非线性波浪绕射问题的数值计算

本文给出非线性波浪绕射问题的计算模型,并用时间步进和边界元法求解。该模型能适用于严重非线性情形,且能满足初始条件和辐射条件。作为对该模型的检验,我们对孤立波绕过穿刺水面的直立圆柱的算例进行了计算,并同Isaacson的解析解、李宝元的差分解进行了比较,结果吻合很好。此外我们还用数值方法同时模拟造波机造波和求该波与直立圆柱的相互作用。结果表明,数值波浪水池能够以尽可能短的暂态过程,模拟波浪与物体的相互作用,提供良好的初始条件。数值波浪水池还能用于任意水深、任意水底形状下的相互作用问题。本文的计算模型和算法具有机时省,计算稳定的优点。     

应用时域格林函数方法模拟有限水深中波浪对结构物的作用

该文采用时域内满足自由水面条件的格林函数方法对无限和有限水深中波浪与任意形状三维物体相互作用所产生的绕射和辐射问题进行了理论研究和数值计算。建立了不包含自由水面积分的积分方程,消除了自由项系数。文中计算了各种形状三维物体在无限水深和有限水深情况下所受到的绕射和辐射波浪力,并与解析解以及频域理论进行了对比,结果符合良好,验证了本文所提理论的正确性。     

波浪对圆柱外接圆弧型防波堤绕射的解析计算

在微幅波绕射理论的基础上,使用特征函数展开法,推导了圆柱外接圆弧型防波堤复合结构的水波绕射的解析解,并据此计算了该结构所受到的波浪载荷以及绕射波面分布。计算结果表明:与单一圆柱相比,外接圆弧型防波堤的存在可明显降低作用于圆柱的波浪载荷和圆柱表面的波浪爬高;采用外接堤表面密实或透空而内圆柱表面透空的结构形式可以取得圆柱防浪的较佳效果;结构透空系数、波浪入射角度、外接堤张角、外堤半径与水深比、水深与波长比等因素的变化对绕射波浪作用均存在一定影响。     

LATTICE BOLTZMANN SIMULATIONS OF TRIAGULAR CAVITY FLOW AND FREE-SURFACE PROBLEMS

The Lattice Boltzmann Method (LBM) was investigated to solve triangular cavity flow and free-surface problems in hydraulic dynamics. Some cases of triangular cavity flow and backward step flow were simulated to show the efficiency and stability of this method. Two-dimensional partial dam breaking problem and the propagation and diffraction of dam-break wave around rectangular and circular cylinder were numerically studied successfully. Excellent agreement was obtained between numerical predictions and available results.     

A 3-D numerical study of solitary wave interaction with vertical cylinders using a parallelised particle-in-cell solver

This paper aims to provide a better understanding of the interaction between solitary waves and vertical circular cylinders. This is achieved via process based numerical modelling using the parallel particle-in-cell based incompressible flow solver PICIN. The numerical model solves the Navier-Stokes equations for free-surface flows and incorporates a Cartesian cut cell method for fluid-structure interaction. Solitary waves are generated using a piston-type wave paddle. The PICIN model is first validated using a test case that involves solitary wave scattering by a single vertical cylinder. Comparisons between the present results and experimental data show good agreement for the free surface elevations around the cylinder and the horizontal wave force on the cylinder. The model is then employed to investigate solitary wave interaction with a group of eleven vertical cylinders. The wave run-up and wave forces on the cylinders are discussed.     

EXPERIMENTAL STUDY ON THE SECOND-ORDER DIFFRACTION WAVE PRESSURE AND FORCE ON A CIRCULAR CYLINDER UNDER STOKES WAVE ACTION

This paper presents the model test to measure the second-order wave pressureand forces on a circular cylinder fixed in Stokes wave with a given draught.The distributions ofsecond-order oscillating and steady wave pressure on the wet surface of the cylinder and secondorder oscillating wave forces were obtained in this test,but the second-order steady wave forcewas not able to be measured due to its very small magnitude.The test results also show thatthird-order wave force may be greater than the second-order force when wave frequencies arehigh.The experimental results were compared with the corresponding calculation results of Ref-erence[3].     

