Towards a model of hydrodynamic damping for a circular cylinder with helical strakes at low KC

This paper investigates the hydrodynamic damping of a circular cylinder with helical strakes at Keulegan-Carpenter (KC) number from 0.07 to 3 in the presence of steady currents. Experiments were performed with a straked cylinder oscillating in either in-line or cross currents over Reynolds number (based on the oscillating velocity amplitude) varying from 1260 to 54,000. With in-line current being present, the measured drag coefficients of the straked cylinder are found to depend on the ratio between the oscillating velocity amplitude and the steady current velocity. This phenomenon is further confirmed by computational fluid dynamics using large-eddy simulations. The drag coefficients obtained from the numerical simulations agree well with the experimentally determined values. Similar phenomenon is observed for the cases with cross background current. Based on the experimental data, empirical formulae are proposed to evaluate drag coefficients. These results are of importance in estimating the resonant motion and the fatigue life of risers, e.g. water intake risers, in the flow regime of low KC. Finally, recommendations are provided for fatigue analysis of risers with helical strakes from the perspective of engineering practice.     

Application of analytical model in the prediction of dynamic responses and fatigue damage of flexible risers: Part II – Dynamic analysis of flexible risers in large-scale domain using a direct moment correction method

In recent years, the dynamic responses of flexible risers have been the focus of many researchers. Most flexible risers undergo a substantial level of irregular motion from environmental loadings, which involves a continuous slip of helical wires. The slip of helical wires especially leads to a hysteretic effect by reducing the bending stiffness, making it hard to predict the dynamic responses of flexible risers. The current study, as an extension to Part I, presents a new large-scale dynamic analysis method for flexible risers. The suggested method creates a large-scale model for the dynamic analysis that considers a geometric and bending nonlinearity of flexible risers. The kinematics of each beam element is formulated based on a Green-Lagrangian strain and the interaction with the seabed, providing a realistic analysis of flexible risers. In particular, the current study introduces a direct moment correction method that modifies the internal force vector using an improved analytical model. The improved analytical model is assigned at each node of the large-scale model and estimates an accurate bending hysteresis curve considering the effect of shear deformation and varying tension. The suggested method corrects the bending moment and shear force of all beam elements based on the bending hysteresis curves obtained from the improved analytical model, by which a complex bending behavior of flexible risers is reflected in a large-scale domain. As a result, this study achieves a more accurate prediction of the dynamic responses and fatigue damage of flexible risers. A new dynamic analysis program, called OPFLEX, is developed herein based on the suggested analysis method. Using the developed program, the current study conducts several numerical investigations to identify the effect of the shear deformation and varying tension. Consequently, it is confirmed that the shear deformation of internal layers reduces the fatigue damage of helical wires by delaying the increase of internal stress. It is also identified that the effect of varying tension deteriorates the fatigue life of flexible risers through a continuous change of contact pressure during bending.     

深水钻井立管建模与角度安全控制

从水面钻井平台与水下立管联合作业的安全角度出发,提出一种将钻井立管的力学响应限制特性引入水面平台动力定位闭环控制中的位置保持方法,实现水面钻井平台（或船舶）基于立管角度响应的动态定位。利用有限元方法建立包括立管系统质量、系统刚度、结构阻尼和水动力载荷在内的立管运动控制模型。联合水面浮体和水下立管的低频运动特性建立水面浮体运动偏移与水下立管顶端角度及末端角度的相对运动关系模型。在此基础上,设计基于立管运行响应的动力定位控位方法,实现对立管顶端角度及末端角度的安全控制。仿真结果表明,所提出的方法可行,在外界突变的环境载荷瞬时作用于水面浮体时,能更快地跟踪新的期望最优位置,保证钻井立管运行在安全界限内。     

深海系泊浮体物面非线性时域耦合动力分析

文章基于三维时域势流理论和弹性细长杆理论,研究并提出了深海系泊浮体物面非线性时域耦合动力分析方法。该方法采用时域物面非线性理论方法在瞬态位置直接时域模拟系泊浮体所需水动力,结合有限元方法计算系泊缆索的动力响应,利用异步耦合方法实现浮体和系泊缆索的时域耦合动力求解。既满足系泊浮体时域水动力耦合,又满足系泊浮体和系泊缆索动力耦合。通过对二阶非线性不规则波作用下深海系泊半潜式平台的时域耦合响应特性进行研究,将不同海况下物面非线性时域耦合静力响应和动力响应与间接时域耦合动力响应的三种方法计算结果进行比较。研究结果表明,系泊缆索动力响应明显,平台瞬态空间位置对垂荡低频运动影响较大,有必要在平台瞬时湿表面采用动力响应方法进行深海系泊浮体时域耦合响应分析。     

