Prediction of hydrodynamic forces on submarine pipelines using an improved Wake II Model

The hydrodynamic force model for prediction of forces on submarine pipelines as described includes flow history effect (wake effects) and time dependence in the force coefficients. The wake velocity correction is derived by using a closed-form solution to the linearized Navier–Stokes equations for oscillatory flow. This is achieved by assuming that the eddy viscosity in the wake is only time dependent and of a harmonic sinusoidal form. The forces predicted by the new Wake (Wake II) Model have been compared to Exxon Production Research Company Wake Model in terms of time histories (force shape) and magnitudes of peak forces. Overall, the model predictions by the Wake II Model are satisfactory and represent a substantial improvement over the predictions of the conventional models. The conventional force models representing adaptations of Morison's equation with ambient velocity and constant coefficients give predictions that are in poor agreement with the measurements especially for the lift force component. The Wake II Force Model can be used for submarine pipeline on-bottom stability design calculations for regular waves with various pipe diameters.     

Prediction of hydrodynamic forces on submarine pipelines using an improved Wake II Model

The hydrodynamic force model for prediction of forces on submarine pipelines as described includes flow history effect (wake effects) and time dependence in the force coefficients. The wake velocity correction is derived by using a closed-form solution to the linearized Navier–Stokes equations for oscillatory flow. This is achieved by assuming that the eddy viscosity in the wake is only time dependent and of a harmonic sinusoidal form. The forces predicted by the new Wake (Wake II) Model have been compared to Exxon Production Research Company Wake Model in terms of time histories (force shape) and magnitudes of peak forces. Overall, the model predictions by the Wake II Model are satisfactory and represent a substantial improvement over the predictions of the conventional models. The conventional force models representing adaptations of Morison's equation with ambient velocity and constant coefficients give predictions that are in poor agreement with the measurements especially for the lift force component. The Wake II Force Model can be used for submarine pipeline on-bottom stability design calculations for regular waves with various pipe diameters.     

Allowable span length of submarine pipeline in shallow water

Because of the complex geological conditions of the seabed, submarine pipelines buried beneath the ocean floor become suspended over the seabed under the long-term scour of waves eroding the surrounding sediment. Further, most oil fields were built in offshore areas while the country was developing. This gives the waves seen in shallow water obvious nonlinear features, and the abnormal characteristics of these waves must be considered when calculating their hydrodynamic forces. Particularly under such conditions, these suspended spans of submarine pipelines are prone to damage caused by the action of the external environment load. Such damages and eventual failures may result not only in great property losses but also pollution of the marine environment. The span length of these areas is a key predictive factor in pipeline damages. Therefore, determining the allowable span length for these submarine pipelines will allow future projects to avoid or prevent damage from excessive suspended span lengths. Expressions of the hydrodynamic loads placed on suspended spans of pipeline were developed in this work based on the first-order approximate cnoidal wave theory and Morison equation. The formula for the allowable free span length was derived for the common forms of free spanning submarine pipeline based on the point where maximum bending stresses remain less than the material’s allowable stress. Finally, the allowable free span length of real-world pipelines was calculated for a subsea pipeline project in Bohai Bay. This research shows that, with consideration for the complicated marine environment, existing suspended spans are within allowable length limitations. However, continuing to limit the length of these submarine pipeline spans in the Nanpu oil field will require ongoing attention.     

Wake II model for hydrodynamic forces on marine pipelines including waves and currents

The Wake II model for the determination of the hydrodynamic forces on marine pipelines is extended to include currents and waves. There are two main differences between the Wake II and the traditional model. First, in the Wake II model the velocity is modified to include the pipe's encounter with the wake flow when the velocity reverses. Second, the model uses time dependent drag and lift coefficients. The flow field is assumed to be the linear superposition of regular waves and uniform current and is treated as wave only but in two different phases. The model requires eight empirical parameters that are obtained from comparisons with field data for various Keulegan–Carpenter numbers and current to wave ratios. The effective velocity and the force predictions are compared with field data from Exxon Production Research Company and with the conventional model. The model gives satisfactory results and predicts lift forces that in shape, magnitude and phase relative to the velocity are in very close agreement with measured forces. For the horizontal forces the results are very accurate. A substantial improvement is obtained over the predictions with the conventional model. This work is applicable to the design of submarine pipelines laying on the sea bottom in water depths where waves or waves and currents contribute to the hydrodynamic forces.     

