柔性立管涡激振动时域响应分析
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摘要
地球的表面约70%为海洋，蕴藏在海洋里的资源将成为人类赖以生存的重要保障。就目前国际工业发展趋势而言，对能源的需求量，特别是石油的需求量日益增大，深海石油的开采已成为解决石油能源危机的主要途径。与深海石油工业密切相关的一个国际性的难题便是输油立管的涡激振动问题。
立管的涡激振动是指洋流流经圆柱状细长柔性立管时，由于压力的不均将产生交替脱落的漩涡，由泻涡诱发的非定常流体力会引起立管的振动响应。在一定来流条件下，泻涡将使立管产生强烈的振动，由于泻涡的周期较短，涡激振动成为立管疲劳损伤导致结构破坏的主要因素。涡激振动是一个强非线性的的流固耦合问题，特别是涉及到高雷诺数条件下湍流的研究。
本文作为国家自然科学基金专项基金项目“深海平台的动力特性研究”（项目编号：50323004）和上海市专项基金项目（项目编号：05DJ14001）的组成部分，旨在通过数值计算方法来研究湍流，并在湍流的基础上实现流固耦合的计算，即实现深海立管涡激振动的数值模拟，建立深海立管涡激振动时域预报模型。为了更接近深海立管实时作业环境，数值计算实现了均匀来流和剪切来流条件下细长柔性立管的时域响应预报。
本文参考了国际上有关湍流研究和细长柔性立管涡激振动的最新研究成果，对研究湍流理论的主要数值计算方法进行了比较和讨论，并对细长柔性立管涡激振动的热点问题展开了深入的研究，其主要内容可以概括如下:
1总结了深海立管涡激振动响应的频域和时域预报模型，对深海立管涡激振动响应的实验进行了归纳，指出现有涡激振动预报模型的缺陷和实验研究的主要方向。对研究湍流理论的三种主要数值计算方法进行综合评述，阐述了湍流的本质以及各湍流研究数值计算方法的优缺点，着重对直接数值模拟方法和雷诺平均法计算湍流的主要思想和基本理论进行了详细的介绍。
2采用直接数值模拟对低雷诺数条件下圆柱绕流进行了研究，其中来流条件分别为对均匀来流、横向剪切流和平面剪切流来流。数值计算成功再现了实验中观测到的三维尾涡结构，这在国内数值研究报道中纯属首次。分析和讨论了三维圆柱绕流的物理特性诸如流体动能、雷诺应力、泻涡频率、边界层以及圆柱体表面的压力系数，探究了剪切流对流体流动和泻涡模式的影响。基于直接数值模拟对三维流体流动计算的优越性，用数值实验的方法成功解析了物理实验结果与二维数值计算结果之间存在差异的原因。
3采用雷诺平均方法结合湍流模式对低质量比弹性支撑圆柱体的涡激振动进行了计算。数值模拟考虑了圆柱体横向和流向的振动对横向振幅幅值的影响，并与限制流向运动时的结果进行了比较。数值计算找出了横向和流向自由度条件下，产生较大横向振幅幅值时所对应的圆柱体的临界质量比。本文的数值结果成功呈现了物理实验中观测到的各种尾涡模式，并得出了均匀来流条件下实验中常见的圆柱体的运动轨迹。
4在横向剪切来流条件下，对两向自由度弹性支撑圆柱体的涡激振动进行了计算。数值模拟得到的横向振幅、运动轨迹、升力系数和位移时历曲线的结果表明，对于不同的雷诺数，存在一个剪切率锁定区间。在横向来流剪切率较小时，圆柱体的运动轨迹与均匀来流条件下的运动轨迹一致。随着剪切率的增加，圆柱体的运动形式表现出一种全新的轨迹。
5基于切片理论并结合有限体积法和动力有限元方法，成功建立了深海立管涡激振动响应的时域计算模型。对阶梯状来流以及轴向剪切流条件下深海立管涡激振动响应进行了时域计算，分析了立管在不同来流条件下所激发的振型和模态。本时域预报模型还记录了沿立管轴向分布的不同尾涡结构，重现了物理实验中所观测到的一系列流体流动现象。
6尽管在阶梯状来流条件下所预报的高阶模态响应与实验结果之间还存在一定差异，但本文的时域预报模型在轴向剪切流条件下所得到的低阶模态响应与实验结果吻合较好，且比同类时域模型和频率模型预报的结果更为精确。
7考虑雷诺数和质量阻尼比对自激振动系统横向振幅幅值的影响，并应用受迫振动的实验数据，从理论上建立了弹性支撑圆柱体涡激振动振幅幅值的预报模型。该理论模型所预报的结果能与现有大部分物理实验结果相吻合，同时可为细长立管频率预报模型考虑雷诺数和质量阻尼比的影响提供参考。
以上对本文研究的主要内容与进行了概述，本论文的结论主要有以下几个方面：
1首次用直接数值模拟方法对各种流条件下的圆柱饶流进行了计算。在低雷诺数条件下，成功再现了均匀来流下的三维尾涡模式；如Mode A和Mode B。在横向剪切来流条件下，与来流速度较低一侧对应的尾涡能量在流体运动过程中逐渐衰减；与来流速度较高一侧对应的尾涡能量在流体运动过程中逐渐增强，以至于在尾流较远处只剩下能量较强的尾涡。横向剪切流对圆柱绕流的影响还体现在边界层和表面压强系数的改变。数值计算结果表明，圆柱体表面的边界层和压强系数在横向剪切流作用下沿轴向出现偏转，这与流体流动的物理特性相一致。而在轴向剪切流条件下，泻涡形式沿轴向倾斜，顺时针和逆时针旋转的尾涡不存在能量的衰减或增强，脱落后的尾涡在流向方向依然保持平行。在横向-轴向组合剪切来流条件下，尾涡的运动不仅偏向于来流速度较低的一侧，而且沿轴向倾斜脱落。组合剪切流可看做是单个横向剪切流和轴向剪切流作功的叠加，但不会出现横向剪切流和轴向剪切流之间相互抑制的现象。