Improving longitudinal motion prediction of hybrid monohulls with the viscous effect

A new method improves prediction of the motion of a hybrid monohull in regular waves. Stem section hydrodynamic coefficients of a hybrid monohull with harmonic oscillation were computed using the Reynolds Averaged Navier-Stokes Equations (RANSE). The governing equations were solved using the finite volume method. The VOF method was used for free surface treatment, and RNGК-ε turbulence model was employed in viscous flow calculation. The whole computational domain was divided into many blocks each with structured grids, and the dynamic process was treated with moving grids. Using a 2-D strip method and 2.5D theory with the correction hydrodynamic coefficients allows consideration of the viscous effect when predicting longitudinal motion of a hybrid monohull in regular waves. The method is effective at predicting motion of a hybrid monohull, showing that the viscous effect on a semi-submerged body cannot be ignored.     

一种新型延展式张力腿平台及其水动力性能

文章提出了一种由四个立柱和一个环形浮箱（四个方型截面梁组成）组成的新型延展式张力腿平台。与传统延展式张力腿平台相比,新型延展式张力腿平台有更少的组块和组块间焊缝,因此它的建造成本更低、建造周期更短。新型延展式张力腿平台将延展式结构改进为浮箱的一部分,这就解决了传统平台的延展式结构与浮箱连接处焊缝疲劳损伤问题。文中对结构进行了水动力性能分析以证明其动态响应可靠性。基于三维势流理论对新型平台进行频域内的数值模拟,得到了新型平台的附加质量和势流阻尼。考虑新型平台和张力筋腱系统的耦合作用,分析了新型平台在风、浪、流联合作用下的非线性动态响应。时域分析得到了新型平台在时域内的位移响应。水动力分析结果证明了新型延展式张力腿平台有可靠的水动力性能,并且满足在南海环境条件下的安全要求。     

桁架式Spar平台与系泊/立管系统的全时域非线性耦合动态分析

开发了对浮式平台系统进行耦合动态分析的全时域程序。采用二阶时域方法计算水动力荷载,在此方法中,对物面边界条件和自由水面边界条件进行泰勒级数展开,利用Stokes摄动展开分别建立相应的一阶、二阶边值问题,而且此边值问题的计算域不随时间变化。采用高阶边界元方法计算每一时刻流场中的速度势,利用四阶预报校正法对二阶自由水面边界条件进行数值积分。在自由表面加入一个人工阻尼层来避免波浪的反射。对于系泊缆索/立管/张力腿的动力分析,在一个总体坐标系中对控制方程进行描述,采用基于细长杆理论的有限元方法进行求解。在耦合动态分析中,采用Newmark方法对平台和系泊缆索/立管/张力腿的运动方程同时进行求解。利用开发的耦合分析程序对一个桁架式Spar平台的运动响应进行了数值模拟,给出了平台的位移和系泊缆索/立管上端点的张力,并得到了一些重要结论。     

Vortex-induced vibrations of piggyback pipelines near the horizontal plane wall in the upper transition regime

Slender subsea structures like pipelines, jumpers and umbilicals when exposed to currents may experience vortex-induced vibrations (VIV), which can shorten their fatigue life and increase the risk of structural failure. In the present study, flow around different configurations of a piggyback pipeline close to a flat seabed has been investigated using the two-dimensional (2D) Unsteady Reynolds-Averaged Navier Stokes (URANS) equations with the k − ω Shear Stress Transport (SST) turbulence model. The Reynolds number (based on the free stream velocity and large cylinder diameter) is equal 3.6 × 10⁶ corresponding to upper-transition regime. The drag forces acting on the cylinders and base pressure coefficient value are well predicted by the present simulations, while the other hydrodynamic quantities (root-mean-square lift coefficient, Strouhal number) are predicted reasonably well as compared to published experimental data. The piggyback pipeline in the present study is modeled as two circular cylinders with a diameter ratio d/D = 0.2 (D denoting diameter of the large cylinder, d is diameter of the small cylinder). These two cylinders are clamped together at a distance G/D = 0.2. The two rigidly coupled cylinders are elastically supported and free to vibrate in two degrees of freedom. The effects on the vibration amplitudes and hydrodynamic forces are analyzed. The flow structures around the cylinders are investigated to explain the variations in observed structural responses. Depending on the angular position (α) of the small cylinder, the lock-in regime is narrower (α = 0°) or significantly wider (α = 180°) when compared to that of a single cylinder.     

