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.     

Investigation of motions of catamarans in regular waves—II

By extending the linear frequency domain theory, a quasi-non-linear time-domain technique has been developed to investigate the large amplitude motions of catamarans in regular waves. The non-linearity of hydrodynamic forces included in this practical method comes from variations of a ship's submerged portion. These forces are obtained from a database generated by the linear frequency domain method at each time step. The coupled equations, heave and pitch, are solved in the time domain by using the Runge-Kutta method with proper initial values. In order to investigate the non-linear effects of large amplitude motions of the V-1 catamaran in the head-sea condition, numerical results obtained from the linear and non-linear strip methods have been compared with those obtained from a series of experiments carried out in the towing tank of the Hydrodynamics Laboratory at the University of Glasgow. Based on the comparative studies, the numerical results obtained from the time-domain program can provide better predictions for the large amplitude motions of catamarans than the linear frequency domain method. It is concluded that the non-linear effects are significant when the model speeds and wave amplitudes increase. The peak values of large amplitude motions around the resonance frequencies, as obtained from the non-linear time-domain predictions as well as from measurements, are smaller than those obtained from the linear theory.     

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.     

Direct time domain analysis of floating structures with linear and nonlinear mooring stiffness in a 3D numerical wave tank

In this paper, motion response of a moored floating structure interacting with a large amplitude and steep incident wave field is studied using a coupled time domain solution scheme. Solution of the hydrodynamic boundary value problem is achieved using a three-dimensional numerical wave tank (3D NWT) approach based upon a form of Mixed-Eulerian–Lagrangian (MEL) scheme. In the developed method, nonlinearity arising due to incident wave as well as nonlinear hydrostatics is completely captured while the hydrodynamic interactions of radiation and diffraction are determined at every time step based on certain simplifying approximations. Mooring lines are modelled as linear as well as nonlinear springs. The horizontal tension for each individual mooring line is obtained from the nonlinear load-excursion plot of the lines computed using catenary theory, from which the linear and nonlinear line stiffness are determined. Motions of three realistic floating structures with different mooring systems are analyzed considering various combinations of linear and approximate nonlinear hydrodynamic load computations and linear/nonlinear mooring line stiffness. Results are discussed to bring out the influence and need for consideration of nonlinearities in the hydrodynamics and hydrostatics as well as the nonlinear modelling of the line stiffness.     

Regular waves onto a truncated circular column: A comparison of experiments and simulations

Accurate prediction of hydrodynamic forces on offshore structures is critical for safe and cost effective design of fixed and floating offshore structures exposed to a harsh environment. In the present paper, nonlinear interactions between regular waves and a single surface-piercing truncated circular column have been investigated using a frequency domain potential flow solver (DIFFRACT) and a full CFD solver in OpenFOAM for direct comparisons. Both the predicted free surface elevation around the column and the total force acting on the column have been analysed and compared with experimental data from MOERI. The degree of non-linearity and the contribution of each harmonic to the free surface run-up and wave forces have been examined, and evaluations of the accuracy and computational efficiency of the potential flow solver and the full CFD solver are provided and compared in the paper. Also of note are the local forms of the scattered waves around the column in numerical simulations, which are consistent with the Type-1 and Type-2 patterns identified in physical experiments at Imperial College.     

垂荡板对半潜式风机基础拖航过程中水动力性能及运动响应的影响分析

垂荡板对半潜式风机基础水动力性能有极大的影响,从而影响基础拖航安装过程的安全。为了研究垂荡板对半潜式基础拖航过程中运动响应的影响,建立了拖缆—WindFloat浮式风机半潜式基础拖航系统模型。首先,基于三维势流理论,采用AQWA开展了拖航系统的频域水动力分析,分析了垂荡板的尺寸及形状对基础水动力性能的影响规律;进一步采用时域方法对拖航系统的运动响应进行分析,探究了垂荡板的尺寸及形状在不同浪向下对基础运动响应的影响规律。结果表明：垂荡板能有效抑制基础的垂荡RAO,但垂荡板形状对基础的水动力性能无明显影响;具有圆形垂荡板的半潜式基础在拖航过程中的运动性能略优于六边形垂荡板,在原设计基础上继续增大垂荡板尺寸对基础运动响应的抑制效果呈现先增大后减小的趋势,说明半潜式风机基础存在一个最优的垂荡板尺寸。     

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.     

Time-domain simulation of wave–structure interaction based on multi-transmitting formula coupled with damping zone method for radiation boundary condition

Based on the Rankine source, this paper proposed a time-domain method for analyzing the three-dimensional wave–structure interaction problem in irregular wave. A stable integral form of the free-surface boundary condition (IFBC) is employed to update the velocity potential on the free surface. A multi-transmitting formula, with an artificial wave speed, is used to eliminate the wave reflection for radiation condition on the artificial boundary. An effective multi-transmitting formula, coupled with damping zone method, is further used to analyze the irregular wave diffraction at the artificial boundary. We investigate hydrodynamic forces on floating structure and compare our solution to the frequency-domain solution. It is shown that long time simulation can be done with high stability and the numerical results agree well with the solution obtained under the frequency domain. The efficiency of the proposed multi-transmitting formula and the coupled methods for radiation boundary make them promising candidates in studying the irregular water wave problem in time domain.     

