Effect of internal sloshing on added resistance of ship

The motion responses of ships carrying liquid cargo are affected not only by external wave excitation, but also by internal sloshing-induced forces and moments. Sloshing flow is coupled with the ship motion. This means the added resistance in waves may change when sloshing occurs inside the tank of the ship. In this study, the motion responses and added resistance of a ship, coupled with the sloshing-induced internal forces and moments are considered by using the linear potential theory. The three-dimensional Rankine panel method, in which the physical quantities are represented by using B-spline basis function, is applied. The sloshing flow of inner tanks is also simulated by using the Rankine panel method and linearized boundary value problem. To study the added resistance, a near-field method, which integrates the second-order pressure on a body surface, is applied. The model ship is a blunt modified Wigley model with two inner tanks. Numerical results obtained without inner tanks are compared with the experimental data, and then the effect of filling ratio of inner tanks on ship motion and added resistance are observed. The components that induce added resistance are examined, and the effects of surge motion on sloshing flow and added resistance are briefly considered. This study shows that the sloshing flow inside the inner tanks may significantly influence not only the motion responses, but also added resistance, especially, when the incident wave frequency approaches the resonance frequency of the sloshing flow.     

NUMERICAL SIMULATION OF SLOSHING IN RECTANGULAR TANK WITH VOF BASED ON UNSTRUCTURED GRIDS

A new method for sloshing simulation in a sway tank is present, in which the two phase interface is treated as a physical discontinuity, which can be captured by a well-designed high order scheme. Based on Normalized Variable Diagram (NVD), a high order discretization scheme with unstructured grids is realized, together with a numerical method for free surface flow with a fixed grid. This method is implemented in an in-house code General Transport Equation Analyzer (GTEA) which is an unstructured grids finite volume solver. The present method is first validated by available analytical solutions. A simulation for a 2-D rectangular tank at different excitation frequencies of the sway is carried out. A comparison with experimental data in literature and results obtained by commercial software CFX shows that the sloshing load on the monitor points agrees well with the experimental data, with the same grids, and the present method gives better results on the secondary peak. It is shown that the present method can simulate the free surface overturning and breakup phenomena.     

超谐共振横摇下液舱晃荡特性数值研究

该文从船舶非线性横摇运动方程出发,采用多尺度法,获得其在正横规则波中的超谐共振稳态解,并将其作为液舱运动的外部激励。在此基础上,基于Open FOAM开源代码,采用基于VOF的两相流模型模拟液舱内气液运动,研究了船舶在超谐共振横摇条件下的液舱晃荡动特性问题。结果表明,在超谐共振横摇条件下,自由液面易出现翻卷、破碎等强非线性现象,舱壁压力时历表现出多峰型特征,其峰值要远大与简谐激励的情况,而且舱内液体晃荡在两个谐波成分的差频附近发生共振响应。     

URANS simulations of ship motion responses in long-crest irregular waves

In this paper, numerical prediction of ship motion responses in long-crest irregular waves by the URANS-VOF method is presented. A white noise spectrum is applied to generate the incoming waves to evaluate the motion responses. The procedure can replace a decade of simulations in regular wave with one single run to obtain a complete curve of linear motion response, considerably reducing computation time. A correction procedure is employed to adjust the wave generation signal based on the wave spectrum and achieves fairly better results in the wave tank. Three ship models with five wave conditions are introduced to validate the method. The computations in this paper are completed by using the solver naoe-FOAM-SJTU, a solver developed for ship and ocean engineering based on the open source code OpenFOAM. The computational motion responses by the irregular wave procedure are compared with the results by regular wave, experiments and strip theory. Transfer functions by irregular wave closely agree with the data obtained in the regular waves, showing negligible difference. The comparison between computational results and experiments also show good agreements. The results better predicted by CFD method than strip theories indicate that this method can compensate for the inaccuracy of the strip theories. The results confirm that the irregular wave procedure is a promising method for the accurate prediction of motion responses with less accuracy loss and higher efficiency compared with the regular wave procedure.     

