An iterative Rankine boundary element method for wave diffraction of a ship with forward speed

A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.     

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.     

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.     

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.     

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.     

用时域法求解二维二阶非线性水波的绕射问题

本文用二阶理论在时期围内研究非线性水波的绕射问题。一、二阶问题分别满足各自的自由表面条件和物面条件。用一阶Ａｄａｍｓ格式并配合时步处理来计算自由表面上的波高和速度势，而流场内的速度势通过求解有限元方法得到。采用人工阻尼区来吸收反射波，对水平半圆柱在水面的绕射问题进行了计算，得到了自由表面波高时间历程和圆柱所受到的波浪力，计算结果和有关文献进行了比较，其符合程度是令人满意的。     

NUMERICAL RESEARCH ON UNSTEADY SHIP WAVE-MAKING PROBLEMS IN TIME-DOMAIN

A time-domain Kelvin source high-order panel method based on NURBS is developed and applied to solve the unsteady wave-making problems. Numerical results of instant wave resistance and free surface elevation are presented and compared with the availaby results by other authors, for submerged spheroid and sphere beneath the free surface and for surface ship of Wigley models moving with unsteady speed,The agreement is satisfying.     

WAVE MAKING COMPUTATION IN TIME DOMAIN FOR MULTI-HULL SHIPS

1. INTRODUCTION For high-speed displacement ships, the wave making at the free surface is an important hydro- dynamic performance. The wave making reduction has attracted more attention for ship designers. The ship wave resistance and ship hull form improvement have been widely investigated. The thin ship theory adopting the Havelock source distribution on the ship centerline plane can be used to analyze the ship wave making profile and the ship wave resistance may be obtained by ship wav…     

Ship bow waves

The bow wave generated by a ship hull that advances at constant speed in calm water is considered. The bow wave only depends on the shape of the ship bow (not on the hull geometry aft of the bow wave). This basic property makes it possible to determine the bow waves generated by a canonical family of ship bows defined in terms of relatively few parameters. Fast ships with fine bows generate overturning bow waves that consist of detached thin sheets of water, which are mostly steady until they hit the main free surface and undergo turbulent breaking up and diffusion. However, slow ships with blunt bows create highly unsteady and turbulent breaking bow waves. These two alternative flow regimes are due to a nonlinear constraint related to the Bernoulli relation at the free surface. Recent results about the overturning and breaking bow wave regimes, and the boundary that divides these two basic flow regimes, are reviewed. Questions and conjectures about the energy of breaking ship bow waves, and free-surface effects on flow circulation, are also noted.     

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.     

造波板运动造波的实时模拟

基于势流理论和时域高阶边界元方法,建立了完全非线性数值波浪水槽模型,通过实时模拟造波板运动来产生波浪.采用混合欧拉-拉格朗日方法追踪流体瞬时水面,运用四阶Runga-Kutta方法更新下一时间步的波面和速度势,同时应用镜像格林函数消除了水槽两个侧面和底面上的积分,在水槽末端布置人工阻尼层消除反射波浪,通过加速势的方法准确计算速度势的时间导数.利用所建模型分别对规则波和不规则波进行了模拟研究,得到了稳定的波形,与试验结果、理论结果和已发表结果均吻合良好,同时计算了造波板做单一频率运动产生的非线性波浪力.     

孤立波与潜水台阶相互作用的数值研究

本文用完整二维Navier-Stokes方程和VOF方法研究孤立波与潜水台阶障碍物相互作用问题.本文的计算结果与Seabra-Santos,Penouard and Temperville(1987)的实验结果有较好的一致性,与Germain(1984)基于势流浅水理论的结果较为接近,同时能更好模拟出前传演化波的衰减.只要给出初始孤立波波幅,静水深和潜水台阶障碍物的高度,利用本文方法就能模拟出演化波、分裂波和反射波的波形,并给出每一时刻的自由面形状、流场、涡量和压力的分布.     

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

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Finite element analysis of second order wave radiation by a group of cylinders in the time domain

A finite element based numerical method is employed to analyze the wave radiation by multiple or a group of cylinders in the time domain. The nonlinear free surface and body surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a Finite Element Method (FEM). The matrix equation of the FEM is solved through iteration and the initial solution is obtained from the result at the previous time step. The three-dimensional (3-D) mesh required is generated based on a two-dimensional (2-D) hybrid mesh on a horizontal plane and its extension in the vertical direction. The hybrid mesh is generated by combining an unstructured grid away from cylinders and two structured grids near the cylinder and the artificial boundary. The fluid velocity on the free surface and the cylinder surface are calculated by using a differential method. Results for various configurations including the cases of two cylinders and four cylinders and a group of eighteen cylinders are obtained to show the joint influences of cylinders on the first- and second-order waves and forces, including the effects of spacing ratios and wave frequency on the second order waves and the mean force, in particular.     

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.     

兴波阻力数值预报方法研究及其在集装箱船船型优化中的应用

集装箱船作为一种中高速船，其兴波阻力在总阻力中所占比例较高。从某种意义上讲，船型优化就是寻求最小兴波阻力的船型。本文采用基于势流理论的面元法预报集装箱船的兴波阻力，对两种计算兴波阻力的方法进行了研究比较：第一种是改进的Dawson方法，传统的Dawson方法采用静水面上的叠模流线网格，而改进的Dawson方法是采用静水面上的贴体网格来计算兴波阻力；第二种方法是单模流动法。文中利用这两种方法计算了两条集装箱船，通过和试验值比较，发现这两种方法在设计航速附近的一定范围内都能正确地识别船型变化对兴波阻力的影响，验证了这两种数值预报方法都可以用于船型优化。但是改进的Dawson方法的计算结果更接近实验值，因此改进的Dawson方法更适用于船型优化。     

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

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移动边界的有限体积KFVS方法在一维溃坝波计算中的应用

本文从Boltzmaun方程出发，采用有限体积KFVS（Kinetic flux-vector splitting）方法，对微观粒子的速度分布进行组合，给出了模拟河道洪水演进时干湿交界处移动边界的一种新方法。并成功地模拟了大坝下游为干河道的一维溃坝模型，通过和精确解的比较得出，此方法在处理河道移动边界问题上是成功和有效的。     

戽流消能沿程水面波动特性研究

为探究采用戽流消能方式时下游河道水面波动的情况,结合某实际工程建立了1∶60整体物理模型,应用DJ800多功能采集系统对自由戽流、附着戽流、临界戽流及淹没戽流时下游山区河道内沿程水面波动特性进行了模拟,并对沿程波高、周期、波长、波速及波动概率密度等特征参数进行统计。研究结果表明:戽流消能形成的涌浪在x/D20的范围内衰减明显,之后衰减明显减缓;稳定戽流时,坝下水面波动周期、波长及波速较其余戽流流态均明显变小,且河道平面转弯对波浪的衰减影响有限,波浪传播较远;不同戽流流态河道内波动主要分布在±3σ范围内,基本符合正态分布。研究成果可为类似工程的防波设计提供参考依据。     

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。