悬跨海底管道疲劳寿命分析研究

海底管道在服役期间由于各种原因会在某些管段形成悬跨。这些悬跨在海流力作用下，将产生涡激振动。这种涡激振动最终可能导致管道疲劳失效。管道在海流力作用下发生的涡激振动是管道振动和漩涡尾流振动耦合的结果。在建立管道振动模型和Matteoluca尾流振子模型基础上，对管道涡激振动动力响应特性进行分析。依据Miner线性损伤累积理论，采用S—N曲线法分析计算管道疲劳寿命。最后，针对海洋油气开发与生产，提出延长海底管道疲劳寿命的方法和措施。     

Effect of Internal Flow on Vortex-Induced Vibration of Submarine Free Spanning Pipelines

At present, most researches on the vortex-induced vibration of submarine free spanning pipelines ignore the effect of internal flowing fluid; furthermore, there are no research reports considering the coupling effect of internal and external fluid with the free span. In this paper, combining Iwan‘s wake oscillator model with the differential equation derived for the dynamic response of submarine free spanning pipelines with inclusion of internal flow, the pipe-fluid coupling equations are developed to investigate the effect of internal flow on the vortex-induced vibration of the free spans. The finite dement approximation is implemented to derive the matrix equations of equilibrium. The Newmark method combined with simple iteration is used to solve the system of equations. The results indicate that the internal fluid flow may cause the shift of resonance band to the lower frequency and a slight decrease in the peak value; the effect will be mare pronounced with the increase of the span length and can be weakened in the presence of the axial tension.     

考虑阻尼海底悬跨段管道的动力特性及允许悬空长度

以海底悬跨段输液管道为研究对象,考虑管道结构阻尼、流体附加阻尼、管内流体流动及管道轴向力和压强的作用,对其进行受力分析,导出管道振动微分方程,进而得到管道动力特性方程。用Hermit插值函数对管道的动力特性方程进行离散得到有限元表达式,采用复模态分析法,求得管道的自振频率。为防止管道发生横向涡激振动,用约化速度作为控制条件,确定管道允许悬空长度。结果表明,管道允许悬空长度随着内流流速、轴向压力和管内压强的增加而减小,随着轴向拉力的增加而加大。     

Experimental Study on Free Spanning Submarine Pipeline Under Dynamic Excitation

Seismic load has a significant effect on the response of a free spanning submarine pipeline when the pipeline is con-structed in a seismically active region. The model experiment is performed on an underwater shaking tahle to simulate the response of submarine pipelines under dynamic input. In consideration of the effects of the terrestrial and submarine pipeline , water depth, support condition, distance from seabed, empty and full pipeline, and span on dynamic response, 120 groups of experiments are conducted. Affecting factors are analyzed and conclusions are drawn for reference. For the con-trol of dynamic response, the span of a submarine pipeline is by far more important than the other factors. Meanwhile, the rosponse difference between a submarine pipeline under sine excitation and that under random excitation exists in ex-periments.     

Wave forces on submarine pipelines near a plane boundary

Forces induced by regular waves on submarine pipelines resting on as well as near a plane boundary and aligned parallel to wave fronts of the oncoming waves are investigated experimentally. The inline hydrodynamic coefficients of drag and inertia are evaluated through the use of Morison equation and the least squares method. The transverse force is analysed in terms of maximum transverse force and transverse root mean square (r.m.s.) coefficients. The resulting inline and transverse hydrodynamic coefficients are correlated with the period parameter or Keulegan-Carpenter number and relative clearance of the pipeline from the plane boundary. The effect of depth parameter on these coefficients and the correlation between maximum transverse force and transverse r.m.s. coefficients are also reported.     

Hydrodynamic Forces and Instability of Submarine Pipelines Under Waves and Currents： A Review

Stability design of submarine pipelines is a very important procedure in submarine pipeline engineering design. The calculation of hydrodynamic forces caused by waves and currents acting on marine pipelines is an essential step in pipeline design for stability. The hydrodynamic forces-induced instabilities of submarine pipelines should be regarded as a wave/ current-pipeline-seabed interaction problem. This paper presents a review on hydrodynamic forces and stability research of submarine pipelines under waves and currents. The representative progress including the improved design method and guideline has been made for the marine pipelines engineering design through experimental investigations, numerical simulations and analytical models. Finally, further studies on this issue are suggested.     