Hydrodynamic damping of a circular cylinder at low KC: Experiments and an associated model

This paper investigates the hydrodynamic damping of a smooth circular cylinder undergoing forced oscillations at Keulegan-Carpenter (KC) numbers smaller than 5 and Reynolds (Re) numbers from 10³–10⁵ with and without background steady currents. A series of experiments are conducted with a circular cylinder oscillating in still water, in-line currents and cross currents. The measured drag coefficients of the smooth cylinder in the still water condition match with the well-published results and the theoretical solution of Stokes and Wang at very small KC numbers. The hydrodynamic damping increases with the in-line steady current whereas it remains almost constant at small transverse velocities and increases notably when the latter becomes large. To predict the hydrodynamic damping in in-line steady currents, the performance of the Morison equation based on relative velocity and independent velocity is explored, respectively. The latter model, by separating the drag into two independent parts, leads to a better fit of the drag force than the former, which is not surprising. However, the former is still a preferable option for engineering design due to its simplicity. The experimental data suggest that the existing design guidelines such as ISO-19902 or DNVGL-RP-C205 should be used with caution for KC < 5.     

带舭龙骨柱体的横摇阻尼的粘性流计算

文章用RANSE求解器计算在自由面上带舭龙骨二维柱体的横摇水动力系数(附加惯量和阻尼).采用有限体积法(VOF)和两相流技术在时间域内求解柱体横摇强迫振荡所扰动的带自由面粘性流场.由柱体所受到的横摇水动力矩的时间历程导出横摇水动力系数.文中所给算例与已公开发表的试验结果吻合令人满意.     

超深水钻井隔水管动力分析理论研究与数值模拟

随着钻井作业向深水(500～1 500m)和超深水(1 500m以上)发展,在交变海洋环境载荷波浪力、海流力和浮式钻井平台运动的共同作用下,隔水管的动态响应更加显著.文中探讨了隔水管侧向振动的数学模型、动态特性分析中的结构与环境载荷建模技术及其非线性动力分析方法,研究并对比了不同分析方法在计算效率、计算精度和工程适用性等方面的差异.介绍了时域内应用ABAQUS软件进行超深水钻井隔水管非确定性动力分析的算法与详细流程,算例比较了不同边界条件对深水钻井隔水管动态特性的影响.研究表明,时域非确定性分析最为精确但需要时间最长,且只能采用线性AIRY波浪理论;理论上,海流主要引起隔水管动态响应的时不变部分,但该时不变部分不等同于海流引起的隔水管静态响应,一种简化方法只将海浪与钻井船运动作为动载荷而不考虑海流对动态响应的贡献;钻井船运动和波浪载荷是隔水管动态响应分析主要的动载荷,对于超深水隔水管来说,钻井船运动是首要的动载荷,其慢漂运动对隔水管性能有重要影响,而波浪仅对隔水管局部产生作用.     

Fatigue damage from time domain simulation of combined in-line and cross-flow vortex-induced vibrations

A semi-empirical method for time domain simulation of vortex-induced vibrations (VIV) is used to calculate the in-line and cross-flow fatigue damage of a tensioned riser in uniform and sheared flow. Simulations are run for flow velocities ranging from 0.3 m/s to 2.4 m/s, and a detailed comparison with experimental observations is performed. Results are reported in terms of dominating frequency, mode of vibration and mean of r.m.s. of displacement, as well as fatigue damage distribution along the length of the structure and maximum fatigue damage rates for each case. Fatigue damage is calculated by rainflow counting of the strain time series together with an idealized S–N curve with slope m = 3. The results show that the model reproduces the measured fatigue damage with a satisfactory level of realism, using a consistent set of parameters. This indicates that the model is usable for calculation of riser VIV fatigue damage in various current conditions, assuming the Reynolds number is in the subcritical range.     