新型浮式基础的海上风机系统动力响应研究

概念性地设计了一种新型半潜—Spar混合浮式基础,以5 MW水平轴风机为例,研究了该新型浮式基础支撑的浮式风力机系统的动力响应。基于三维势流理论和Morison公式,应用SESAM软件建立浮式基础模型,在频域内计算了该浮式基础的水动力参数和响应算子,分析了浮式基础的运动性能。考虑叶片气动载荷和浮式基础波浪载荷,应用FAST软件对风机—浮式基础系统进行时域计算,分析风力机系统的运动性能。结果显示,该浮式基础运动幅值较小,具有良好的运动性能。     

半潜式平台运动及系泊系统特性研究

针对深海半潜式平台及其系泊系统的水动力特性,运用时域耦合的分析方法,对一座水深为1 000 m的半潜式平台,及其悬链线式系泊系统的水动力性能进行探索,获得频域和时域响应结果。同时阐述了平台系泊系统的设计流程,并通过系泊系统参数的变化,研究其特性寻找影响系泊系统作用的一般规律,为平台及其系泊系统设计提供参考。     

海上风机稳桩施工平台吊装过程中的多船水动力干扰特性与动力响应分析

建立双臂起重船从运输船上起吊大型稳桩施工平台的吊装系统模型,其中,起重船与运输船呈T型布置。首先基于势流理论,采用专业水动力分析软件AQWA开展了双船系统的频域水动力分析,分析双船起吊系统的水动力干扰特性和遮蔽效应,并对双船间隙自由液面进行黏性修正从而提高频域多体水动力分析的精度。进一步采用频域—时域方法对起吊耦合系统进行参数分析,探究起吊速度、波浪周期等对吊索张力和起重船运动的影响规律。分析多个工况下运输船的遮蔽效应对起吊系统的影响。结果表明,对间隙流体施加阻尼自由液面边界条件可以一定程度提高计算模型的精度,在某些周期的迎浪条件下运输船对起重船的遮蔽效应可以降低吊装系统的响应;起吊速度对时域动力响应的影响较小;周期为8 s的规则波引起过大的动力响应。     

Hydrodynamic interactions between two ships advancing in waves

In this paper the hydrodynamic problems between two moving ships in waves are analyzed using a three-dimensional potential-flow theory based on the source distribution technique. The potential is presented by a distribution of source over the ship hull. The corresponding Green functions and their derivatives can be easily solved numerically by using the series expansions of Telste and Noblesse's algorithm for the Cauchy principal value integral of unsteady flow. The numerical solution is evaluated by applying the present method to two pairs of models and compared with experimental data and strip theory. From the comparisons, it shows that the hydrodynamic interactions are generally important. In the resonance region, the hydrodynamic interaction calculated by the 3D method is more reasonable, which is not so significant as that by the 2D method. The technique developed here may serve as a more rigorous tool to analyze the related problems of two ships doing underway replenishment in waves.     

Numerical and Experimental Study on Hydrodynamic Performance of A Novel Semi-Submersible Concept

The Multiple Column Platform (MCP) semi-submersible is a newly proposed concept, which differs from the conventional semi-submersibles, featuring centre column and middle pontoon. It is paramount to ensure its structural reliability and safe operation at sea, and a rigorous investigation is conducted to examine the hydrodynamic and structural performance for the novel structure concept. In this paper, the numerical and experimental studies on the hydrodynamic performance of MCP are performed. Numerical simulations are conducted in both the frequency and time domains based on 3D potential theory. The numerical models are validated by experimental measurements obtained from extensive sets of model tests under both regular wave and irregular wave conditions. Moreover, a comparative study on MCP and two conventional semi-submersibles are carried out using numerical simulation. Specifically, the hydrodynamic characteristics, including hydrodynamic coefficients, natural periods and motion response amplitude operators (RAOs), mooring line tension are fully examined. The present study proves the feasibility of the novel MCP and demonstrates the potential possibility of optimization in the future study.     

Hydrodynamic interactions between two vertical circular cylinders in linear oscillatory flow

Linear potential theory is used to investigate the hydrodynamic interactions between two vertical cylinders in harmonic flow. The behaviour of the added mass and damping is studied for various cylinder diameters, lengths of immersion and spacing between the cylinders. In practice, the results have relevance to the fluid loading on offshore structural members, such as risers and platform legs, and pipeline bundles. On a more theoretical level, comparisons are possible between the results of a three-dimensional diffraction program and various asymptotic expressions to establish the range of validity of the latter and the need, where appropriate, of the former.     