A numerical study of violent sloshing problems with modified MPS method

A numerical study on violent liquid sloshing phenomenon in a partially filled rectangular container is carried out by using moving particle semi-implicit(MPS) method. The present study deals with the implementation of five modifications all together over the original MPS method. The modifications include improved source terms for pressure Poisson equation, special approximation technique for the representation of gradient differential operator, collective action of mixed free surface particle identification boundary conditions, effecting Neumann boundary condition on solving the PPE and fixing judiciously the parting distance among particles to prevent collision. The suitability of the kernel function used in the original MPS method along with these five modifications is investigated for violent sloshing problems. The present model ensures a good agreement between numerical results with the existing experimental observations. The model is successfully applied to a partially filled tank undergoing horizontal sinusoidal excitation to compute the sloshing wave amplitudes and pressure on tank walls. The assessment of dynamic behaviour manifested in terms of base shear, overturning moment and impact pressure load exerted on tank ceiling induced by violent sloshing motion using MPS method is not reported in the open literature and has been efficiently carried out in the present study.     

Shallow-water sloshing motions in rectangular tank in general motions based on Boussinesq-type equations

Based on the highly accurate Boussinesq-type equations in terms of velocity potential, the shallow-water sloshing in a two-dimensional rectangular tank is studied. The rectangular tank in harmonic sway, heave and roll motions with small excitation amplitudes is considered. The total velocity potential is divided into two parts: the particular solution and the remaining part to be determined by the Boussinesq-type equations. The Stokes-Joukowski potential is adopted in the particular solution for the roll excitation motion. The comparisons of the numerical results indicate that the shallow-water sloshing motions in a rectangular tank can be predicted well based on the Boussinesq-type equations.     

EXPERIMENTAL INVESTIGATION OF EFFECTS OF INNER-TANK SLO-SHING ON HYDRODYNAMICS OF AN FLNG SYSTEM

The present research focuses on experimentally clarifying the effect of inner-tank sloshing on the hydrodynamics of an Floating Liquefied Natural Gas(FLNG)system.Through the comparisons of the results obtained from the model tests carried out with the vessel model ballasted with liquid and solid cargo separately,the effects of the inner-tank sloshing on the hydrodynamics of an FLNG system are highlighted and presented.Statistical languages of the maximum,minimum,mean values and the standard deviations and power density spectra calculated with the help of the algorithm of Fast Fourier Transformation(FFT)are provided.It is concluded that the effects of the inner-tank sloshing on the responses of the FLNG system are sensitive to wave excitation frequencies,and that the effects of the inner-tank sloshing play an important role,particularly in the roll motion of the FLNG hull.The outcome of the proposed technique would offer constructive feedback,which can lead to more practical applications and can serve as a reference for the verification of the potential numerical simulations by other researchers.     

NUMERICAL SIMULATION OF TRANSIENT FLOW AROUND A SHIP IN UNSTEADY BERTHING MOTION

Ship berthing is a specific maneuver operation. The flow around a berthing ship and the forces acting on the hull are quite different from those for a ship in normal navigation. By solving the unsteady Reynolds-Averaged Navier-Stokes (RANS) equations, the transient flow field around a ship undergoing unsteady lateral motion is simulated and the varying lateral hydrodynamic force acting on the hull is evaluated in this article. The numerical results obtained with different turbulence models are analyzed and compared with experimental results and other numerical results published in literature, and a turbulence model more suitable for simulation of the viscous flow around a ship undergoing unsteady berthing is determined.     

Numerical prediction of hydrodynamic forces on a ship passing through a lock with different configurations简

A CFD method is used to numerically predict the hydrodynamic forces and moments acting on a ship passing through a lock with a constant speed. By solving the RANS equations in combination with the RNG k-e turbulence model, the unsteady viscous flow around the ship is simulated and the hydrodynamic forces and moments acting on the ship are calculated. UDF is com-piled to define the ship motion. Meanwhile, grid regeneration is dealt with by using the dynamic mesh method and sliding interface technique. Under the assumption of low ship speed, the effects of free surface elevation are neglected in the numerical simulation. A bulk carrier ship model is taken as an example for the numerical study. The numerical results are presented and compared with the available experimental results. By analyzing the numerical results obtained for locks with different configurations, the influences of approach wall configuration, lock configuration symmetry and lock chamber breadth on the hydrodynamic forces and moments are demonstrated. The numerical method applied in this paper can qualitatively predict the ship-lock hydrodynamic interaction and pro-vide certain guidance on lock design.     

