A nonlinear viscoelastic bend stiffener steady-state formulation

Bend stiffeners are essential components of a flexible riser system, employed to ensure a smooth transition at the upper connection and to protect the riser against over bending and from accumulation of fatigue damage. The highly nonlinear rate dependent behavior of these structures directly affects the integrity assessment of the riser in one of its most critical regions, the top connection. A steady-state formulation (disregarding inertial forces) and numerical solution procedure is developed in this work employing the perturbation method for a nonlinear viscoelastic bend stiffener large deflection beam model subjected to harmonic loading conditions. For stochastic loading conditions, the response is calculated employing the superposition principle by summing up the steady-state result of a number of individual frequency components. A time domain formulation is also derived employing the state-variable approach for the numerical solution of the resulting hereditary integral in the governing equations. A case study is presented for the top connection system of a 4″ ID flexible riser using relaxation and tensile experimental data obtained from a typical class of bend stiffener polyurethane. Harmonic and stochastic input loading conditions are employed for time and frequency domain model comparison/validation and to assess loading history and frequency influence in the curvature response.     

Random dynamic response of a tethered buoyant platform production riser

A new normal mode spectral analysis method is presented for calculating r.m.s. riser deflections, bending stresses and lower ball joint angles. Forces on the riser consist of: (a) non-linear fluid drag taking account of the relative velocity due to tethered buoyant platform (TBP) motion, riser elastic deflection and wave induced fluid velocity, (b) wave induced fluid acceleration, (c) inertia forces due to TBP acceleration, and (d) buoyancy. The non-linear fluid drag forces are linearized using Tung and Wu's approximation based on the r.m.s. relative fluid velocity and current. A wide range of results is presented for risers in water depths up to 1000 m and it is observed that 6 normal modes are sufficient for calculating bending stresses. A static analysis is also presented for bending stresses due to wave and current induced drag forces and riser offset.     

考虑内流的海洋立管动力特性和动力响应的实验研究

本文考虑管内流体和管外流体的共同作用,对海洋立管进行试验研究。试验在中国海洋大学物理海洋试验室进行,通过试验得到了立管的一些有价值的规律:随着外流流速逐渐增大,立管的一阶激振频率也逐渐增大,在一定的外流速下,会激起立管的二阶激振频率甚至于三阶激振频率,由于立管的刚度较大,内流对立管的影响并不明显。但是当外流达到一定流速,这种影响就会显现出来,内流的存在会降低海洋立管的振动频率。     

Dynamic Characteristics of Marine Risers Conveying Fluid

The lateral vibration differential equation for a marine riser conveying fluid is derived by useof the small deflection theory.and the effect of internal flow velocity and top tension on the natural fre-quency of the riser is studied by use of FEM.At the same time,the preliminary relationship between thenatural frequency and riser span under different internal flow velocities is obtained,the effect of riser sup-ports on the vibration frequency is computed.It is found that the natural frequency of the marine riser in-creases with the increase of top tension.however decreases with the increase of internal flow velocity.In ad-dition,the frequency decreases drastically with the increase of riser span.     

深海悬链线立管涡激疲劳损伤研究

讨论海洋平台钢质悬链线式立管SCR(Steel Catenary Riser)的涡激疲劳损伤问题。对于悬链线立管外的流体,给出涡脱落频率和升力对立管作用的计算方法。悬链线立管采用索结构模型,进行动力学分析并利用模态叠加法对其进行动力响应分析。根据Palmgren-Miner线性累积损伤准则并结合S-N曲线,分析在不同流速下立管的涡激疲劳损伤。以工程中实际使用的1 500 m Spar海洋平台悬链线立管为例,对立管的涡激疲劳损伤进行了预报。并通过立管的参数研究,分别就立管外不同来流速度、立管壁厚、内部流体密度和柔性接头刚度对其疲劳损伤的影响进行了分析,得到了一些有意义的研究结果。     

An updated Lagrangian finite element formulation for large displacement dynamic analysis of three-dimensional flexible riser structures

An updated Lagrangian finite element formulation of a three-dimensional annular section beam element is presented for large displacement and large rotation dynamic analyses of flexible riser structures. In this formulation a new linearization method is used to avoid inaccuracies normally associated with other linearization schemes. The effects of buoyancy force as well as steady state current loading are considered in the finite element solution for riser structures response. The formulation has been implemented in a nonlinear finite element code and the results are compared with those obtained from other schemes reported in the literature.     

