管土耦合边界下海底悬跨管道涡激振动研究
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摘要
在管道工程中,海床的凹凸不平和冲刷容易产生悬跨,并引发泄涡频率与结构频率的锁定,产生涡激振动疲劳。悬跨设计一直是管道设计的一个挑战,除了涡激振动系统海流与悬跨运动的相互作用,管土耦合的影响也不容忽视。正确地认识和描述悬跨跨肩管土耦合作用下悬跨VIV,合理的评估悬跨涡激振动疲劳,对保证海底管道经济效应和在服役期间安全运行有着重要意义。
本文针对管土耦合边界下海底悬跨管道的涡激振动,分别采用基于弱耦合算法的CFD模型、半经验模型以及尾流振子模型,建立了管土耦合非线性作用下悬跨涡激振动预报方法,并探讨多跨多模态涡激振动疲劳损伤的评估方法。论文的主要内容和成果可以归纳为以下五个方面：
(1)基于时域弱耦合算法,采用动网格技术模拟圆柱运动带来的流域边界的变化,开发出涡激振动的CFD数值程序。程序有效地实现了二维以及三维圆柱的涡激振动的数值模拟。流场求解选取有限体积法结合RANS方程与SST湍流模式离散,圆柱运动采用四阶Runge-Kutta求解,首次展开了对二维自激数值模拟的可靠性、有效性和不确定因数研究,指出了时间步长对计算结果的不确定性,以及流向自由度和高雷诺数对响应幅值的放大效应。
(2)首次应用尾流振子模型以及弱耦合算法的二维CFD数值方法,模拟了理想塑性非线性弹簧支撑刚性圆柱的涡激振动响应。两者方法的预报结果一致显示：在锁定初始阶段,当弹簧变形进入塑性阶段后,圆柱振动响应产生突变,产生较大振幅的振动；且整个锁定区域的响应幅值的峰值较线性弹簧下要低；CFD数值方法还模拟出非线性弹簧变形进入塑性区后,相位角由0突变到180附件,频率锁定在空气中的固有频率附近。
(3)利用2D刚性柱实验数据建立水动力经验模型,发展适合管土耦合边界下悬跨管道自身特点的简易预报频域程序。VIV响应频率的预报简化为在一定附加质量影响下的特征值求解问题；利用能量平衡原理,建立频域幅值迭代预报简易程序。最后在频域预报结果基础上,对管土耦合非线性作用下涡激振动应力响应进行时域分析。非线性的引入对跨肩最大应力幅值的影响十分显著,能够更现实的反应实际环境。(4)运用有限元法对输液张紧悬跨管道进行空间离散,并应用Facchinetti等发展的尾流振子模型和切片假定模拟每个有限单元上的涡激振动水动力,开发了一种基于尾流振子模型的悬跨管道-海床-海流多场耦合的非线性时域预报程序。在合理改进尾流振子模型附加水动力阻尼参数的基础上,应用程序时域上预报了线性、理想塑性和张力截断弹簧模型下悬跨管道的涡激振动响应。研究发现在锁定范围内非线性弹簧支撑情况下的最大幅值峰值较线性时要低,但出现的峰值时的流速要小。此时,若按照线性弹簧支撑柱的响应规律进行工业设计,很可能会低估了非线性情况下低流速下的响应幅值,而高估了幅值的峰值。
(5)针对长期作业的海底多跨管道的多模态涡激振动,联合考虑遭遇海流流速变化以及涡激振动响应本身的随机性,发展了一种基于离散流速的多跨多模态VIV疲劳损伤预报方法。采用Weibull分布描述流速长期变化,并将涡激振动引起的交变应力进程看作是零均值的窄带的平稳正态随机进程。从工程应用实践出发,在深入的研究DNV规范响应模型的基础上,结合离散流速VIV疲劳损伤预报流程,实现海底多跨管道的多模态VIV疲劳损伤预报,可以直接方便的应用于实际的管道设计。分析结果显示：疲劳损伤对土壤刚度选取敏感；DNV RP-105规范中多模态响应缩减系数较振幅权重形式要保守；用Rayleigh分布描述涡激振动响应进程较用横幅稳态振动描述得到的结果,在工程应用上更安全。
总之,本文的工作涉及到圆柱体以及海洋管道涡激振动研究的诸多方面,对许多重要的概念与现象给出了独到的解释与分析。从简单线性、非线性弹簧支撑刚性柱的二维涡激振动机理,到三维悬跨管道在复杂边界条件下的涡激振动响应预报,以及悬跨管道复杂振动响应下的涡激振动疲劳损伤,这些理论模型与经验为进一步的研究以及管道悬跨设计提供了有益的参考。
Free spans often become a challenge in the pipeline design and operation due to pipeline installation on uneven seabed or seabed scouring effects. Amplified responses due to resonance between the vortex shedding frequency and natural frequency of the free spans may cause fatigue damage. And a whole free span VIV system should include three parts:pipe, seabed and current. Hence, improving the knowledge about the effect of pipe-seabed interaction on VIV is quite important for free spanning pipelines, which are often highly nonlinear due to interaction with the seabed. A reasonable VIV analysis model based pipe-seabed interaction is helpful for VIV fatigue estimation, then provide the support for safe operation and cost reduction of submarine pipeline design
In the presented VIV response analysis of free span under pipe-soil interaction boundary, three prediction models were adopted respectively, including CFD model based on loose coupling algorithms, semi-empirical model and wake oscillator model. And a fatigue analysis method is established for multi-spans pipeline VIV.
