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.     

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     

Second-order sum-frequency wave diffraction by a truncated surface-piercing cylinder in bichromatic waves

This work considers the second-order sum-frequency diffraction problem for a stationary truncated surface-piercing circular cylinder in bichromatic waves. The solution method was based on a semianalytical formulation of the second-order sum-frequency diffraction potential. The boundary conditions were properly satisfied by introducing the “locked” and the “free” wave components of the nonlinear velocity potential. The method was validated by comparing the calculated results with numerical data previously reported by other authors. Particular attention was paid to the second-order sum-frequency heave forces and the change in the wave run-up configuration due to the existence of the lower fluid domain underneath the truncated cylinder.     

水波传播与变形的数值模拟(英文)

A numerical approach was performed to predict the propagation and transformation of nonlinear water waves. A numerical wave flume was developed based on the non-periodic high-order spectral (HOS) method. The flume was applied to analyze the effect of wave steepness and wavelength on the propagation of nonlinear waves. The results show that for waves of low steepness, the wave profile and the wave energy spectrum are stable, and that the propagation can be predicted by the linear wave theory. For waves of moderate steepness and steep waves, the effects associated with the interactions between waves in a wave group become significant and a train of initially sinusoidal waves may drastically change its form within a short distance from its original position.     

基于双层Boussinesq方程的聚焦波数值模型

基于高精度双层Boussinesq方程,建立了聚焦波的时域波浪数值水槽。时间积分采用混合4阶Adams-BashforthMoulton预报-校正格式,聚焦波生成则采用累加不同频率规则波的内部造波源项法。针对Baldock等的聚焦波试验进行数值计算,计算结果与试验数据吻合较好。利用验证后模型进一步考察了非线性对数值计算聚焦波的影响,其中考虑了强非线性、弱非线性以及线性3种情况,结果表明非线性对精确模拟聚焦波至关重要,强非线性模型给出的结果最好,弱非线性次之,线性最差。     

椭圆余弦波理论在波峰面上升高度计算中的应用

在开敞式高桩码头的设计中,波峰面上升高度是确定上部结构顶面高程的重要因素。针对波峰面上升高度的计算理论问题,对二阶斯托克斯波和椭圆余弦波理论进行论述。结合西非某工程案例,采用不同理论计算各控制点的波要素。结果表明:在长周期波浪作用海域,计算波峰面上升高度前应首先计算相对水深,当d0.125L时,采用二阶斯托克斯波理论计算结果误差较大,采用椭圆余弦波理论计算结果更符合实际情况。     

不规则波在斜坡地形破碎区波高分布的数值试验研究

在近岸浅水波浪分布的研究中,格鲁霍夫斯基给出适用于深水波至破碎波的整个浅水域(相对水深η>2)的波高经验分布公式,但该式在波浪发生破碎后的适用性研究欠缺。基于FLOW-3D软件对深水不规则波传播到斜坡地形上波浪发生破碎进行模拟,验证波高沿程分布与试验值的一致性,并模拟在130斜坡地形条件下波浪从有限水深传播到近岸破碎区的沿程波高分布变化。结果表明,在该坡度相对水深η<2.75情况下,格鲁霍夫斯基经验分布公式出现较大误差,不再适用;破碎区各累积率波高与平均波高的比值随相对水深变小呈递减趋势,经验公式值与之相比,总体上呈现出大波偏大、小波偏小的情况。     

孤立波作用于V形薄壁防波堤的绕射波浪力

在一定条件下浅水波可能以孤立波形态作用于离岸结构。基于波浪绕射理论,推导V形薄壁防波堤的一阶孤立波绕射理论解。通过对孤立波作用于防波堤的波浪力进行计算,研究孤立波对V形防波堤的作用规律。通过对180°张角的有限长薄壁V形堤足够长时的绕射波浪力计算,与无限长直立薄壁堤的孤立波反射波浪力进行有效的相似性比较。结果表明:孤立波的最大无量纲波浪力明显大于相同浅水条件下Airy微幅波理论的对应结果,由此反映浅水波的非线性效应;孤立波入射角、V形堤张角、防波堤臂长与水深比以及孤立波特征参数等因素的变化均将对波浪荷载产生一定的影响。     

