 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.
[107]R. Govardhan, C. H. K. Williamson. Critical mass in vortex-induced vibration of a cylinder [J]. European Journal of Mechanics-B/Fluids,2004,23(1):17-27.
[108]J. Carberry, R. Govardhan, J. Sheridan. Wake states and response branches of forced and freely oscillating cylinders [J]. European Journal of Mechanics-B/Fluids,2004, 23(1):89-97.
[109]N. Jauvtis, C. H. K. Williamson. Vortex-induced vibration of a cylinder with two degrees of freedom [J]. Journal of Fluids and Structures,2003,17(7):1035-1042.
[110]R. Govardhan, C. H. K. Williamson.Resonance forever:Existence of a critical mass and an infinite regime of resonance in vortex-induced vibration [J]. Journal of Fluid Mechanics,2002,473:147-166.
[111]R. Govardhan, C. H. K. Williamson. Mean and fluctuating velocity fields in the wake of a freely-vibrating cylinder [J]. Journal of Fluids and Structures,2001,15(3-4): 489-501.
[112]R. Govardhan, C. H. K. Williamson.Modes of vortex formation and frequency response of a freely vibrating cylinder [J]. Journal of Fluid Mechanics,2000,420(85):85-130.
[113]A. Khalak, C. H. K. Williamson. 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.
[114]C. H. K. Williamson. Advances in our understanding of vortex dynamics in bluff body wakes [J]. Journal of Wind Engineering and Industrial Aerodynamics,1997,69-71:3-32.
[115]A. Khalak, C. H. K. Williamson. Fluid forces and dynamics of a hydroelastic structure with very low mass and damping [J]. Journal of Fluids and Structures,1997,11(8): 973-982.
[116]A. Khalak, C. H. K. Williamson. Investigation of relative effects of mass and damping in vortex-induced vibration of a circular cylinder [J]. Journal of Wind Engineering and Industrial Aerodynamics,1997,69-71:341-350.
[117]A. Khalak, C. H. K. Williamson. Dynamics of a hydroelastic cylinder with very low mass and damping [J]. Journal of Fluids and Structures,1996,10(5):455-472.
[118]R. Gopalkrishnan. Vortex-induced forces on oscillating bluff cylinders [D]. Massachusetts Institute of Technology,1993.
[119]C. H. K. Williamson, A. Roshko. Vortex formation in the wake of an oscillating cylinder [J]. Journal of Fluids and Structures,1988,2(4):355-381.
[120]梁在朝.工程湍流[M].华中理工大学出版社,1999.
[121]是勋刚.湍流[M].天津大学出版社,1994.
[122]林建中.湍动力学[M].浙江大学出版社,2000.
[123]许维德.流体力学[M].国防工业出版社,1989.
[124]V. Yakhot, S. A. Orszag. Renormalization group analysis of turbulence. [J]. Journal of Scientific Computing,1986,1(1):3-51.
[125]H. Schlichting. Boundary layer theory [M]. Nueva York, EUA:McGraw-Hill.1979.
[126]A. Roshko. Perspectives on bluff body aerodynamics [J]. Journal of Wind Engineering and Industrial Aerodynamics,1993,49(1-3):79-100.
[127]E. Achenbach. Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re= 5×106 [J]. Journal of Fluid Mechanics,1968,34(4): 625-639.
[128]C. Norberg. Flow around a circular cylinder:aspects of fluctuating lift [J]. Journal of Fluids and Structures,2001,15(3-4):459-469.
[129]H. M. Blackburn, W. H. Melbourne. The effect of free-stream turbulence on sectional lift forces on a circular cylinder [J]. Journal of Fluid Mechanics,1996,306: 267-292.
[130]G. Schewe. On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers [J]. Journal of Fluid Mechanics, 1983,133:265-285.
[131]U.0. Onal, M. Atlar. Effect of turbulence modelling on the computation of the near-wake flow of a circular cylinder [J]. Ocean Engineering,2010,37(4):387-399.
[132]P. Parnaudeau, J. Carlier, D. Heitz. Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900 [J]. Physics of Fluids,2008,20(8): 85-101.