The main contents and contributions of this thesis may be summarized as follows:
(1) Dynamic mesh technology wase adopted to achieve the simulation of moving wall boundary. And computational fluid dynamics (CFD) techniques, which analytically solve the viscous Navier-Stokes equations in order to obtain the hydrodynamic forces directly, were developed based on loose coupling algorithms in time domain. The codes can simulate successfully the VIV response of rigid and flexible rigid in 2-dimension and 3-dimension flow fluid domain. In the study, a research was implemented to analysis the reliability, validity and uncertainty of 2D VIV coupling code. the turbulence was presented by SST model, and fourth order Runge-Kutta algorithm used for cylinder movement resolution. The results show that time step is one of uncertain factors during CFD simulation, and amplified responses will come forth due to free in-line degree of freedom or high Reynolds number.
(2) The vortex induced vibration response of a rigid cylinder supported by perfectly plastic nonlinear spring in a fluid flow was simulated for the first time. Wake-oscillator prediction model and 2D CFD method based on loose coupling algorithms were adopted. The results of above two methods all showed that, vibration amplitude jumps to a maximum value when cylinder movement exceeds the nonlinear spring limited displacement, then decreases with velocity increasing. The response peak value for nonlinear spring case is higher than linear spring, but at the lower flow velocity. As the same time, the simulation of CFD presented that vibration frequency for synchronization is close to vortex shedding frequency at the beginning, and then switch to above the natural frequency in air when the amplitude reaches a peak value, while the phase angle of displacement and lift force transfer from 0 to 180 degree.
(3) An empirical hydrodynamic coefficient models based on the data from 2D rigid cylinder vibration experiments were used to predict the vortex-induced vibrations response of free spans under pipe-soil interaction boundary. The response frequencies were resolved from a eigenvalue problems of free spans with some certain added mass. And response amplitude could be received from a iteration process, which based on energy balance. After response frequency and hydrodynamic coefficients, were determined by use of above linear response model. This result is then used in a time domain model that can handle non-linear boundary conditions at the span shoulders. The results demonstrate that non-linear effects can be significant, in particular for pipe stress in the span shoulder. The significance of the new method is that displacements, and hence also stresses, in the pipe at the shoulders will be far better described by the non-linear method than what is possible from linear theory.
(4) And a time domain analysis method for non-linear pipe-seabed-interaction analysis of free spanning pipelines under VIV conditions has been developed. The flow is modeled by a van-der-Pol wake oscillator developed by Facchinetti et al. And the stall parameter is taken into account in the general form of the VIV amplitude and the response frequency, which can successful model the VIV response amplitude comparing with a constant. After the free spanning pipeline discrtized into the finite elements, the average acceleration method is chosen to integrate the equations of motion. Three types of pipe-seabed-interaction (linear spring, perfectly plastic nonlinear spring, and tension cut-off nonlinear spring) are considered. The results show that the presented time domain method can capture the non-linear interaction between the pipeline and the seabed at the free span shoulders. And the maximum response amplitude of nonlinear case is lower than the one with linear spring. Hence, the response will be underestimated at low current velocity, or overestimated at high current velocity.
(5) When the eigen-frequencies are close, several potential vibration modes of multi-spans can become active at a given low flow velocity, i.e. multi-mode vortex induced vibration. Considered for statistical distributions of current speed and VIV response of free spans in long-term operating condition, in the study, a fatigue assessment method for multi-spans was developed. It can provide a reference on the initial design of free spanning pipeline. At last, the fatigue damage due to multi-mode vortex induced vibration was investigated. It is to assume that the stress ranges are narrow-banded and Rayleigh-distributed, and a 3-parameter Weibull distribution is appropriate for modeling of the long-term statistics for the current velocity. The results based on the Response Model in DNV rules were shown that soil stiffness is sensitive. For reduction coefficient of multi-mode response, it is more conservative to use the DNV RP-105 than the weight of response amplitude. If the structure vibrates in a purely sinusoidal fashion with constant amplitude, then the calculation based on the Rayleigh distribution overestimates the damage rate.