2采用直接数值模拟法研究了无滑移边界条件和自由表面边界条件对尾涡的影响，找出了物理实验结果Kiya et al (1980)与近年来数值模拟结果Kang (2007)存在较大差异的主要原因。指出无滑移边界条件将能有效抑制尾涡的脱落，而自由表面边界条件则对尾涡的脱落没有多大的影响。因而，物理实验的实施必须考虑到无滑移边界条件的影响，而数据的采集应尽量避免处在无滑移边界条件影响的区域之内。
3数值计算得出了两向自由度弹性支撑圆柱体产生较大横向振幅的临界质量比* m = 3.5。当圆柱体的质量比高于临界质量比时，限制流向运动对横向振幅幅值的影响不大；当质量比降至临界质量比时，流向和横向的振动将激发出更大的横向振幅幅值，流向运动对横向振幅的影响在此凸现。数值计算还重现了实验中不同横向振幅响应分支对应的尾涡模式，特别是与超上端分支对应的2T尾涡模式。在均匀来流条件下，数值模拟还成功得出了圆柱体“8”型的运动轨迹。
4在横向剪切来流条件下，两向自由度弹性支撑圆柱体的涡激振动存在一个剪切率的锁定区间。剪切率锁定区间与雷诺数的大小成正比。在剪切率的锁定区间内，横向振幅增大；脱离剪切率锁定区间后，横向振幅迅速下降。在横向来流剪切率较小时，圆柱体的运动轨迹与均匀来流条件下的“8”型的运动轨迹一致。随着剪切率的增加，圆柱体“8”型运动轨迹上端消失而表现为“小雨点”的外形。
5在阶梯状来流条件下，立管的响应在时域内并不表现为单一模态，而是在各个模态之间进行跳转。当某一激发模态的权重占绝对主导地位时，立管的变形与该激发模态下的形状一致；而当立管激发各模态的权重并不由唯一的激发模态所主导时，立管的响应形式将在占主导地位的几种激发模态之间跳转。通过记录时域内沿立管轴向分布的流体力，发现流体力沿立管轴向具有分段相关性，这为本文基于切片法所建立的时域预报模型的合理性提供了依据。沿立管轴向分布的附加质量系数存在波动区间，这与立管呈现的多模态响应相关联。当立管的涡激振动表现为多模态响应时，本文提出了附加质量系数的计算应当根据激发模态的权重来考虑各个模态所对应附加质量系数的贡献。数值计算沿立管轴向同时捕捉到了2S和2P尾涡模式，重现了这一经典的物理现象；在不同的立管截面之间，还观测到尾涡泻涡时间的切换现象。
6在轴向剪切来流条件下，本文的时域预报模型所得到的低阶模态响应与实验结果吻合较好。本文采用的时域模型采用了较多的切片数量来考虑流体力的轴向相关性，利用动网格和变形网格来模拟流固耦合运动对流体流动的影响，还同步考虑到立管的变形引起的总体刚度矩阵的非线性性。因而，本文所预报的结果较同类切片模型和频率预报模型的结果更为精确。
7通过沟通受迫振动和自激振动内在联系，建立理论模型成功实现了由受迫振动实验数据来预报自激振动圆柱体的横向振幅幅值。该理论模型可同时考虑到雷诺数和质量阻尼比对横向振幅幅值的影响，同时也再次证明雷诺数是影响涡激振动横向振幅的一个重要参数。本文的理论预报模型可为深海立管频域预报模型的发展和完善提供理论依据。
通过对本文主要内容和结论的阐述，可以反映出该论文的创新点表现在以下几个方面：
1利用直接数值模拟方法首次对横向剪切来流条件下的圆柱绕流进行了计算，对尾涡模式和流体流动的物理特性进行了详细探讨。
2对两向自由度弹性支撑圆柱体在均匀来流和横向剪切流条件下进行了数值模拟，得出了均匀来流条件下产生较大横向振幅所对应的临界质量比为3.5；得出横向剪切流条件下存在剪切流的锁定区间，并发现了一种全新的“小雨点”运动轨迹。
3建立了柔性立管涡激振动时域响应预报模型，在时域内成功预报了立管的模态响应。
4发展和完善了频域预报模型。在受迫振动实验数据基础上，考虑了雷诺数和质量阻尼比得出了自激振动横向振幅峰值的理论预报公式。
总而言之，本文从简单的圆柱绕流开始，逐步考虑到弹性支撑圆柱体和柔性立管的涡激振动响应，并成功建立了柔性立管涡激振动的时域预报模型。本文时域模型的预报结果能准确地反映出物理实验中的诸多现象和结论，同时，从本文时域模型得到的结论中可为完善和发展柔性立管频率预报模型提供思路和参考。
Around seventy percent of the Earth surface is covered by water and huge amount of natural resources such as gas and oil are richly stored in the deep ocean. With the fast industry development, the sharp increasing demand of consuming energy, especially the oil and gas, has become bottle-neck issue for both developing and developed countries. Deep-water petroleum industry could be a good way to solve the global energy crisis in future. One of the technique challenges, related to deep-water petroleum industry, is the Vortex-Induced Vibration (VIV for short) of flexible riser.
