NONLINEAR WAVE INDUCED BY AN ACCELERATING CYLINDRICAL TANK

This paper presents a method of solving Lagrangian version of governing equations that allows boundary conditions at the free surface to be satisfied exactly, which is a three-dimensional generalization of a method first put forward by Stoker. Analytical expressions of nonlinear hydrodynamic pressure up to the third order and of free surface displacement up to the fourth order of an accelerating cylindrical tank were obtained. Here only the motions of objects in their early stage after initial impulses was considered. As a justification of the method, the importment special case when the ratio of tank diameter to fluid depth tends to infinity was taken as an exainple, which shows that the linear hydrodynamic pressure obtained agrees completely with Westergaard or von Karman's classical result.     

FINITE ELEMENT ANALYSIS OF A VERTICAL RECTANGULAR PLATE COUPLED WITH AN UNBOUNDED FLUID DOMAIN ON ONE SIDE USING A TRUNCATED FAR BOUNDARY

The dynamic pressure distribution on a rectangular plate attached to a rigid wall and supporting an infinitely large extent of fluid subjected to a harmonic ground excitation is evaluated in the time domain. Governing equations for the fluid domain are set considering the compressibility of the fluid with negligibly small change in density and a linearized free surface. A far boundary condition for the three-dimensional fluid domain is developed so that the far boundary is truncated at a closer proximity to the structure. The coupled problem is solved independently for the structure and the fluid domain by transferring the acceleration of the plate to the fluid and pressure of the fluid to the plate in sequence. Helmholtz equation for the three-dimensional fluid domain and Mindlin's theory for the two-dimensional plate are used for the solution of the interacting domains. Finite element technique is adopted for the solution of this problem with pressure as nodal variable for the fluid domain and displacement for the plate. The time dependent equations are solved in each of the interacting domain using Newmark-b method. The effectiveness of the technique is demonstrated and the influences of surface wave, exciting frequency and flexibility of the plate on dynamic pressure are investigated.     

LARGE EDDY SIMULATION FOR PLUNGING BREAKER WAVE

1 .　INTRODUCTIONInthenear shoreregion ,aswavespropagateintoshallowwater ,theprocessofshoalingleadstotheincreaseofwaveheight ,however ,thisprocesscannotcontinue ,andatacertain positionthewavebreaks .Inpractice ,breakingwavesarepow erfulagentsforgeneratingturbulence ,whichplaysanimportantroleinmostofthefluiddynamicalprocessesthroughoutthesurfzone ,suchaswavetransformation ,generationofnear shorecurrent ,diffusionofmaterials ,andsedimenttransporta tion .Manynumericalstudieshavebeenconductedt…     

THE VOF METHOD FOR STUDY OF WAVE RUN-UP AND BREAKING ON A SLOPING STRUCTURE

The volume of fluid method(VOF method)for numerical simulations describing wave run-up on a sloping structure including the overturning,breaking and.merging phenomena is presented.The flow motions are governed by the classical,two-dimen-sional Navier-Stokes equation for incompressible fluid.Computational results concerning the time evolution of the free surface and pressure distribution along water bed and slope boundary are given,showing how an initial solitary wave undergoes run-up,overturning,breaking and merging on the slope.It is found that most of the wave energy is lost after the wave breaking and merging.     

用MPS方法数值模拟低充水液舱的晃荡

液体晃荡是一种非线性的自由面流动现象.在低充水率下,由于液体具有很大的运动空间,晃荡现象具有强烈的非线性特征,自由面的变形较大,剧烈时甚至会翻卷和破碎,这给数值模拟带来很大挑战.本文基于移动粒子半隐式法(Moving Particle Semi-Implicit,MPS)对低充水率的液舱晃荡问题进行了数值模拟.结果表明:当激励频率等于共振频率时,液体撞击到了液舱的顶板,并出现了飞溅现象,此时液体对侧舱壁产生了较大的抨击压力;在低于共振频率时,自由面出现了破碎波及波前的翻卷和融合等现象,抨击压力相对较小.计算结果表明,MPS方法能够很好地预测晃荡引起的拍击现象,数值计算得到的压力能够与实验结果很好地吻合.在自由面的追踪上,MPS方法具有很大的灵活性,能够很好地处理自由面的破碎、融合及液体的飞溅等流动现象.     

