Nonlinear wave effect on the slow drift motion of a floating body

The slow drift motion of a floating body in a two-dimensional wave field has been investigated using a time-domain, fully nonlinear numerical model with non-reflective open boundaries. Preliminary computations were conducted for incident bichromatic waves, in which wave theories with different orders were applied in generating the waves required. The results show that the use of low-order theories generates undesirable free waves, and that fourth-order terms contribute markedly to low-frequency input. The motion of a rectangular floating body in response to nonlinear bichromatic waves was computed. The numerical results for small-amplitude incident waves agree reasonably well with the second-order approximation for both the steady and difference-frequency (Δσ) components in the body's motion. For relatively large waves, however, the 2Δσ component becomes predominant compared with the Δσ component. The motion of the body in irregular waves with different wave parameters has also been presented in order to discuss the validity range of a second-order approximation.     

On the use of the capability polar plots program for dynamic positioning systems for marine vessels

As the capability of polar plots becomes better understood, improved dynamic positioning (DP) systems are possible since the control algorithms greatly depend on the accuracy of the aerodynamic and hydrodynamic models. The measurements and estimation of the environmental disturbances have an important role in the optimal design and selection of a DP system for a marine vessel. The main objective of this work is to present a new software program capable of estimating the environmental forces, thrusters capability calculations, and capability polar plots for marine vessels. A flowchart illustrating the logic and data flow of a developed software program, the Capability Polar Plot Program (CPPP), and the estimated results for two case studies for a scientific drilling vessel and a survey vessel are presented. It is obvious from the obtained results that the developed program has a future potential for the estimation of the Capability Polar Plots for marine vessels. Moreover, the developed software program would be considered as a marine tool for the thrusters' selection and their configuration for marine vessels and floating production units for the Oil and Gas industries.     

Feedback control system for blow-out preventer positioning

During the drilling of ultra-deep-water subsea petroleum wells, a blow-out preventer (BOP), a piece of safety equipment, must be assembled on the wellhead. The BOP is suspended using the drilling riser during the wellhead approach operation, and the riser's top end is connected to the floating platform rig. This article presents a feedback control system for the automatic approach of the BOP to the wellhead. Compared to state-of-the-art controls, ours does not require ancillary thrusters installed alongside the riser nor inclination sensors atop of the drilling riser. Additionally, our proposed control embeds a closed-loop dynamic positioning system, thus retaining the characteristics of the original control system and adding an extra closed-loop. This eases implementation of the BOP approach control to an existing platform. To calculate the optimal gains for the BOP controller, we assume a linear system for the riser, including only the pendulum-shape. The simulation is carried out using nonlinear models for both riser and floating platform. We assume an International Towing Tank Conference standard semi-submersible platform, coupled with a 3000-m free-hanging vertical riser for the time-domain simulation. The results show the BOP tracking to be a step-shaped input signal under current and wave loads. A discussion of the performance of feedback control under different environmental loads is also included.     

畸形波作用下张力腿浮式风力机动力响应特性

针对张力腿系泊浮式风力机的基础运动,忽略柔性构件的影响,建立气动—水动—系泊非线性耦合运动方程。在运动控制方程中包含张力腿系泊系统的非线性回复刚度,桨距角控制以及浮式基础运动对空气动力载荷的影响。在波浪载荷的计算中考虑二阶波浪载荷的作用。采用随机频率相位角调制法生成畸形波波面时历,计算在畸形波作用下张力腿型浮式风力机的动力响应特性。数值模拟结果表明,在畸形波作用下,浮式基础的运动及空气动力性能均受到了显著的影响。其中浮式基础的纵荡和纵摇运动分别受二阶差频与和频波浪力的影响,而垂荡运动的增加则主要是受下沉运动的影响。在畸形波经过的时刻,风力机的功率系数迅速下降,水平方向的风载荷波动先减小,随后其数值急剧下降,而垂直方向的风载荷波动增大。     

Hull/mooring/riser coupled dynamic analysis and sensitivity study of a tanker-based FPSO

A computer program is developed for hull/mooring/riser coupled dynamic analysis of a tanker-based turret-moored FPSO (Floating Production Storage and Offloading) in waves, winds, and currents. In this computer program, the floating body is modeled as a rigid body with six degrees of freedom. The first- and second-order wave forces, added mass, and radiation damping at various yaw angles are calculated from the second-order diffraction/radiation panel program WAMIT. The wind and current forces for various yaw angles of FPSO are modeled following the empirical method suggested by OCIMF (Oil Company International Marine Forum).