VIV happens while flow over the flexible riser and the structure is excited by the unsteady fluid fore which is generated by the periodic shedding vortex. The flexible riser will vibrate frequently with large amplitude under certain incoming flow conditions. Great damage to the riser would be resulted from the VIV due to the high vortex shedding frequency. Having a good understanding of the VIV mechanism could be helpful to reduce the damage effect on the riser, and also a quite kind strategy to the environments. However, VIV can be regarded as a complex fluid-structure coupling problem and the equations solving the flow domain and the structure bare strong non-linearity. The flow could turn into turbulence according to the high Reynolds number theory and how to revolve the turbulence accurately in a numerical way is still a big challenge world wild.
The present research described in this thesis is a part of the project“Research on Dynamic Response of Platforms in Deep-water”supported by the National Natural Science Foundation of China under Grant No.50323004 and also supported by Shanghai Scientific Fund under Grant No. 05DJ14001. The purpose of the research is to study turbulence and to construct a numerical model to predict the VIV response of flexible riser under uniform and shear flow conditions in the time domain.
Based on the latest achievements on turbulence research and VIV response of flexible riser, the present thesis focuses on the most interested points which include numerical tools for turbulence simulation and the VIV response of flexible riser under stepped and shear flow conditions. The main contents of the present thesis can be summarized as follows:
1, A review on the turbulence research and the existed models for VIV response prediction has been conducted. A brief introduction to the numerical research tools on turbulence including RANS、LES and DNS is described, especially the DNS and RANS being used in the present thesis are compared in a detail way. Empirical model and time-domain model for VIV response are also introduced. Most of the latest experimental results on VIV of flexible riser are concluded and constructive suggestion is made for the future research.
2, Three dimensional numerical simulation on shear flow over a circular cylinder has been studied by applying DNS. Shear effort on the three dimensional vorticity structure behind the circular cylinder has been intensively investigated. The physics of the fluid such as turbulence energy, kinetic energy, Reynolds stress, shedding frequency, boundary layer and pressure coefficient is also conducted and compared with the results of other sources. The discrepancy between the physical experiment and two dimensional simulations could be well resolved by applying the three dimensional numerical experiments.
3, Two-degrees-freedom VIV of a spring constrained rigid circular cylinder with low mass and damping ratio has been analyzed using RANS solver combined with turbulence model for the Navier-Stoke equation. The vibration in streamwise and transverse direction is considered to have a limited effect on the peak transverse amplitude of the spring mounted circular cylinder with moderate mass ratio. It is interesting to find the critical mass ratio under which the supper upper branch could appear accordingly in the current numerical results. The time-trace circular cylinder movement and vorticity structure which obtained in physical experiments are also captured in the present simulation.
4, Another numerical investigation is also conducted on VIV response of an elastic mounted circle cylinder under planar shear flow conditions. A planar shear ratio lock-in range can be concluded from the data analysis in transverse response, fluid force and time trace displacement at moderate Reynolds number. The figure“8”trace movement could be observed under small planar shear flow conditions while a completely new style time-trace circular cylinder movement is discovered as the planar shear ratio increases.
5, Based on the strip theory and the combination of the Finite Volume Method and Dynamic Finite Element Method, a numerical model which can be used to predict the VIV response of a flexible riser in time-domain is successfully constructed. VIV response of a flexible riser under stepped and shear flow conditions is calculated and extensive investigation on the mechanics of the VIV is carried out by applying the research on the time-trace of the transverse response and fluid forces along the axis of the riser. The multi-modal response is obtained and two typical vortex shedding modes are observed at the same time in the spanwise direction as the riser is set in a stepped flow.
