Three-dimensional numerical wave tank simulations on fully nonlinear wave–current–body interactions

A finite-difference scheme and a marker-and-cell (MAC) method are used for numerical wave tank (NWT) simulations to investigate the characteristics of nonlinear wave motions and their interactions with a stationary three-dimensional body in the presence of steady uniform currents. The Navier–Stokes (NS) equation is solved in the computational domain, and the boundary values are updated at each time-step by a finite-difference time-marching scheme in the frame of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is satisfied by the marker–density function technique developed for two fluid layers. The incident waves are generated from the inflow boundary by prescribing a velocity profile resembling the motions of a flexible flap wavemaker, and the outgoing waves are numerically dissipated inside an artificial damping zone located at the end of the tank. Using the NS–MAC NWT, nonlinear wave and current interactions around a stationary vertical truncated circular cylinder are studied, and the results are compared with the experimental results of Mercier and Niedzwecki, a time-domain NWT based on linear potential theory, a fully nonlinear NWT, and a second-order diffraction computation. Received: July 3, 2001 / Accepted: September 25, 2001     

Hydrodynamic forces acting on a circular cylinder oscillating in waves and a small current

A complete theory to obtain semianalytical solutions of the wave drift damping for a circular cylinder freely oscillating in waves is developed. The wave drift damping can be significantly increased by heave and pitch motions. Effects of the draft of the cylinder and effects of the water depth are shown. The effective evaluation of the free-surface integral and the corner problem are also discussed, and the computed results of the far and near field formulations are compared. These semianalytical solutions may prove to be important in providing validation of results obtained by numerical techniques such as the higher-order boundary element method.     

全非线性方法对于沉浸双圆柱定常前行运动引起自由表面流的研究（英文）

The free surface flow generated by twin-cylinders in forced motion submerged beneath the free surface is studied based on the boundary element method. Two relative locations, namely, horizontal and vertical, are examined for the twin cylinders. In both cases, the twin cylinders are starting from rest and ultimately moving with the same constant speed through an accelerating process. Assuming that the fluid is inviscid and incompressible and the flow to be irrotational, the integral Laplace equation can be discretized based on the boundary element method. Fully-nonlinear boundary conditions are satisfied on the unknown free surface and the moving body surface. The free surface is traced by a Lagrangian technique. Regriding and remeshing are applied, which is crucial to quality of the numerical results. Single circular cylinder and elliptical cylinder are calculated by linear method and fully nonlinear method for accuracy checking and then fully nonlinear method is conducted on the twin cylinder cases, respectively. The generated wave elevation and the resultant force are analysed to discuss the influence of the gap between the two cylinders as well as the water depth. It is found that no matter the kind of distribution, when the moving cylinders are close to each other, they suffer hydrodynamic force with large absolute value in the direction of motion. The trend of force varying with the increase of gap can be clearly seen from numerical analysis. The vertically distributed twin cylinders seem to attract with each other while the horizontally distributed twin cylinders are opposite when they are close to each other.     

三维完全非线性波浪水槽的数值模拟

用有限元求解拉普拉斯方程,采用满足完全非线性自由表面条件的半拉格朗日法追踪流体自由表面,离散单元采用20节点的六面体二次等参数单元,建立了三维完全非线性数值波浪水槽.把数值计算结果与水面初始升高产生箱体内流体运动解析解和二阶斯托克波理论解进行了对比,结果表明该模型是稳定的、守恒的,能精确模拟非线性波浪的产生和传播,为今后研究非线性波浪对船舶等非规则物体的作用提供了参考.     