Effect of upward internal flow on dynamics of riser model subject to shear current

Numerical study about vortex-induced vibration(VIV) related to a flexible riser model in consideration of internal flow progressing inside has been performed.The main objective of this work is to investigate the coupled fluid-structure interaction(FSI) taking place between tensioned riser model,external shear current and upward-progressing internal flow(from ocean bottom to surface).A CAE technology behind the current research which combines structural software with the CFD technology has been proposed.According to the result from dynamic analysis,it has been found that the existence of upward-progressing internal flow does play an important role in determining the vibration mode(/dominant frequency),vibration intensity and the magnitude of instantaneous vibration amplitude,when the velocity ratio of internal flow against external current is relatively high.As a rule,the larger the velocity of internal flow is,the more it contributes to the dynamic vibration response of the flexible riser model.In addition,multi-modal vibration phenomenon has been widely observed,for asymmetric curvature along the riser span emerges in the case of external shear current being imposed.     

Filtering inertia-gravity waves from the initial conditions of the linear shallow water equations

A method for filtering inertia-gravity waves from elevation and depth-averaged velocity is described. This filtering scheme is derived from the linear shallow water equations for constant depth and constant Coriolis frequency. The filtered solution is obtained by retaining only the eigenvectors corresponding to the geostrophic equilibrium and by discarding explicitly the eigenvectors corresponding to the fast moving inertia-gravity waves. An alternative formulation is derived using a variational approach. Both filtering methods are tested numerically for a periodic domain with constant depth and the variational approach is implemented for a closed domain with large topographic variations. The filtering methods significantly reduce the amplitudes of the inertia-gravity waves while preserving the mean flow. The variational method is compared to the Incremental Analysis Update technique and the benefits of the variational filter are presented.     

Cross-Flow VIV-Induced Fatigue Damage of Deepwater Steel Catenary Riser at Touch-Down Point简

A prediction model of the deepwater steel catenary riser VIV is proposed based on the forced oscillation test data, taking into account the riser-seafloor interaction for the cross-flow VIV-induced fatigue damage at touch-down point （TDP）. The model will give more reasonable simulation of SCR response near TDP than the previous pinned truncation model. In the present model, the hysteretic riser-soil interaction model is simplified as the linear spring and damper to simulate the seafloor, and the damping is obtained according to the dissipative power during one periodic riser-soil interaction. In order to validate the model, the comparison with the field measurement and the results predicted by Shear 7 program of a full-scale steel catenary riser is carried out. The main induced modes, mode frequencies and response amplitude are in a good agreement. Furthermore, the parametric studies are carried out to broaden the understanding of the fatigue damage sensitivity to the upper end in-plane offset and seabed characteristics. In addition, the fatigue stress comparison at TDP between the truncation riser model and the present full riser model shows that the existence of touch-down zones is very important for the fatigue damage assessment of steel catenary riser at TDP.     

海洋立管复模态动力特性分析

考虑阻尼的影响,研究海洋立管的动力特性。通过分析管内流体及管外海洋环境荷载的共同作用,建立海洋立管涡激振动偏微分方程,进而得到立管动力特性方程,用复模态分析法求解动力特性方程得到立管考虑阻尼的自振频率。算例计算表明:考虑阻尼的立管自振频率略小于不考虑阻尼的立管自振频率;立管的自振频率随着内流流速的增加而减小,但内流流速不大时,影响较小;管道长度对立管的自振频率影响较大。     

多频参激—涡激联合作用下顶张力立管分岔分析

复杂海洋环境中,顶张力立管顶部平台受到不同分量叠加的波浪作用,导致其轴向张力与多个频率相关,系统产生多频参激与涡激的联合振动,其动力学行为变得更为复杂,尤其是分岔和混沌等非线性振动特性有待进一步分析。首先,基于欧拉—伯努利梁理论,引入范德波尔尾流振子,建立和推导受多频参激—涡激联合作用下立管的动力学模型及其运动微分方程;接着,利用伽辽金法得到离散后的常微分方程组,采用多尺度法得到系统共振响应的调谐方程;最后,通过数值算例探究系统在多源和多频载荷联合作用下的共振响应。结果表明：对于多频参数激励,其中一个参数激励幅值在立管振动中起主导作用,而另一个会引起分岔的位置、数量和性质发生改变;随质量—阻尼参数增大,系统共振响应幅值整体先增大后减小,各分岔点出现的位置整体先向泄涡频率较大处移动,随后向泄涡频率较小处移动;质量—阻尼参数的变化还可能诱使系统发生倍周期分岔和混沌现象,危害结构安全。此外,采用直接数值积分求解微分方程组,验证近似分析结果,两者吻合较好。     

Experimental Investigation on Vortex-Induced Vibration of Deep-Sea Risers of Different Excitation Water Depths