6, The same numerical model is applied to predict the VIV response of a flexible riser under the axis shear flow condition. Compared to the results by other CFD model and empirical model, the present results are more rational and accuracy in agreement with the experimental results in the deforming modal shapes.
7, The Reynolds number effect and mass-damping ratio effect on the peak transverse response amplitude of a freely vibrating circular cylinder is well studied based on the forced oscillation experimental data. A theory model which can be used to predict the peak transverse response is constructed. This model could be considered as an update to the empirical model for the prediction of the response of the flexible riser. According to the research work mentioned above, main conclusion can be drawn as follows:
1, The vorticity structure such as Mode A and Mode B is successfully recorded under uniform inflow at low Reynolds numbers. Oblique vortex shedding in streamwise direction is observed by applying DNS calculation on planar shear flow over a circular cylinder. The vorticity energy corresponding to the higher velocity side becomes stronger and the vorticity energy in the other side will decay to be totally destroyed as it moves down in the far wake of the circular cylinder. The planar shear flow will affect the boundary layer and pressure coefficient around the surface of the circular cylinder, but no effect on the shedding frequency. Oblique vortex shedding in the spanwise direction and dislocations could be observed under the spanwise shear inflow over a circular cylinder. The two shear flow results could be regarded as a combination of the planar shear and the spanwise shear flow cases, and it can be inferred that the planar shear and the spanwise shear do affect the flow motion separately but without any interaction effect.
2, DNS calculation is conducted to study the no-slip and free slip boundary conditions on the suppression effort in vortex shedding phenomenon under the planar shear flow over a circular cylinder. The discrepancy between the experimental results by Kiya et al (1980) and recently two dimensional numerical results by Kang (2007) is well explained according to the three dimensional DNS results. The no-slip boundary condition will have a great effect on vortex shedding suppression while very limited effect in free slip boundary condition
3, The streamewise vibration has a limited effect on the peak transverse response of the circular cylinder with moderate mass ratio. Larger transverse response could be excited as the mass ratio is below the critical mass ratio m* cri= 3.5for the circular cylinder with two degree-freedom rather than the streamewise vibration is constrained. The vortex shedding mode, such as SS, 2S and 2P, corresponding to different transverse response branch is observed; especially the classical 2T mode appearing at the supper upper branch in the experiment by Jauvtis & Williamson (2003) is reproduced in the present numerical simulation. The figure“8”traces movement for the VIV response is also captured successfully.
4, The results form the two dimensional planar shear flow over an elastic mounted circular cylinder infer that there exits a planar shear ratio lock-in range in which the transverse amplitude grows rapidly and the amplitude would decrease sharply as it goes out of the shear ratio lock-in range. The lock-in range becomes wider as the Reynolds number grows. The figure“8”time trace movement can be seen as the planar shear flow ratio is small, while a new time trace movement which is named as“water drop”shape is discovered.
5, The multi-modal response of the flexible riser is obtained under the stepped inflow condition. The excited model for the long flexible riser can jump from one model to another one in the time domain while the deforming shape of the riser appears to be the dominated excited modal shape. It is can be inferred from the time trace contour of the lift or drag coefficient that the fluid force correction length along the axis of the riser could be given a strong supportive evidence for the present multi-strip numerical model. The added mass is not equally distributed along the axis of the riser but vibrates a lot according to the multi-modal response. It is suggested that the added mass distribution should take into account of the contributions separately from the main excited modals. The“2S”and“2P”vorticity structures are observed along the axis of the riser at the same time due to the small or large amplitude of the riser in various excited models. The switching phenomenon in the vortex shedding is observer in the present CFD model.
6, The predicted VIV response of the riser agrees well with the experimental results as the riser is excited at low modal response in the spanwise shear flow. Compared to other multi-strip model or empirical model, the present CFD model could be recognized as a more accurate and rational multi-strip model for more strips are used to consider the fluid force correction along the axis the riser and the deforming mesh is applied to simulate the fluid-structure coupling movement in the current model. Furthermore, the non-linear global stiffness matrix is updated in the time domain as the riser deforms.
7, Potential relationship between the freely vibration and the forced oscillation has been investigated and a theory model is successfully constructed. Reynolds number effect and mass-damping effect are considered to predict the peek transverse amplitude of a freely vibrating cylinder by applying the force oscillation experimental results. It is concluded that the Reynolds number ignored previously in the forced oscillation is a quite important parameter in the freely vibration case. The general idea in the current theory model could provide a strong background for the empirical model of VIV response of a flexible riser.
In a word, the present paper starts with the simple case in flow over a circular cylinder, and then focuses on the VIV of a spring mounted circular to the VIV response of a flexible riser finally. A CFD model is successfully constructed and it can be used to predict the VIV response of a flexible riser in the time domain Most of the experimental results or vortex shedding phenomenon could be accurately reproduced in the current CFD model. It can be inferred that the main conclusions drawn from the present CFD model could provide a constructive way to improve the empirical model in VIV response prediction.
