基于粘性流模型的筒型基础防波堤波浪力数值分析

筒型基础防波堤是一种新型港口海岸工程结构,其基础上部是由连续排列的圆筒构成的直立防浪墙.采用粘性流数值模型,研究连续圆筒防波堤上波浪力竖向分布、水平(沿圆筒环向)分布和波浪力合力特性,并对粘性流数值模型计算的平面直墙波浪力与海港水文规范方法计算结果;粘性流数值模型计算的连续圆筒墙面波浪力与平面直墙波浪力;无限长连续圆筒墙面波浪力与有限长连续圆筒墙面波浪力进行比较分析.针对所选工程算例,建议按<海港水文规范>中平面直墙波浪力计算方法确定连续圆筒防波堤上的波浪力时,波峰时考虑0.90左右的折减系数,波谷时考虑0.95左右的折减系数.     

双层直立圆弧型防波堤上绕射波浪力的解析计算

基于微幅波绕射理论,应用特征函数展开法,推导了双层直立圆弧型透空防波堤的波浪绕射解析解,从而将已有的比例边界有限元法拓展为解析算法,并据此对外层与内层防波堤所受波浪载荷进行了解析计算。计算结果表明:应用本文方法对直立透空圆环柱的绕射波浪载荷进行验证计算,所得结果与现有的解析解完全吻合,说明方法可靠。双层堤较单层堤能更有效地减弱波浪作用。波浪的入射角度和特征参数、防波堤张角与半径、防波堤透空系数以及水深等因素的相对变化对双层堤的波浪作用均存在一定影响。     

Experimental and Theoretical Investigation of Wave Forces on A Partially-Perforated Caisson Breakwater with A Rock-Filled Core

1.IntroductionVertical breakwaters are widely used for harbor and coastline protection in coastal engineering.Recently,perforated breakwaters have been often used in practice as they can effectively reduce thewaveforces actingon,the wave reflectionfromand…     

Numerical investigation on the dynamics of a vertical wall defenced by an offshore breakwater

The numerical and experimental investigations on the performance of an offshore-submerged breakwater in reducing the wave forces and wave run-up on vertical wall are presented. A two-dimensional finite-element model is employed to study the hydrodynamic performance of the submerged breakwater under the action of regular and random waves. The numerical prediction has been supported with experimental measurements. The wave forces and wave run-up on the vertical wall were measured for different breakwater configurations. The applicability of linear theoretical model in the prediction of wave forces on the wall by a submerged breakwater has been discussed.     

A finite difference method for effective treatment of mild-slope wave equation subject to non-reflecting boundary conditions

A numerical model for coastal water wave motion that includes an effective method for treatment of non-reflecting boundaries is presented. The second-order one-way wave equation to approximate the non-reflecting boundary condition is found to be excellent and it ensures a very low level of reflection for waves approaching the boundary at a fairly wide range of the incidence angle. If the Newman approximation is adopted, the resulting boundary condition has a unique property to allow the free propagation of wave components along the boundary. The study is also based on a newly derived mild-slope wave equation system that can be easily made compatible to the one-way wave equation. The equation system is theoretically more accurate than the previous equations in terms of the mild-slope assumption. The finite difference method defined on a staggered grid is employed to solve the basic equations and to implement the non-reflecting boundary condition. For verification, the numerical model is then applied to three coastal water wave problems including the classical problem of plane wave diffraction by a vertical circular cylinder, the problem of combined wave diffraction and refraction over a submerged hump in the open sea, and the wave deformation around a detached breakwater. In all cases, the numerical results are demonstrated to agree very well with the relevant analytical solutions or with experimental data. It is thus concluded that the numerical model proposed in this study is effective and advantageous.     

