双自由度涡激振动的涡强尾流振子模型研究
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摘要
涡激振动是导致深水立管疲劳损伤的一个重要因素，关于圆柱状结构体涡激振动机理的研究正逐步趋于完善。现阶段提出的大量涡激振动预报模型主要针对圆柱体的单自由度横向振动，而结构在顺流向上的振动往往被限制或者忽略。最近的研究表明，对于海洋立管这种低质量比结构，涡激振动导致顺流向的疲劳损伤与横向上的疲劳损伤在同一量级。因此，正确地认识和描述顺流向和横向的双向涡激振动特性，全面地预报和评估立管结构的综合疲劳寿命，对保证海洋工程结构物的经济效益和服役期的安全运行有着重要的意义。
本文针对结构的双向涡激振动问题开展了一系列研究，建立了一种具有工程实际意义的半经验模型来预报刚性圆柱体和细长柔性立管的顺流向和横向涡激振动响应。论文的主要内容和成果包括：
(1)系统地归纳和评述了圆柱体双向涡激振动的研究现状和成果，阐释了涡激振动相关的若干物理概念和基本物理参数，总结了现有的涡激振动半经验性模型。
(2)基于二维离散点涡方法推导出流体对刚性圆柱体在顺流向和横向的脉动水动力，重新定义了传统尾流振子控制变量的含义，采用范德波尔方程描述近壁点涡的非线性特征，进而建立了一种能够预报双自由度涡激振动响应的涡强尾流振子模型，并给出了模型中经验参数的确定方法。利用本文模型预报了刚性圆柱体的双向涡激振动响应，得到的横向锁定、顺流向初始响应峰值、运动相位角以及“8”字形运动轨迹等的变化规律与实验结果吻合，同时讨论了质量比和阻尼比对结构顺流向和横向振幅响应的影响。
(3)针对水平放置的外径5cm，长120cm的刚性圆柱体开展了顺流向和横向在不同频率比条件下的双自由度涡激振动模型试验。试验中发现频率比可能对结构的涡激振动特性产生显著影响。当频率比在1.0附近时，圆柱的涡激振动特性与等频率比双自由度圆柱的结果没有明显不同，但随着频率比的增加顺流向和横向振幅以及两者之间的相位差发生了显著改变。利用涡强尾流振子模型预报了不同频率比的圆柱体涡激振动响应，分析了频率比和质量比对响应振幅和运动轨迹的影响。
(4)使用切片法建立了可以预报细长弹性体双向涡激振动的三维时域半经验模型。将该模型应用到研究在阶梯状来流作用下的顶部张紧式立管的涡激振动响应，结果显示顺流向振幅峰值小于横向振幅峰值，但是顺流向激活模态的阶数大约为横向振动的2倍。两个方向上的振动中均存在驻波和行波，当顺流向振动的模态较高时，处于静水中的立管上半段表现为驻波振动状态，截面的运动轨迹沿管变化较大，而处于均匀流的作用下的立管下半段将以行波振动为主，截面的运动轨迹更趋于均匀，模型预报的振动特性与实验结果吻合。
(5)利用三维涡强尾流振子模型分析了深水钢悬链立管的双向涡激振动响应。在自由剪切流的作用下，立管各节点的运动轨迹可能不会形成稳定的“8”字形，响应振幅和相位角随时间改变。顺流向的振动模态显著高于横向的振动模态，除靠近触地点立管段处于驻波振动，立管大部分中间段的行波效应明显。由于顺流向具有高频高模态的振动特性，该方向的涡激振动疲劳损伤与横向疲劳损伤在同一量级，且沿管的分布不同，因此考虑顺流向的影响将益于全面地评估立管的涡激振动疲劳损伤。
VIV is an important factor leading to the fatigue damage of deepwater riser, the VIVmechanism research on cylindrical structure is gradually tending to be perfect. A large numberof VIV prediction models proposed at the present stage mainly focus on thesingle-degree-of-freedom CF vibration of cylinder, while the IL vibration of the structure isoften restricted or ignored. Recent studies have indicated that, for the low mass ratio structurelike marine riser, the IL fatigue damage caused by VIV is in the same order of magnitude asthe CF’s. Therefore, correctly understand and describe the bidirectional VIV characteristics ofIL and CF, while forecast and assess the comprehensive fatigue life of riser structure in detail,which is of great significance for ensuring the economic benefit and safe operation duringservice of offshore structures.
This paper has carried out a series of in-depth research on the structure bidirectional VIVproblems, proposing a semi-empirical model with practical significance of engineering toforecast the IL and CF VIV response of rigid cylinder and slender flexible riser. The maincontents and results include:
(1) Systematically induce and review the research status and achievements of thecylinder bidirectional VIV, explain related certain physical concepts and basic physicalparameters of VIV, and summarize the existing semi-empirical models of VIV.
