Study on coupling effects of ship motion and sloshing

This study considers the coupling effects of ship motion and sloshing. The linear ship motion is solved using an impulse-response-function (IRF) method, while the nonlinear sloshing flow is simulated using a finite-difference method. The IRF method requires the frequency-domain solution prior to conversion to time domain, but the computational effort is much less than that of direct time-domain approaches. The developed scheme is verified by comparing the motion RAOs between the frequency-domain solution and the solution obtained by the IRF method. Furthermore, a soft-spring concept and linear roll damping are implemented to predict more realistic motions of surge, sway, yaw, and roll. For the simulation of sloshing flow in liquid tanks, a physics-based numerical approach adopted by Kim [2001. Numerical simulation of sloshing flows with impact load. Applied Ocean Research 23, 53–62] and Kim et al. [2004. Numerical study on slosh-induced impact pressures on three-dimensional prismatic tanks. Applied Ocean Research 26, 213–226] is applied. In particular, the present method focuses on the simulation of the global motion of sloshing flow, ignoring some local phenomena. The sloshing-induced forces and moments are added to wave-excitation forces and moments, and then the corresponding body motion is obtained. The developed schemes are applied for two problems: the sway motion of a box-type barge with rectangular tanks and the roll motion of a modified S175 hull with rectangular anti-rolling tank. Motion RAOs are compared with existing results, showing fair agreement. It is found that the nonlinearity of sloshing flow is very important in coupling analysis. Due to the nonlinearity of sloshing flow, ship motion shows a strong sensitivity to wave slope.     

A 3D fully coupled analysis of nonlinear sloshing and ship motion

This study investigates the coupling effects of six degrees of freedom in ship motion with fluid oscillation inside a three-dimensional rectangular container using a novel time domain simulation scheme. During the time marching, the tank-sloshing algorithm is coupled with the vessel-motion algorithm so that the influence of tank sloshing on vessel motions and vice versa can be assessed. Several factors influencing the dynamic behavior of tank–liquid system due to moving ship are also investigated. These factors include container parameters, environmental settings such as the significant wave height, current velocity as well as the direction of wind, wave and flow current acting on the ship. The nonlinear sloshing is studied using a finite element model whereas nonlinear ship motion is simulated using a hybrid marine control system. Computed roll response is compared with the existing results, showing fair agreement. Although the two hull forms and the sea states are not identical, the numerical result shows the same trend of the roll motion when the anti-rolling tanks are considered. Thus, the numerical approach presented in this paper is expected to be very useful and realistic in evaluating the coupling effects of nonlinear sloshing and 6-DOF ship motion.     

Coupled analysis of nonlinear sloshing and ship motions

A coupled numerical model considering nonlinear sloshing flows and the linear ship motions has been developed based on a boundary element method. Hydrodynamic performances of a tank containing internal fluid under regular wave excitations in sway are investigated by the present time-domain simulation model and comparative model tests. The numerical model features well the hydrodynamic performance of a tank and its internal sloshing flows obtained from the experiments. In particular, the numerical simulations of the strong nonlinear sloshing flows at the natural frequency have been validated. The influence of the excitation wave height and wave frequency on ship motions and internal sloshing has been investigated. The magnitude of the internal sloshing increases nonlinearly as the wave excitation increases. It is observed that the asymmetry of the internal sloshing relative to still water surface becomes more pronounced at higher wave excitation. The internal sloshing-induced wave elevation is found to be amplitude-modulated. The frequency of the amplitude modulation envelope is determined by the difference between the incident wave frequency and the natural frequency of the internal sloshing. Furthermore, the coupling mechanism between ship motions and internal sloshing is discussed.     

Application of an improved semi-Lagrangian procedure to fully-nonlinear simulation of sloshing in non-wall-sided tanks

The semi-Lagrangian procedure is widely used for updating the fully-nonlinear free surface in the time domain. However, this procedure is only available to cases when the body surface is vertical near the waterline. Present study introduces an improved semi-Lagrangian procedure which removes this ‘vertical-wall’ limitation. Coupling with the boundary element method, the improved semi-Lagrangian procedure is applied to the simulation of fully-nonlinear sloshing waves in non-wall-sided tanks. From the result comparison with the open source CFD software OpenFOAM, it is confirmed that this numerical scheme could guarantee a sufficient accuracy. Further series studies on 2D and 3D fully-nonlinear sloshing waves in wedged tanks are performed. Featured phenomena are observed which are distinct from those in wall-sided tanks.     