[133]P. Catalano, M. Wang, G. Iaccarino. Numerical simulation of the flow around a circular cylinder at high Reynolds numbers [J]. International Journal of Heat and Fluid Flow, 2003,24(4):463-469.
[134]L.Ong, J. Wallace. The velocity field of the turbulent very near wake of a circular cylinder [J]. Experiments in Fluids,1996,20(6):441-453.
[135]王福军.计算流体动力学分析—CFD软件原理与应用[M].清华大学出版社,2006.
[136]J. Lighthill. Fundamentals concerning wave loading on offshore structures [J].Journal of Fluid Mechanics,1986,173:667-681.
[137]F. R. Menter. Two-equation eddy-viscosity models for engineering applications [J]. AIAA Journal,1994,32:1598-1605.
[138]J. G. Wissink, W. Rodi. Numerical study of the near wake of a circular cylinder [J]. International Journal of Heat and Fluid Flow,2008,29(4):1060-1070.
[139]A. Elbanhawy, A. Turan. On two-dimensional predictions of turbulent cross-flow induced vibration:Forces on a cylinder and wake interaction [J]. Flow, Turbulence and Combustion,2010,85(2):199-224.
[140]D. M. F. Gao, C. G. Mingham. Numerical and experimental investigation of turbulent flow around a vertical circular cylinder [C].20th International Offshore and Offshore and Polar Engineering Conference Proceedings,2010,639-643.
[141]R. M. C. So, Y. Zhou, M. H. Liu. Free vibrations of an elastic cylinder in a cross flow and their effects on the near wake [J]. Experiments in Fluids,2000,29(2): 130-144.
[142]R. D. Blevins, J. F. Saint-Marcoux. Wake of a vibrating cylinder at Re=105 [C]. Proceedings of the 30th International Conference on Offshore Mechanics and Arctic Engineering,2011,97-103.
[143]J. Xu, D. Spencer, A. Gardner. Wake fields behind risers undergoing vortex-induced vibration [C]. Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering,2008,539-546.
[144]A. G. Kravchenkoa, P. Moin. Numerical studies of flow over a circular cylinder at Re=3900 [J]. Physics of Fluids,2000,12(2):403-417.
[145]林海花.浪流共同作用下隔水管涡激动力响应分析[J].哈尔滨工程大学学报,2008,29(2)：121-125.
[146]林海花.波流共同作用下隔水管动力响应非线性分析[J].船舶力学,2009,13(2)：189-195.
[147]王勖成.有限单元法基本原理和数值方法[M].清华大学出版社,1988.
[148]殷有泉.非线性有限元法基础[M].北京大学出版社,2007.
[149]贾星兰, 方华灿.海洋钻井隔水管的动力响应[M].石油机械,1995.
[2]康庄.深海工程中的立管系统研究,http://www. deepwatercenter. com.
[3]黄维平,李华军.深水开发的新型立管系统——钢悬链线立管(SCR)[J].中国海洋大学学报,2006,36(5)：775-780.
[3]杨明华.海洋油气管道工程[M].天津大学出版社,1994.
[5]Y. Bai. Pipelines and risers [M]. Elsevier,2001.
[6]聂武.海洋工程结构动力分析[M].哈尔滨工程大学出版社,2002.
[7]C. Norberg. Fluctuating lift on a circular cylinder:Review and new measurements [J]. Journal of Fluids and Structures,2003,17(1):57-96.
[8]孔珑.工程流体力学[M].中国电力出版社,2007.
[9]R. D. Blevins. Flow-induced vibration [M]. Van Nostrand Reinhold,1990.
[10]R. N. Govardhan, C. H. K. Williamson. Defining the'modified griffin plot'in vortex-induced vibration:Revealing the effect of Reynolds number using controlled damping [J]. Journal of Fluid Mechanics,2006,561:147-180.
[11]J. T. Klamo, A. Leonard, A. Roshko. On the maximum amplitude for a freely vibrating cylinder in cross-flow [J]. Journal of Fluids and Structures,2005,21(4):429-434.
[12]K. Raghavan, M. M. Bernitsas. Experimental investigation of Reynolds number effect on vortex induced vibration of rigid circular cylinder on elastic supports [J]. Ocean Engineering,2011,38(5-6):719-731.