大型海洋结构物的非线性绕射效应

本文在空间上应用面源法,在时间域上应用步进法,数值处理了三维物体与非线性波浪的相互干扰,研究了结构物的非线性绕射效应。首先,作为比较,求解了正弦波列和孤立波绕射垂直桩柱的情形。接着,进一步求解了大振幅波浪绕射固定在自由面上的大型浮动码头的工程实例。结果表明,非线性波浪绕射力与线性结果,有一定的差别。有时,尽管从总体效应来看,这种差别不十分明显,但从上浪、出水和波的爬高以及局部应力等局部效应来看,这种差别可能很明显。     

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。     

有限深两层流体中水波与水平圆柱潜体的相互作用

研究了有限深两层流体中表面波模态和内波模态的水波与水平圆柱潜体的相互作用问题。在线性势流理论框架内,建立了两种模态入射波作用下,水平圆柱体绕射势的多极展开求解理论。基于所建立的求解模型,对作用在圆柱体上的波浪力进行了数值计算分析,并且与均匀流中情况进行了比较。结果表明了,在入射波的某个频率范围内,流体的分层效应对圆柱体波浪力的影响是不可忽略的。同时,对流域内的绕射速度矢量场进行了数值分析。     

二阶波浪力的切片理论与潜体上的垂向定常力

二阶波浪力的三维理论基本上是对无航速的结构物建立起来的，航速的影响不甚清楚，一些理论问题，例如二阶绕射势辐射条件的提法，直到最近才得以澄清，即使如此，用三维方法完整地求取物体上的二阶波浪力仍十分费时，本文中对有航速的细长物体建立了二阶波浪力的切片理论，旨在提供理论上合理，实用上相对简便的二阶力计算方法，作为完整的二阶波浪力的一个组成部分，文中给出了细长潜体在不同潜深和浪向角时所受的垂向常力及变化趋     

用格子Boltzmann方法模拟涌波的反射与绕射

本文应用格子Boltzmann模型建立离散动力学模型,并利用Chapman Enskog对模型的方程组进行展开,建立了模拟二维浅水动力学的方程组。在从理论上证明了它严格地满足质量和动量的基本守恒定律的基础上,应用所建立的模型进行数值试验,模拟了溃坝涌波现象及其与固壁和建筑物的相互作用。利用这一模型计算了溃坝波与水中方柱和圆柱的相互作用,以及明渠内的涌波的反射和绕射复杂流场。该模型具有显式的表达形式,易于编程应用;粒子运动是彼此独立的,适合于并行数值计算;边界条件易于处理;易于处理多相流动微观机制等优点。     

THE RADIATION AND DIFFRACTION OF WATER WAVES BY A BOTTOM-MOUNTED CIRCULAR CYLINDER IN A TWO-LAYER FLUID

An analytical method was proposed to analyze the radiation and diffraction of water waves by a bottom-mounted circular cylinder in a two-layer fluid. Analytical expressions for added mass and damping coefficients, as well as the wave excitation forces of the circular cylinder were obtained by an eigenfunction expansion method. The hydrodynamic forces on the bottom-mounted circular cylinder in a two-layer fluid include not only the added mass and damping coefficients, but also the wave forces of the surface and internal-wave modes. This is different from the case of a homogenous fluid. Some examples were given, showing that density stratification can have a relative large effect on these hydrodynamic forces over a wide range of frequencies.     

Three-dimensional steep wave impact on a vertical cylinder

In the present study we investigate the 3-D hydrodynamic slamming problem on a vertical cylinder due to the impact of a steep wave that is moving with a steady velocity.The linear theory of the velocity potential is employed by assuming inviscid,incompressible fluid and irrotational flow.As the problem is set in 3-D space,the employment of the Wagner condition is essential.The set of equations we pose,is presented as a mixed boundary value problem for Laplace’s equation in 3-D.Apart from the mixedtype of boundary conditions,the problem is complicated by considering that the region of wetted surface of the cylinder is a set whose boundary depends on the vertical coordinate on the cylinder up to the free-surface.We make some simple assumptions at the start but otherwise we proceed analytically.We find closed-form relations for the hydrodynamic variables,namely the time dependent potential,the pressure impulse,the shape of the wave front(from the contact point to beyond the cylinder) and the slamming force.     