An approximation to energy dissipation in time domain simulation of sloshing waves based on linear potential theory

This paper proposes a new approximation to energy dissipation in time domain simulation of sloshing waves by use of a linear potential theory.The boundary value problem is solved by the NURBS(non-uniform rational B-spline) higher-order panel method,in which a time-domain Green function is employed.The energy dissipation is modeled by changing the boundary condition on solid boundaries.Model experiments are carried out in a partially filled rectangular tank with forced horizontal motion.Sloshing-induced internal pressures and horizontal force obtained numerically and experimentally are compared with each other.It is observed that the present energy dissipation approximation can help produce a fair agreement between experimental forces and those of numerical simulations.     

MPS方法数值模拟液舱晃荡问题

基于无网格粒子法MPS方法(moving particle semi-implicit method)研究了液舱晃荡问题。针对二维矩形液舱晃荡问题进行了数值验证,结果表明MPS方法能够很好地计算晃荡产生的拍击压力。同时将MPS方法应用到带隔板的液舱晃荡问题计算中,分析了二维和三维带隔板液舱晃荡问题。计算结果表明:隔板的存在很大程度地限制了流体的水平运动,隔板附近出现了自由面的翻卷、破碎和融合现象,MPS方法能够很好地模拟这些流动现象。计算得到的波高与实验测得的波高吻合较好,表明MPS方法模拟带隔板的晃荡问题具有一定的可靠性。     

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。     

Boundary element analysis of liquid sloshing characteristics in axisymmetric tanks with various porous baffles

This paper aims to investigate the effects of the porous baffles on the suppression of sloshing for the tanks with axisymmetric geometries under lateral excitation. Based on the assumptions of inviscid, irrotational, incompressible liquid and small amplitude sloshing, an axisymmetric boundary element method (BEM) for 3D Laplace equation is derived by using the Green's theorem together with the weighted residual method. And a zoning method is employed to model fluid domain in the tanks with complex porous baffles. Meanwhile, the porous baffles are treated motioning together with the tanks, and the velocity across the porous baffle is assumed to be linearly proportional to the pressure gradient between each side of the porous baffle. And the mechanism of suppressing the sloshing response is mainly the energy dissipation of the fluid passing through the porous baffle. Moreover, the linear free surface boundary conditions are also used to solve the governing equations. Compared with other numerical methods, the most prominent advantage of the BEM in solving axisymmetric potential problem is that only the boundaries of half the cross-section instead of the entire problem domain should be discretized, which can cut down large amount of memory and time costs. The present method is verified by comparing the numerical results with the existing literatures, and excellent agreements are obtained. Meanwhile, the proposed models are applied to investigate the effects of the porous baffles on sloshing response in circular cylindrical, annular cylindrical and conical tanks. The effects of the porous baffle length, porous-effect parameter, installation angle and baffle height on the sloshing force, natural frequency and surface elevation are studied. Additionally, some typical sloshing pressure distributions, velocity potential contours and velocity fields are plotted. The results show that swirls at the tips of the baffles can be observed in many cases, and the top-mounted porous baffle makes more significant suppression effects on sloshing response than that of bottom-mounted porous baffle, while increasing the number of ring porous baffles can achieve better restraint effects on sloshing response. And increasing the baffle length of the horizontal wall-mounted ring porous baffle can significantly decrease the sloshing frequencies, as well as the first non-dimensional natural frequency decreases with decrease in porous-effect parameter of the coaxial porous baffle. In addition, remarkable effects on sloshing can be obtained when reasonable designed by selecting the optimal porous-effect parameter, installation angle and baffle height. And this paper can be a useful guide for the seismic design and analysis of many actual liquid storage tanks (such as the Advanced Passive PWR, large water cooling tower, etc.).     

Design of passive anti-roll tanks for roll stabilization in the nonlinear range

The best way of reducing roll motion is by increasing roll damping. Bilge keels are the most common devices for increasing roll damping. If more control is required, anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. Our objective is to develop design procedures for passive tanks for roll reduction in rough seas. This paper focuses on the design of passive U-tube tanks. The tank-liquid equation of motion is integrated simultaneously with the six-degree-of-freedom (6DOF) equations of the ship motion. The coupled set of equations is solved by using the Large Amplitude Motion Program ‘LAMP’, which is a three-dimensional time-domain simulation of the motion of ships in waves. The unstabilized and stabilized roll motions of a S60-70 ship with forward speed and beam waves have been analyzed. For high-amplitude waves, the unstabilized roll angle exhibits typical nonlinear phenomena: a shift in the resonance frequency, multi-valued responses, and jumps. The performance of a S60-70 ship with a passive tank is investigated in various sea states with different encounter wave directions. It is found that passive anti-roll tanks tuned in the linear or nonlinear ranges are very effective in reducing the roll motion in the nonlinear range. The effect of the tank damping, frequency, and mass on the tank performance is studied. Also, it is found that passive anti-roll tanks are very effective in reducing the roll motion for ships having a pitch frequency that is nearly twice the roll frequency in sea states 5 and 6.     

Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank

A time-independent finite-difference method and a fifth-order Runge–Kutta–Felhberg scheme were used to analyze the dynamic responses of sea-wave-induced fully non-linear sloshing fluid in a floating tank. The interaction effect between the fully non-linear sloshing fluid and the floating tank associated with coupled surge, heave and pitch motions of the tank are analyzed for the first time in the present pilot study. For the analysis of fluid motion in the tank, the coordinate system is moving (translating and rotating) with tank motion. The time-dependent water surface of the sloshing fluid is transformed to a horizontal plane and the flow field is mapped on to a rectangular region. The Euler equations as well as the fully non-linear kinematic free surface condition were used in the analysis of the sloshing fluid. The strip theory for linearized harmonic sea-wave loading was adopted to evaluate the regular encounter wave force. In addition, the dynamic coefficients used in the dynamic equations of tank motion were also derived based on strip theory and a harmonic motion of the tank. The characteristics of free and forced tank motions with and without the sloshing effect are studied. By the damping effect, the response of free oscillation will damp out and that of forced oscillation will approach a steady state. Without sea-wave action, the contribution of the sloshing load would enlarge the angular response of tank motion as well as the rise of free surface and the sloshing effect will delay the damping effect on angular displacement. On the contrary, under sea-wave action, the sloshing effect will decrease the dynamic response of tank motion and rise of free surface. The interaction, sloshing and coupling effects are found to be significant and should be considered in the analysis and design of floating tanks.     

Motion responses of barge carrying liquid tank

The interaction between the liquid sloshing in a rectangular tank equipped inside the barge and the barge responses has been investigated through a comprehensive experimental program. The barge was subjected to both regular and random wave excitations under beam sea condition. Three relative fill levels (h_s/l) with liquid fill depth (h_s) to length of tank (l) ratio of 0.163, 0.325 and 0.488 were considered. In addition, the barge responses of equivalent dry weight condition corresponding to each fill level were measured to understand the influence of sloshing. While the excitation wave frequency equals to first mode natural sloshing frequency, a noticeable decrease in the sway response has been observed. However, the effect of sloshing oscillation on the heave response is insignificant. A split up of roll resonance was observed for the aspect ratio of 0.163 due to the coupling effect of roll motion and sloshing.     

容器固有频率对液体晃荡的影响

针对矩形容器内液体晃荡问题,采用了时域高阶边界元方法建立自由水面满足完全非线性边界条件的数学模型。求解中采用混合欧拉-拉格朗日方法追踪流体瞬时水面,运用四阶龙格库塔方法更新下一时间步的波面和速度势。通过将计算得到的波面结果与实验数据、解析解和已发表结果对比,吻合良好,验证了本方法的准确性。进而采用谱分析方法分析了波面时间历程,得到容器各阶固有频率对液体晃荡的影响。研究发现,基频对液体晃荡的影响最大,且非线性越强,更高阶容器固有频率的影响越大。     

Hydroelastic analysis of floating structures with liquid tanks and comparison with experimental tests

In this study, we develop a numerical method for a 3D linear hydroelastic analysis of floating structures with liquid tanks subjected to surface regular water waves and compare the numerical results with experimental tests. Considering direct couplings among structural motion, sloshing, and water waves, a mathematical formulation and a numerical method extended from a recent work [1] are developed. The finite element method is employed for the floating structure and internal fluid in tanks, and the boundary element method is used for the external fluid. The resulting formulation completely incorporates all the interaction terms including hydrostatic stiffness and the irregular frequency effect is removed by introducing the extended boundary integral equations. Through various numerical tests, we verify the proposed numerical method. We also performed 3D hydroelastic experimental tests of a floating production unit (FPU) model in an ocean basin. The measured dynamic motions are compared with the numerical results obtained using the proposed method.     

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.     

A time-domain prediction method of ship motions

A time-domain analysis is used to predict wave loading and motion responses for a ship traveling at a constant speed in regular oblique waves. Considered as a distribution of normal velocities on the wetted hull surface, the combined diffraction and radiation perturbations caused by the forward moving ship and her motions are determined simultaneously. This way, the ship-hull boundary condition is exactly fulfilled. The 3-D time domain Green's function is used to express the combined diffraction/radiation potential in terms of impulsive and memory potentials. Application of the Bernoulli equation yields the pressure distribution and accordingly, the necessary hydrodynamic forces. The equations of motion of the ship are then developed and solved in the time domain.Forces and motions at forward speed are predicted for a Wigley ship-hull in head waves and for a catamaran-ferry in oblique waves. Comparison is made with published theoretical and experimental results for the Wigley ship-hull, and the agreement is good. For the catamaran, a self-propelled model is built and tested both in a large towing tank and in a seakeeping basin in order to measure the six-degrees-of-freedom forces, moments and motions at forward speed in regular waves of different directions. For the longitudinal motions, the agreement between measurements and predictions is generally good. For the transverse motions, however, acceptable discrepancy exists. The discrepancy is thought to be mainly due to the exclusion from the analysis of the rudder forces and viscous damping. The inclusion of such nonlinear effects in the time domain simulation involves complex analysis and this problem is left to a future research.     