(2) Deduce the IL and CF fluctuating hydrodynamic acting on rigid cylinder by fluidbased on two-dimensional discrete point vortex method, redefine the meaning of the controlvariables of traditional wake oscillator, and adopt van der Pol equation describe the nonlinearcharacteristics of the near-wall point vortex, thereby establishing a vortex strength wakeoscillator model which can forecast the VIV response of the two degrees of freedom, andproviding the method to determine the experience parameters in the model. Employ the modelto predict the bidirectional VIV response of rigid cylinder, the variation of obtained CFlock-in, IL initial response peak, phase angle of movement and "8"shape trajectory etc.coinciding with the experimental results, while discuss the effect of mass ratio and dampingratio on the IL and CF amplitude response of the structure.
(3) Carry out bidirectional VIV model experiment with different IL and CF frequencyratio for the horizontally arranged outer diameter of5cm, length of120cm rigid cylinder. It is found in the experiment that the frequency ratio may have a significant impact on the VIVcharacteristics of the structure. when the frequency ratio is near1.0, there is no significantdifference between the conclusions of cylinder VIV characteristics and the two degrees offreedom cylinder with the equal frequency ratio, but with the increase in frequency ratio, theIL and CF amplitude together with the phase difference between them change significantly.Apply the vortex strength wake oscillator model to forecast the VIV response of the cylinderwith different frequency ratio, which indicates that under the specific frequency ratio, whileanalyze the effect of frequency ratio and mass ratio on the response amplitude and trajectory.
(4) Adopt section method establish the semi-empirical model of three-dimensional time-domainwhich can forecast the bidirectional VIV of slender elastomer. Apply the model to the study onthe VIV response of TTR under the action of step flow, which indicates that the IL amplitudepeak is less than the CF’s, but the order of IL activation mode is about2times the CF. Thevibration in two directions both exists the standing wave and traveling wave, when the IL is inrelatively high vibration mode, the upper half of the riser in the still water presents a standingwave vibration mode and the section trajectory along the pipe is rather changeable, while thelower half of the riser in the uniform flow is mainly on traveling wave vibration and thesection trajectory tends to be more uniform, the vibration characteristics forecast by modelcoinciding with the experimental results.
(5) Employ three-dimensional vortex strength wake oscillator model to forecast thebidirectional VIV response of deepwater SCR. Under the action of free shear flow, thetrajectory of each riser node may not form a steady "8" shape, while the response amplitudeand phase angle change with time. The IL vibration mode is significantly higher than the CF’s,and in addition to the riser section near the touchdown point which is in standing wavevibration, the traveling wave has significant effect on the most part of the intermediate sectionof the riser. Due to the high-frequency and high-modal vibration characteristics of IL, thefatigue damage in IL direction is in the same order of magnitude as the CF’s, and has differentdistribution along the pipe, so taking the effect of IL into consideration benefits thecomprehensive assessment of the VIV fatigue damage in riser section.
本文针对结构的双向涡激振动问题开展了一系列研究，建立了一种具有工程实际意义的半经验模型来预报刚性圆柱体和细长柔性立管的顺流向和横向涡激振动响应。论文的主要内容和成果包括：
(1)系统地归纳和评述了圆柱体双向涡激振动的研究现状和成果，阐释了涡激振动相关的若干物理概念和基本物理参数，总结了现有的涡激振动半经验性模型。
(2)基于二维离散点涡方法推导出流体对刚性圆柱体在顺流向和横向的脉动水动力，重新定义了传统尾流振子控制变量的含义，采用范德波尔方程描述近壁点涡的非线性特征，进而建立了一种能够预报双自由度涡激振动响应的涡强尾流振子模型，并给出了模型中经验参数的确定方法。利用本文模型预报了刚性圆柱体的双向涡激振动响应，得到的横向锁定、顺流向初始响应峰值、运动相位角以及“8”字形运动轨迹等的变化规律与实验结果吻合，同时讨论了质量比和阻尼比对结构顺流向和横向振幅响应的影响。
(3)针对水平放置的外径5cm，长120cm的刚性圆柱体开展了顺流向和横向在不同频率比条件下的双自由度涡激振动模型试验。试验中发现频率比可能对结构的涡激振动特性产生显著影响。当频率比在1.0附近时，圆柱的涡激振动特性与等频率比双自由度圆柱的结果没有明显不同，但随着频率比的增加顺流向和横向振幅以及两者之间的相位差发生了显著改变。利用涡强尾流振子模型预报了不同频率比的圆柱体涡激振动响应，分析了频率比和质量比对响应振幅和运动轨迹的影响。
(4)使用切片法建立了可以预报细长弹性体双向涡激振动的三维时域半经验模型。将该模型应用到研究在阶梯状来流作用下的顶部张紧式立管的涡激振动响应，结果显示顺流向振幅峰值小于横向振幅峰值，但是顺流向激活模态的阶数大约为横向振动的2倍。两个方向上的振动中均存在驻波和行波，当顺流向振动的模态较高时，处于静水中的立管上半段表现为驻波振动状态，截面的运动轨迹沿管变化较大，而处于均匀流的作用下的立管下半段将以行波振动为主，截面的运动轨迹更趋于均匀，模型预报的振动特性与实验结果吻合。
(5)利用三维涡强尾流振子模型分析了深水钢悬链立管的双向涡激振动响应。在自由剪切流的作用下，立管各节点的运动轨迹可能不会形成稳定的“8”字形，响应振幅和相位角随时间改变。顺流向的振动模态显著高于横向的振动模态，除靠近触地点立管段处于驻波振动，立管大部分中间段的行波效应明显。由于顺流向具有高频高模态的振动特性，该方向的涡激振动疲劳损伤与横向疲劳损伤在同一量级，且沿管的分布不同，因此考虑顺流向的影响将益于全面地评估立管的涡激振动疲劳损伤。