月池对FDPSO水动力性能的影响分析

采用数值模拟的方法,分析了不同尺寸、位置、吃水的月池对FDPSO船体附加质量和阻尼系数的影响。建立FDPSO三维水动力模型,采用水动力计算软件AQWA,研究了月池在不同尺寸、位置、吃水情况下对FDPSO横荡、垂荡、横摇附加质量和阻尼力的影响。结果表明：月池内流体的“活塞”振荡会增大船体的垂荡运动;FDPSO船体附加质量和阻尼力在频域范围内存在极值,垂向附加质量和阻尼力极值对应的波浪频率位置与月池尺寸、吃水有关,与位置无关。     

Fatigue damage induced by vortex-induced vibrations in oscillatory flow

Vortex-induced vibration (VIV) of a flexible cylinder in oscillatory flow was experimentally investigated in an ocean basin. An intermittent VIV was confirmed to have occurred during the tests. The fatigue damage caused by VIV was calculated based on rainflow counting and a standard S–N curve. There are 3 main observations for fatigue damage from VIV in oscillatory flow: 1) the damage varied significantly with the KC number, which is a unique feature for VIV in oscillatory flow. 2) Fatigue damage at small KC number cases was found to be larger compared to those at large KC numbers owing to the fact that number of vortex shedding cycles per half of the motion cycle is low, and damping within half of the motion cycle will hence become low. The fact that vortices from the previous cycle still are active during the next may also contribute to the large response at small KC numbers. 3) ‘Amplitude modulation’ and ‘mode transition’, two specific features for VIV in oscillatory flow, were found to have a strong influence on fatigue. Fatigue damage has also been calculated by an empirical VIV prediction model assuming that all cases have steady flow at an equivalent velocity. Finally, a simplified method for calculating fatigue damage from VIV in oscillatory flow based on steady flow conditions is proposed. A modification factor diagram is presented, but the scope of the present study is too limited to provide a good basis for a general model for this factor. A general model for how to apply results from constant current analysis to predict fatigue in oscillatory flow will therefore need further research.     

Mathematical modelling of response amplitude operator for roll motion of a floating body: Analysis in frequency domain with numerical validation

This paper investigates mathematical modelling of response amplitude operator （RAO） or transfer function using the frequency-based analysis for uncoupled roll motion of a floating body under the influence of small amplitude regular waves. The hydrodynamic coefficients are computed using strip theory formulation by integrating over the length of the floating body. Considering sinusoidal wave with frequency （ω ） varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed, analytical expressions of RAO in frequency domain is obtained. Using the normalization procedure and frequency based analysis, group based classifications are obtained and accordingly governing equations are formulated for each case. After applying the fourth order Runge-Kutta method numerical solutions are obtained and relative importance of the hydrodynamic coefficients is analyzed. To illustrate the roll amplitude effects numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave with a fixed wave height. The effect of viscous damping on RAO is evaluated and the model is validated using convergence, consistency and stability analysis. This modelling approach could be useful to model floating body dynamics for higher degrees of freedom and to validate the result.     

台风条件下TLP串行立管系统碰撞分析

TLP立管系统以丛式方阵排列,台风条件下立管在波浪、海流及平台的联合作用下可能发生碰撞,有必要深入研究TLP串行立管系统的碰撞情况。文章基于DNV-RP-F203规范和Huse半经验尾流模型,提出台风条件下串行立管下游立管来流速度计算方法和立管系统碰撞分析方法,建立串行立管—井口—导管系统耦合有限元模型,研究台风条件下串行生产立管系统碰撞时的力学特性,在整体碰撞分析的基础上进行立管局部碰撞精细化分析,对比分析立管局部碰撞理论解和仿真解的不同。结果表明:下游立管来流速度的计算至少采用文中建立的方法迭代3次。串行立管发生碰撞时的最大应力发生在泥面导管处,碰撞位置应力发生了突变;立管发生碰撞的位置在水深100-120 m范围内。立管局部碰撞分析的理论解和仿真解基本吻合。     

Effects of roughness on hydrodynamic characteristics of a submerged floating tunnel subject to steady currents