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…     

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.     

NUMERICAL SIMULATION OF IRREGULAR WAVE-SIMULATING IRREGULAR WAVE TRAIN

In real sea states, damage incidents on offshore floating structures are not due to the whole time series of wave elevation characterized as statistical one but due to few extreme waves or wave groups in irregular wave train. So, using CFD tools to precisely simulate predetermined irregular wave train will lay sound basis for understanding the local characteristic of the flow field and impact loads on offshore floating structures when damage incidents occur. In this article, the generation of single extreme wave is investigated in a numerical wave tank. First, experimental irregular wave train is decomposed into certain number of small-amplitude waves. The Fourier series expansion is performed to determine the amplitude and initial phase angle of each wave component. A hydrodynamic transfer function is used to calculate the amplitude of wave-maker motion associated with each wave component. Then superposition is carried out on all of the wave-maker motion components to get the final wave-maker motion. With the wave-maker motion as input, simulation of the single extreme irregular wave train is modeled successfully. Then the method is applied to simulating a much more complicated irregular wave train. Once again main features of the complicated irregular wave train are reproduced compared with experiment carried out in the new deepwater experimental basin at Shanghai Jiao Tong University. In the simulation, dynamic mesh method is enabled to model the piston-type wave-maker, the Volume Of Fluid (VOF) method is employed to capture the free surface and a dissipation zone is introduced to deal with wave reflection.     

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.     

WAVE FORCES ON INCLINED CYLINDER IN REGULAR WAVES

Through a series of model tests,the wave forces on horizontal and inclined circularcylinders are measured and analyzed.Based on Morison Equation and Stokes second order wavetheory,the relationship between the hydrodynamic force coefficients with KC number and sub-merged water depth as well for horizontal cylinders are analyzed,also the relationship betweenthe hydrodynamic force coefficients with KC number,inclined angle and the effect of water freesurface as well for the inclined cylinders are investigated.     

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].     

WAVE EQUATION MODEL FOR SHIP WAVES IN BOUNDED SHALLOW WATER

1.　 INTRODUCTIONIn the recentyears,waves in coastal shallow water,generated by marine traffic and in-tensified by port expansion,interaction with structures and reflection of land boundaries,has become a crucial factor affecting waterenvironmentsand engineering operation.In com-parison with the wind waves and ocean swells,waves inside harbor exhibitanomalous waveheight in certain areas.The dominantship waves are hardly dissipated in the harbor due tothe interaction with shorelines,and may…     

Pressure Management Model for Urban Water Distribution Networks

A technique for leakage reduction is pressure management, which considers the direct relationship between leakage and pressure. To control the hydraulic pressure in a water distribution system, water levels in the storage tanks should be maintained as much as the variations in the water demand allows. The problem is bounded by minimum and maximum allowable pressure at the demand nodes. In this study, a Genetic Algorithm (GA) based optimization model is used to develop the optimal hourly water level variations in a storage tank in different seasons in order to minimize the leakage level. Resiliency and failure indices of the system have been considered as constraints in the optimization model to achieve the minimum required performance. In the proposed model, the results of a water distribution simulation model are used to train an Artificial Neural Network (ANN) model. Outputs of the ANN model as a hydraulic pressure function is then linked to a GA based optimization model to simulate hydraulic pressure and leakage at each node of the water distribution network based on the water level in the storage tank, water consumption and elevation of each node. The proposed model is applied for pressure management of a major pressure zone with an integrated storage facility in the northwest part of Tehran Metropolitan area. The results show that network leakage can be reduced more than 30% during a year when tank water level is optimized by the proposed model.     

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.     