具有隔板容器中液体晃荡的数值模拟

在容器中装置隔板来抑制液体晃荡是一种常见的工程措施。此文针对具有隔板的矩形容器中液体晃荡问题,采用时域高阶边界元方法建立了自由水面满足完全非线性边界条件的数学模型。求解中采用了半混合欧拉-拉格朗日方法追踪流体瞬时水面,并运用四阶龙格库塔方法更新下一时间步的波面和速度势。通过与文献的数值结果的对比,验证了本模型的准确性。通过大量数值试验,研究了隔板位置、尺寸和形式等因素对容器内晃荡液体运动特性、动力特性和容器固有频率的影响。     

The dynamics of the floodwater and the damaged ship in waves

The interaction between the dynamics of the floodwater and the damaged ship in waves is investigated by applying an integrated method, which couples a seakeeping solver and a Navier-Stokes solver. To reveal the effects of the water flooding and the sloshing on the damaged ship behaviour, the motion of a Ro-Ro ferry in regular beam seas is simulated, including the ship under the intact condition with and without internal water and the ship under a damaged condition. It is found that the shift of the natural roll frequency of a damaged ship and the decrease of its roll response are mainly due to the water sloshing inside the compartment. The effect of the resonant sloshing leads to the presence of a ship's second peak response at higher frequencies and it is significantly reduced by the water flooding through the damaged opening. The influence of the flooding and the sloshing on the ship behaviour is small with a further increase of the wave frequency.     

带自由液面 Navier-Stokes 流动问题的ALE 分步有限元方法

将任意的拉格朗日 欧拉 (ArbitraryLagrange Euler,简称ALE)描述引入到Navier Stokes方程中 ,以速度和压力为基本变量 ,在时间域上采用分步求解格式 ,利用Galerkin加权余量法推导了分步格式的ALE有限元数值离散方程。并对带有自由液面的Navier Stokes流动问题的定解条件进行了分析讨论。最后利用所得到的ALE分步有限元方法对二维及三维不可压粘性液体大幅晃动问题进行了算例数值模拟 ,数值计算结果验证了本文方法及计算机仿真软件的正确性与可靠性     

浅窄航道会遇船舶水动力相互作用数值计算

该文应用CFD软件对两船在浅窄航道中会遇时的水动力相互作用进行数值研究,通过求解非定常RANS方程并结合RNG k-ε湍流模型,采用动网格技术及UDF进行船舶运动过程中的网格更新,对两船沿平行直线航行时的三维非定常黏性流场进行数值模拟,并对其相互作用水动力进行了计算。首先通过计算结果与试验数据进行对比,验证了数值方法的可行性和有效性;随后对四种船型在不同水深、航道宽度、两船航速比和船-船横向间距下的水动力进行了系列计算,通过结果分析得出了以上因素对两船会遇水动力相互作用的影响规律。     

高雷诺数下带自由表面的重力波的有限元数值模型

本文基于扩展的虚拟浓度和Sommerfeld线性辐射边界条件建立了数值波浪水槽。用有限元方法结合大涡模拟（LES）湍流模型在Euler坐标系统中求解了二维不可压粘性流体的N－S方程，而自由表面函数方程是在沿流体质点迹线定义的Lagrange系统中求解的。为了检验该数值波浪模型的有效性，本文中用该数值波浪水槽进行了海底管线在波浪场中受力的数值实验，并与物模实验的结果做了对比，其雷诺数Re为10700。     

Practical evaluation of the drag of a ship for design and optimization

We consider two major components of the drag of a ship, the“friction drag”and the“wave drag”, that are related to vis-cous friction at the hull surface and wavemaking, and mostly depend on the Reynolds...     

