An iterative Rankine BEM for wave-making analysis of submerged and surface- piercing bodies in finite water depth

A 3-D iterative Rankine Boundary Element Method （BEM） for seakeeping problem in time domain is developed in the framework of linear potential theory. Waves generated by both submerged and surface-piercing bodies moving at a constant forward speed in otherwise calm water, and the resultant steady wave pattern, wave profile and resistance are computed to validate this newly-developed code. A rectangular computational domain moving with the same forward speed as the body is introduced, in which an artificial damping beach is installed at an outer portion of the free surface except the downstream side for satisfying the radiation condition. The velocity potential on the ship hull and the normal velocity on the free surface are obtained directly by solving the boundary integral equation, with the Rankine source used as the kernel function. An iterative time-marching scheme is employed for updating both kinematic and dynamic free surface boundary conditions to stabilize the calculation. Extensive results including the wave patterns, wave profiles and wave resistances for a submerged spheroid and a Wigley hull with forward speed are presented to validate the efficiency of the proposed 3-D time-domain higher-order approach. Finally, the sensitivity of ship-generated waves to the water depth is investigated. Computed results show satisfactory agreement with the corresponding experimental data and other numerical solutions.     

Iterative Rankine HOBEM analysis of hull-form effects in forward-speed diffraction problem

A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constant forward speed in incident waves and the resultant diffraction forces acting on the hull are computed to investigate the hull-form effects on the hydrodynamic forces. A rectangular computational domain travelling at ship's speed is considered. An artificial damping beach for satisfying the radiation condition is installed at the outer portion of the free surface except the downstream side. An iterative time-marching scheme is employed for updating both kinematic and dynamic free-surface boundary conditions for numerical accuracy and stability. The boundary integral equation is solved by distributing higher-order boundary elements over the wetted body surface and the free surface. The hull-form effects on the naval hydrodynamics are investigated by comparing three different Wigley models. Finally, the corresponding unsteady wave patterns and the wave profiles around the hulls are illustrated and discussed.     

FULLY NONLINEAR WAVE COMPUTATIONS FOR ARBITRARY FLOATING BODIES USING THE DELTA METHOD

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NUMERICAL STUDY OF SQUARE-STERN SHIP WAVE IN SHALLOW WATER

This paper employed shallow water equations with moving pressure to calculate water waves generated by a square-stern ship in shallow water. The moving ship is considered as moving pressure on free surface. The finite element method with moving grids is used to solve the shallow water equations based on wave equation model [3]. A non-reflection boundary condition [5]is imposed on open boundaries surrounding the ship. 3-D surface elevations, depth-averaged horizontal velocities are presented. The numerical solutions are physically reasonable. It is found that wave resistance coefficients, draftchange and pitch angle vary rapidly in neighborhood of critical flow (Fh=u/ gh= 0. 9 -1. 1). The numerical results also indicate that the wave resistance coefficients, draft change and pitch angle of square-stern ship are larger than those of sharp-stern ship with the same hull structure at the same speed.     

ON THE 3-D PULSATING SOURCE OF MICHELL TYPE WITH FORWARD SPEED

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COMPUTATIONAL RESEARCH ON WAVE MAKING OF MOVING WIGLEY HULL IN TIME DOMAIN

Based on Green＇s theorem, a time domain numerical model was constructed to simulate wave making phenomenon caused by a moving ship. In this article, the Rankine sources and dipoles were placed on boundary surfaces （i.e., the ship surface and free surface）, and a time-stepping scheme was employed. Its unique characteristic is that steady state can be realized from initial value by employing the time-stepping scheme and unsteady free surface conditions. In time domain, if the results of unsteady flow problem tend to data stabilization after many time steps of computation, they could be regarded as the data of steady ones. This model could be employed to steady or unsteady problems. Theoretical reasoning and computational process of this method was described in detail The linear and nonlinear boundary conditions on body surface were studied, and the relative means to realize these boundary conditions in iterative computation were also discussed. Some proper parameters about the model of the Wigley hull were determined by many numerical tests, and their influences on wave making resistance and wave pattern were discussed. According to the comparison between numerical results and data available in relative references, the method used in this work is proven to be a reliable method in time domain. And the lattice reorganization in every time step computation is a feasible numerical approach.     

THE OPTIMIZATION OF THE HULL FORM WITH THE MINIMUM WAVE MAKING RESISTANCE BASED ON RANKINE SOURCE METHOD

The hull form optimization concerns one of the most important applications of wave making resistance theories. In order to obtain a hull form with the minimum wave making resistance, an optimization design method based on the CFD is proposed, which combines the Rankine source method with the nonlinear programming (NLP). The bow-body shape is optimized with the minimum wave making resistance as the objective function. A hull form modification function is introduced to represent an improved hull surface, which can be used to generate a new smooth hull surface by multiplying it by the offset data of the original hull surface. The parameters of the hull form modification function are taken as the design variables. Other constraint conditions can also be considered, for example, in optimizing the lines of the bow, appropriate displacements can be taken as the basic constraints. S60 hull form is selected as the original hull. Three improved hulls are obtained by optimal design. Rankine source method proves to be an effective method in ship form optimization based on analysis of the resistance performance and lines of the improved hull.     

Time domain simulations of radiation and diffraction by a Rankine panel method

The radiation and the diffraction of a ship with a forward speed are studied by using a time domain Rankine panel method. The free surface conditions are linearized onto an undisturbed free surface based on the double body flow. The linearized body boundary condition is applied on the mean wetted hull surface. The fluid domain boundary is discretized by a collection of quadric panels. The unknown quantities, including the free surface elevation, the normal flux over the free surface and the potential on the fluid domain boundary, are determined at each time step. The numerical results are compared with experimental data and other numerical solutions, showing satisfactory agreements.     