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.     

Numerical analysis and validation of weakly nonlinear ship motions and structural loads on a modern containership

This paper aims to validate a numerical seakeeping code based on a 3D Rankine panel method by comparing its results with experimental data. Particularly, the motion response and hull-girder loads on a real modern ship, a 6500 TEU containership, are considered in this validation study. The method of solution is a 3D Rankine panel method which adopts B-spline basis function in the time domain. The numerical code is based on the weakly nonlinear scheme which considers nonlinear Froude-Krylov and restoring forces. The main focus of this study is given to investigate the nonlinear characteristics of wave-induced loads, and to validate this present scheme for industrial use in the range of low Froude number. The comparisons show that the nonlinear motions and hull-girder loads, computed by the present numerical code, have good overall agreements with experimental results. It is found that, for the better accuracy of computational results, particularly at extreme waves in oblique seas, the careful treatment of soft-spring (or compatible) system is recommended to the control of non-restoring motions such as surge, sway, and yaw.     

A comparative study of numerical simulations for fluid–structure interaction of liquid-filled tank during ship collision

Although International Maritime Organization (IMO) has taken many measures to minimize ship collisions, ships carrying liquid cargo sometimes do get struck by other vessels. The outflow of crude oil causes very serious consequences to the environment. In such cases it is necessary to analyze the response of structure of struck liquid cargo-filled tank to account for fluid–structure interaction accurately. In this paper, numerical simulation of collision between a container ship with double hull very large crude carrier (VLCC) is presented. Three different numerical simulation mothods were adopted to model fluid–structure interaction in liquid-filled cargo tank, namely arbitrary Lagrangian–Eulerian finite element method, Lagrangian finite element method and linear sloshing model. The numerical simulation results reveal that the fluid–structure interaction of liquid cargo-filled tank has a significant effect on the motion and structural response of the struck cargo tank. Compared with the calculation results of ALE FE method, the linear sloshing model underestimates the influence of fluid–structure interaction of liquid cargo tank while the Lagrangian–Eulerian finite element method may be considered as the practical method for engineering applications as it provided more reasonable results with a relatively low central processing unit (CPU) time.     

Time-Domain Simulation for Coupled Motions of Three Barges Moored Side-by-Side in Floatover Operation

Simulating the coupled motions of multiple bodies in the time domain is a complex problem because of the strong hydrodynamic interactions and coupled effect of various mechanical connectors. In this study, we investigate the hydrodynamic responses of three barges moored side-by-side in a floatover operation in the frequency and time domains. In the frequency domain, the damping lid method is adopted to improve the overestimated hydrodynamic coefficients calculated from conventional potential flow theory. A time-domain computing program based on potential flow theory and impulse theory is compiled for analyses that consider multibody hydrodynamic interactions and mechanical effects from lines and fenders. Correspondingly, an experiment is carried out for comparison with the numerical results. All statistics, time series, and power density spectra from decay and irregular wave tests are in a fairly good agreement.     

Motion response simulation of a twin-hulled semi-submersible

The purpose of the study was to develop a prediction technique to simulate the motion response of a damaged platform under wave, wind and current forces. The equations of motion were obtained using Newton's second law and the numerical solution technique of non-linear equations of motion is explained for intact and damaged cases. The analysis technique employs large displacement non-linear equations of motion. Solutions were obtained in the time-domain to predict the motion characteristics. In this study, analysis procedures were developed to calculate: (a) wave loading on asymmetrical structural configurations; (b) hydrodynamic reaction forces (inertia or moment of inertia, damping and restoring forces) on asymmetrical shapes. During the damage simulation, change in the mass of the structure as well as wave and hydrodynamic reaction forces, were taken into account. The computer program developed for the time-domain simulation is introduced. In order to avoid slowly decaying transient motions of the structure due to wave excitation forces, an exponential ramp function is used. The application of a ramp function enables a quick convergence in the time-domain solution of equations of motion. Results of a numerical motion simulation program and the experimental studies are also presented in order to make comparisons. Comparison of the test results with the numerical simulations shows good agreement for heave, roll and pitch motions. The formulations and the computational procedures given in this paper provide useful tools for the investigation of the non-linear dynamic stability characteristics of floating structures in waves for intact, damaged and post-flooding conditions in six-degrees of freedom.