Nonlinear response of membranes to ocean waves using boundary and finite elements

The behavior of a highly deformable membrane to ocean waves was studied by coupling a nonlinear boundary element model of the fluid domain to a nonlinear finite element model of the membrane. The hydrodynamic loadings induced by water waves are computed assuming large body hydrodynamics and ideal fluid flow and then solving the transient diffraction/radiation problem. Either linear waves or finite amplitude waves can be assumed in the model and thus the nonlinear kinematic and dynamic free surface boundary conditions are solved iteratively. The nonlinear nature of the boundary condition requires a time domain solution. To implicitly include time in the governing field equation, Volterra's method was used. The approach is the same as the typical boundary element method for a fluid domain where the governing field equation is the starting point. The difference is that in Volterra's method the time derivative of the governing field equation becomes the starting point.The boundary element model was then coupled through an iterative process to a finite element model of membrane structures. The coupled model predicts the nonlinear interaction of nonlinear water waves with highly deformable bodies. To verify the coupled model a large scale test was conducted in the OH Hinsdale wave Research Laboratory at Oregon State University on a 3-ft-diameter fabric cylinder submerged in the wave tank. The model data verified the numerical prediction of the structure displacements and of the changes in the wave field.The boundary element model is an ideal modeling technique for modeling the fluid domain when the governing field equations is the Laplace equation. In this case the nonlinear boundary element model was coupled with a finite element model of membrane structures, but the model could have been coupled with other finite element models of more rigid structures, such as a pontoon floating breakwater.     

基于能量竞争载荷模型的海洋立管双向涡激振动时域预报方法研究

海洋立管是深海油气开发中用于连接海底井口和水面浮体的唯一通道。立管在洋流作用下极易发生涡激振动（vortex-induced vibration,简称VIV）,发展快速经验性涡激振动时域预报方法对立管的安全设计具有重要意义。通过柔性立管模型试验,结合载荷重构方法和最小二乘法,识别建立了能量竞争载荷模型下的经验水动力载荷系数模型。应用识别建立的经验水动力载荷系数模型,发展形成了海洋立管顺流向及横流向双向涡激振动时域预报方法。将预报结果与试验结果对比,结果表明：基于能量竞争载荷模型的海洋立管双向涡激振动预报方法能够有效预报海洋立管涡激振动主导模态、主导频率、流向平均位移响应和涡激振动位移响应等力学行为特性。研究成果对发展更为有效的涡激振动预报手段具有有益参考。     

Extending a time/frequency domain hybrid method for riser fatigue analysis

Fully coupled time domain analysis of a floating system is rigorous but time-consuming, thus an efficient hybrid method was developed in a prior work. The method simulates the coupled slow-drift responses in the time domain and analyzes the wave-frequency dynamics in the frequency domain. The hybrid method was shown to compare well with time domain analysis in predicting the mean-square vessel motions and line tensions. In this paper, the hybrid method is extended for the fatigue analysis of moorings and risers. The fatigue damage thus calculated is found to closely agree with the result from time domain analysis in conjunction with rainflow counting. Several spectral fatigue techniques are also compared, and these methods are significantly less accurate, thus attesting to the complexity of the problem.     

Coupled dynamic analysis of deep-sea mining support vessel with dynamic positioning

Deep-sea mining (DSM) is an advanced concept. A simulation method of coupled vessel/riser/body system in DSM combined with dynamic positioning (DP) is proposed. Based on the three-dimensional potential flow theory, lumped mass method, and Morison’s equations the dynamic models of the production support vessel, riser and slurry pump are established. A proportion integration differentiation (PID) controller with a nonlinear observer and a thrust allocation unit are used to simulate the DP system. Coupled time domain simulation is implemented with the vessel operated in two DP modes. Results of the vessel and pump motions, riser tension, and thruster forces are obtained. It shows that the pump will be lifted by the riser when the vessel is chasing the next set point. Riser tension is influenced by the wave frequency motions of the vessel in positioning mode and low-frequency motions in tracking mode. The proposed simulation scheme is practical to study the DSM operation.     

The hydrodynamics of thin floating plates

The radiation and diffraction problems are considered in the frequency domain for a thin elastic plate of rectangular planform floating in an irrotational, incompressible ocean of infinite depth. The inner potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion which suits the geometry and zero-draft nature of the plate. Problems associated with distributing sources in the free surface are avoided. The Chen and Mei variational principle is used to weakly match this inner solution and its normal derivative to an outer field described by distributing sources on the exterior of the hemisphere. The validity of the procedure is first illustrated by considering a heaving circular disk. Numerous hydrodynamic coefficients are presented as benchmark data for floating flexible structures. The transient motion of the plate is simulated using rational approximations (in the frequency domain) to the radiation impedance and diffraction mapping which are implemented as ODE's in the time domain.