The mooring/riser dynamics are modeled using a rod theory and finite element method (FEM), with the governing equations described in a generalized coordinate system. The dynamics of hull, mooring lines, and risers are solved simultaneously at each time step in a combined matrix for the specified connection condition. For illustration, semi-taut chain-steel wire-chain mooring lines and steel catenary risers are employed and their effects on global FPSO hull motions are investigated. To better understand the physics related to the motion characteristics of a turret-moored FPSO, the role of various hydrodynamic contributions is analyzed and assessed including the effects of hull and mooring/riser viscous damping, second-order difference-frequency wave-force quadratic transfer functions, and yaw-angle dependent wave forces and hydrodynamic coefficients. To see the effects of hull and mooring/riser coupling and mooring/riser damping more clearly, the case with no drag forces on those slender members is also investigated. The numerical results are compared with MARIN's wave basin experiments.     

Incorporating irregular nonlinear waves in coupled simulation and reliability studies of offshore wind turbines

Design of an offshore wind turbine requires estimation of loads on its rotor, tower and supporting structure. These loads are obtained by time-domain simulations of the coupled aero-servo-hydro-elastic model of the wind turbine. Accuracy of predicted loads depends on assumptions made in the simulation models employed, both for the turbine and for the input wind and wave conditions. Currently, waves are simulated using a linear irregular wave theory that is not appropriate for nonlinear waves, which are even more pronounced in shallow water depths where wind farms are typically sited. The present study investigates the use of irregular nonlinear (second-order) waves for estimating loads on the support structure (monopile) of an offshore wind turbine. We present the theory for the irregular nonlinear model and incorporate it in the commonly used wind turbine simulation software, FAST, which had been developed by National Renewable Energy Laboratory (NREL), but which had the modeling capability only for irregular linear waves. We use an efficient algorithm for computation of nonlinear wave elevation and kinematics, so that a large number of time-domain simulations, which are required for prediction of long-term loads using statistical extrapolation, can easily be performed. To illustrate the influence of the alternative wave models, we compute loads at the base of the monopile of the NREL 5MW baseline wind turbine model using linear and nonlinear irregular wave models. We show that for a given environmental condition (i.e., the mean wind speed and the significant wave height), extreme loads are larger when computed using the nonlinear wave model. We finally compute long-term loads, which are required for a design load case according to the International Electrotechnical Commission guidelines, using the inverse first-order reliability method. We discuss a convergence criteria that may be used to predict accurate 20-year loads and discuss wind versus wave dominance in the load prediction. We show that 20-year long-term loads can be significantly higher when the nonlinear wave model is used.     

Difference-frequency wave loads on a large body in multi-directional waves

The second-order difference-frequency wave forces on a large three-dimensional body in multi-directional waves are computed by the boundary integral equation method and the so-called FML formulation (assisting radiation potential method). Semi-analytic solutions for a bottom-mounted vertical circular cylinder are also developed to validate the numerical method. Difference-frequency wave loads on a bottom-mounted vertical cylinder and stationary four legs of the ISSC tension-leg platform (TLP) are presented for various combinations of incident wave frequencies and headings. These force quadratic transfer functions (QTF) can directly be used in studying slowly varying wave loads in irregular short-crested seas described by a particular directional spectrum. From our numerical results, it is seen that the slowly varying wave loads are in general very sensitive to the directional spreading function of the sea, and therefore wave directionality needs to be taken into account in relevant ocean engineering applications. It is also pointed out that the uni-directionality of the sea is not necessarily a conservative assumption when the second-order effects are concerned.     