[13]黄智勇.柔性立管涡激振动时域响应分析[D].上海交通大学,2008.
[14]P. W. Bearman. Vortex shedding from oscillating bluff bodies [J]. Annual Review of Fluid Mechanics,1984,16(1):195-222.
[15]C. H. K. Williamson, R. Govardhan. Vortex-induced vibrations [J]. Annual Review of Fluid Mechanics,2004,36:413-455.
[16]P. W. Bearman. Circular cylinder wakes and vortex-induced vibrations [J]. Journal of Fluids and Structures,2011,27(5-6):648-658.
[17]T. Sarpkaya. A critical review of the intrinsic nature of vortex-induced vibrations [J]. Journal of Fluids and Structures,2004,19(4):389-447.
[18]X. Wu, F. Ge, Y. Hong. A review of recent studies on vortex-induced vibrations of long slender cylinders [J]. Journal of Fluids and Structures,2012,28:292-308.
[19]R. D. Gabbai, H. Benaroya.An overview of modeling and experiments of vortex-induced vibration of circular cylinders [J]. Journal of Sound and Vibration,2005,282(3-5): 575-616.
[20]C. H. K. Williamson, R. Govardhan. A brief review of recent results in vortex-induced vibrations [J].Journal of Wind Engineering and Industrial Aerodynamics,2008,96(6-7): 713-735.
[21]C. M. Larsen, K. H. Halse. Comparison of models for vortex induced vibrations of slender marine structures [J]. Marine Structure,1997,10:413-441.
[22]G. Parkinson. Phenomena and modelling of flow-induced vibrations of bluff bodies [J]. Progress in Aerospace Sciences,1989,26(2):169-224.
[23]M. A. Tognarelli, S. T. Slocum, W. R. Frank. VIV response of a long flexible cylinder in uniform and linearly sheared currents [C]. Offshore Technology Conference. Houston, Texas.2004.
[24]A. D. Trim, H. Braaten, H. Lie. Experimental investigation of vortex-induced vibration of long marine risers [J]. Journal of Fluids and Structures,2005,21(3):335-361.
[25]J. R. Chaplin, P. W. Bearman. Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current [J]. Journal of Fluids and Structures, 2005,21(1):3-24.
[26]H. Lie, K. E. Kaasen. Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow [J]. Journal of Fluids and Structures,2006,22(4): 557-575.
[27]F. J. Huera-Huarte, P. W. Bearman. Wake structures and vortex-induced vibrations of a long flexible cylinder—part 1:Dynamic response [J]. Journal of Fluids and Structures,2009,25(6):969-990.
[28]F. J. Huera-Huarte, P. W. Bearman. Wake structures and vortex-induced vibrations of a long flexible cylinder—part 2:Drag coefficients and vortex modes [J]. Journal of Fluids and Structures,2009,25(6):991-1006.
[29]H. Marcollo, H. Chaurasia, J. K. Vandiver. Phenomena observed in VIV bare riser field tests [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering,2007,989-995.
[30]J. K. Vandiver, V. Jaiswal, S. B. Swithenbank. Fatigue damage from high mode number vortex-induced vibration [C]. Proceedings of the 25th International Conference on Offshore Mechanics and Arctic Engineering,2006,1-9.
[31]J. K. Vandiver, H. Marcollo, S. Swithenbank. High mode number vortex-induced vibration field experiments [C]. Offshore Technology Conference. Houston, Texas.2005.
[32]J. Xu, M. He, N. Bose. Vortex modes and vortex-induced vibration of a long, flexible riser [J]. Ocean Engineering,2009,36(6-7):456-467.
[33]J. K. Vandiver, V. Jaiswal, V. Jhingran. Insights on vortex-induced, traveling waves on long risers [J]. Journal of Fluids and Structures,2009,25(4):641-653.
[34]S. Pasto. Vortex-induced vibrations of a circular cylinder in laminar and turbulent flows [J]. Journal of Fluids and Structures,2008,24(7):977-993.