Nonlinear hydrodynamic responses of submerged moving payload in vicinity of a crane barge in waves

The wave interaction with a submerged cylindrical payload subjected to constrained motions in presence of a nearby floating crane barge is investigated in the three-dimensional numerical wave tank using a fully nonlinear potential flow model in the time domain. Numerical simulations are carried out to investigate the hydrodynamic features of this submerged payload under pendulum motion in water waves as well as while it moves towards the sea bed at a constant vertical velocity. It is known that the presence of multiple side by side floating bodies in waves can create significant drift motion. In the present study the similar drift motion is observed for the side by side floating barge and submerged payload and it appears that the submerged payload under constrained motions may face a very large mean drift motion of nearly seven times that of the incident wave amplitude in the beam sea upstream condition. Emphasis is also given towards investigating and understanding the influences of natural frequency of the payload and shielding effect due to the presence of the floating barge. It is found that natural frequency coupled with shielding effect generates remarkable low frequency components in payload responses both in the head sea and the beam sea situations. The effect of different cable lengths, wave maker frequencies and downward moving velocities on payload responses under several geometric setups are studied and compared, and interesting features such as increased low frequency movement of the payload near the natural frequency region and existence of considerable low frequency motions even at a greater depth (while the payload is quite below the free surface) are observed.     

港湾内非线性波浪对船剖面作用的时域计算模型(英文)

文中用边界元数值求解复速度势模拟了波浪对船剖面的时域作用力,采用满足运动学和动力学条件的半拉朗格朗日法跟踪流体的自由表面.推导了适用本数值模型的辐射边界条件,此边界条件和海绵层边界条件组成的出口边界条件,可以使波浪很好地被吸收或传播出去.进行了相关物理模型实验,数值计算结果和实验结果的对比表明此模型能精确模拟波浪对船的作用力.     

内孤立波作用下水下潜器的载荷特性数值分析

为了研究海洋内孤立波作用下潜器的载荷特性,以RANS方程为控制方程,依据Kdv,eKdv和mKdv三类内孤立波理论计算速度入口,建立两层流体中内孤立波与水下潜器相互作用的数值模拟方法,计算分析内孤立波作用下潜器的水平力、垂向力和力矩的变化规律.结果表明,数值模拟得到的内孤立波波形及振幅与其对应理论解和文献中实验结果吻合良好.潜器的受力变化规律与内孤立波波幅、上下层水深比和潜器潜深有关.     

斜浪中二维潜体的二阶定常力

本文主要研究斜浪中作用于二维潜体（或看作为无限长的潜没柱体）上二阶定常波浪力的的力学机理和计算方法．研究表明．对圆柱而言，水平方向定常力在任意浪向中均可忽略．文中进而考察了潜没深度、浪向角和波浪频率对潜体垂向定常力的影响．同时，附带地证明了用于斜浪中二维绕射问题求解的格林函数在浪向角趋于横浪情况时可退化成横浪二维绕射问题中的格林函数．     

迎浪规则波中小水线面双体船纵向运动及波浪载荷非线性特性数值分析

基于RANS方程和VOF模型求解船体粘性兴波流场,开展了小水线面双体船(Small Waterplane Area Twin Hulls,SWATH)迎浪规则波中纵向运动及波浪载荷的非线性特性研究.通过数值计算结果与模型试验结果的对比分析,验证了文中方法的有效性;在此基础上,较为系统地分析了SWATH船的垂荡及纵摇运动响应、垂向加速度和波浪载荷的一阶及二阶量随入射波高的变化规律,指出SWATH船的运动响应及载荷与波高存在非线性的关系,尤其体现在响应共振区附近;相比于船体垂荡和纵摇运动,垂向加速度及波浪载荷的非线性特性更为显著.     

Second-order wave run-up on a vertical cylinder adjacent to a plane wall based on the application of quadratic transfer function in bi-directional waves

A numerical model was developed in this study to simulate the wave diffraction caused by an arbitrarily shaped structure in the presence of bi-directional incident waves based on a higher-order boundary element method (HOBEM). Based on the developed model, the wave elevation quadratic transfer function (QTF) in bi-directional waves, which is defined as the second-order wave elevation caused by two incident waves of unit amplitude from two directions, can be determined. The developed model was subsequently used to investigate the wave interaction with a cylinder situated near a vertical wall. The image principle was applied to transform the original problem into an equivalent one of wave diffraction caused by two symmetrical cylinders in open seas exposed to bi-directional incident waves. The second-order wave run-up on the cylinder can then be determined using the wave elevation QTF obtained from an analysis of the equivalent problem. A detailed numerical analysis was then conducted. Numerical results revealed that the presence of the vertical wall can apparently disturb the wave diffraction process from the cylinder, and lead to significantly amplified second-order wave elevation within the region between the wall and cylinder. In addition, the respective contribution from the first- and second-order components to the overall wave elevation around the cylinder was discussed.     

