Viscosity and nonlinearity effects on the forces and waves generated by a floating twin hull under heave oscillation

Nonlinear hydrodynamics of a twin rectangular hull under heave oscillation is analyzed using numerical methods. Two-dimensional nonlinear time-domain solutions to both inviscid and viscous problems are obtained and the results are compared with linear, inviscid frequency-domain results obtained in [26] to quantify nonlinear and viscous effects. Finite-difference methods based on boundary-fitted coordinates are used for solving the governing equations in the time domain [2]. A primitive-variables based projection method [6] is used for the viscous analysis and a mixed Eulerian–Lagrangian formulation [11] for inviscid analysis. The algorithms are validated and the order of accuracy determined by comparing the results obtained from the present algorithm with the experimental results of Vugt [22] for a heaving rectangle in the free surface. The present study on the twin-hull hydrodynamics shows that at large and non-resonant regular frequencies, and small amplitude of body oscillation, the fluid viscosity does not significantly affect the wave motion and the radiation forces. At low frequencies however the viscosity effect is found to be significant even for small amplitude of body oscillation. In particular, the hydrodynamic force obtained from the nonlinear viscous analysis is found to be closer to the linear inviscid force than the nonlinear inviscid force to the linear inviscid force, the reason for which is attributed to the wave dampening effect of viscosity. Since the wave lengths generated at smaller frequencies of oscillation are longer and therefore the waves could have a more significant effect on the dynamic pressure on the bottom of the hulls which contribute to the heave force, the correlation between the heave force and the wave elevation is found to be larger at smaller frequencies. Because of nonlinearity, the wave radiation and wave damping force remained nonzero even at and around the resonant frequencies – with the resonant frequencies as determined in [26] using linear potential flow theory. As to be expected, the nonlinear effect on the wave force is found to be significant at all frequencies for large amplitude of oscillation compared to the hull draft. The effect of viscosity on the force, by flow separation, is also found to be significant for large amplitude of body oscillation.     

Nonlinear heave radiation forces on two-dimensional single and twin hulls

A study of nonlinear heave radiation of two-dimensional single and double hulls has been carried out in the time domain. The problem is analyzed by means of a fully nonlinear mathematical model, referred to as the mixed Eulerian–Lagrangian (MEL) model, which is based on an integral relation formulation coupled with time-integration of the nonlinear free-surface boundary conditions. The integral equation solver is based on a cubic-spline boundary-element scheme in which both potential and velocity continuity conditions can be enforced through the intersection points. The body undergoes periodic forced heave oscillation. By implementing effective wave-absorbing beaches at the two ends of the rectangular numerical tank, long-term steady-state force-histories could be achieved consistently in all computations.Results in terms of radiation forces for rectangular and triangular single- and twin-hull geometries are presented and discussed. Linear hydrodynamic forces in terms of added-mass and damping are validated for the rectangular hull. The Fourier-analyzed results reveal the extent of nonlinear (higher-order) components in the force-signals over different parameters which include the amplitudes of oscillation, hull-spacing for the twin-hulls and water depth.     

随机波浪下Truss Spar平台垂荡运动时域分析

研究Truss Spar平台在随机波浪下的垂荡运动特性。采用ITTC双参数谱,考虑绕射作用,数值计算了平台所受的随机波浪力。利用已有的水动力试验和数值模拟结果及Morison方程,估计了Truss Spar平台垂荡方向的附加质量和粘滞阻尼大小。考虑非线性阻尼和瞬时波面的影响,运用Runge-Kutta数值迭代算法,比较了不同随机波浪参数对平台运动响应的影响,特别是波浪特征周期接近垂荡固有周期时。结果表明,当波浪特征周期接近平台垂荡固有周期时,平台产生大幅垂荡运动,频域的运动分析结果比时域结果偏小。     

A modified scaled boundary finite-element method for problems with parallel side-faces. Part II. Application and evaluation