立管的涡激振动是指洋流流经圆柱状细长柔性立管时，由于压力的不均将产生交替脱落的漩涡，由泻涡诱发的非定常流体力会引起立管的振动响应。在一定来流条件下，泻涡将使立管产生强烈的振动，由于泻涡的周期较短，涡激振动成为立管疲劳损伤导致结构破坏的主要因素。涡激振动是一个强非线性的的流固耦合问题，特别是涉及到高雷诺数条件下湍流的研究。
本文作为国家自然科学基金专项基金项目“深海平台的动力特性研究”（项目编号：50323004）和上海市专项基金项目（项目编号：05DJ14001）的组成部分，旨在通过数值计算方法来研究湍流，并在湍流的基础上实现流固耦合的计算，即实现深海立管涡激振动的数值模拟，建立深海立管涡激振动时域预报模型。为了更接近深海立管实时作业环境，数值计算实现了均匀来流和剪切来流条件下细长柔性立管的时域响应预报。
本文参考了国际上有关湍流研究和细长柔性立管涡激振动的最新研究成果，对研究湍流理论的主要数值计算方法进行了比较和讨论，并对细长柔性立管涡激振动的热点问题展开了深入的研究，其主要内容可以概括如下:
1总结了深海立管涡激振动响应的频域和时域预报模型，对深海立管涡激振动响应的实验进行了归纳，指出现有涡激振动预报模型的缺陷和实验研究的主要方向。对研究湍流理论的三种主要数值计算方法进行综合评述，阐述了湍流的本质以及各湍流研究数值计算方法的优缺点，着重对直接数值模拟方法和雷诺平均法计算湍流的主要思想和基本理论进行了详细的介绍。
2采用直接数值模拟对低雷诺数条件下圆柱绕流进行了研究，其中来流条件分别为对均匀来流、横向剪切流和平面剪切流来流。数值计算成功再现了实验中观测到的三维尾涡结构，这在国内数值研究报道中纯属首次。分析和讨论了三维圆柱绕流的物理特性诸如流体动能、雷诺应力、泻涡频率、边界层以及圆柱体表面的压力系数，探究了剪切流对流体流动和泻涡模式的影响。基于直接数值模拟对三维流体流动计算的优越性，用数值实验的方法成功解析了物理实验结果与二维数值计算结果之间存在差异的原因。
3采用雷诺平均方法结合湍流模式对低质量比弹性支撑圆柱体的涡激振动进行了计算。数值模拟考虑了圆柱体横向和流向的振动对横向振幅幅值的影响，并与限制流向运动时的结果进行了比较。数值计算找出了横向和流向自由度条件下，产生较大横向振幅幅值时所对应的圆柱体的临界质量比。本文的数值结果成功呈现了物理实验中观测到的各种尾涡模式，并得出了均匀来流条件下实验中常见的圆柱体的运动轨迹。
4在横向剪切来流条件下，对两向自由度弹性支撑圆柱体的涡激振动进行了计算。数值模拟得到的横向振幅、运动轨迹、升力系数和位移时历曲线的结果表明，对于不同的雷诺数，存在一个剪切率锁定区间。在横向来流剪切率较小时，圆柱体的运动轨迹与均匀来流条件下的运动轨迹一致。随着剪切率的增加，圆柱体的运动形式表现出一种全新的轨迹。
5基于切片理论并结合有限体积法和动力有限元方法，成功建立了深海立管涡激振动响应的时域计算模型。对阶梯状来流以及轴向剪切流条件下深海立管涡激振动响应进行了时域计算，分析了立管在不同来流条件下所激发的振型和模态。本时域预报模型还记录了沿立管轴向分布的不同尾涡结构，重现了物理实验中所观测到的一系列流体流动现象。
6尽管在阶梯状来流条件下所预报的高阶模态响应与实验结果之间还存在一定差异，但本文的时域预报模型在轴向剪切流条件下所得到的低阶模态响应与实验结果吻合较好，且比同类时域模型和频率模型预报的结果更为精确。
7考虑雷诺数和质量阻尼比对自激振动系统横向振幅幅值的影响，并应用受迫振动的实验数据，从理论上建立了弹性支撑圆柱体涡激振动振幅幅值的预报模型。该理论模型所预报的结果能与现有大部分物理实验结果相吻合，同时可为细长立管频率预报模型考虑雷诺数和质量阻尼比的影响提供参考。
以上对本文研究的主要内容与进行了概述，本论文的结论主要有以下几个方面：
1首次用直接数值模拟方法对各种流条件下的圆柱饶流进行了计算。在低雷诺数条件下，成功再现了均匀来流下的三维尾涡模式；如Mode A和Mode B。在横向剪切来流条件下，与来流速度较低一侧对应的尾涡能量在流体运动过程中逐渐衰减；与来流速度较高一侧对应的尾涡能量在流体运动过程中逐渐增强，以至于在尾流较远处只剩下能量较强的尾涡。横向剪切流对圆柱绕流的影响还体现在边界层和表面压强系数的改变。数值计算结果表明，圆柱体表面的边界层和压强系数在横向剪切流作用下沿轴向出现偏转，这与流体流动的物理特性相一致。而在轴向剪切流条件下，泻涡形式沿轴向倾斜，顺时针和逆时针旋转的尾涡不存在能量的衰减或增强，脱落后的尾涡在流向方向依然保持平行。在横向-轴向组合剪切来流条件下，尾涡的运动不仅偏向于来流速度较低的一侧，而且沿轴向倾斜脱落。组合剪切流可看做是单个横向剪切流和轴向剪切流作功的叠加，但不会出现横向剪切流和轴向剪切流之间相互抑制的现象。
2采用直接数值模拟法研究了无滑移边界条件和自由表面边界条件对尾涡的影响，找出了物理实验结果Kiya et al (1980)与近年来数值模拟结果Kang (2007)存在较大差异的主要原因。指出无滑移边界条件将能有效抑制尾涡的脱落，而自由表面边界条件则对尾涡的脱落没有多大的影响。因而，物理实验的实施必须考虑到无滑移边界条件的影响，而数据的采集应尽量避免处在无滑移边界条件影响的区域之内。