浮式直立圆柱体辐射问题研究

采用特征函数展开及边界匹配的方法求解流场各子区域速度势的展开系数,得到了浮式直立圆柱体在静水面作纵荡,垂荡和纵摇运动时引起的水动力系数,分析了所取截断项数对计算结果的影响,所需最少截断项数取决于水深半径比和吃水半径比。讨论了水深对水动力系数的影响,得到了可近似表示深水情况的水深半径比。     

Slow drift damping force acting on a horizontal cylinder

The hydrodynamic forces acting on a circular cylinder and a rectangular cylinder undergoing slow drift oscillation in regular waves were investigated experimentally and numerically. Forced oscillation tests with low frequency and large amplitude in regular waves and forced two-harmonic oscillation with combined low and high frequencies were carried out in the experimental study. In the numerical study a finite-difference method was used to simulate viscous flow around a two-dimensional oscillating cylinder. The results of experiments showed that a horizontal rectangular cylinder oscillating slowly in waves has much higher damping coefficients than one oscillating in two-harmonic mode, while the numerical study indicated that such differences in the damping coefficient arise partly from the different effects of one-direction harmonic flow and rotating flow on the vortex shedding caused by the slow drift oscillation.     

直立圆柱体内孤立波载荷特性数值模拟

以三类内孤立波理论(KdV、eKdV和MCC)的适用性条件为依据,将内孤立波诱导上下层深度平均水平速度作为入口条件,采用Navier-Stokes方程为流场控制方程,建立了两层流体中内孤立波对直立圆柱体强非线性作用的数值模拟方法.结果表明,数值模拟所得内孤立波波形及其振幅与相应理论和实验结果一致,并且直立圆柱体内孤立波水平力、垂向力及其力矩数值模拟结果与实验结果吻合.直立圆柱体内孤立波载荷由波浪压差力、粘性压差力和摩擦力构成,其中摩擦力很小,可以忽略;对于水平力,其波浪压差力与粘性压差力量级相当,流体粘性的影响显著;对于垂向力,粘性压差力很小,流体粘性影响可以忽略.此外,直立圆柱体对内孤立波的波形及其诱导流场的影响很小,因此采用Morison公式和傅汝德—克雷洛夫力分别计算其内孤立波水平力和垂向力是可行的.     

Trapped Modes in a Three-Layer Fluid

In this work, trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities. The impermeable cylinder is fully immersed in either the bottom layer or the upper layer. The effect of surface tension at the surface of separation is neglected. In this set-up, there exist three wave numbers: the lowest one on the free surface and the other two on the internal interfaces. For each wave number, there exist two modes for which trapped waves exist. The existence of these trapped modes is shown by numerical evidence. We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth. We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity. The existence of trapped modes shows that in general, a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.     

三层流体中的捕获模态分析（英文）

In this work, trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities. The impermeable cylinder is fully immersed in either the bottom layer or the upper layer. The effect of surface tension at the surface of separation is neglected. In this set-up, there exist three wave numbers: the lowest one on the free surface and the other two on the internal interfaces. For each wave number, there exist two modes for which trapped waves exist. The existence of these trapped modes is shown by numerical evidence. We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth. We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity. The existence of trapped modes shows that in general, a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.     