Comparative study of MPS method and level-set method for sloshing flows

This paper presents a comparative study of a meshless level-set method in the simulation of sloshing flows. The numerical moving particle semi-implicit （MPS） method and a grid based schemes of the MPS and level-set methods are outlined and two violent sloshing cases are considered. The computed results are compared with the corresponding experimental data for validation. The impact pressure and the deformations of free surface induced by sloshing are comparatively analyzed, and are in good agreement with experimental ones. Results show that both the MPS and level-set methods are good tools for simulation of violent sloshing flows. However, the second pressure peaks as well as breaking and splashing of free surface by the MPS method are captured better than by the level-set method.     

用MPS方法数值模拟低充水液舱的晃荡

液体晃荡是一种非线性的自由面流动现象.在低充水率下,由于液体具有很大的运动空间,晃荡现象具有强烈的非线性特征,自由面的变形较大,剧烈时甚至会翻卷和破碎,这给数值模拟带来很大挑战.本文基于移动粒子半隐式法(Moving Particle Semi-Implicit,MPS)对低充水率的液舱晃荡问题进行了数值模拟.结果表明:当激励频率等于共振频率时,液体撞击到了液舱的顶板,并出现了飞溅现象,此时液体对侧舱壁产生了较大的抨击压力;在低于共振频率时,自由面出现了破碎波及波前的翻卷和融合等现象,抨击压力相对较小.计算结果表明,MPS方法能够很好地预测晃荡引起的拍击现象,数值计算得到的压力能够与实验结果很好地吻合.在自由面的追踪上,MPS方法具有很大的灵活性,能够很好地处理自由面的破碎、融合及液体的飞溅等流动现象.     

粘性流中的二维兴波水翼水动力特性研究

本文采用边界层的概念来研究粘性流中的二维兴波水翼之水动力特性的数值计算方法。考虑到边界层与外部势流的相互干扰，运用了势流与边界层的相互迭代计算，从而求得两者相互匹配的解。用势流解求得的水翼升力系数往往比实验值明显偏大。而用本文的方法，从算例来看，计算结果比势流解减小１５％左右，而与实验值比较接近。本文还讨论了兴波阻力的计算方法，并有算例。     

高速船甲板上浪的水体流动与冲击

针对高速船舶的甲板上浪,综合考虑船体外飘、船艏波面升高、波浪传播与船体运动等相关因素的影响,采用势流理论计算和CFD技术相结合的方法,建立了计入整船运动的船艏上浪计算模型,计算模拟并分析了甲板上水体流动形态及其对甲板结构的冲击作用。计算中船体运动通过势流理论给定,势流理论计算通过用户自定义函数嵌入Fluent软件,并通过二次开发实现了上浪现象的模拟。文中就迎浪状态下高速行驶的S175船甲板上浪进行了三维数值模拟研究,结果表明甲板上水体的流动及其对结构物的冲击载荷与试验吻合良好,该方法能够对上浪机理给出较为清晰的描述,能够分析预报甲板上浪对浮体结构物的破坏作用,为工程应用提供了良好的方法和途径。     

三体船在斜浪规则波中运动响应预报方法研究

对于三体船在波浪中的水动力预报,航速效应和主体与片体间水动力干扰效应是水动力载荷合理预报的关键之处,需合理考虑.二维半势流理论可较为准确反映上述效应,已在三体船顶浪中垂向运动响应理论预报上获得了较为满意的结果.在此基础上,该文探讨了该方法在三体船斜浪中运动特别是横摇预报上的应用.为较准确获得三体船横摇运动时粘性阻尼贡献,采用三体船模静水中自由横摇衰减试验获得了自由横摇运动衰减曲线,并经能量法处理获得了船舶横摇阻尼系数.然后,结合二维半理论,获得了三体船运动数值解.数值解与斜浪规则波中运动响应模型试验结果符合较好,反映本文所采用的数值方法可较好地预测三体船斜浪中水动力载荷和运动,可用于三体船在波浪中耐波性评估.