[35]Z. J. Ding, S. Balasubramanian, R. T. Lokken. Lift and Damping Characteristics of Bare and Straked Cylinders at Riser Scale Reynolds Numbers [C]. Offshore Technology Conference. Houston, Texas.2004.
[36]J. K. Vandiver, A. Marcollo. High mode number VIV experiments [C]. IUTAM Symposium on Integrated Modeling of Fully Coupled Fluid Structure Interactions Using Analysis, Computations and Experiments. Springer Netherlands.2003:211-231.
[37]E. Huse, F. G. Nielsen, T. Soreide. Coupling between in-line and transverse VIV response [C]. Proceedings of the 21th International Conference on Offshore Mechanics and Arctic Engineering,2002,835-847.
[38]D. W. Allen, D. L.Henning. Prototype vortex-induced vibration tests for production risers [C]. Offshore Technology Conference. Houston, Texas.2001.
[39]K. Vikestad. Multi-frequency response of a cylinder subjected to vortex shedding and support motions [D]. Norwegian University of Science and Technology,1998.
[40]E. Huse, G. Kleiven, F.G.Nielsen. Large scale model testing of deep sea risers [C]. Offshore Technology Conference. Houston, Texas.1998.
[41]唐国强,吕林,滕斌.大长细比柔性杆件涡激振动实验[J].海洋工程,2011,1：18-25.
[42]黄维平,曹静,张恩勇,唐世振.大柔性圆柱体两自由度涡激振动试验研究[J].力学学报,2011,43(2)：436-440.
[43]郭海燕,董文乙,娄敏.海中输流立管涡激振动试验研究及疲劳寿命分析[J].中国海洋大学学报(自然科学版),2008,162(3)：503-507.
[44]E. Guilmineau, P. Queutey. Numerical simulation of vortex-induced vibration of a circular cylinder with low mass-damping in a turbulent flow [J]. Journal of Fluids and Structures,2004,19(4):449-466.
[45]J. B. V. Wanderley, G. H. B. Souza, S. H. Sphaier. Vortex-induced vibration of an elastically mounted circular cylinder using an upwind TVD two-dimensional numerical scheme [J]. Ocean Engineering,2008,35(14-15):1533-1544.
[46]Z. Y. Pan, W. C. Cui, Q. M. Miao. Numerical simulation of vortex-induced vibration of a circular cylinder at low mass-damping using rans code [J]. Journal of Fluids and Structures,2007,23(1):23-37.
[47]J. B. V. Wanderley, S. H. Sphaier, C. Levi. A numerical investigation of vortex induced vibration on an elastically mounted rigid cylinder [C]. Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering,2008,703-711.
[48]P. Bhattacharjee, K. K. Nielsen, G. Stewart. Numerical simulation of pipeline VIV for steady and unsteady flow [C].Proceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering,2009,843-851.
[49]A. Sanchis, G. Salevik, J. Grue. Two-degree-of-freedom vortex-induced vibrations of a spring-mounted rigid cylinder with low mass ratio [J]. Journal of Fluids and Structures,2008,24(6):907-919.
[50]Z. S. Chen, W. J, Kim, D. Y. Yu. Numerical simulation of a large-scale riser with vortex-induced vibration [C]. Proceedings of the 8th ISOPE Pacific/Asia Offshore Mechanics Symposium.2008,121-128.
[51]J. B. V. Wanderley, G. H. B. Souza, C. Levi.Two-dimensional numerical simulation of vortex induced vibration of a circular cylinder [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering,2007,623-632.
[52]J. P. Pontaza, H. C. Chen. Three-dimensional numerical simulations of circular cylinders undergoing two degree-of-freedom vortex-induced vibrations [J]. Journal of Offshore Mechanics and Arctic Engineering,2007,129(3):158-164.
[53]A. Placzek, J. F. Sigrist, A. Hamdouni. Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number:Forced and free oscillations [J]. Computers & Fluids,2009,38(1):80-100.
[54]K. Huang, H. C. Chen, C. R. Chen. Riser VIV analysis by a CFD approach [C].17th International Offshore and Offshore and Polar Engineering Conference Proceedings, 2007,2723-2729.