不同间距下大直径圆筒防波堤波吸力试验研究

防波堤的波浪力计算对防波堤的设计和稳定具有重要意义。针对目前圆筒防波堤波吸力的设计计算方法尚未成熟,通过开展物理模型试验,进行不规则波作用下不同间距下大直径圆筒结构波吸力的分布规律、影响因素和计算方法研究。结果表明:波谷作用下,大直径圆筒结构波吸力的横向分布规律与圆筒的间距有关,纵向分布规律表现为随着水深增加先线性增大然后线性减小,且最大波吸力的位置出现在静水位一倍波高以下。圆筒的相对间距、相对水深以及波陡对不同间距大直径圆筒防波堤的波吸力影响较大。基于直立墙结构波吸力公式给出折减系数的拟合公式,用以计算圆筒周身迎浪面的波吸力。     

Numerical simulation with a macroscopic CFD method and experimental analysis of wave interaction with fixed porous cylinder structures

Porous structures have been widely applied in the coastal and ocean engineering due to their wave energy dissipation mechanism. The macroscopic computational fluid dynamics (CFD) approach where the quadratic pressure drop condition of porous surface is introduced to model the wave interaction with porous cylinders. A series of CFD simulations of waves interacting with a single porous cylinder and the combined structure of a porous cylinder with a concentric inner solid column are performed, with corresponding tank tests conducted. The CFD method is compared with experiments, linear potential model, and the quadratic BEM (boundary element method) model. The effects of porosity and porous cylinder radius on wave force and wave heights inside porous cylinder are analyzed to evaluate the performance of porous shell reducing wave loads and wave surface elevation, and the wave force variation with incident wave amplitudes are also investigated. The results demonstrate that the established CFD model is reliable for engineering analysis and thereby being of great significance for reference purpose in the CFD simulations of waves interacting with porous structures.     

考虑定常兴波影响的辐射问题去奇Rankine源方法数值计算

随着中高速船舶在海洋资源开发中的广泛应用,航速对船舶在波浪中摇荡运动的影响受到重视。本文基于势流理论,采用非均匀有理B样条(NURBS)表达物面,应用去奇Rankine源方法求解流场速度势;推导了兴波问题的二阶近似非线性自由面边界条件,以及考虑二阶近似非线性兴波影响的辐射速度势的线性自由面和物面边界条件。本文编程首先数值计算了Wigley船型的近似非线性兴波问题,将计算的线性和非线性兴波阻力系数与文献结果做了比较;然后数值计算了计及线性定常兴波影响的下潜圆球有航速辐射问题,将计算的附加质量和阻尼系数与文献结果比较。本文计算结果与文献结果吻合程度较好,验证了本文数值计算方法的有效性。文中还给出了兴波波形和辐射波形。     

Nonlinear wave forces on large-scale submerged tunnel element

This paper presents parametric studies of nonlinear wave forces on large-scale submerged tunnel element. A transportation project of submerged tunnel element under irregular wave conditions is taken as the research background. Three-dimensional diffraction potential and radiation potential associating with the motion of the floating body are utilized, and an efficient three dimensional Green function is implemented to solve the radiation-diffraction problem. A computational method for calculating the nonlinear wave forces of the submerged tunnel element is developed. The present method is validated by the existed methods and experimental data, and good agreements are observed for all test models. The effects of wave parameters and structural parameters on the second-order nonlinear wave forces are studied. Results from the present study can provide valuable recommendations for the weather window and downtime frequencies, the configuration of tugboats, the arrangement of sea-route, and the size and type of the design and construction of the submerged tunnel element.     

直接边界元法时域全非线性兴波计算

文章在时域中采用直接边界元的方法计算模拟了以稳定航速运动的近水面潜体全非线性兴波现象.从格林定理出发,在边界面上布置Rankine源和偶极子,采用时间步进的方法计算模拟潜体近自由面运动的兴波现象.每个时步自由面上的势和节点位置采用全非线性拉格朗日自由面边界条件求解,重新生成自由面网格准备下一个时步计算的初始条件.文中给出了数值计算的结果并与试验和线性计算的结果相比,证实了该方法是可靠的,并可以利用该方法建立数值波浪水池.