Dynamic Analysis of Semi-Submersible Production Platform Under the Failure of Mooring Lines

This paper quantitatively studies the transient dynamic response of a semi-submersible production platform with the loss of one or several positioning mooring lines.A semi-submersible platform,production risers,and positioning mooring lines are all included in the numerical simulation.Increased motion of the semi-submersible platform,tension variation of the remaining mooring lines/risers and the risk of mooring line or riser clashing are all investigated through fully coupled time-domain analysis.Combined environmental loads are selected from irregular waves and the steady current varying from very rough to extreme sea conditions.Three dimension radiation/diffraction theories and Morison’s equation are applied to calculate first-order wave force and second-order mean drift force of floating semi-submersible platform.Nonlinear time-domain finite element methods are employed to analyze the behavior of mooring lines and risers.Results show that the failure of mooring lines seriously reduce the platform’s stability performance.The tension of the rest lines is also increased accordingly.Remaining lines which are closer to the failed lines will have larger tension increase to compensate.Line-Line distance provides practical information for the risk of clashing investigation.     

码头-缆绳-动力定位船舶耦合系统的时频特性分析

为研究系泊状态下动力定位船舶与码头及缆绳间的耦合作用,采取凝集质量法计算系泊缆索有效张力,设置弹簧阻尼单元用以计算码头碰垫间的非线性反力,应用比例-积分-微分控制系统(PID)进行推力控制。在系泊状态下,以动力定位船舶和无动力定位船舶为研究对象,分析了耦合系统中侧推器对消除因一阶波浪载荷而引起的船舶运动影响的作用;针对动力定位船舶,讨论了码头-缆绳及目标位置两个因素对动力定位船舶的定位能力及侧推器性能的影响。结果表明,在选取合理目标位置的情况下,耦合系统中的侧推器性能及动力定位船舶的定位能力均得到了有效提高。     

Predicting the capability-polar-plots for dynamic positioning systems for offshore platforms using artificial neural networks

As the capability of polar plots becomes better understood, improved dynamic positioning (DP) systems are possible as the control algorithms greatly depend on the accuracy of the aerodynamic and hydrodynamic models. The measurements and estimation of the environmental disturbances have an important role in the optimal design and selection of a DP system for offshore platforms. The main objective of this work is to present a new method of predicting the Capability-Polar-Plots for offshore platforms using the combination of the artificial neural networks (NNs) and the capability polar plots program (CPPP). The estimated results from a case study for a scientific drilling vessel are presented. A trained artificial NN is designed in this work and is able to predict the maximum wind speed at which the DP thrusters are able to maintain the offshore platform in a station-keeping mode in the field site. This prediction for the maximum wind speed will be a helpful tool for DP operators in managing station-keeping for offshore platforms in an emergency situation where the automation of the DP systems is disabled. It is obvious from the obtained results that the developed technique has potential for the estimation of the capability-polar-plots for offshore platforms. This tool would be suitable for DP operators to predict the maximum wind speed and direction in a very short period of time.     

超大型和大型半潜浮式海上风力机动力响应对比

以超大型风力机(DTU 10 MW)为研究对象,对现有的大型(NREL 5 MW)无撑杆半潜浮式风力机支撑平台进行放大设计,用于支撑超大型风力机,基于气动-水动-伺服-弹性全耦合计算模型,根据设定的典型工况,使用FAST软件对超大型和大型无撑杆的半潜浮式风力机系统进行时域耦合分析,并依据计算结果对超大型和大型浮式风力机系统的运动响应和结构动力反应等特性进行对比分析。研究发现:半潜浮式风力机大型化后,气动荷载效应对风力机系统的激励作用更为突出,使得浮式平台运动由风荷载激励的低频共振反应比例增大,波频运动比例减小,这也导致由浮式平台低频运动激励的锚链张力反应增大。此外,高倍的飞轮转动频率对大型半潜浮式风力机叶片、塔架结构的激励作用较超大型半潜浮式风力机更为显著。     

A novel decomposition of the quadratic transfer function (QTF) for the time-domain simulation of non-linear wave forces on floating bodies

In the present study, a novel method is proposed for the separation of the second-order sum- and difference-frequency wave forces—that is, quadratic transfer functions (QTFs)—on a floating body into three components due to wave–wave, wave–motion, and motion–motion action. By applying the new QTF components, the second-order wave forces on a floating body can be strictly computed in the time domain. In this work, the boundary value problems (BVPs) corresponding to the three kinds of QTF components were derived, and non-homogeneous boundary conditions on the free surface and the body surface were obtained. The second-order diffraction potentials were determined using the boundary integral equation method. In the solution procedure, the highly oscillatory and slowly converging integral on the free surface was evaluated in an accurate and effective manner. Furthermore, the application of the QTF components in the time domain was demonstrated. The second-order exciting forces in the time domain were divided into three parts. Each part of these forces was computed via a two-term Volterra series model based on the incident waves, the first-order motion response, and the QTF components. This method was applied to several numerical examples. The results demonstrated that this decomposition yields satisfactory results.     