VIV is an important factor leading to the fatigue damage of deepwater riser, the VIVmechanism research on cylindrical structure is gradually tending to be perfect. A large numberof VIV prediction models proposed at the present stage mainly focus on thesingle-degree-of-freedom CF vibration of cylinder, while the IL vibration of the structure isoften restricted or ignored. Recent studies have indicated that, for the low mass ratio structurelike marine riser, the IL fatigue damage caused by VIV is in the same order of magnitude asthe CF’s. Therefore, correctly understand and describe the bidirectional VIV characteristics ofIL and CF, while forecast and assess the comprehensive fatigue life of riser structure in detail,which is of great significance for ensuring the economic benefit and safe operation duringservice of offshore structures.
This paper has carried out a series of in-depth research on the structure bidirectional VIVproblems, proposing a semi-empirical model with practical significance of engineering toforecast the IL and CF VIV response of rigid cylinder and slender flexible riser. The maincontents and results include:
(1) Systematically induce and review the research status and achievements of thecylinder bidirectional VIV, explain related certain physical concepts and basic physicalparameters of VIV, and summarize the existing semi-empirical models of VIV.
(2) Deduce the IL and CF fluctuating hydrodynamic acting on rigid cylinder by fluidbased on two-dimensional discrete point vortex method, redefine the meaning of the controlvariables of traditional wake oscillator, and adopt van der Pol equation describe the nonlinearcharacteristics of the near-wall point vortex, thereby establishing a vortex strength wakeoscillator model which can forecast the VIV response of the two degrees of freedom, andproviding the method to determine the experience parameters in the model. Employ the modelto predict the bidirectional VIV response of rigid cylinder, the variation of obtained CFlock-in, IL initial response peak, phase angle of movement and "8"shape trajectory etc.coinciding with the experimental results, while discuss the effect of mass ratio and dampingratio on the IL and CF amplitude response of the structure.
(3) Carry out bidirectional VIV model experiment with different IL and CF frequencyratio for the horizontally arranged outer diameter of5cm, length of120cm rigid cylinder. It is found in the experiment that the frequency ratio may have a significant impact on the VIVcharacteristics of the structure. when the frequency ratio is near1.0, there is no significantdifference between the conclusions of cylinder VIV characteristics and the two degrees offreedom cylinder with the equal frequency ratio, but with the increase in frequency ratio, theIL and CF amplitude together with the phase difference between them change significantly.Apply the vortex strength wake oscillator model to forecast the VIV response of the cylinderwith different frequency ratio, which indicates that under the specific frequency ratio, whileanalyze the effect of frequency ratio and mass ratio on the response amplitude and trajectory.
(4) Adopt section method establish the semi-empirical model of three-dimensional time-domainwhich can forecast the bidirectional VIV of slender elastomer. Apply the model to the study onthe VIV response of TTR under the action of step flow, which indicates that the IL amplitudepeak is less than the CF’s, but the order of IL activation mode is about2times the CF. Thevibration in two directions both exists the standing wave and traveling wave, when the IL is inrelatively high vibration mode, the upper half of the riser in the still water presents a standingwave vibration mode and the section trajectory along the pipe is rather changeable, while thelower half of the riser in the uniform flow is mainly on traveling wave vibration and thesection trajectory tends to be more uniform, the vibration characteristics forecast by modelcoinciding with the experimental results.
(5) Employ three-dimensional vortex strength wake oscillator model to forecast thebidirectional VIV response of deepwater SCR. Under the action of free shear flow, thetrajectory of each riser node may not form a steady "8" shape, while the response amplitudeand phase angle change with time. The IL vibration mode is significantly higher than the CF’s,and in addition to the riser section near the touchdown point which is in standing wavevibration, the traveling wave has significant effect on the most part of the intermediate sectionof the riser. Due to the high-frequency and high-modal vibration characteristics of IL, thefatigue damage in IL direction is in the same order of magnitude as the CF’s, and has differentdistribution along the pipe, so taking the effect of IL into consideration benefits thecomprehensive assessment of the VIV fatigue damage in riser section.
引文
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