海洋立管涡致耦合振动CFD数值模拟研究
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摘要
本文基于计算流体力学（CFD）与计算结构动力学（CSD）方法，对圆柱体的涡激振动响应进行数值模拟，研究不同工况下柱体受力系数、振动幅值以及尾流漩涡脱落模式等变化规律，探索海洋立管的涡激振动机理；并进一步研究带抑振装置圆柱体的涡激振动及抑振效果；在此基础上，对多个圆柱体涡激振动的干涉问题进行了数值模拟研究；最后对深水立管结构进行准三维涡激振动数值模拟。具体内容如下：
1、流体—圆柱体结构耦合振动数值模拟方法研究
在总结分析国内外对CFD流固耦合研究现状的基础上，本文考虑了涡激振动参数并结合CFD方法，建立流固耦合系统的涡致振动无量纲数值模型。选择SST k模型模拟流场变化，同时采用Newmark-β法控制柱体边界的运动。最后给出流固耦合求解的具体实现方法，确定流固耦合数值模拟的求解流程，并编制相应的计算程序。
2、单圆柱体涡激耦合振动数值模拟
首先，以单圆柱体为基础建立了单柱体涡激振动CFD数值模型，并编制fsi-xy.c结构运动程序。通过得到的受力系数与振幅变化规律，分析圆柱体在流体作用下的运动规律。给出尾流涡结构，揭示柱体振动与漩涡脱落模式间的关系。
3、带抑振装置柱体涡激耦合振动数值模拟
应用流体—柱体结构耦合振动数值模拟方法研究带抑振装置单柱体的二维涡激振动响应。分别建立尾翼为14mm、10mm的带三角导流板柱体以及带板状导流板柱体的流固耦合数值模型，并根据流固耦合系统求解流程对其进行模拟。分别将模拟得到的带抑振柱体振动幅值与受力系数的变趋势、振动响应时程曲线、质心运动轨迹以及不同截面柱体尾流漩涡脱落模式等结果与单圆柱体模拟结果进行比较，分析不同抑振装置的工作原理。
4、群柱体系干扰效应数值模拟
针对实际海洋工程中常见的串联与并列两种形式圆柱体进行涡激振动数值模拟。分别建立柱间距比L/D=3~10串联排列，以及柱距比G/D=5~10的并列排列两圆柱体流固耦合数值模型，编制fsi-2c-xy.c结构运动程序，并采用特殊宏同时控制同一时间步内的两柱体的运动。通过求解雷诺数范围为6300~18000时流体与柱体的耦合响应，分析不同排列形式下，柱间距比与流速对两柱体横向与顺流向振幅、受力系数以及质心运动轨迹的影响规律。结果表明：两种排列方式的干扰效应明显不同。
5、立管结构准三维涡激振动数值模拟
为更准确的模拟立管在诸多因素（如雷诺数，结构性质，流体作用等）的影响下的复杂耦联振动，同时为避免三维流场模拟计算量大、结果不易收敛等缺点，本文以静力等效为基础，将三维结构与二维流体相结合，建立准三维涡激振动流固耦合数值模型。将两端固定连接的立管简化为多质点模型，各质点在二维平面上均被视为弹簧—阻尼模型，弹簧刚度基于静力等效计算得到。分别对各质点进行二维流固耦合模拟，最终得到立管结构整体的涡激振动响应。
最后，进行立管涡激振动无比尺实验，以验证建立的准三维数值模型。通过对比立管涡激振动物理模型实验与数值分析结果发现，两者得到的结构振动响应的变化规律基本一致。
Based on Computational fluid dynamics (CFD) and Computational structuredynamics (CSD), the vortex induced vibration (VIV) of circular cylinder is simulatednumerically. The variation regularity of the force coefficients, the amplitude ofvibration and the patterns of vortex shedding in different cases are studied, and thephenomenon of marine risers under vortex induced vibration is explored. The VIVmotion of cylinder with suppressions is analyzed, and the effect of suppressions isdiscussed. Furthermore, the interference among multi-cylinder with VIV is involved,and the quasi-3D study on the VIV motion of the deepwater risers is established. Themain content of this dissertation is as follows:
1. Study on the numerical simulation of the fluid-structure interaction
Based on summarizing and analyzing the CFD research status of thefluid-structure interaction both at home and abroad, a dimensionless numerical modelfor the analysis of the vortex-induced vibration of fluid-structure interaction(FSI) isestablished. Based on the coefficients of VIV and CFD method, the SST k modelis chose for the establishment the model of fluid field, and the boundary motion of thecylinder is simulated by the Newmark-β method. Finally, a computational procedureon FSI is given to solve the dynamic response of cylinder.