A hybrid time/frequency domain approach for efficient coupled analysis of vessel/mooring/riser dynamics

The dynamic analysis of a deepwater floating structure is complex due to dynamic coupling between the platform and the moorings/risers. Furthermore, the system response at the incident wave frequency and at the resonant low frequency is coupled due to geometric and hydrodynamic nonlinearities. As such, it is generally held that a fully coupled time-domain analysis should be used for an accurate prediction of the dynamic response. However, in a recent work, it is found that for an ultra-deepwater floating system, a fully coupled frequency-domain analysis can provide highly accurate response predictions. One reason is the accuracy of the drag linearization procedure over the motions at two time scales, another is the minimal geometric nonlinearity of the moorings/risers in deepwater. In this paper, the frequency-domain approach is investigated for intermediate water depths, and it is found that the accuracy reduces substantially as geometric nonlinearity becomes important. Therefore, a novel hybrid approach is developed, in which the low-frequency motion is simulated in the time domain while the wave frequency motion is solved in the frequency domain at regular intervals. Coupling between the two analyses is effected by the fact that (i) the low-frequency motion affects the line geometry for the wave frequency motion, and (ii) the wave frequency motion affects the modeling of the drag forces, which damp the low-frequency motion. The method is found to be nearly as accurate as fully coupled time domain analysis even for a system with a preponderance of nonlinear and coupling effects, but requiring only one-tenth of the computational effort.     

Analysis of the extreme wave elevation due to second-order diffraction around a vertical cylinder

Statistical analysis of nonlinear random waves is important in coastal and ocean engineering. One approach for modeling nonlinear waves is second-order random wave theory, which involves sum- and difference-frequency interactions between wave components. The probability distribution of the non-Gaussian surface elevation can be solved using a technique developed by Kac and Siegert [21]. The wave field can be significantly modified by wave diffraction due to a structure, and the nonlinear diffracted wave elevation can be of interest in certain applications, such as the airgap prediction for an offshore structure. This paper investigates the wave statistics due to second-order diffraction, motivated by the scarcity of prior research. The crossing rate approach is used to evaluate the extreme wave elevation over a specified duration. The application is a bottom-supported cylindrical structure, for which semi-analytical solutions for the second-order transfer functions are available. A new efficient statistical method is developed to allow the distribution of the diffracted wave elevation to be obtained exactly, accounting for the statistical dependency between the linear, sum-frequency and difference-frequency components. Moreover, refinements are proposed to improve the efficiency for computing the free surface integral. The case study yields insights into the problem. In particular, the second-order nonlinearity is found to significantly amplify the extreme wave elevation, especially in the upstream region; conversely, the extreme elevation at an oblique location downstream is attenuated due to sheltering effects. The statistical dependency between the linear and sum-frequency components is also shown to be important for the extreme wave statistics.     

Fatigue damage induced by nonGaussian bimodal wave loading in mooring lines

Catenary mooring lines are typically subjected to bimodal loads, comprising of a wave frequency (WF) component due to the first-order wave forces and a low frequency (LF) component induced by the second-order wave forces. For moored vessels, the LF forces due to current and wind also play a role. Only dynamic wave loads are considered herein, while current and wind loads are modeled as constant forces. Because of the nonlinearities of the mooring line characteristics, the dynamic line tension and the second-order responses, both the WF and LF line tensions are in principle nonGaussian. These facts make it difficult to estimate the combined fatigue damage of mooring lines in the frequency domain. A fatigue combination rule based on the Jiao and Moan’s theory has been extended to cover the nonGaussian case. The purpose of this paper is to improve and validate the frequency-domain method by time-domain analysis based on a simplified, but accurate mechanical model of the dynamic line tension. Improvements on the LF and combined fatigue damage estimation have been made by considering the nonsymmetrical property of the LF line tension distribution. Both the WF and LF mooring line tensions due to wave loading have been simulated in the time domain for different sea states and the combined fatigue damage has been estimated by using the rainflow cycle counting algorithm. The accuracy of the frequency-domain method for estimating the bimodal nonGaussian fatigue damage of mooring lines has been verified by the time-domain simulations and is considered to be acceptable.     