Numerical simulation of nonlinear wave force on a quasi-ellipse caisson

A three dimensional numerical model of nonlinear wave action on a quasi-ellipse caisson in a time domain was developed in this paper. Navier-Stokes equations were solved by the finite difference method, and the volume of fluid (VOF) method was employed to trace the free surface. The partial cell method was used to deal with the irregular boundary typical of this type of problem during first-time wave interaction with the structure, and a satisfactory result was obtained. The numerical model was verified and used to investigate the effects of the relative wave height H/d, relative caisson width kD, and relative length-width ratio B/D on the wave forces of the quasi-ellipse caisson. It was shown that the relative wave height H/d has a significant effect on the wave forces of the caisson. Compared with the non-dimensional inline wave force, the relative length-width ratio B/D was shown to have significant influence on the non-dimensional transverse wave force.     

Time domain springing analysis on a floating barge under oblique wave

This paper studies the springing response of a flexible floating barge under an oblique wave. A time domain Rankine panel method was used to represent fluid motion surrounding a flexible seagoing vessel, and a finite element method was used for structural response. For accurate prediction of the structural response under an oblique wave, special attention was given to the structural model, such as the effect of warping distortion and bending-torsion coupling. The Vlasov assumption was followed for a deformable beam element to take into account the effect of warping distortion so that the cross section of the beam deforms out of its original plane without changing its cross-section contour. The coupled equation for both the fluid and structural domain was solved by using the implicit iterative method. A fixed point iteration with a relaxation scheme was employed in this study with the aid of the Aitken δ² process seeking acceleration of solution convergence. Accuracy of a developed computer program was verified through the comparison with experimental work done by Remy et al. (Experimental and numerical study of the wave response of a flexible barge, Hydroelasticity in Marine Technology, Wuxi, 2006) resulting in good correspondence between the two results.     

破碎波对随机波统计特性影响的实验研究(英文)

The influence of wave breaking on wave statistics for finite-depth random wave trains is investigated experimentally. This paper is to investigate the influence of wave breaking and water depth on the wave statistics for random waves on water of finite depth. Greater attention is paid to changes in wave statistics due to wave breaking in random wave trains. The results show skewness of surface elevations is independent of wave breaking and kurtosis is suppressed by wave breaking. Finally, the exceedance probabilities for wave heights are also investigated.     

高阶谱数值方法及其应用

高阶谱方法是一种快速模拟波浪运动的有效方法,它基于小波陡对速度势展开,通过快速Fourier变换解决了自由面波动问题.文中基于高阶谱方法,建立了模拟波浪运动的数值模型,通过与Stokes波理论值比较,验证了方法的合理性;并应用于波浪的色散聚集和Stokes波不稳定性研究,通过与其它结论的比较,验证了结果的正确性.     

近水面椭球体非线性兴波的数值模拟

本文开发了一种去奇异面元法用于计算以定常前进速度运动的近水面椭球体引起的三维非线性自由面势流.采用求解非线性深水波的Stokes理论求解该定常非线性问题;物面用NURBS(非均匀有理B样条)表达;孤立的Rankine源分布在物体内部和自由面上方.给出了波型、波阻以及收敛特性随一些参数的变化规律.波阻计算结果和他人的其它数值结果进行了比较,其吻合程度令人满意.     

透空式梳式防波堤的数值模拟和波浪透射系数的研究

基于FLUENT求解器,采用源函数造波方法建立了三维数值波浪水槽,应用不同的造波源函数生成线性波浪、二阶Stokes波浪和不规则波浪.建立了规则波浪和不规则波浪与梳式防波堤相互作用的数值模型,验证了水平波浪力折减系数和堤前反射率的数值结果;并对梳式防波堤有效减小波浪力的机理进行数值解释.对透空式梳式防波堤的透浪特性进行...     