In conclusion, from both the numerical and the experimental empirical models, the research in this thesis sets out from the VIV of a two dimensional circular cylinder supported by linear or nonlinear spring, ends up with the prediction of VIV of slender pipelines under more complicated pipe-soil interaction boundary. Many experience and findings will be helpful for the future work. It can provide a reference on the initial design of free spanning pipeline.
本文针对管土耦合边界下海底悬跨管道的涡激振动,分别采用基于弱耦合算法的CFD模型、半经验模型以及尾流振子模型,建立了管土耦合非线性作用下悬跨涡激振动预报方法,并探讨多跨多模态涡激振动疲劳损伤的评估方法。论文的主要内容和成果可以归纳为以下五个方面：
(1)基于时域弱耦合算法,采用动网格技术模拟圆柱运动带来的流域边界的变化,开发出涡激振动的CFD数值程序。程序有效地实现了二维以及三维圆柱的涡激振动的数值模拟。流场求解选取有限体积法结合RANS方程与SST湍流模式离散,圆柱运动采用四阶Runge-Kutta求解,首次展开了对二维自激数值模拟的可靠性、有效性和不确定因数研究,指出了时间步长对计算结果的不确定性,以及流向自由度和高雷诺数对响应幅值的放大效应。
(2)首次应用尾流振子模型以及弱耦合算法的二维CFD数值方法,模拟了理想塑性非线性弹簧支撑刚性圆柱的涡激振动响应。两者方法的预报结果一致显示：在锁定初始阶段,当弹簧变形进入塑性阶段后,圆柱振动响应产生突变,产生较大振幅的振动；且整个锁定区域的响应幅值的峰值较线性弹簧下要低；CFD数值方法还模拟出非线性弹簧变形进入塑性区后,相位角由0突变到180附件,频率锁定在空气中的固有频率附近。
(3)利用2D刚性柱实验数据建立水动力经验模型,发展适合管土耦合边界下悬跨管道自身特点的简易预报频域程序。VIV响应频率的预报简化为在一定附加质量影响下的特征值求解问题；利用能量平衡原理,建立频域幅值迭代预报简易程序。最后在频域预报结果基础上,对管土耦合非线性作用下涡激振动应力响应进行时域分析。非线性的引入对跨肩最大应力幅值的影响十分显著,能够更现实的反应实际环境。(4)运用有限元法对输液张紧悬跨管道进行空间离散,并应用Facchinetti等发展的尾流振子模型和切片假定模拟每个有限单元上的涡激振动水动力,开发了一种基于尾流振子模型的悬跨管道-海床-海流多场耦合的非线性时域预报程序。在合理改进尾流振子模型附加水动力阻尼参数的基础上,应用程序时域上预报了线性、理想塑性和张力截断弹簧模型下悬跨管道的涡激振动响应。研究发现在锁定范围内非线性弹簧支撑情况下的最大幅值峰值较线性时要低,但出现的峰值时的流速要小。此时,若按照线性弹簧支撑柱的响应规律进行工业设计,很可能会低估了非线性情况下低流速下的响应幅值,而高估了幅值的峰值。
(5)针对长期作业的海底多跨管道的多模态涡激振动,联合考虑遭遇海流流速变化以及涡激振动响应本身的随机性,发展了一种基于离散流速的多跨多模态VIV疲劳损伤预报方法。采用Weibull分布描述流速长期变化,并将涡激振动引起的交变应力进程看作是零均值的窄带的平稳正态随机进程。从工程应用实践出发,在深入的研究DNV规范响应模型的基础上,结合离散流速VIV疲劳损伤预报流程,实现海底多跨管道的多模态VIV疲劳损伤预报,可以直接方便的应用于实际的管道设计。分析结果显示：疲劳损伤对土壤刚度选取敏感；DNV RP-105规范中多模态响应缩减系数较振幅权重形式要保守；用Rayleigh分布描述涡激振动响应进程较用横幅稳态振动描述得到的结果,在工程应用上更安全。
总之,本文的工作涉及到圆柱体以及海洋管道涡激振动研究的诸多方面,对许多重要的概念与现象给出了独到的解释与分析。从简单线性、非线性弹簧支撑刚性柱的二维涡激振动机理,到三维悬跨管道在复杂边界条件下的涡激振动响应预报,以及悬跨管道复杂振动响应下的涡激振动疲劳损伤,这些理论模型与经验为进一步的研究以及管道悬跨设计提供了有益的参考。
Free spans often become a challenge in the pipeline design and operation due to pipeline installation on uneven seabed or seabed scouring effects. Amplified responses due to resonance between the vortex shedding frequency and natural frequency of the free spans may cause fatigue damage. And a whole free span VIV system should include three parts:pipe, seabed and current. Hence, improving the knowledge about the effect of pipe-seabed interaction on VIV is quite important for free spanning pipelines, which are often highly nonlinear due to interaction with the seabed. A reasonable VIV analysis model based pipe-seabed interaction is helpful for VIV fatigue estimation, then provide the support for safe operation and cost reduction of submarine pipeline design
In the presented VIV response analysis of free span under pipe-soil interaction boundary, three prediction models were adopted respectively, including CFD model based on loose coupling algorithms, semi-empirical model and wake oscillator model. And a fatigue analysis method is established for multi-spans pipeline VIV.