A NEW MEASURE FOR DIRECT MEASUREMENT OF THE BED SHEAR STRESS OF WAVE BOUNDARY LAYER IN WAVE FLUME

In this article, a shear plate was mounted on the bottom in a wave flume and direct measurements of the smooth and rough bed shear stress under regular and irregular waves were conducted with the horizontal force exerted on the shear plates by the bottom shear stress in the wave boundary layer. Under immobile bed condition, grains of sand were glued uniformly and tightly onto the shear plate, being prevented from motion with the fluid flow and generation of sand ripples. The distribution of the bottom mean shear stress varying with time was measured by examining the interaction between the shear plate and shear transducers. The relation between the force measured by the shear transducers and its voltage is a linear one. Simultaneous measurements of the bottom velocity were carried out by an Acoustic Doppler Velocimeter (ADV), while the whole process was completely controlled by computers, bottom shear stress and velocity were synchronously measured. Based on the experimental results, it can be concluded that (1) the friction coefficient groews considerably with the increase of the Reynolds number, (2) the shear stress is a function varying with time and linearly proportional to the velocity. Compared with theoretical results and previous experimental data, it is shown that the experimental method is feasible and effective, A further study on the bed shear stress under regular or irregular waves can be carried out. And applicability to the laboratory studies on the initiation of sediments and the measurement of the shear stress after sediment imigration.     

APPLICATION OF MAXIMUM ENTROPY PRINCIPLE METHOD TO THE STUDY OF WAVE CLIMATE STATISTICAL CHARACTERISTICS

The Maximum Entropy Principle (MEP) method is elaborated, and the corresponding probability density evaluation method for the random fluctuation system is introduced, the goal of the article is to find the best fitting method for the wave climate statistical distribution. For the first time, a kind of new maximum entropy probability distribution (MEP distribution) expression is deduced in accordance with the second order moment of a random process. Different from all the fitting methods in the past, the MEP distribution can describe the probability distribution of any random fluctuation system conveniently and reasonably. If the moments of the random signal is limited to the second order, that is, the ratio of the root-mean-square value to the mean value of the random variable is obtained from the random sample, the corresponding MEP distribution can be computed according to the deduced expression in this essay. The concept of the wave climate is introduced here, and the MEP distribution is applied to fit the probability density distributions of the significant wave height and spectral peak period. Take the Mexico Gulf as an example, three stations at different locations, depths and wind wave strengths are chosen in the half-closed gulf,the significant wave height and spectral peak period distributions at each station are fitted with the MEP distribution, the Weibull distribution and the Log-normal distribution respectively, the fitted results are compared with the field observations, the results show that the MEP distribution is the best fitting method, and the Weibull distribution is the worst one when applied to the significant wave height and spectral peak period distributions at different locations, water depths and wind wave strengths in the Gulf. The conclusion shows the feasibility and reasonability of fitting wave climate statistical distributions with the deduced MEP distributions in this essay, and furthermore proves the great potential of MEP method to the study of wave statistical properties.     

A numerical study of violent sloshing problems with modified MPS method

A numerical study on violent liquid sloshing phenomenon in a partially filled rectangular container is carried out by using moving particle semi-implicit(MPS) method. The present study deals with the implementation of five modifications all together over the original MPS method. The modifications include improved source terms for pressure Poisson equation, special approximation technique for the representation of gradient differential operator, collective action of mixed free surface particle identification boundary conditions, effecting Neumann boundary condition on solving the PPE and fixing judiciously the parting distance among particles to prevent collision. The suitability of the kernel function used in the original MPS method along with these five modifications is investigated for violent sloshing problems. The present model ensures a good agreement between numerical results with the existing experimental observations. The model is successfully applied to a partially filled tank undergoing horizontal sinusoidal excitation to compute the sloshing wave amplitudes and pressure on tank walls. The assessment of dynamic behaviour manifested in terms of base shear, overturning moment and impact pressure load exerted on tank ceiling induced by violent sloshing motion using MPS method is not reported in the open literature and has been efficiently carried out in the present study.     

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。     

NUMERICAL SIMULATIONS OF WATER WAVE DYNAMICS BASED ON SPH METHODS

A numerical model was established for simulating water wave dynamic problems by adopting the Smoothed Particle Hydrodynamics (SPH) methods of iterative solution of Poisson's equation for pressure field, and meanwhile the sub-grid turbulence model was applied in the simulation so as to more accurately describe the turbulence characteristics at the time of wave breaking. In this article, simulation of the problem of the dam collapsing verifies the compoting accuracy of this method, and its results can be identical with the results of VOF method and the experimental results by comparison. Numerical simulations of the course of solitary wave and cnoidal wave run-up breaking on beaches were conducted, and the results are basically consistent with experimental results. This indicates that the SPH method is effective for the numerical simulation of the complex problems of water wave dynamics.     

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.