Variational principles in water-wave problems (wave radiation conditions and their variational treatment)

To discuss water-wave problems in unlimited waters, it is important to know what type of wave radiation condition should be placed on a virtual surface corresponding to infinity. For this kind of problem, the Sommerfeld radiation condition is well known. In this article, the condition is extended to treat a case with an incident wave. Furthermore, a more general wave radiation condition is introduced from a different point of view. The above-mentioned wave radiation conditions are introduced into the variational principles of the Kelvin, Hellinnger–Reissner, and Dirichlet type. The Dirichlet-type variational principles are then used in numerical calculations for bending waves in a bar, and the effectiveness of the wave radiation conditions and the variational principles is shown. The numerical results for one-dimensional water-wave problems are then given. As expected, the region required for the numerical solution is reduced drastically compared with that required by the Sommerfeld-type formulation. Furthermore, the amplitude of the diverging wave is obtained in the process of reaching the variational solution. Finally, two-dimensional water-wave problems are briefly discussed. Received: August 9, 2001 / Accepted: September 17, 2001     

Water wave scattering by a sphere submerged in uniform finite depth water with an ice-cover

Using the multipole method, we formulate the problem of water wave scattering by a submerged sphere in uniform finite water depth with an ice-cover, the ice-cover being modelled as an elastic plate of very small thickness. This leads to an infinite system of linear equations which are solved numerically by standard techniques. The vertical and horizontal forces on the sphere are obtained and depicted graphically against the wave number for various values of the depth of water and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover and also the effect of varying depth of water on these quantities. When the flexural rigidity is taken to be zero, the numerical results exactly coincide with the curves of the vertical and horizontal forces on the sphere for the cases of uniform finite depth water with a free surface.     

Estimation of the response of a deeply immersed cylinder to the shock wave generated by an underwater explosion

The work presented in this paper is focused on the development of a simplified method to study the structural response of a deeply immersed cylinder subjected to the primary shock wave generated by an underwater explosion. The proposed analytical model is based on the string-on-foundation method initially developed by Hoo Fatt and Wierzbicki, who converted the two dimensional boundary value problem of a cylindrical shell to an equivalent one-dimensional problem of a plastic string on a plastic foundation. This method has already been extended by the authors to study the shock wave response of an unstiffened cylinder immersed in shallow water. The present work focuses on deep-immersed cylinders subjected to both high hydrostatic pressure and explosion shock wave. The elastic deformation energy of the cylinder under hydrostatic pressure is first calculated and used to determine the initial conditions of the dynamic problem. Cylinder deflection and plastic deformation energy are then calculated for various immersion depths. When confronted to numerical results, the proposed model appears to underestimate the increase of deflection and absorbed energy with the immersion depth. A thorough analysis of the results post-processed from Ls-Dyna/USA finite element simulations highlights a new mechanism which is due to the action of hydrostatic pressure that continues to push inward the immersed cylinder. In order to improve the analytical model, a correction factor on the hydrostatic pressure is introduced but it is finally concluded that a new mechanism dedicated to the late action of the hydrostatic pressure still needs to be developed.     

A comparative study on 3D wave load and pressure computations for different level of modelling of nonlinearities

This paper presents a comparative study on the vertical bending moment and pressures between different levels of modelling of nonlinearities based on a 3D time-domain solution scheme. The basic solution method and its successive extensions to model the nonlinear effects are similar to the code LAMP and its various versions [Lin WM, Meinhold M, Salvesen N, Yue DKP. Large amplitude motions and wave loads for ship design. 20th ONR Sym. on Naval Hydrodynamics, Washington D.C.: National Academy Press; 1994. pp. 205–226] although their numerical implementations may differ in details. Results are presented for a large tanker hull and the S175 container hull. It is found that the predictions from the different levels of computations may differ considerably, particularly for the pressures. In general the level 2 computation, which considers modelling of only the nonlinear Froude-Krylov and hydrostatic effects, over-predicts the loads and pressures compared to the most advanced ‘body-exact’ level considered in this paper, where the nonlinearities in the diffraction effect are modelled within certain approximations.     

斜坡型潜导堤波浪力特性的数值研究

为研究各水位期不同波高作用条件下,斜坡型潜堤所受波浪力的特性,基于某潜导堤工程设计与物理模型资料,采用FLUENT软件建立二维波浪数值水槽,用物理模型试验数据验证模型的可靠性,对不同淹没水深和波高下斜坡型潜导堤所受波浪力进行数值计算,分析波浪力与相对波高、相对淹没水深之间的关系,结合其他形式潜堤波浪力的经验计算公式拟合得出该斜坡型潜导堤堤顶面最大波浪力计算公式。结果表明:波浪力大小受相对波高、相对淹没水深的影响较为显著,其影响机理与波浪场流体运动特征相关;相对于波高的变化,波浪力对淹没水深的变化更为敏感,且波浪力在不同的淹没水深区间和不同的作用位置均呈现出不同的变化规律。