3数值计算得出了两向自由度弹性支撑圆柱体产生较大横向振幅的临界质量比* m = 3.5。当圆柱体的质量比高于临界质量比时，限制流向运动对横向振幅幅值的影响不大；当质量比降至临界质量比时，流向和横向的振动将激发出更大的横向振幅幅值，流向运动对横向振幅的影响在此凸现。数值计算还重现了实验中不同横向振幅响应分支对应的尾涡模式，特别是与超上端分支对应的2T尾涡模式。在均匀来流条件下，数值模拟还成功得出了圆柱体“8”型的运动轨迹。
4在横向剪切来流条件下，两向自由度弹性支撑圆柱体的涡激振动存在一个剪切率的锁定区间。剪切率锁定区间与雷诺数的大小成正比。在剪切率的锁定区间内，横向振幅增大；脱离剪切率锁定区间后，横向振幅迅速下降。在横向来流剪切率较小时，圆柱体的运动轨迹与均匀来流条件下的“8”型的运动轨迹一致。随着剪切率的增加，圆柱体“8”型运动轨迹上端消失而表现为“小雨点”的外形。
5在阶梯状来流条件下，立管的响应在时域内并不表现为单一模态，而是在各个模态之间进行跳转。当某一激发模态的权重占绝对主导地位时，立管的变形与该激发模态下的形状一致；而当立管激发各模态的权重并不由唯一的激发模态所主导时，立管的响应形式将在占主导地位的几种激发模态之间跳转。通过记录时域内沿立管轴向分布的流体力，发现流体力沿立管轴向具有分段相关性，这为本文基于切片法所建立的时域预报模型的合理性提供了依据。沿立管轴向分布的附加质量系数存在波动区间，这与立管呈现的多模态响应相关联。当立管的涡激振动表现为多模态响应时，本文提出了附加质量系数的计算应当根据激发模态的权重来考虑各个模态所对应附加质量系数的贡献。数值计算沿立管轴向同时捕捉到了2S和2P尾涡模式，重现了这一经典的物理现象；在不同的立管截面之间，还观测到尾涡泻涡时间的切换现象。
6在轴向剪切来流条件下，本文的时域预报模型所得到的低阶模态响应与实验结果吻合较好。本文采用的时域模型采用了较多的切片数量来考虑流体力的轴向相关性，利用动网格和变形网格来模拟流固耦合运动对流体流动的影响，还同步考虑到立管的变形引起的总体刚度矩阵的非线性性。因而，本文所预报的结果较同类切片模型和频率预报模型的结果更为精确。
7通过沟通受迫振动和自激振动内在联系，建立理论模型成功实现了由受迫振动实验数据来预报自激振动圆柱体的横向振幅幅值。该理论模型可同时考虑到雷诺数和质量阻尼比对横向振幅幅值的影响，同时也再次证明雷诺数是影响涡激振动横向振幅的一个重要参数。本文的理论预报模型可为深海立管频域预报模型的发展和完善提供理论依据。
通过对本文主要内容和结论的阐述，可以反映出该论文的创新点表现在以下几个方面：
1利用直接数值模拟方法首次对横向剪切来流条件下的圆柱绕流进行了计算，对尾涡模式和流体流动的物理特性进行了详细探讨。
2对两向自由度弹性支撑圆柱体在均匀来流和横向剪切流条件下进行了数值模拟，得出了均匀来流条件下产生较大横向振幅所对应的临界质量比为3.5；得出横向剪切流条件下存在剪切流的锁定区间，并发现了一种全新的“小雨点”运动轨迹。
3建立了柔性立管涡激振动时域响应预报模型，在时域内成功预报了立管的模态响应。
4发展和完善了频域预报模型。在受迫振动实验数据基础上，考虑了雷诺数和质量阻尼比得出了自激振动横向振幅峰值的理论预报公式。
总而言之，本文从简单的圆柱绕流开始，逐步考虑到弹性支撑圆柱体和柔性立管的涡激振动响应，并成功建立了柔性立管涡激振动的时域预报模型。本文时域模型的预报结果能准确地反映出物理实验中的诸多现象和结论，同时，从本文时域模型得到的结论中可为完善和发展柔性立管频率预报模型提供思路和参考。
Around seventy percent of the Earth surface is covered by water and huge amount of natural resources such as gas and oil are richly stored in the deep ocean. With the fast industry development, the sharp increasing demand of consuming energy, especially the oil and gas, has become bottle-neck issue for both developing and developed countries. Deep-water petroleum industry could be a good way to solve the global energy crisis in future. One of the technique challenges, related to deep-water petroleum industry, is the Vortex-Induced Vibration (VIV for short) of flexible riser.