The modified scaled boundary finite-element method (SBFEM), keeping the advantages of the original SBFEM, eliminates the restriction of the scaling center location so that this approach can solve two-dimensional problems with parallel side-faces. In this paper, the modified SBFEM is applied to solutions of two types of problems—wave diffraction by a single and twin surface rectangular obstacles and wave radiation induced by an oscillating mono-hull and twin-hull structures in a finite depth of water. For wave diffraction problems, numerical results agree extremely well with the analytic solution for the single obstacle case and other numerical results of a different approach for the twin obstacle case. For wave radiation problems, the particular solutions to the scaled boundary finite-element equation are presented for cases of heave, sway and roll motions. The added mass and damping coefficients for heave, sway and roll motions of a two-dimensional rectangular container are computed and the numerical results are compared with those from independent analytical solution and numerical solution using the boundary element method (BEM). It is found that the SBFEM method achieves equivalent accuracy to the conventional BEM with only a few degrees of freedom. In the last example, wave radiation by a two-dimensional twin-hull structure is analyzed. Comparisons of the results with those obtained using conventional Green's function method (GFM) demonstrate that the method presented in this paper is free from the irregular frequency problems.     

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.     

A new concept of a hull form to improve wave response characteristics for marine construction barges

The object of the new hull form is to provide a single hull which possesses long natural periods of roll and heave and has substantially reduced motion response amplitudes in very high sea states. Model tests and preliminary estimates indicated that the new hull form can be designed for roll and heave motions nearly equivalent to those of much larger semisubmersible units.All existing conventional marine construction barges have rectangular cross section hull. The new hull form consists of a system of upper side tanks and lower side tanks added onto a rectangular cross section hull. The upper tanks and lower tanks form longitudinal troughs on the port and starboard sides. Structural grillage of any open type is to connect the upper and lower tanks at the side of the vessel. Figure 1 indicates a profile and a typical transverse section of the new hull form. The new hull comprises the concept of reduced water plane area which is turn results in low transverse metacentric height and low tons per in. immersion. The novel features of combining low GM_T and low TPI with extremely heavy damping and added mass of the entrained water characteristics result in very long natural periods of roll and heave and considerably small rolling and heaving amplitudes in high sea states. The open side shell plating on the side of the vessel functions to dissipate wave energy at the side of the vessel which would have otherwise been transmitted to the vessel and caused the vessel to respond. This paper presents the conceptual foundation and outline of the new hull form. Model test results are presented and implemented. Also presented is the design philosophy.     

Experimental investigation of nonlinearities of ship responses in head waves

The present study focuses on building a systematic approach to identify, from experimental results, the nonlinearity in the dynamic system of a high-speed ship. The experimental program consists of tests in both regular and irregular head waves, and the measured quantities included wave elevation, vertical motions, and hull pressures. By contrasting these results to the quasi-linear behaviors of heave motion, the nonlinear behaviors of pressure are highlighted and presented. Three nonlinear assessments, the probability density function, and the variance spectra are provided. Based on these investigations, we conclude that the pressures, particularly, at the ship’s bow contain more nonlinearities than just the heave motion. They are identified mainly by the large amplitude of the higher harmonics and also by the large asymmetry in the measured signals. Furthermore, the coherence spectrum obtained from the third-order orthogonal frequency-domain Volterra model provides information regarding the magnitude of each order at the corresponding frequency, which serves as a strategy to simplify a complex problem or to achieve a balance between regular and irregular waves. The overall results show that the higher-order components are significant for the pressure system and the outcome of the proposed model can offer constructive feedback, which can lead to more practical applications.     

