钢悬链线输流立管非线性振动数值模拟
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摘要
钢悬链线立管大量的优点使其成为深水油气资源开发的首选立管系统。作为海面与海底的一种联系通道,它既可用于浮式海洋平台,又可用于固定式平台及钻探船舶。钢悬链线立管内部一般有高压的油或气流过,外部承受波浪、海流作用,当波浪、海流流经立管时,在一定的流速下会产生涡旋脱落,使立管发生涡激振动,当海洋立管自振频率与旋涡脱落频率接近时,振动会迫使旋涡脱落频率固定在结构自振频率附近,发生频率锁定(lock—in)现象,引起管道振动加强。所以,在钢悬链线立管的设计中,涡激振动是一个非常重要的问题。另外,钢悬链线立管在触地点附近的管土相互作用、以及触地点弯矩的动力放大等问题,多数是由顶部浮体的运动引起的。因此钢悬链线立管的动力分析需要深入研究立管系统在涡激升力以及在顶部浮体激励下的动力响应。
当管内介质流经挠曲的管道时,由于管道曲率的变化和管道的横向振动,流体发生加速,这些加速的力会反过来作用在管道上,引起管道的附加振动。钢悬链线输流立管在涡激振动和管内流体流动的共同作用下可能引起大幅度的振动,使得应力加大,易引起管道的疲劳破坏。目前,同时考虑管道内外流共同作用的涡激振动理论研究较少。因此,考虑管内流体流动及管外海洋环境共同作用的钢悬链线输流立管理论研究,不仅有重要的科学意义,在工程上亦有较大的应用价值。
本文利用虚功原理,其中包括轴向应变能和弯曲应变能所做的虚功以及重力、惯性力、外部流体作用力和结构阻尼所做虚功,建立了适用于计算分析自由悬挂钢悬链线立管的三维动力学数学模型。将Euler方程联合平衡方程得到了立管在笛卡尔坐标系内的整体耦合运动方程。利用Galerkin有限元法得到质量、阻尼和刚度矩阵,通过计算矩阵的特征值来确定立管的固有频率以及模态形状。通过数值计算验证模型的正确性,并且分析各种参数变化对钢悬链线立管动力特性的影响。
用Matteoluca尾流振子模型来模拟流体对立管的涡激振动作用力,求解立管涡激振动响应；将顶部浮体的运动简化为正弦运动施加于立管顶部,求解立管的动力响应。与相关的研究结果进行比较,验证本文模型的有效性,并用Matlab编制计算程序,分析了内流流速、顶部张力以及外部流体对立管动力响应的影响。结果表明：不同外流流速钢悬链线立管的涡激振动出现不同的多阶模态的耦合振动,内流流速和顶部张力的变化会改变立管的涡激振动响应频率、幅值以及应力和弯矩。顶部浮体激励频率的变化会改变立管的应力和弯矩的分布,特别是顶部和底部的变化较大。激励幅值和内流、顶部张力以及外流的存在对响应应力和弯矩都有不同程度的影响。
Steel catenary risers are the main connecter between a platform and the mouth of a well in the seabed and can be applied to floating platform, fixed platform and drilling shipping systems. The risers generally contain flowing oil or high pressure gas and bear the action of wave and current outside. When current or wave flows across the risers at certain speed, there will appear vortex shedding, and if the frequency of the risers is close to that of the vortex shedding, oscillation will make the vortex shedding frequency fixed nearby to the structural natural frequency and cause large amplitude vibration which is called 'lock-in' state. So the vortex-induced vibration is an important factor in the design of steelcatenary riser system. Otherwise some indicative examples include the riser-soil interaction effects in bottoms of practically unknown contour, the ill-understood vortex induced vibration (VIV) effects and the floater vortex induced motion (VIM) induced riser fatigue, extreme dynamic amplification of bending moments at the touch-down region, etc. Some of these issues are related to the dynamic response of the riser under imposed excitation applied at the top of the structure, which represents the motions of the floating vessel. Therefore the dynamic analysis of steel catenary risers is a key issue that requires deep and comprehensive investigation of the associated system, proper formulation of the theoretical model and finally, the use of an efficient solution method.
When internal fluid travels along the curved path inside the deflected risers, it experiences centrifugal and coriolis accelerations because of the curvature of the risers and the relative motion of fluid to the time dependent risers motion, respectively. Those accelerations exert against the risers and, in turn, affect the dynamic behavior of the risers and cause additional vibrations. Steel catenary risers subjected to the vortex-induced vibration and the internal fluid may experience large response which gives rise to oscillatory stresses and cause fatigue damage. The numerical studies that were focused on the VIV considering internal flowing have not been carried out yet. So the numerical simulation on VIV considering internal flow flowing has both scientific and practical value.
This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of inclined extensible steel catenary risers. The virtual work-energy functional, which involves strain energy due to axial stretching and bending moment of the riser and virtual work done by the gravitational, inertial, and external hydrostatic and drag forces, is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler's equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass damping and stiffness matrices. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of steel catenary risers.