The effects of LNG-tank sloshing on the global motions of LNG carriers

The coupling and interactions between ship motion and inner-tank sloshing are investigated by a time-domain simulation scheme. For the time-domain simulation, the hydrodynamic coefficients and wave forces are obtained by a potential-thoery-based three-dimensional (3D) diffraction/radiation panel program in frequency domain. Then, the corresponding simulations of motions in time domain are carried out using convolution integral. The liquid sloshing in a tank is simulated in time domain by a Navier–Stokes solver. A finite difference method with SURF scheme is applied for the direct simulation of liquid sloshing. The computed sloshing force and moment are then applied as external excitations to the ship motion. The calculated ship motion is in turn inputted as the excitation for liquid sloshing, which is repeated for the ensuing time steps. For comparison, we independently developed a coupling scheme in the frequency domain using a sloshing code based on the linear potential theory. The hydrodynamic coefficients of the inner tanks are also obtained by a 3D panel program. The developed schemes are applied to a barge-type FPSO hull equipped with two partially filled tanks. The time-domain simulation results show similar trend when compared with MARIN's experimental results. The most pronounced coupling effects are the shift or split of peak-motion frequencies. It is also found that the pattern of coupling effects between vessel motion and liquid sloshing appreciably changes with filling level. The independent frequency-domain coupled analysis also shows the observed phenomena.     

Coupled dynamic analysis for wave interaction with a truss spar and its mooring line/riser system in time domain

A full time-domain analysis program is developed for the coupled dynamic analysis of offshore structures. For the hydrodynamic loads, a time domain second order method is developed. In this approach, Taylor series expansions are applied to the body surface and free-surface boundary conditions, and the Stokes perturbation procedure is then used to establish the corresponding boundary value problems with time-independent boundaries. A higher-order boundary element method (HOBEM) is developed to calculate the velocity potential of the resulting flow field at each time step. The free-surface boundary condition is satisfied to the second order by fourth order Adams–Bashforth–Moultn method. An artificial damping layer is adopted on the free surface to avoid the wave reflection. The mooring-line/tendon/riser dynamics are based on the rod theory and the finite element method (FEM), with the governing equations described in a global coordinate system. In the coupled dynamic analysis, the motion equation for the hull and dynamic equations for mooring-lines/tendons/risers are solved simultaneously using the Newmark method. The coupled analysis program is applied for a truss Spar motion response simulation. Numerical results including motions and tensions at the top of mooring-lines/risers are presented, and some significant conclusions are derived.     

Extreme wave run-up and pressure on a vertical seawall

The performance of coastal vertical seawalls in extreme weather events is studied numerically, aiming to provide guidance in designing and reassessing coastal structures with vertical wall. The extreme wave run-up and the pressure on the vertical seawall are investigated extensively. A time-domain higher-order boundary element method (HOBEM) is coupled with a mixed Eulerian-Lagrangian technique as a time marching technique. Focused wave groups are generated by a piston wave-maker in the numerical wave tank using a wave focusing technique for accurately reproducing extreme sea states. An acceleration-potential scheme is used to calculate the transient wave loads. Comparisons with experimental data show that the extended numerical model is able to accurately predict extreme wave run-ups and pressures on a vertical seawall. The effects of the wave spectrum bandwidth, the wall position and the wave nonlinearity on the wave run-up and the maximum wave load on the vertical seawall are investigated by doing parametric studies.     

波浪与带窄缝方箱作用共振现象的数值模拟

By introducing a source term into the Laplace equation, a two-dimensional fully nonlinear time-domain numerical wave flume (NWF) is developed to investigate the resonance induced by the interaction bet...