The vortex-induced vibration test of the deep-sea riser was carried out with different excitation water depths in the wave-current combined water flume.By dimensionally changing the multi-stage water depth and hydrodynamic parameters such as outflow velocity at various water depths,the dynamic response parameters such as dominant frequency,dimensionless displacement and vibration trajectory evolution process of the riser under different excitation water depths were explored to reveal the sensitive characteristics of the dynamic response of vortexinduced vibration of the risers under different excitation water depths.The results show that different excitation water depths will change the additional mass of the riser and the fluid damping and other parameters,which will affect the spatial correlation and stability of the vortex shedding behind the riser.In the lock-in region,the distribution range of the characteristic frequency becomes narrow and centered on the lock-in frequency.The increase of the excitation water depth gradually advances the starting point of the lock-in region of the riser,and at the same time promotes the excitation of the higher-order vibration frequency of the riser structure.Within the dimensionless excitation water depth,the dominant frequency and dimensionless displacement are highly insensitive to the excitation water depth at high flow velocity.The change of the excitation water depth will interfere with the correlation of the non-linear coupling of the riser.The“8-shaped”gradually becomes irregular,and the vibration trajectories of the riser show“O-shape”,“X-shape”and“Crescent-shape”.     

Numerical Investigation on Severe Slugging in A Catenary Riser

A mathematical model is presented to study the main characteristics of severe slugging in a downward inclined pipeline followed by a catenary riser. In this model, both simplified transient model and phase distribution model are included so that the flow characteristics of each stage for severe slugging can be accurately reproduced, especially for blowout stage. The results show that the flow features of severe slugging can be simulated by the proposed mathematical model. A good agreement between the experimental data and the numerical results is observed. The model can predict the transient fluctuation of many respects, such as the superficial gas velocity at the bottom of the riser and the average velocity at the outlet of the riser.     

Experimental and Computational Investigations on Severe Slugging in A Catenary Riser

Severe slugging can occur in a pipeline-riser system at relatively low liquid and gas flow rates during gas-oil transportation, possibly causing unexpected damage to the production facilities. Experiments with air and water are conducted in a horizontal and downward inclined pipeline followed by a catenary riser in order to investigate the mechanism and characteristics of severe slugging. A theoretical model is introduced to compare with the experiments. The results show that the formation mechanism of severe slugging in a catenary riser is different from that in a vertical riser due to the riser geometry and five flow patterns are obtained and analyzed. A gas-liquid mixture slug stage is observed at the beginning of one cycle of severe slugging, which is seldom noticed in previous studies. Based on both experiments and computations, the time period and variation of pressure amplitude of severe slugging are found closely related to the superficial gas velocity, implying that the gas velocity significantly influences the flow patterns in our experiments. Moreover, good agreements between the experimental data and the numerical results are shown in the stability curve and flow regime map, which can be a possible reference for design in an offshore oil-production system.     

海洋环境荷载下输液立管的静、动力特性研究

考虑管内流动流体和管外海洋环境荷载共同作用 ,建立海洋立管侧向运动微分方程。用Hermite插值函数离散 ,在微机上编写海洋立管静、动力分析程序 ,通过计算分析研究管内流体对立管侧向变形和应力的作用 ;另外 ,探讨管内流体的流动速度和立管顶端的预张力对立管动力特性的影响。结果表明 ,立管变形和应力均随管内流体流动速度增加而增大 ,同时内流速度的增大会降低立管的固有频率 ,但适当增大立管顶端预张力会抵消内流流速增加引起的固有频率下降。     

Experimental Investigation of Vibration Response of A Free-Hanging Flexible Riser Induced by Internal Gas-Liquid Slug Flow

The vibration response of a free-hanging flexible riser induced by internal gas-liquid slug flow was studied experimentally in a small-diameter tube model based on Froude number criterion. The flow regime in a curved riser model and the response displacements of the riser were simultaneously recorded by high speed cameras. The gas superficial velocity ranges from 0.1 m/s to 0.6 m/s while the liquid superficial velocity from 0.06 m/s to 0.3 m/s. Severe slugging type 3, unstable oscillation flow and relatively stable slug flow were observed in the considered flow rates. Severe slugging type 3 characterized by premature gas penetration occurs at relatively low flow rates. Both the cycle time and slug length become shorter as the gas flow rate increases. The pressure at the riser base undergoes a longer period and larger amplitude of fluctuation as compared with the other two flow regimes. Additionally, severe slugging leads to the most vigorous in-plane vibration. However, the responses in the vertical and horizontal directions are not synchronized. The vertical vibration is dominated by the second mode while the horizontal vibration is dominated by the first mode. Similar to the vortex-induced vibration, three branches are identified as initial branch, build-up branch and descending branch for the response versus the mixture velocity of gas-liquid flow.     