Experimental studies of a damaged ship section in forced heave motion

This work documents a detailed series of experiments performed in a wave flume on a thin walled prismatic hull form. The model consists of a rectangular opening located on the side. The length of the model is slightly smaller than the flume breadth to achieve two-dimensional (2D) behavior in the experiments. Forced oscillatory heave tests in calm water have been carried out by varying the model-motion parameters and examining both intact and damaged conditions. Video recordings, measurements of the wave elevation inside the damaged compartment and of the force on the model were performed in all the experiments. The effect of damage opening in the model on hydrodynamic loads is examined by comparing with an intact section. A theoretical analysis is used to explain the behavior of added mass and damping coefficients in heave for a 2D damaged section. The presented results demonstrate occurrence of sloshing and piston mode resonances in the tests and their influence on the hydrodynamics loads of a damaged ship. Detailed physical investigations are presented at these resonance frequencies for the damaged section. Effect of filling level in the damage compartment, damage-opening length and air compressibility in the airtight compartment is examined. Nonlinear effects are documented and appear dominant, especially, for lowest filling level where we have shallow-water depth conditions in the damaged compartment. Resonance phenomena that can lead to significant local loads are identified for the shallow water condition. Air compressibility in the airtight compartment and floodwater act as a coupled system and influence inflow/outflow of floodwater in the compartment. It has a significant effect on local floodwater behavior in the damaged compartment.     

Time-domain computation of large amplitude 3D ship motions with forward speed

Time-domain computations of 3D ship motions with forward speed are presented in this paper. The method of computation is based upon transient Green function. Both linear and nonlinear (large-amplitude) computations are performed where the included nonlinearities are those arising from the incident wave, but the diffraction and radiation forces are otherwise retained as linear. The incident wave can be described by any explicit nonlinear model. Computations over a variety of wave and speed parameters establish the robustness of the algorithm, which include high speed and following waves. Comparison of linear and nonlinear computations show that nonlinearities have a considerable influence on the results, particularly in predicting the instantaneous location of the hull in relation to the wave, which is crucial in determining forefoot emergence and deck wetness.     

孤立波与升沉水平板相互作用数值模拟研究

合理的刚度和潜深设计可以使升沉水平板获得优异的消浪性能。基于考虑流体黏性的二维不可压缩Navier-Stokes方程,以高阶紧致插值CIP(constrained interpolation profile)方法求解方程对流项,采用VOF(volume of fluid)方法重构自由液面,构建二维数值波浪水槽。采用试验数据验证模型后,研究孤立波与升沉水平板相互作用,分析相对刚度K*、相对潜深d/h、相对波高H/h对于升沉板的消浪性能和运动响应的影响,揭示升沉板对孤立波的消浪机理。研究表明:在孤立波通过时,升沉板会经历一个先上升后下降的运动,随后非线性自由振动,板下方水体近似均匀流动,且水流的垂向流动与板的垂荡方向一致;升沉板主要通过不对称涡旋脱落、浅水变形、波浪反射与辐射波转化等方式消耗孤立波能量;一定条件下,采用最优相对刚度K*=4.0和最优相对潜深d/h=0.52可以取得良好的消浪效果,此时透射系数最小,同时升沉板的运动响应在合理的范围内。     

An Irregular Wave Generating Approach Based on naoe-FOAM-SJTU Solver

In this paper, a wave generating approach for long-crest irregular waves in a numerical tank by our in-house solver naoe-FOAM-SJTU is presented. The naoe-FOAM-SJTU solver is developed using an open source tool kit, OpenFOAM. Reynolds-averaged Navier?Stokes (RANS) equations are chosen as governing equations and the volume of fluid (VOF) is employed to capture the two phases interface. Incoming wave group is generated by imposing the boundary conditions of the tank inlet. A spectrum based correction procedure is developed to make the measured spectrum approaching to the target spectrum. This procedure can automatically adjust the wave generation signal based on the measured wave elevation by wave height probe in numerical wave tank. After 3 to 4 iterations, the measured spectrum agrees well with the target one. In order to validate this method, several wave spectra are chosen and validated in the numerical wave tank, with comparison between the final measured and target spectra. In order to investigate a practical situation, a modified Wigley hull is placed in the wave tank with incoming irregular waves. The wave-induced heave and pitch motions are treated by Fourier analysis to obtain motion responses, showing good agreements with the measurements.     