The main contents and contributions of this thesis may be summarized as follows:
(1) Dynamic mesh technology wase adopted to achieve the simulation of moving wall boundary. And computational fluid dynamics (CFD) techniques, which analytically solve the viscous Navier-Stokes equations in order to obtain the hydrodynamic forces directly, were developed based on loose coupling algorithms in time domain. The codes can simulate successfully the VIV response of rigid and flexible rigid in 2-dimension and 3-dimension flow fluid domain. In the study, a research was implemented to analysis the reliability, validity and uncertainty of 2D VIV coupling code. the turbulence was presented by SST model, and fourth order Runge-Kutta algorithm used for cylinder movement resolution. The results show that time step is one of uncertain factors during CFD simulation, and amplified responses will come forth due to free in-line degree of freedom or high Reynolds number.
(2) The vortex induced vibration response of a rigid cylinder supported by perfectly plastic nonlinear spring in a fluid flow was simulated for the first time. Wake-oscillator prediction model and 2D CFD method based on loose coupling algorithms were adopted. The results of above two methods all showed that, vibration amplitude jumps to a maximum value when cylinder movement exceeds the nonlinear spring limited displacement, then decreases with velocity increasing. The response peak value for nonlinear spring case is higher than linear spring, but at the lower flow velocity. As the same time, the simulation of CFD presented that vibration frequency for synchronization is close to vortex shedding frequency at the beginning, and then switch to above the natural frequency in air when the amplitude reaches a peak value, while the phase angle of displacement and lift force transfer from 0 to 180 degree.
(3) An empirical hydrodynamic coefficient models based on the data from 2D rigid cylinder vibration experiments were used to predict the vortex-induced vibrations response of free spans under pipe-soil interaction boundary. The response frequencies were resolved from a eigenvalue problems of free spans with some certain added mass. And response amplitude could be received from a iteration process, which based on energy balance. After response frequency and hydrodynamic coefficients, were determined by use of above linear response model. This result is then used in a time domain model that can handle non-linear boundary conditions at the span shoulders. The results demonstrate that non-linear effects can be significant, in particular for pipe stress in the span shoulder. The significance of the new method is that displacements, and hence also stresses, in the pipe at the shoulders will be far better described by the non-linear method than what is possible from linear theory.
(4) And a time domain analysis method for non-linear pipe-seabed-interaction analysis of free spanning pipelines under VIV conditions has been developed. The flow is modeled by a van-der-Pol wake oscillator developed by Facchinetti et al. And the stall parameter is taken into account in the general form of the VIV amplitude and the response frequency, which can successful model the VIV response amplitude comparing with a constant. After the free spanning pipeline discrtized into the finite elements, the average acceleration method is chosen to integrate the equations of motion. Three types of pipe-seabed-interaction (linear spring, perfectly plastic nonlinear spring, and tension cut-off nonlinear spring) are considered. The results show that the presented time domain method can capture the non-linear interaction between the pipeline and the seabed at the free span shoulders. And the maximum response amplitude of nonlinear case is lower than the one with linear spring. Hence, the response will be underestimated at low current velocity, or overestimated at high current velocity.
(5) When the eigen-frequencies are close, several potential vibration modes of multi-spans can become active at a given low flow velocity, i.e. multi-mode vortex induced vibration. Considered for statistical distributions of current speed and VIV response of free spans in long-term operating condition, in the study, a fatigue assessment method for multi-spans was developed. It can provide a reference on the initial design of free spanning pipeline. At last, the fatigue damage due to multi-mode vortex induced vibration was investigated. It is to assume that the stress ranges are narrow-banded and Rayleigh-distributed, and a 3-parameter Weibull distribution is appropriate for modeling of the long-term statistics for the current velocity. The results based on the Response Model in DNV rules were shown that soil stiffness is sensitive. For reduction coefficient of multi-mode response, it is more conservative to use the DNV RP-105 than the weight of response amplitude. If the structure vibrates in a purely sinusoidal fashion with constant amplitude, then the calculation based on the Rayleigh distribution overestimates the damage rate.
In conclusion, from both the numerical and the experimental empirical models, the research in this thesis sets out from the VIV of a two dimensional circular cylinder supported by linear or nonlinear spring, ends up with the prediction of VIV of slender pipelines under more complicated pipe-soil interaction boundary. Many experience and findings will be helpful for the future work. It can provide a reference on the initial design of free spanning pipeline.
引文
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