[55]Y. Constantinides, H. Owen, J. Oakley. CFD high L/D riser modeling study [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering,2007,715-722.
[56]J. B. V. Wanderley, G. H. B. Souza, C. Levi.Numerical simulation of vortex induced vibration using the k-epsilon model [C]. Proceedings of the 25th International Conference on Offshore Mechanics and Arctic Engineering,2006,607-614.
[57]J. R. Meneghini, F. Saltara, R. D. A. Fregonesi. Numerical simulations of VIV on long flexible cylinders immersed in complex flow fields [J]. European Journal of Mechanics-B/Fluids,2004,23(1):51-63.
[58]H. Al-Jamal, C. Dalton. Vortex induced vibrations using large eddy simulation at a moderate Reynolds number [J]. Journal of Fluids and Structures,2004,19(1):73-92.
[59]D. Shiels, A. Leonard, A. Roshko. Flow-induced vibration of a circular cylinder at limiting structural parameters [J]. Journal of Fluids and Structures,2001,15(1): 3-21.
[60]H. M. Blackburn, R. N. Govardhan, C. H. K. Williamson. A complementary numerical and physical investigation of vortex-induced vibration [J]. Journal of Fluids and Structures,2001,15(3-4):481-488.
[61]D. Sampaio. Simulating vortex shedding at high Reynolds numbers [C].10th International Offshore and Offshore and Polar Engineering Conference Proceedings, 2000,461-466.
[62]C. Evangelinos, D. Lucor, G. E. Karniadakis. DNS-derived force distribution on flexible cylinders subject to vortex-induced vibration [J]. Journal of Fluids and Structures,2000,14(3):429-440.
[63]B. C. Ferreira, M. A. Vitola, J. B. V. Wanderley. A numerical investigation of the response of an elastically mounted rigid cylinder with two degrees of freedom [C]. Proceedings of the 29th International Conference on Offshore Mechanics and Arctic Engineering,2010,383-392.
[64]C. T. Yamamoto, J. R. Meneghini, F. Saltara. Numerical simulations of vortex-induced vibration on flexible cylinders [J]. Journal of Fluids and Structures,2004,19(4): 467-489.
[65]Z. Huang, C. M. Larsen. Numerical simulation on vortex-induced vibration of an elastically mounted circular cylinder with two degrees-of-freedom [C]. Proceedings of the 30th International Conference on Offshore Mechanics and Arctic Engineering, 2011,447-455.
[66]J. S. Wang, H. Liu, S. Q. Jiang. Vortex-induced vibration on 2D circular riser using a high resolution numerical scheme [J]. Journal of Hydrodynamics, Ser B,2010,22(5): 954-959.
[67]L.F. N. Soares, J. B. V. Wanderley, M. Vitola. The response of an elastically mounted rigid cylinder subjected to vortex shedding and support motion [C]. Proceedings of the 29th International Conference on Offshore Mechanics and Arctic Engineering,2010, 393-400.
[68]王成官,王嘉松.海洋隔水管涡激振动的三维数值模拟研究[J].水动力学研究与进展,2011,6(4)：437-443.
[69]陶实, 周力,宗智.基于格子Boltzmann方法的圆柱两自由度涡激振动的研究[J].水动力学研究与进展,2013,28(2)：167-175.
[70]艾尚茂,孙丽萍.时间步长对低质量比圆柱涡激振动数值结果的影响[J].船海工程,2011,40：168-171.
[71]潘志远,崔维成,刘应中.低质量—阻尼因子圆柱体的涡激振动预报模型[J].船舶力学,2005,5：115-124.
[72]王成官,王嘉松.不同预紧力时隔水管涡激振动特性三维数值模拟研究[J].中国海上油气,2011,6：415-419.
[73]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,2009,5：613-619.
[74]赵静,吕林,董国海.亚临界雷诺数下圆柱受迫振动的数值研究[J].计算力学学报,2012,1：74-80.
[75]M. L. Facchinetti. Coupling of structure and wake oscillators in vortex-induced vibrations [J]. Journal of Fluids and Structures,2004,19(2):123-140.
[76]M. L Facchinetti, E. de Langre, F. Biolley. Vortex-induced travelling waves along a cable [J]. European Journal of Mechanics-B/Fluids,2004,23(1):199-208.