An irregular wave generating approach based on naoe-FOAM-SJTU solver

In this paper, a wave generating approach for long-crest irregular waves in a numerical tank by our in-house solver naoe-FOAM-SJTU is presented. The naoe-FOAM-SJTU solver is developed using an open source tool kit, OpenFOAM. Reynolds-averaged Navier-Stokes (RANS) equations are chosen as governing equations and the volume of fluid (VOF) is employed to capture the two phases interface. Incoming wave group is generated by imposing the boundary conditions of the tank inlet. A spectrum based correction procedure is developed to make the measured spectrum approaching to the target spectrum. This procedure can automatically adjust the wave generation signal based on the measured wave elevation by wave height probe in numerical wave tank. After 3 to 4 iterations, the measured spectrum agrees well with the target one. In order to validate this method, several wave spectra are chosen and validated in the numerical wave tank, with comparison between the final measured and target spectra. In order to investigate a practical situation, a modified Wigley hull is placed in the wave tank with incoming irregular waves. The wave-induced heave and pitch motions are treated by Fourier analysis to obtain motion responses, showing good agreements with the measurements.     

基于非线性数学模型的半潜式平台共振运动特性研究

共振运动是深海浮式平台设计的关键考虑因素之一,对海洋平台的作业具有重要影响。采用半潜式平台运动的非线性耦合数学模型,考虑浮筒和横撑出入水以及垂荡、横摇和纵摇运动耦合对平台浮力和恢复力的影响,研究半潜式平台非线性共振运动特性,以及不规则波浪参数对运动的影响。研究表明:在非线性耦合运动和浮力变化的影响下,半潜式平台纵摇和垂荡运动的固有周期会随运动幅值的增大而逐渐减小,且最终趋于稳定,对纵摇运动周期的影响更为显著;非线性效应会使半潜式平台产生显著的低频纵摇共振响应,以及共振频率漂移的现象,且受随机种子和波浪周期的影响较小。     

一种新型干树式半潜平台设计

开发了一种新型的深吃水干树式半潜生产平台(TCDD-Semi),该平台可用于中国南海深水区域的油气田开发。它的一个显著特点是立柱的截面形状呈现为渐变形式,而非传统的等截面形式。立柱的底部最大,向上逐渐变小,再结合适当的下浮体设计,能够为平台在服役前期及在位状态时提供足够的浮力以及稳性。最重要的是这种新型立柱的设计能够明显地减小平台在恶劣海况时的垂向运动,从而使在平台上布置具有干式采油树的TTR立管系统成为可能。此外,这种渐变式的立柱设计也有利于减弱平台在流作用下的涡激诱导运动(VIM)。分析结果表明这种渐变式立柱半潜平台可以明显降低平台的垂向运动,也可以在码头组装时提供足够的浮力以及在平台下沉过程中提供足够的稳性。平台优越的垂向运动性能可以使顶部张紧式立管的行程范围限制在10.5 m之内(包括平台偏移、垂荡运动、潮汐影响、海床沉降、热膨胀等因素)。分析结果表明平台的垂荡范围、水平偏移、倾侧角度、上部模块重心处的加速度等可以满足设计要求,证明了这种新型干树式半潜平台的可行性。     

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

Time-domain numerical and segmented ship model experimental analyses of hydroelastic responses of a large container ship in oblique regular waves

Real sea conditions are characterized by multidirectional sea waves. However, the prediction of hull load responses in oblique waves is a difficult problem due to numeral divergence. This paper focuses on the investigation of numerical and experimental methods of load responses of ultra-large vessels in oblique regular waves. A three dimensional nonlinear hydroelastic method is proposed. In order to numerically solve the divergence problem of time-domain motion equations in oblique waves, a proportional, integral and derivative (PID) autopilot model is applied. A tank model measurement methodology is used to conduct experiments for hydroelastic responses of a large container ship in oblique regular waves. To implement the tests, a segmented ship model and oblique wave testing system are designed and assembled. Then a series of tests corresponding to various wave headings are carried out to investigate the vibrational characteristics of the model. Finally, time-domain numerical simulations of the ship are carried out. The numerical analysis results by the presented method show good agreement with experimental results.     