WAVE-CURRENT INTERACTIONS WITH THREE-DIMENSIONAL FLOATING BODIES

A Time-domain Higher-Order Boundary Element Method (THOBEM) is developed for simulating wave-current interactions with 3-D floating bodies. Through a Taylor series expansion and a perturbation procedure, the model is formulated to the first-order in the wave steepness and in the current velocity, respectively. The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem. Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching. An artificial damping layer is adopted to dissipate the scattering waves. Different from the other time-domain numerical models, which are often focused on the wave-current interaction with restrained bodies, the present model deals with a floating hemisphere. The numerical results of wave forces, wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods. The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry. In this work, the regular and focused wave combined with current interacting with a truss-spar platform is investigated.     

粗糙床面振荡紊流边界层运动的三维格子玻尔兹曼模拟

该文采用格子玻尔兹曼(LB)方法建立了紧密排列颗粒粗糙床面振荡紊流边界层模拟的三维数学模型。收集粗糙床面波浪水槽实验结果,对水槽实验条件下的振荡流边界层进行模拟,模拟得到的平均流速、紊动特性、等效粗糙高度、摩阻系数和边界层厚度等与实验结果进行了全面对比,并对三维涡旋结构进行了分析。结果表明,所建立的LB数学模型可以合理模拟粗糙床面振荡流边界层流动,能够反映三维涡旋特性,可进一步应用于粗糙床面振荡流紊动特性以及床面粗糙参数的研究。     

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。     

HYDRODYNAMIC BEHAVIOR OF FPSO UNDER VARIUS LOADING IN SURVIVAL STORMS IN SHALLOW WATER

The motion performance and clearance between the hull and seabed of a FPSO (Floating, Production, Storage and Offloading units) in survival storm conditions are closely related to its safety during the operation in shallow water. As an example the behavior of a 160 kDWT FPSO with single point mooring system in shallow water was investigated in this paper. Calculation for the FPSO is made based on the 3-D linear potential flow theory and time-domain numerical simulation method and corresponding model test is carried out in the wave basin at Shanghai Jiaotong University. Both the calculated and experimental results indicate that the heave, roll and pitch motions of FPSO become lazy with the increase of the draft. And the fully loaded FPSO in survival storm touched seabed few times. Therefore, it is concluded that the FPSO should be less loaded than that in the fully loaded condition when the survival storm is coming.     

二维半理论的船舶运动及波浪增阻计算适用性研究

波浪增阻是计算船舶能效指标中气象因子w_f的关键。该文基于二维半理论(又称高速细长体理论)实现了船舶运动响应预报并采用辐射能量法开发了波阻增加计算程序。通过对不同航速下Wigley III和S175船的水动力、运动和波浪增阻的细致计算与分析,并与切片理论和三维航速修正法求解的结果及试验值进行了比较,验证该方法的可靠性和适用性。研究表明二维半理论适用于船舶运动与波浪增阻的计算,相较于工程上常用的切片理论和航速修正方法,计算结果准确性适用性更高,为船舶波阻增加预报提供了快速有效的手段。     

动水压力波高阶双渐近时域平面透射边界Ⅱ:计算性能

为了准确模拟动水压力波在半无限水库中传播引起的辐射阻尼，本文基于比例边界有限单元法构造了高阶双渐近时域平面透射边界。首先将描述半无限水库的连续波动方程转化为半离散的比例边界有限单元方程描述，然后通过特征模态变换将以动力刚度矩阵形式表达的控制方程解耦，获得了模态动力刚度的连分式解答，再通过引入辅助变量将透射边界在频域的动力刚度表达等效为一个高阶矩阵方程，对其施加傅立叶逆变换后即得到时域透射边界条件。频域模态动力刚度的计算结果表明：该双渐近透射边界可以在全频范围内迅速的逼近准确解，表现出优良的收敛性能。     

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。     

STUDY OF TRIMARAN WAVEMAKING RESISTANCE WITH NUMERICAL CALCULATION AND EXPERIMENTS

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计及定常流的三维物体的辐射问题

本文对在波浪中以定常速度般行的物体建立了拟线性理论，在此基础上采用基本源法，利用高边元划分网格，计算了有定常航速物体的附加质量和阻尼系系数，从与实验值及其它计算方法的计算值的比较可看出，本文提供的计算方法是成功的。     

自由面区域变换法解三体船兴波问题

为求解三体船兴波问题,基于线性自由面条件的势流兴波理论Rankine源方法,利用物理平面与计算平面的转换关系计算自由面上物理量的导数,开发了三体船兴波阻力预报程序.采用该方法和程序,对不同侧体布局的Wigley三体船兴波阻力及波形进行计算,并将计算结果与模型试验结果、其他作者数值计算结果进行比较,验证了该方法对三体船的适用性,表明采用贴水线网格及自由面区域变换法解三体船兴波问题可提高三体船兴波问题求解效率.     

NUMERICAL SIMULATIONS OF WAVE-INDUCED SHIP MOTIONS IN TIME DOMAIN BY A RANKINE PANEL METHOD

A time domain prediction of wave-induced ship motions by a Rankine panel method is investigated. Linear boundary conditions on free surface and mean wetted body surface are adopted, while the numerical damping method is used for the radiation conditions. The motions of two ships in regular head waves are computed by the present method. The related numerical results are compared with the experiment data and those from linear strip theory. The comparison shows satisfactory agreements for pitch and heave transfer functions.     

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.