Try to simulate the fluid induced vibration of riser vortex force by Matteoluca wake oscillator model, solving riser vortex induced vibration. The motion of the floating body is simplified as sinusoidal excitation imposed on the riser at the top, solving the dynamic response of riser. And related research results were compared to verify the validity of this model. The program in Matlab was complied, detailed analysis of the dynamic response of riser influenced by the internal fluid velocity, the top tension and the external fluid. The results indicate that:steel catenary riser has different multi-modal coupling vortex induced vibrations under different external fluid velocity. Internal fluid velocity and top tension may change the riser vortex induced vibration frequency, amplitude, dynamic stress and bending moment. Top floating-body excitation frequency may change the distribution of dynamic stress and bending moment of the riser, and large changes in the top and bottom. Excitation amplitude, internal fluid velocity, top tension and the existence of external fluid may change the dynamic stress and bending moment of the response in different degrees.
当管内介质流经挠曲的管道时,由于管道曲率的变化和管道的横向振动,流体发生加速,这些加速的力会反过来作用在管道上,引起管道的附加振动。钢悬链线输流立管在涡激振动和管内流体流动的共同作用下可能引起大幅度的振动,使得应力加大,易引起管道的疲劳破坏。目前,同时考虑管道内外流共同作用的涡激振动理论研究较少。因此,考虑管内流体流动及管外海洋环境共同作用的钢悬链线输流立管理论研究,不仅有重要的科学意义,在工程上亦有较大的应用价值。
本文利用虚功原理,其中包括轴向应变能和弯曲应变能所做的虚功以及重力、惯性力、外部流体作用力和结构阻尼所做虚功,建立了适用于计算分析自由悬挂钢悬链线立管的三维动力学数学模型。将Euler方程联合平衡方程得到了立管在笛卡尔坐标系内的整体耦合运动方程。利用Galerkin有限元法得到质量、阻尼和刚度矩阵,通过计算矩阵的特征值来确定立管的固有频率以及模态形状。通过数值计算验证模型的正确性,并且分析各种参数变化对钢悬链线立管动力特性的影响。
用Matteoluca尾流振子模型来模拟流体对立管的涡激振动作用力,求解立管涡激振动响应；将顶部浮体的运动简化为正弦运动施加于立管顶部,求解立管的动力响应。与相关的研究结果进行比较,验证本文模型的有效性,并用Matlab编制计算程序,分析了内流流速、顶部张力以及外部流体对立管动力响应的影响。结果表明：不同外流流速钢悬链线立管的涡激振动出现不同的多阶模态的耦合振动,内流流速和顶部张力的变化会改变立管的涡激振动响应频率、幅值以及应力和弯矩。顶部浮体激励频率的变化会改变立管的应力和弯矩的分布,特别是顶部和底部的变化较大。激励幅值和内流、顶部张力以及外流的存在对响应应力和弯矩都有不同程度的影响。
Steel catenary risers are the main connecter between a platform and the mouth of a well in the seabed and can be applied to floating platform, fixed platform and drilling shipping systems. The risers generally contain flowing oil or high pressure gas and bear the action of wave and current outside. When current or wave flows across the risers at certain speed, there will appear vortex shedding, and if the frequency of the risers is close to that of the vortex shedding, oscillation will make the vortex shedding frequency fixed nearby to the structural natural frequency and cause large amplitude vibration which is called 'lock-in' state. So the vortex-induced vibration is an important factor in the design of steelcatenary riser system. Otherwise some indicative examples include the riser-soil interaction effects in bottoms of practically unknown contour, the ill-understood vortex induced vibration (VIV) effects and the floater vortex induced motion (VIM) induced riser fatigue, extreme dynamic amplification of bending moments at the touch-down region, etc. Some of these issues are related to the dynamic response of the riser under imposed excitation applied at the top of the structure, which represents the motions of the floating vessel. Therefore the dynamic analysis of steel catenary risers is a key issue that requires deep and comprehensive investigation of the associated system, proper formulation of the theoretical model and finally, the use of an efficient solution method.
When internal fluid travels along the curved path inside the deflected risers, it experiences centrifugal and coriolis accelerations because of the curvature of the risers and the relative motion of fluid to the time dependent risers motion, respectively. Those accelerations exert against the risers and, in turn, affect the dynamic behavior of the risers and cause additional vibrations. Steel catenary risers subjected to the vortex-induced vibration and the internal fluid may experience large response which gives rise to oscillatory stresses and cause fatigue damage. The numerical studies that were focused on the VIV considering internal flowing have not been carried out yet. So the numerical simulation on VIV considering internal flow flowing has both scientific and practical value.
This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of inclined extensible steel catenary risers. The virtual work-energy functional, which involves strain energy due to axial stretching and bending moment of the riser and virtual work done by the gravitational, inertial, and external hydrostatic and drag forces, is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler's equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass damping and stiffness matrices. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of steel catenary risers.
Try to simulate the fluid induced vibration of riser vortex force by Matteoluca wake oscillator model, solving riser vortex induced vibration. The motion of the floating body is simplified as sinusoidal excitation imposed on the riser at the top, solving the dynamic response of riser. And related research results were compared to verify the validity of this model. The program in Matlab was complied, detailed analysis of the dynamic response of riser influenced by the internal fluid velocity, the top tension and the external fluid. The results indicate that:steel catenary riser has different multi-modal coupling vortex induced vibrations under different external fluid velocity. Internal fluid velocity and top tension may change the riser vortex induced vibration frequency, amplitude, dynamic stress and bending moment. Top floating-body excitation frequency may change the distribution of dynamic stress and bending moment of the riser, and large changes in the top and bottom. Excitation amplitude, internal fluid velocity, top tension and the existence of external fluid may change the dynamic stress and bending moment of the response in different degrees.
引文
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