指数剪切流作用下海洋立管振动特性研究

细长海洋立管在复杂来流作用下的涡激振动（VIV）是海洋工程领域备受关注的热点问题。采用双向流—固耦合方法,对立管在指数剪切来流作用下的涡激振动实施了数值仿真研究。基于均方根振幅包络图的显性模态分析发现,与线性剪切流工况相比,当流速较小时,立管模型在指数剪切流作用下振幅最大值相对较小;流速较大时,指数剪切流的非线性分布致使立管的振动响应增强。通过对立管模型均方根振幅包络峰、谷处的振动响应频率分析发现,在波峰位置处振动频率单一且较为稳定,而在相邻波谷位置处多频共存现象显著,两者有显著差异。沿管的轴向波形主要表现为驻波主导和驻波—行波混合模式,行波一般间歇发生,流速越大发生频次愈高,其在横流向的传播方向通常由高流速区段传递至低流速区段。指数剪切流作用下,沿管体轴向各截面位置处的旋涡脱落模式差异显著,高流速段尾流区的旋涡发放具有较强的周期性,涡管完整且与管轴存在一定偏离角度,低流速段蜂窝状离散涡旋较多。     

Numerical Simulation of the Vortex-Induced Vibration of A Curved Flexible Riser in Shear Flow

A series of fully three-dimensional(3 D) numerical simulations of flow past a free-to-oscillate curved flexible riser in shear flow were conducted at Reynolds number of 185–1015. The numerical results obtained by the two-way fluid–structure interaction(FSI) simulations are in good agreement with the experimental results reported in the earlier study. It is further found that the frequency transition is out of phase not only in the inline(IL) and crossflow(CF) directions but also along the span direction. The mode competition leads to the non-zero nodes of the rootmean-square(RMS) amplitude and the relatively chaotic trajectories. The fluid–structure interaction is to some extent reflected by the transverse velocity of the ambient fluid, which reaches the maximum value when the riser reaches the equilibrium position. Moreover, the local maximum transverse velocities occur at the peak CF amplitudes, and the values are relatively large when the vibration is in the resonance regions. The 3 D vortex columns are shed nearly parallel to the axis of the curved flexible riser. As the local Reynolds number increases from 0 at the bottom of the riser to the maximum value at the top, the wake undergoes a transition from a two-dimensional structure to a 3 D one. More irregular small-scale vortices appeared at the wake region of the riser, undergoing large amplitude responses.     

Dynamic Response Study of Steel Catenary Riser Based on Slender Rod Model

A numerical model of the steel catenary riser(SCR) is built based on the slender rod model. The slender rod model,which describes the behavior of the slender riser in terms of the center line position, can solve the geometrical nonlinearity effectively. In a marine environment, the SCR is under the combined internal flow and external loads,such as wave and current. A general analysis considers only the inertial force and the drag force caused by the wave and current. However, the internal flow has an effect on the SCR; it is essential to explore the dynamic response of the SCR with the internal flow. The SCR also suffers the lift force and the fluctuating drag force because of the current. Finite element method is utilized to solve the motion equations. The effects of the internal flow, wave and current on the dynamic response of the SCR are considered. The results indicate that the increase of the internal flow density leads to the decrease of the displacement of the SCR, while the internal flow velocity has little effect on the SCR. The displacement of the SCR increases with the increase of the wave height and period. And the increasing wave period results in an increase in the vibration period of the SCR. The current velocity changes the displacements of the SCR in x-and z-directions. The vibration frequency of the SCR in y-direction increases with the increase of the current velocity.     

A finite difference approximation for dynamic calculation of vertical free hanging slender risers in re-entry application

The dynamic calculations of slender marine risers, such as Finite Element Method (FEM) or Modal Expansion Solution Method (MESM), are mainly for the slender structures with their both ends hinged to the surface and bottom. However, for the re-entry operation, risers held by vessels are in vertical free hanging state, so the displacement and velocity of lower joint would not be zero. For the model of free hanging flexible marine risers, the paper proposed a Finite Difference Approximation (FDA) method for its dynamic calculation. The riser is divided into a reasonable number of rigid discrete segments. And the dynamic model is established based on simple Euler-Bernoulli Beam Theory concerning tension, shear forces and bending moments at each node along the cylindrical structures, which is extendible for different boundary conditions. The governing equations with specific boundary conditions for riser’s free hanging state are simplified by Keller-box method and solved with Newton iteration algorithm for a stable dynamic solution. The calculation starts when the riser is vertical and still in calm water, and its behavior is obtained along time responding to the lateral forward motion at the top. The dynamic behavior in response to the lateral parametric excitation at the top is also proposed and discussed in this paper.