[77]L. Mathelin, E. de Langre. Vortex-induced vibrations and waves under shear flow with a wake oscillator model [J]. European Journal of Mechanics-B/Fluids,2005,24(4): 478-490.
[78]R. Violette, E. de Langre, J. Szydlowski. Computation of vortex-induced vibrations of long structures using a wake oscillator model:Comparison with DNS and experiments [J]. Computers & Structures,2007,85(11-14):1134-1141.
[79]A. Farshidianfar, N. Dolatabadi. Modified higher-order wake oscillator model for vortex-induced vibration of circular cylinders [J]. Acta Mechanica,2013,1-16.
[80]N. Srinil. Multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures with geometric nonlinearities [J]. Journal of Fluids and Structures,2010,26(7-8):1098-1122.
[81]R. Bourguet, G. E. Karniadakis, M. S. Triantafyllou. Vortex-induced vibrations of a long flexible cylinder in shear flow [J]. Journal of Fluid Mechanics,2011,677: 342-382.
[82]W. Chen, Z. Zheng, M. Li. Effects of varying tension and stiffness on dynamic characteristics and VIV of slender riser [C]. Proceedings of the 30th International Conference on Offshore Mechanics and Arctic Engineering,2011,207-213.
[83]G. F. Rosetti, K. Nishimoto, J. Wilde. Vortex-induced vibrations on flexible cylindrical structures coupled with non-linear oscillators [J]. Proceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering,2009, 217-229.
[84]S. Kaewunruen, J. Chiravatchrade, S. Chucheepsakul. Nonlinear free vibrations of marine risers/pipes transporting fluid [J]. Ocean Engineering,2005,32(3-4):417-440.
[85]A. Farshidianfar, H. Zanganeh. A modified wake oscillator model for vortex-induced vibration of circular cylinders for a wide range of mass-damping ratio [J]. Journal of Fluids and Structures,2010,26(3):430-441.
[86]G. K. Furnes. Flow induced vibrations modeled by coupled non-linear oscillators [C]. 17th International Offshore and Offshore and Polar Engineering Conference Proceedings, 2007,2781-2787.
[87]L. Zhang, W. Chen, Z. Zheng. Controlling parameter for wave types of long flexible cable undergoing vortex-induced vibration [J]. Procedia Engineering,2010,4: 161-170.
[88]W. H. Xu, X. H. Zeng, Y. X. Wu. High aspect ratio (L/D) riser VIV prediction using wake oscillator model [J]. Ocean Engineering,2008,35(17-18):1769-1774.
[89]N. Srinil. Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents [J]. Applied Ocean Research,2011,33(1): 41-53.
[90]F. Ge, W. Lu, L. Wang. Shear flow induced vibrations of long slender cylinders with a wake oscillator model [J]. Acta Mechanica Sinica,2011,27(3):330-338.
[91]R. Bourguet, G. E. Karniadakis, M. S. Triantafyllou. Lock-in of the vortex-induced vibrations of a long tensioned beam in shear flow [J]. Journal of Fluids and Structures, 2011,27(5-6):838-847.
[92]A. Farshidianfar, H. Zanganeh The Lock-in Phenomenon in VIV Using a modified wake oscillator model for both high and low mass-damping ratio [J]. Iranian Journal of Mechanical Engineering,2009,10(2):5-27.
[93]F. Ge, X. Long, L. Wang. Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators [J]. Science China Ser G -Physics, Mechanics & Astronomy,2009,52(7):1086-1093.
[94]R. H. M. Ogink, A. V. Metrikine.A wake oscillator with frequency dependent coupling for the modeling of vortex-induced vibration [J]. Journal of Sound and Vibration,2010, 329(26):5452-5473.
[95]N. Srinil, H. Zanganeh. Modelling of coupled cross-flow/in-line vortex-induced vibrations using double duffing and van der pol oscillators [J]. Ocean Engineering, 2012,53:83-97.
[96]J. Leklong. Dynamic responses of marine risers/pipes transporting fluid subject to top end excitations [C].18th International Offshore and Offshore and Polar Engineering Conference Proceedings,2008,113-120.