Experimental Study and System Identification of Hydrodynamic Force Acting on Heave Damping Plate

Although Morison equation is often applied for simulating hydrodynamic force of marine structure, it may give poor results when non-linear behavior is severe or random wave is encountered. This leads to some modifications of Morison equation or other methods for predicting hydrodynamic force. One of them is the system identification technique. In this paper, NARMAX model theory is firstly used to identify the hydrodynamic system of heave damping plates, which are commonly installed on spar platform. Both linear and non-linear models are obtained. The comparisons between the predieted results and measured data indicate that NARMAX model can predict hydrodynamic force of a heave damping plate very well. The measured data for identification originate from forced oscillation tests, which are random records with given spectrum. The forced oscillation forms in experiment also contain simple harmonic, multi-frequency ones.     

Numerical simulation of a partially buried pipeline in a permeable seabed subject to combined oscillatory flow and steady current

Hydrodynamic forces exerting on a pipeline partially buried in a permeable seabed subjected to combined oscillatory flow and steady current are investigated numerically. Two-dimensional Reynolds-Averaged Navier-Stokes equations with a k−ω turbulent model closure are solved to simulate the flow around the pipeline. The Laplace equation is solved to calculate the pore pressure below the seabed with the simulated seabed hydrodynamic pressure as boundary conditions. The numerical model is validated against the experimental data of a fully exposed pipeline resting on a plane boundary under various flow conditions. Then the flow with different embedment depths, steady current ratios and KC numbers is simulated. The amplitude of seepage velocity is much smaller than the amplitude of free stream velocity as expected. The normalized Morison inertia, drag and lift coefficients based on the corresponding force coefficients of a fully exposed pipeline are investigated. The normalized Morison force coefficients reduce almost linearly with the increase of embedment depth and that the KC only has minor effect on the normalized Morison coefficients. It is also found that the permeable seabed condition causes a slight increase on the inline force and has a little effect on the lift force, compared with corresponding conditions in an impermeable bed.     

New model to determine forces at on-bottom slender pipelines

The present paper proposes a numerical model to determine horizontal and vertical components of the hydrodynamic forces on a slender submarine pipeline lying at the sea bed and exposed to non-linear waves plus a current. The new model is an extension of the Wake II type model, originally proposed for sinusoidal waves (Soedigdo et al., 1999) and for combined sinusoidal waves and currents (Sabag et al., 2000), to the case of periodic or random waves, even with a superimposed current. The Wake II type model takes into account the wake effects on the kinematic field and the time variation of drag and lift hydrodynamic coefficients. The proposed extension is based on an evolutional analysis carried out for each half period of the free stream horizontal velocity at the pipeline. An analytical expression of the wake velocity is developed starting from the Navier–Stokes and the boundary layer equations. The time variation of the drag and lift hydrodynamic coefficients is obtained using a Gaussian integration of the start-up function. A reduced scale laboratory investigation in a large wave flume has been conducted in order to calibrate the empirical parameters involved in the proposed model. Different wave and current conditions have been considered and measurements of free stream horizontal velocities and dynamic pressures on a bottom-mounted pipeline have been conducted. The comparison between experimental and numerical hydrodynamic forces shows the accuracy of the new model in evaluating the time variation of peaks and phase shifts of the horizontal and vertical wave and current induced forces.     

Condition Identification Based on Vibration Measurements for Free Spanning Submarine Pipelines

Free spanning pipelines are suspended between two points on an uneven seaffoor. The variations of structural conditions, such as the changes in soil property, flow velocity, axial force and span length etc., directly affect working performance of the whole submarine pipeline system. But until now few researches have focused on condition identification for free span （CIFS）. A method to identify the operational conditions of free spanning submarine pipelines based on vibration measurements is proposed in this paper. Firstly, the ill-posedness of CIFS is analyzed in detail. Secondly, the framework for CIFS based on the nonlinear kernel discriminant analysis （KDA） is established. Thirdly, the internal structural characteristics of natural frequencies, normalized frequencies and frequency change ratios are studied. And then the condition feature vector for CIFS is extracted by use of the vibration measurements. Finally, the validity of the proposed approach is evaluated by a case study. The results demonstrate that the proposed approach can effectively identify each condition of free span when condition variation occurs even if under measurement noise. It is concluded that the proposed method is a promising tool for CIFS in real applications.     