波流联合作用下的物体上的波浪绕射力

本文研究了在波流联合作用下的任意三维物体的波浪绕射问题,建立了求解物体上的波浪绕射力的时域解理论模型。本文证明了对于任意三维物体,如果在自由面条件简化时,假设定常兴波势为有限量阶,则在波浪绕射力公式中,不存在含有绕射势的水线积分项。从数学上证明了水线积分项反映了自由面条件中定常兴波势和不定常势之间的耦合效应。在此基础上,本文提出了在波流联合作用情况下,作用在物体上的绕射力与辅助辐射势之间的关系式,从而不须求解绕射势便可得到绕射力。     

RADIATION AND DIFFRACTION OF WATER WAVES BY A SUBMERGED CIRCULAR CYLINDER AT FORWARD SPEED

The wave radiation and diffraction by a submerged circular cylinder in deepwater is analysed by the multipole expansion method.The theory is based on the inviscid andlinearized potential flow.     

波浪和水流对大直径圆柱的共同作用力

本文将波流共同对圆柱作用的速度势分成合模势（无自由表面的绕流速度势）、流兴波势和非定常波势三部分。忽略小量的流兴波势，考虑合模势对非定常波势的影响，用直接边界元法求出非定常波势，从而求出波流共同对圆柱的作用力，提出了沿流线的自由表面条件和波流共同作用下散射波的幅射条件。文中给出了波流对大直径圆柱作用力曲线，可供工程设计使用，适用条件是相对水深ｄ／Ｌ＞０．１５，相对流速Ｕ／ｃ＜０．２。     

部分可渗透直立圆柱的消波作用研究

本文导出了线性波浪作用于上部可渗透的直立刚性圆柱体上的水动力的解析解。在线性有势流的假定下，用特征函数展开方法求出了内部和外部流场的解。给出了不同波浪要素及结构尺寸参数下的数值结果。由结果可知，提高可渗透性可以有效消减波幅。     

基于粒子图像测速技术的明渠圆柱上游行近流特征研究

现有实验测量和数值模拟方法难以准确捕获近水面流动特征,为全面掌握墩柱上游行近来流的内部结构和水面特征,通过明渠圆柱绕流试验,采用粒子图像测速技术对柱体上游的对称垂面进行了测量,获得了行近来流的瞬时二维流场和水面线。在此基础上,对圆柱上游的时均流动和壅水特征进行了研究,得出上游行近来流从水面至床面依次由上升流、近水平流和下降流构成,形成典型的三层结构,其中,上升流厚度随柱体雷诺数增加而变厚,下降流无量纲厚度基本不随柱体雷诺数改变。在靠近柱体的床面附近,边界层与床面分离,分离区内为向上游流动的逆流以及一个马蹄涡和一个次生涡;在靠近柱体的水面附近存在表层逆流以及两个逆向涡。研究结果揭示出边界层分离、表层逆流及柱体本身依次促使行近来流减速,使得沿程水深雍高,壅水末端至圆柱迎水面的水面线符合一元四次函数分布,无量纲壅水长度随着柱体雷诺数的增加而延长。研究成果可作为基于流体体积法等具有自由水面计算能力的明渠墩柱绕流数学模型的验证依据。     

CALCULATION OF VISCOUS FLOW AROUND CIRCULAR CYLINDER WITH THREE-DIMENSIONAL NUMERICAL SIMULATION

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The hydrodynamic interactions of an array of truncated circular cylinders as each cylinder oscillates independently with different prescribed modes

An analytical method based on the eigenfunction expansion and the Graf’s addition theorem for Bessel functions is developed to study the hydrodynamic interactions of an array of truncated circular cylinders with each cylinder oscillating independently in different prescribed modes. The hydrodynamic radiation and diffraction of linear waves by such an array of cylinders are investigated and the analytical solutions of the velocity potentials are obtained. After comparisons for degenerated cases and program verifications, several cases for an array of truncated cylinders with each cylinder oscillating independently in surge, sway, heave, roll, and pitch modes with different prescribed amplitudes, are studied and the hydrodynamic forces and moments acting on the cylinders are obtained.