[97]李洪春,郭海燕,李效民.基于Matlab的海洋立管涡激振动数值模拟系统研究[J].中国海洋大学学报(自然科学版),2010,1：207-212.
[98]秦伟,康庄,孙丽萍,宋儒鑫.并列双圆柱涡激振动的经验性模型研究[J].海洋工程,2013,31(2)：11-18.
[99]余建星,俞永清,李红涛,吴海欣.海底管跨涡激振动疲劳可靠性研究[J].船舶力学,2005,2：109-114.
[100]郑仲钦,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,2012,43(4)：37-41.
[101]徐万海,杜杰,余建星.非均匀流中立管涡激振动模型预测分析[J].海洋技术,2011,3：94-96.
[102]饶志标,杨建民,付世晓.剪切流下钢悬链线立管涡激振动响应研究[J].振动与冲击,2010.10：4-8.
[103]葛斐,龙旭,王雷,洪友士.长细比圆柱体顺流向与横向耦合涡激振动的研究[J].中国科学(G辑：物理学力学天文学),2009,5：752-759.
[104]黄维平,刘娟,唐世振.考虑流固耦合的大柔性圆柱体涡激振动非线性时域模型[J].振动与冲击,2012,31：140-143.
[105]C. Feng. The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders [D]. University of British Columbia, 1968.
[106]N. Jauvtis, C. H. K. Williamson. 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.
[107]R. Govardhan, C. H. K. Williamson. Critical mass in vortex-induced vibration of a cylinder [J]. European Journal of Mechanics-B/Fluids,2004,23(1):17-27.
[108]J. Carberry, R. Govardhan, J. Sheridan. Wake states and response branches of forced and freely oscillating cylinders [J]. European Journal of Mechanics-B/Fluids,2004, 23(1):89-97.
[109]N. Jauvtis, C. H. K. Williamson. Vortex-induced vibration of a cylinder with two degrees of freedom [J]. Journal of Fluids and Structures,2003,17(7):1035-1042.
[110]R. Govardhan, C. H. K. Williamson.Resonance forever:Existence of a critical mass and an infinite regime of resonance in vortex-induced vibration [J]. Journal of Fluid Mechanics,2002,473:147-166.
[111]R. Govardhan, C. H. K. Williamson. Mean and fluctuating velocity fields in the wake of a freely-vibrating cylinder [J]. Journal of Fluids and Structures,2001,15(3-4): 489-501.
[112]R. Govardhan, C. H. K. Williamson.Modes of vortex formation and frequency response of a freely vibrating cylinder [J]. Journal of Fluid Mechanics,2000,420(85):85-130.
[113]A. Khalak, C. H. K. Williamson. 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.
[114]C. H. K. Williamson. Advances in our understanding of vortex dynamics in bluff body wakes [J]. Journal of Wind Engineering and Industrial Aerodynamics,1997,69-71:3-32.
[115]A. Khalak, C. H. K. Williamson. Fluid forces and dynamics of a hydroelastic structure with very low mass and damping [J]. Journal of Fluids and Structures,1997,11(8): 973-982.
[116]A. Khalak, C. H. K. Williamson. Investigation of relative effects of mass and damping in vortex-induced vibration of a circular cylinder [J]. Journal of Wind Engineering and Industrial Aerodynamics,1997,69-71:341-350.
[117]A. Khalak, C. H. K. Williamson. Dynamics of a hydroelastic cylinder with very low mass and damping [J]. Journal of Fluids and Structures,1996,10(5):455-472.
[118]R. Gopalkrishnan. Vortex-induced forces on oscillating bluff cylinders [D]. Massachusetts Institute of Technology,1993.
[119]C. H. K. Williamson, A. Roshko. Vortex formation in the wake of an oscillating cylinder [J]. Journal of Fluids and Structures,1988,2(4):355-381.
[120]梁在朝.工程湍流[M].华中理工大学出版社,1999.
[121]是勋刚.湍流[M].天津大学出版社,1994.
[122]林建中.湍动力学[M].浙江大学出版社,2000.