Artificial neural network ability in evaluation of random wave-induced inline force on a vertical cylinder

An approach based on artificial neural network (ANN) is used to develop predictive relations between hydrodynamic inline force on a vertical cylinder and some effective parameters. The data used to calibrate and validate the ANN models are obtained from an experiment. Multilayer feed-forward neural networks that are trained with the back-propagation algorithm are constructed by use of three design parameters (i.e. wave surface height, horizontal and vertical velocities) as network inputs and the ultimate inline force as the only output. A sensitivity analysis is conducted on the ANN models to investigate the generalization ability (robustness) of the developed models, and predictions from the ANN models are compared to those obtained from Morison equation which is usually used to determine inline force as a computational method. With the existing data, it is found that least square method (LSM) gives less error in determining drag and inertia coefficients of Morison equation. With regard to the predicted results agreeing with calculations achieved from Morison equation that used LSM method, neural network has high efficiency considering its convenience, simplicity and promptitude. The outcome of this study can contribute to reducing the errors in predicting hydrodynamic inline force by use of ANN and to improve the reliability of that in comparison with the more practical state of Morison equation. Therefore, this method can be applied to relevant engineering projects with satisfactory results.     

含初始缺陷海底管道侧向屈曲临界力的参数解

未埋设的海底管道在高温高压运行条件下可能发生侧向屈曲,情况严重时影响海底管道的结构安全。侧向屈曲临界力作为判定海底管道发生侧向屈曲的重要依据,主要影响因素有初始缺陷、管土相互作用等。现有关于侧向屈曲临界力的公式并未考虑管土相互作用、缺陷不平直度和管道自身材料特性对侧向屈曲临界力的综合影响。建立含有通用几何初始缺陷海底管道的数值模型,使用Riks算法进行参数分析以研究极限侧向土壤阻力、管道缺陷不平直度和截面几何尺寸对海底管道侧向屈曲的具体影响。基于量纲分析法和多元线性回归,推导出海底管道侧向屈曲临界力关于上述3个影响参数的一般公式,并对该公式进行了检验,结果表明文中推导的公式在参数涵盖的研究范围内有效。     

高雷诺数下近壁圆柱绕流数值模拟与分析

近壁圆柱绕流问题在海底悬跨管道的研究中具有重要的意义。在绕流阻力、升力以及海底土壤的耦合作用下,海底管道所发生的移位、悬跨等现象对于海底管道的安全运行构成了很大的威胁。正确预测各种绕流条件下管流之间的作用力是保证油气管道安全的首要任务。海底管道在极端海洋环境条件下的管、流相互作用为高雷诺数绕流问题,处于高雷诺数下的绕流模拟比处于低雷诺数下的绕流模拟要复杂很多,它需要更精细的网格以及合适的湍流模型。此文对处于悬跨状态下的海底管道进行数值研究,给出不同间隙比下海流绕流海底管道的流场结构形态,分析了间隙比对绕流阻力和绕流升力的影响,为进一步研究海底悬跨管道的受力和变形提供载荷边界数据。     

地震条件下海底双层油气管线的工作理论、强度标准和损伤评价

我国渤海湾是地震多发地区 ,该地区的海底输油管线随时都面临地震的威胁。地震成为渤海输油管线必要的设计条件 ,地震载荷是在役管线安全风险评估必须包括的环境载荷。本文综述了国内外在管线抗震设计及相关研究、双层油气管线的工作理论、强度标准与损伤评判等方面的研究工作 ,对我国制定地震条件下海底管线的评估计算方法、管线的抗震设计准则以及地震灾害的防治与风险分析具有一定的参考价值     

考虑流固耦合时的海底管道悬跨段非线性动力分析

通过对管道的涡激振动试验,提出了考虑流固耦合的非线性涡激升力表达式,并用该式进行了海底管线悬跨段非线性动力响应时程分析。对考虑流固耦合与未考虑流固耦合情况下得到的管道动力响应时程进行对比,算例表明:当管外流场流速与管道顺流向振动速度值较接近时,不考虑流固耦合时的计算结果明显小于考虑流固耦合时的计算结果。分析认为,在管外流场流速与管道顺流向振动速度值较接近的情况下,管道的涡激振动计算宜采用非线性涡激力模型。     

黄河水下三角洲埕岛油田海底管线悬空分析

现代黄河三角洲埕岛油田海底管线的调查发现了许多管线悬空现象。分析表明，悬空主要在3种条件下产生，其中平台周围冲刷坑导致的管线悬空是最主要的。经计算可知，所调查管线的最大允许悬空长度为18．6m，其中有3条管线悬空长度已超过此值，应及时进行治理。