2. Numerical simulation on vortex induced vibration of single cylinder
The numerical model of vortex-induced vibration for single cylinder is established.And the dynamic response of a single cylinder is achieved by employing acombination of program fsi-xy.c and FLUENT. By simulating structure and flowtogether, the force coefficients and the vibration amplitude can be achieved.According to the results, the pattern of oscillating cylinder is analyzed, and therelationship between cylinder vibration and the vortex shedding model is revealed.
3. Numerical simulation on vortex induced vibration of cylinder with suppressiondevice by FSI
The dynamic response of cylinder with suppression device is simulatednumerically by fluid-structure interaction. In this section, three kinds of fairings arestudied, which is triangular fairing of10mm length, triangular fairing of14mm lengthand plate-shaped fairing of18mm. By analyzing numerically based on the procedure above, the dynamic response of cylinders with different cross-section can be achieved.The results show that there is influence on the vibration of cylinder because offairings. And under the effect of vibration of cylinder with fairing, the flow field isdamaged in varying degrees. Compare to the dynamic response of single, the effectsof the fairing are further explained.
4. The effect of the interference of two cylinder in tandem and side-by-sidearrangement.
Based on the FSI model of single cylinder, a numerical calculation method offluid-solid interaction vibration system of multi cylinders under elastic support isdeveloped. Two cylinders are arranged at space interval ratio L/D=3~10in tandemand at space interval ratio G/D=5~10at side-by-side. The motions of two cylinders indifferent arrangement are solved by the programme fsi-2c-xy.c. And depended on thespecial macro, two cylinders move together in the same time step. The range of Re isfrom6300to18000. The results achieved by simulating are the amplitude of vibration,force coefficients and the x-y trajectory, which show that there is different interferenceeffect on the different arrangement.
5. The quasi-3D numerical simulation on dynamic response of the riser
The vibration of riser is more complex under the influence of Reynolds number,characters of structure and fluid. The numerical model in2D can’t solve the problemof the vibration of3D risers well. So in this section a quasi-3D numerical is modeledby CFD. The quasi-3D model is based on the combination of3D structure model and2D fluid model. The riser is transformed into the multi particle model, and every masspoint is considered as the spring-damping vibration model. Based on the FSI model ofsingle cylinder, the dynamic responses of mass points are calculated in2D flow field,respectively. Depended on the results of every mass points, the dynamic response ofthe riser is approximately achieved. In order to verify the quasi-3D model, anexperiment on vortex-induced vibration of rise is conducted. By compared the resultsbetween experiment and numerical simulation, the non dimensionless displacementenvelopes between two studies is similar. It is shown that the quasi-3D model cansimulate the dynamic response of the structure in3D approximately.
1、流体—圆柱体结构耦合振动数值模拟方法研究
在总结分析国内外对CFD流固耦合研究现状的基础上，本文考虑了涡激振动参数并结合CFD方法，建立流固耦合系统的涡致振动无量纲数值模型。选择SST k模型模拟流场变化，同时采用Newmark-β法控制柱体边界的运动。最后给出流固耦合求解的具体实现方法，确定流固耦合数值模拟的求解流程，并编制相应的计算程序。
2、单圆柱体涡激耦合振动数值模拟
首先，以单圆柱体为基础建立了单柱体涡激振动CFD数值模型，并编制fsi-xy.c结构运动程序。通过得到的受力系数与振幅变化规律，分析圆柱体在流体作用下的运动规律。给出尾流涡结构，揭示柱体振动与漩涡脱落模式间的关系。
3、带抑振装置柱体涡激耦合振动数值模拟
应用流体—柱体结构耦合振动数值模拟方法研究带抑振装置单柱体的二维涡激振动响应。分别建立尾翼为14mm、10mm的带三角导流板柱体以及带板状导流板柱体的流固耦合数值模型，并根据流固耦合系统求解流程对其进行模拟。分别将模拟得到的带抑振柱体振动幅值与受力系数的变趋势、振动响应时程曲线、质心运动轨迹以及不同截面柱体尾流漩涡脱落模式等结果与单圆柱体模拟结果进行比较，分析不同抑振装置的工作原理。
4、群柱体系干扰效应数值模拟
针对实际海洋工程中常见的串联与并列两种形式圆柱体进行涡激振动数值模拟。分别建立柱间距比L/D=3~10串联排列，以及柱距比G/D=5~10的并列排列两圆柱体流固耦合数值模型，编制fsi-2c-xy.c结构运动程序，并采用特殊宏同时控制同一时间步内的两柱体的运动。通过求解雷诺数范围为6300~18000时流体与柱体的耦合响应，分析不同排列形式下，柱间距比与流速对两柱体横向与顺流向振幅、受力系数以及质心运动轨迹的影响规律。结果表明：两种排列方式的干扰效应明显不同。
5、立管结构准三维涡激振动数值模拟
为更准确的模拟立管在诸多因素（如雷诺数，结构性质，流体作用等）的影响下的复杂耦联振动，同时为避免三维流场模拟计算量大、结果不易收敛等缺点，本文以静力等效为基础，将三维结构与二维流体相结合，建立准三维涡激振动流固耦合数值模型。将两端固定连接的立管简化为多质点模型，各质点在二维平面上均被视为弹簧—阻尼模型，弹簧刚度基于静力等效计算得到。分别对各质点进行二维流固耦合模拟，最终得到立管结构整体的涡激振动响应。
最后，进行立管涡激振动无比尺实验，以验证建立的准三维数值模型。通过对比立管涡激振动物理模型实验与数值分析结果发现，两者得到的结构振动响应的变化规律基本一致。
Based on Computational fluid dynamics (CFD) and Computational structuredynamics (CSD), the vortex induced vibration (VIV) of circular cylinder is simulatednumerically. The variation regularity of the force coefficients, the amplitude ofvibration and the patterns of vortex shedding in different cases are studied, and thephenomenon of marine risers under vortex induced vibration is explored. The VIVmotion of cylinder with suppressions is analyzed, and the effect of suppressions isdiscussed. Furthermore, the interference among multi-cylinder with VIV is involved,and the quasi-3D study on the VIV motion of the deepwater risers is established. Themain content of this dissertation is as follows:
1. Study on the numerical simulation of the fluid-structure interaction
Based on summarizing and analyzing the CFD research status of thefluid-structure interaction both at home and abroad, a dimensionless numerical modelfor the analysis of the vortex-induced vibration of fluid-structure interaction(FSI) isestablished. Based on the coefficients of VIV and CFD method, the SST k modelis chose for the establishment the model of fluid field, and the boundary motion of thecylinder is simulated by the Newmark-β method. Finally, a computational procedureon FSI is given to solve the dynamic response of cylinder.
2. Numerical simulation on vortex induced vibration of single cylinder
The numerical model of vortex-induced vibration for single cylinder is established.And the dynamic response of a single cylinder is achieved by employing acombination of program fsi-xy.c and FLUENT. By simulating structure and flowtogether, the force coefficients and the vibration amplitude can be achieved.According to the results, the pattern of oscillating cylinder is analyzed, and therelationship between cylinder vibration and the vortex shedding model is revealed.
3. Numerical simulation on vortex induced vibration of cylinder with suppressiondevice by FSI
The dynamic response of cylinder with suppression device is simulatednumerically by fluid-structure interaction. In this section, three kinds of fairings arestudied, which is triangular fairing of10mm length, triangular fairing of14mm lengthand plate-shaped fairing of18mm. By analyzing numerically based on the procedure above, the dynamic response of cylinders with different cross-section can be achieved.The results show that there is influence on the vibration of cylinder because offairings. And under the effect of vibration of cylinder with fairing, the flow field isdamaged in varying degrees. Compare to the dynamic response of single, the effectsof the fairing are further explained.
4. The effect of the interference of two cylinder in tandem and side-by-sidearrangement.
Based on the FSI model of single cylinder, a numerical calculation method offluid-solid interaction vibration system of multi cylinders under elastic support isdeveloped. Two cylinders are arranged at space interval ratio L/D=3~10in tandemand at space interval ratio G/D=5~10at side-by-side. The motions of two cylinders indifferent arrangement are solved by the programme fsi-2c-xy.c. And depended on thespecial macro, two cylinders move together in the same time step. The range of Re isfrom6300to18000. The results achieved by simulating are the amplitude of vibration,force coefficients and the x-y trajectory, which show that there is different interferenceeffect on the different arrangement.
5. The quasi-3D numerical simulation on dynamic response of the riser
The vibration of riser is more complex under the influence of Reynolds number,characters of structure and fluid. The numerical model in2D can’t solve the problemof the vibration of3D risers well. So in this section a quasi-3D numerical is modeledby CFD. The quasi-3D model is based on the combination of3D structure model and2D fluid model. The riser is transformed into the multi particle model, and every masspoint is considered as the spring-damping vibration model. Based on the FSI model ofsingle cylinder, the dynamic responses of mass points are calculated in2D flow field,respectively. Depended on the results of every mass points, the dynamic response ofthe riser is approximately achieved. In order to verify the quasi-3D model, anexperiment on vortex-induced vibration of rise is conducted. By compared the resultsbetween experiment and numerical simulation, the non dimensionless displacementenvelopes between two studies is similar. It is shown that the quasi-3D model cansimulate the dynamic response of the structure in3D approximately.
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[91]曹洪建查晶晶万德成，基于OpenFOAM编程数值模拟双圆柱绕流流动[J]，中国力学学会学术大会'2009论文摘要集。
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[94] Prasanth T. K., Mittal S., Vortex-induced vibration of two circular cylinders at low Reynoldsnumber [J]. Journal of Fluids and Structures,2009,25:731-741.
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[96]徐枫，欧进萍，正三角形排列三圆柱绕流与涡致振动数值模拟[J].空气动力学学报，2010,28(5):582-590.
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