VIV happens while flow over the flexible riser and the structure is excited by the unsteady fluid fore which is generated by the periodic shedding vortex. The flexible riser will vibrate frequently with large amplitude under certain incoming flow conditions. Great damage to the riser would be resulted from the VIV due to the high vortex shedding frequency. Having a good understanding of the VIV mechanism could be helpful to reduce the damage effect on the riser, and also a quite kind strategy to the environments. However, VIV can be regarded as a complex fluid-structure coupling problem and the equations solving the flow domain and the structure bare strong non-linearity. The flow could turn into turbulence according to the high Reynolds number theory and how to revolve the turbulence accurately in a numerical way is still a big challenge world wild.
The present research described in this thesis is a part of the project“Research on Dynamic Response of Platforms in Deep-water”supported by the National Natural Science Foundation of China under Grant No.50323004 and also supported by Shanghai Scientific Fund under Grant No. 05DJ14001. The purpose of the research is to study turbulence and to construct a numerical model to predict the VIV response of flexible riser under uniform and shear flow conditions in the time domain.
Based on the latest achievements on turbulence research and VIV response of flexible riser, the present thesis focuses on the most interested points which include numerical tools for turbulence simulation and the VIV response of flexible riser under stepped and shear flow conditions. The main contents of the present thesis can be summarized as follows:
1, A review on the turbulence research and the existed models for VIV response prediction has been conducted. A brief introduction to the numerical research tools on turbulence including RANS、LES and DNS is described, especially the DNS and RANS being used in the present thesis are compared in a detail way. Empirical model and time-domain model for VIV response are also introduced. Most of the latest experimental results on VIV of flexible riser are concluded and constructive suggestion is made for the future research.
2, Three dimensional numerical simulation on shear flow over a circular cylinder has been studied by applying DNS. Shear effort on the three dimensional vorticity structure behind the circular cylinder has been intensively investigated. The physics of the fluid such as turbulence energy, kinetic energy, Reynolds stress, shedding frequency, boundary layer and pressure coefficient is also conducted and compared with the results of other sources. The discrepancy between the physical experiment and two dimensional simulations could be well resolved by applying the three dimensional numerical experiments.
3, Two-degrees-freedom VIV of a spring constrained rigid circular cylinder with low mass and damping ratio has been analyzed using RANS solver combined with turbulence model for the Navier-Stoke equation. The vibration in streamwise and transverse direction is considered to have a limited effect on the peak transverse amplitude of the spring mounted circular cylinder with moderate mass ratio. It is interesting to find the critical mass ratio under which the supper upper branch could appear accordingly in the current numerical results. The time-trace circular cylinder movement and vorticity structure which obtained in physical experiments are also captured in the present simulation.
4, Another numerical investigation is also conducted on VIV response of an elastic mounted circle cylinder under planar shear flow conditions. A planar shear ratio lock-in range can be concluded from the data analysis in transverse response, fluid force and time trace displacement at moderate Reynolds number. The figure“8”trace movement could be observed under small planar shear flow conditions while a completely new style time-trace circular cylinder movement is discovered as the planar shear ratio increases.
5, Based on the strip theory and the combination of the Finite Volume Method and Dynamic Finite Element Method, a numerical model which can be used to predict the VIV response of a flexible riser in time-domain is successfully constructed. VIV response of a flexible riser under stepped and shear flow conditions is calculated and extensive investigation on the mechanics of the VIV is carried out by applying the research on the time-trace of the transverse response and fluid forces along the axis of the riser. The multi-modal response is obtained and two typical vortex shedding modes are observed at the same time in the spanwise direction as the riser is set in a stepped flow.