圆形数值波浪水池斜向和多向入射波浪模拟研究

为了研究斜向入射波浪,基于三维不可压缩两相流模型,开发了一套圆形数值波浪水池数值模型。在圆形波浪水池中,通过源项造波法成功生成了任意入射方向的波浪,并且利用人工摩擦项模拟阻尼区以数值耗散反射波浪。模型基于嵌入式多块网格体系,采用FVM法(finite volume method)离散Navier-Stokes方程,VOF法(volume of fluid)追踪自由水面。试验结果表明,斜向入射波浪的模拟结果与理论值基本一致,圆形波浪水池在模拟斜向入射波浪时,有效区域的面积较传统波浪水池显著增大,而且有效区域受波浪入射角度的影响也较小。同时,通过叠加多列斜向入射波浪,模拟出了多向交叉波列,并通过与理论结果对比,发现其具有较高的精度。     

Experimental investigation of a fast monohull in forced harmonic motions

The paper presents the results of an experimental investigation of added masses and damping coefficients of a model of a fast monohull. A model of 4.5 m length between perpendiculars was constructed of fiber glass reinforced plastic (FRP) with four segments connected by a backbone. The backbone was instrumented with load cells at the positions of the cuts. This configuration, combined with load cells measuring the force exerted by the forced motion actuators, made it possible to obtain the hydrodynamic coefficients for each of the four hull segments.

The investigation focused on the vertical motions. Thus, the experimental program included forced harmonic heave and pitch motions in calm water (no incident waves). Subtracting inertial and restoring forces from total measured forces, one obtained the hydrodynamic component, which then resulted in the hydrodynamic coefficients. The effects of steady forward speed on the radiation forces were investigated by conducting model tests at four forward speeds. Finally, nonlinear effects were assessed by conducting model tests for three amplitudes of forced heave and forced pitch motions.     

Modelling of a wave energy converter array with a nonlinear power take-off system in the frequency domain

This paper presents a nonlinear frequency domain model and uses this to assess the performance of a wave energy converter (WEC) array with a nonlinear power take-off (PTO). In this model, the nonlinear PTO forces are approximated by a truncated Fourier series, while the dynamics of the WEC array are described by a set of linear motion equations in the frequency domain, and the hydrodynamic coefficients are obtained with the boundary element method. A single heave absorber is firstly investigated to establish the accuracy of the new model in capturing the nonlinear behaviour of the pumping system. Subsequently, simulations of a 2D array with 18 WECs and a pillar in the centre (representing the tower of a wind turbine) are carried out to understand wave interference effects. Several optimisation strategies are proposed to improve the overall performance of the WEC array. These results demonstrate a computationally effective method for accounting for nonlinear effects in large WEC arrays. The proposed approach may potentially be applied for developing control algorithms for the adaptability of a 2D array to incoming wave excitation.     

Effect of wave nonlinearity on fatigue damage and extreme responses of a semi-submersible floating wind turbine

Floating wind turbine has been the highlight in offshore wind industry lately. There has been great effort on developing highly sophisticated numerical model to better understand its hydrodynamic behaviour. A engineering-practical method to study the nonlinear wave effects on floating wind turbine has been recently developed. Based on the method established, the focus of this paper is to quantify the wave nonlinearity effect due to nonlinear wave kinematics by comparing the structural responses of floating wind turbine when exposed to irregular linear Airy wave and fully nonlinear wave. Critical responses and fatigue damage are studied in operational conditions and short-term extreme values are predicted in extreme conditions respectively. In the operational condition, wind effects are dominating the mean value and standard deviation of most responses except floater heave motion. The fatigue damage at the tower base is dominated by wind effects. The fatigue damage for the mooring line is more influenced by wind effects for conditions with small wave and wave effects for conditions with large wave. The wave nonlinearity effect becomes significant for surge and mooring line tension for large waves while floater heave, pitch motion, tower base bending moment and pontoon axial force are less sensitive to the nonlinear wave effect. In the extreme condition, linear wave theory underestimates wave elevation, floater surge motion and mooring line tension compared with fully nonlinear wave theory while quite close results are predicted for other responses.