[123]许维德.流体力学[M].国防工业出版社,1989.
[124]V. Yakhot, S. A. Orszag. Renormalization group analysis of turbulence. [J]. Journal of Scientific Computing,1986,1(1):3-51.
[125]H. Schlichting. Boundary layer theory [M]. Nueva York, EUA:McGraw-Hill.1979.
[126]A. Roshko. Perspectives on bluff body aerodynamics [J]. Journal of Wind Engineering and Industrial Aerodynamics,1993,49(1-3):79-100.
[127]E. Achenbach. Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re= 5×106 [J]. Journal of Fluid Mechanics,1968,34(4): 625-639.
[128]C. Norberg. Flow around a circular cylinder:aspects of fluctuating lift [J]. Journal of Fluids and Structures,2001,15(3-4):459-469.
[129]H. M. Blackburn, W. H. Melbourne. The effect of free-stream turbulence on sectional lift forces on a circular cylinder [J]. Journal of Fluid Mechanics,1996,306: 267-292.
[130]G. Schewe. On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers [J]. Journal of Fluid Mechanics, 1983,133:265-285.
[131]U.0. Onal, M. Atlar. Effect of turbulence modelling on the computation of the near-wake flow of a circular cylinder [J]. Ocean Engineering,2010,37(4):387-399.
[132]P. Parnaudeau, J. Carlier, D. Heitz. Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900 [J]. Physics of Fluids,2008,20(8): 85-101.
[133]P. Catalano, M. Wang, G. Iaccarino. Numerical simulation of the flow around a circular cylinder at high Reynolds numbers [J]. International Journal of Heat and Fluid Flow, 2003,24(4):463-469.
[134]L.Ong, J. Wallace. The velocity field of the turbulent very near wake of a circular cylinder [J]. Experiments in Fluids,1996,20(6):441-453.
[135]王福军.计算流体动力学分析—CFD软件原理与应用[M].清华大学出版社,2006.
[136]J. Lighthill. Fundamentals concerning wave loading on offshore structures [J].Journal of Fluid Mechanics,1986,173:667-681.
[137]F. R. Menter. Two-equation eddy-viscosity models for engineering applications [J]. AIAA Journal,1994,32:1598-1605.
[138]J. G. Wissink, W. Rodi. Numerical study of the near wake of a circular cylinder [J]. International Journal of Heat and Fluid Flow,2008,29(4):1060-1070.
[139]A. Elbanhawy, A. Turan. On two-dimensional predictions of turbulent cross-flow induced vibration:Forces on a cylinder and wake interaction [J]. Flow, Turbulence and Combustion,2010,85(2):199-224.
[140]D. M. F. Gao, C. G. Mingham. Numerical and experimental investigation of turbulent flow around a vertical circular cylinder [C].20th International Offshore and Offshore and Polar Engineering Conference Proceedings,2010,639-643.
[141]R. M. C. So, Y. Zhou, M. H. Liu. Free vibrations of an elastic cylinder in a cross flow and their effects on the near wake [J]. Experiments in Fluids,2000,29(2): 130-144.
[142]R. D. Blevins, J. F. Saint-Marcoux. Wake of a vibrating cylinder at Re=105 [C]. Proceedings of the 30th International Conference on Offshore Mechanics and Arctic Engineering,2011,97-103.
[143]J. Xu, D. Spencer, A. Gardner. Wake fields behind risers undergoing vortex-induced vibration [C]. Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering,2008,539-546.
[144]A. G. Kravchenkoa, P. Moin. Numerical studies of flow over a circular cylinder at Re=3900 [J]. Physics of Fluids,2000,12(2):403-417.
[145]林海花.浪流共同作用下隔水管涡激动力响应分析[J].哈尔滨工程大学学报,2008,29(2)：121-125.
[146]林海花.波流共同作用下隔水管动力响应非线性分析[J].船舶力学,2009,13(2)：189-195.
[147]王勖成.有限单元法基本原理和数值方法[M].清华大学出版社,1988.
[148]殷有泉.非线性有限元法基础[M].北京大学出版社,2007.
[149]贾星兰, 方华灿.海洋钻井隔水管的动力响应[M].石油机械,1995.