6, The same numerical model is applied to predict the VIV response of a flexible riser under the axis shear flow condition. Compared to the results by other CFD model and empirical model, the present results are more rational and accuracy in agreement with the experimental results in the deforming modal shapes.
7, The Reynolds number effect and mass-damping ratio effect on the peak transverse response amplitude of a freely vibrating circular cylinder is well studied based on the forced oscillation experimental data. A theory model which can be used to predict the peak transverse response is constructed. This model could be considered as an update to the empirical model for the prediction of the response of the flexible riser. According to the research work mentioned above, main conclusion can be drawn as follows:
1, The vorticity structure such as Mode A and Mode B is successfully recorded under uniform inflow at low Reynolds numbers. Oblique vortex shedding in streamwise direction is observed by applying DNS calculation on planar shear flow over a circular cylinder. The vorticity energy corresponding to the higher velocity side becomes stronger and the vorticity energy in the other side will decay to be totally destroyed as it moves down in the far wake of the circular cylinder. The planar shear flow will affect the boundary layer and pressure coefficient around the surface of the circular cylinder, but no effect on the shedding frequency. Oblique vortex shedding in the spanwise direction and dislocations could be observed under the spanwise shear inflow over a circular cylinder. The two shear flow results could be regarded as a combination of the planar shear and the spanwise shear flow cases, and it can be inferred that the planar shear and the spanwise shear do affect the flow motion separately but without any interaction effect.
2, DNS calculation is conducted to study the no-slip and free slip boundary conditions on the suppression effort in vortex shedding phenomenon under the planar shear flow over a circular cylinder. The discrepancy between the experimental results by Kiya et al (1980) and recently two dimensional numerical results by Kang (2007) is well explained according to the three dimensional DNS results. The no-slip boundary condition will have a great effect on vortex shedding suppression while very limited effect in free slip boundary condition
3, The streamewise vibration has a limited effect on the peak transverse response of the circular cylinder with moderate mass ratio. Larger transverse response could be excited as the mass ratio is below the critical mass ratio m* cri= 3.5for the circular cylinder with two degree-freedom rather than the streamewise vibration is constrained. The vortex shedding mode, such as SS, 2S and 2P, corresponding to different transverse response branch is observed; especially the classical 2T mode appearing at the supper upper branch in the experiment by Jauvtis & Williamson (2003) is reproduced in the present numerical simulation. The figure“8”traces movement for the VIV response is also captured successfully.
4, The results form the two dimensional planar shear flow over an elastic mounted circular cylinder infer that there exits a planar shear ratio lock-in range in which the transverse amplitude grows rapidly and the amplitude would decrease sharply as it goes out of the shear ratio lock-in range. The lock-in range becomes wider as the Reynolds number grows. The figure“8”time trace movement can be seen as the planar shear flow ratio is small, while a new time trace movement which is named as“water drop”shape is discovered.
5, The multi-modal response of the flexible riser is obtained under the stepped inflow condition. The excited model for the long flexible riser can jump from one model to another one in the time domain while the deforming shape of the riser appears to be the dominated excited modal shape. It is can be inferred from the time trace contour of the lift or drag coefficient that the fluid force correction length along the axis of the riser could be given a strong supportive evidence for the present multi-strip numerical model. The added mass is not equally distributed along the axis of the riser but vibrates a lot according to the multi-modal response. It is suggested that the added mass distribution should take into account of the contributions separately from the main excited modals. The“2S”and“2P”vorticity structures are observed along the axis of the riser at the same time due to the small or large amplitude of the riser in various excited models. The switching phenomenon in the vortex shedding is observer in the present CFD model.
6, The predicted VIV response of the riser agrees well with the experimental results as the riser is excited at low modal response in the spanwise shear flow. Compared to other multi-strip model or empirical model, the present CFD model could be recognized as a more accurate and rational multi-strip model for more strips are used to consider the fluid force correction along the axis the riser and the deforming mesh is applied to simulate the fluid-structure coupling movement in the current model. Furthermore, the non-linear global stiffness matrix is updated in the time domain as the riser deforms.
7, Potential relationship between the freely vibration and the forced oscillation has been investigated and a theory model is successfully constructed. Reynolds number effect and mass-damping effect are considered to predict the peek transverse amplitude of a freely vibrating cylinder by applying the force oscillation experimental results. It is concluded that the Reynolds number ignored previously in the forced oscillation is a quite important parameter in the freely vibration case. The general idea in the current theory model could provide a strong background for the empirical model of VIV response of a flexible riser.
In a word, the present paper starts with the simple case in flow over a circular cylinder, and then focuses on the VIV of a spring mounted circular to the VIV response of a flexible riser finally. A CFD model is successfully constructed and it can be used to predict the VIV response of a flexible riser in the time domain Most of the experimental results or vortex shedding phenomenon could be accurately reproduced in the current CFD model. It can be inferred that the main conclusions drawn from the present CFD model could provide a constructive way to improve the empirical model in VIV response prediction.
引文
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