The effects of surface roughness as induced by marine fouling on the hydrodynamic forces on a submerged floating tunnel (SFT) are experimentally and numerically investigated in detail at Reynolds numbers Re = 8.125 × 10³–5.25 × 10⁴. A sensitivity analysis to different roughness parameters including roughness height, skewness, coverage ratio, and spatial arrangement is performed. In addition, an optimized parametric cross-section for an SFT is proposed, and the hydrodynamic performance of the parametric shape and circular SFT cross-section shape with roughness elements is compared. The pressure distribution along the SFT, flow separation and wake characteristics are analyzed to provide a systematic insight into the fundamental mechanism relating the roughness parameters and flow around an SFT. In order to better understand the nonlinear relationships among structural geometry, roughness parameters, flow states, and structural response, an artificial intelligence method using Random Forest (RF) for feature importance ranking is applied. The results show that with the parametric shape, the hydrodynamic forces on the fouled SFT can be effectively mitigated. The roughness height and coverage ratio affect the equivalent blockage and hence, change flow separation and recirculation length in the wake. Lower skewness of the roughness elements can increase the critical Re by changing the relative roughness parameter. Horizontal arrangement of the roughness elements on an SFT generally results in the largest hydrodynamic forces, compared to staggered and vertical distributions. Throughout the feature importance ranking, the flow regime is found to be the most important feature of the hydrodynamics of the SFT. In addition, the SFT cross-section shape and roughness coverage ratio play a dominant role.     

双浮体波浪能装置的振荡和能量转换特性研究（英文）

In this study, we investigated the hydrodynamic and energy conversion performance of a double-float wave energy converter(WEC) based on the linear theory of water waves. The generator power take-off(PTO) system is modeled as a combination of a linear viscous damping and a linear spring. Using the frequency domain method, the optimal damping coefficient of the generator PTO system is derived to achieve the optimal conversion efficiency(capture width ratio).Based on the potential flow theory and the higher-order boundary element method(HOBEM), we constructed a threedimensional model of double-float WEC to study its hydrodynamic performance and response in the time domain. Only the heave motion of the two-body system is considered and a virtual function is introduced to decouple the motions of the floats. The energy conversion character of the double-float WEC is also evaluated. The investigation is carried out over a wide range of incident wave frequency. By analyzing the effects of the incident wave frequency, we derive the PTO's damping coefficient for the double-float WEC's capture width ratio and the relationships between the capture width ratio and the natural frequencies of the lower and upper floats. In addition, it is capable to modify the natural frequencies of the two floats by changing the stiffness coefficients of the PTO and mooring systems. We found that the natural frequencies of the device can directly influence the peak frequency of the capture width, which may provide an important reference for the design of WECs.     

VIV response of a flexible cylinder with varied coverage by buoyancy elements and helical strakes

Many significant engineering challenges have emerged as the petroleum industry has moved their field development and production activities into increasingly deeper water depths. The design of deepwater marine risers presents the combined challenges to minimize top tensioning requirements, mitigate any flow-induced vibrations, and if possible to increase the expected fatigue life of these slender structural members. As part of the design process to achieve these goals external buoyancy modules and strakes have been employed. To gain insight into the complex multi-mode response behavior a recent experimental study was performed and the analysis of selected data sets is presented. In the experiments a horizontal cylinder with a length to diameter ratio of 263 was fitted with a variety of strake and buoyancy element configurations. The models were towed at uniform speeds ranging from 0.4 to 2.0 m/s and fiber optic strain gages were used to measure both in-line and cross-flow strain response. The resulting time series information was processed utilizing the method of time domain decomposition formulated for strain data input and the introduction of modal assurance criterion to resolve the modal strain information that included frequency, mode shape, and critical damping ratio information. The pre-tensioned cylinder without appendages was used as a base case and the results were basically consistent with expectations. In the case of 0.8 m/s low-tension test, multiple closely spaced non-overlapping peaks were observed in both in-line and cross-flow directions and were identified as being of the same mode with mode shapes distorted away from purely sinusoidal behavior. The test data for the 100% coverage by helical stakes demonstrated the effectiveness of that suppression device over the range of current velocities investigated. The most interesting case was that of a staggered combination of helical strakes and buoyancy element whose total for each type of coverage was equal. This effective asymmetric VIV suppression approach is presented and discussed in detail.     

西非海域FPSO多点系泊系统的疲劳寿命分析

文章首先采用三维频域理论分析西非海域FPSO的水动力性能,得到船体各自由度的运动响应,慢漂载荷,附加质量和势流阻尼等;随后,利用分块法将波浪散点图离散为若干个海况,基于准动态方法对多点系泊系统进行分析,得到各海况下船体的漂移和各系泊缆的张力;最后,结合前两步的计算结果,采用T-N曲线,雨流计数和Miner线性累计损伤理论对系泊缆的疲劳寿命进行预报。研究结果表明,各系泊缆的疲劳寿命沿长度方向的分布趋势基本一致,锚链顶端和触底部分的疲劳寿命较短。此外,西非海域的涌浪对系泊缆的疲劳损伤较大,系泊设计时应予以重点关注。