波浪作用下涵洞式直立堤水体交换特性研究

基于计算流体力学(CFD)数值模拟和物理模型试验结合的方式,开展涵洞式直立堤在波浪作用下的水体交换研究。CFD数值模拟采用VPM (volume-average/point-value method)-THINC (tangent of hyperbola for interface capturing)/QQ (quadratic surface representation and Gaussian quadrature)模型,并在此基础上提出一种能够标记涵洞内外水体变化的双液相流体体积模型(VOF)方法,定性及定量描述涵洞内外水体的交换特性;物理模型试验主要用来验证数值模型的准确性。研究表明,在波浪的作用下,涵洞内部会形成一股往复振荡的水流,对水体交换起到重要的作用。该振荡流主要受到涵洞高度、波浪周期以及波高的影响,涵洞深度对其影响不大。在波浪长时间的作用下,涵洞式直立堤能有效地增强港池内外水体交换。     

不完全立波的二维数值波浪水槽模拟

利用二维数值波浪水槽研究波浪在防波堤前的运动状态.模型选用Navier-Stokes方程作为基本方程,以有限元法对基本方程进行离散.以直立堤前完全立波和越浪条件的不完全立波、斜坡堤前的不完全立波等典型情况的模拟为基础,组合这些典型情况模拟削角堤前不完全立波运动,探讨其堤前波面、波节点及波腹点位置、波压力等特性变化.     

Dynamic Response Analysis for Embedded Large-Cylinder Breakwaters Under Wave Excitation

1 .IntroductionThestaticmethodsarecommonlyusedinthestabilityanalysisofembeddedlarge cylinderbreak waters .Thestaticanalysismodelscanbedividedintotwocategories :simplifiedmodels (Zhouetal.,1 995;WangandZhu ,2 0 0 2 )andfiniteelementmodels (MengandWang ,1 999) .Thesimplifiedmodelsinheritthetraditionalengineeringexperiencesandareconvenienttouseinengineeringprac tice.However,itisdifficultforthesimplifiedmodelstodepictthegeometricandphysicalpropertiesofastructure soilsystemprecisely .Thefiniteel…     

Deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on a sloping bed

This study investigates the wave deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on the slope. Experiments were conducted in a three-dimensional wave basin equipped with a multi-directional random wave generator. Measurements of the free surface elevations around an impermeable submerged breakwater were carried out using 19 capacitance-type wave gages. In addition, a numerical model is proposed in three-dimensional random wave field. It is shown that the numerical results reproduce the general trend of the experimental results well. Investigations are made to study the effect of the spreading parameter S_max and bottom topography (bottom slope and submerged breakwater) on the wave deformation. It is pointed out that concentration of wave energy with larger values of the spreading parameter S_max is located within narrow limits in onshore side of the submerged breakwater. Furthermore, the supplementary discussion is made by means of numerical results.     

Numerical study on the characteristics of flow field and wave propagation near submerged breakwater on slope

In this study,characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical twodimensional model are Reynolds Averaged Navier Stokes equations. The Reynolds stress terms are closed by a nonlinear k ε turbulence transportation model. The free surface is traced through the PILC-VOF method. The proposed numerical model is verified with experimental results. The numerical result shows that the wave profile may become more asymmetrical when wave propa-gates over breakwater. When wave crest propagates over breakwater,the anticlockwise vortex may generate. On the contrary,when wave hollow propagates over breakwater,the clockwise vortex may generate. Meanwhile,the influenced zone of vortex created by wave crest is larger than that created by wave hollow. All the maximum values of the turbulent kinetic energy,turbulent dissi-pation and eddy viscosity occur on the top of breakwater. Both the turbulent dissipation and eddy viscosity increase as the turbulent kinetic energy increases. Wave energy may rapidly decrease near the breakwater because turbulent dissipation increases and energy in lower harmonics is transferred into higher harmonics.     

Three-dimensional numerical simulation on the interaction of solitary waves and porous breakwaters

A three-dimensional (3D) large-eddy-simulation model with macroscopic model equations of porous flow is proposed to investigate solitary waves interacting with permeable breakwaters. The major objective of this paper is twofold. First, we seek to evaluate the present model through the comparison with available simulated and measured data in the literature. The second aim, given the 3D nature of flow past a permeable breakwater, the variations of permeable breakwater modeled on both macroscopic and microscopic scales are examined. First validation is carried out with experiments on solitary wave propagation in a 3D wave basin and then runup on a vertical permeable breakwater with a gap in the lateral direction. A satisfactory agreement on the free surface elevation time series is obtained between model and measured results. Second, we replicate the experiments on a solitary wave interaction with a submerged permeable breakwater in a two-dimensional narrow wave flume. The porous medium is composed of spheres with a uniform size and arranged in a non-staggered regular pattern such that the porous medium can thus be modeled on macroscopic and microscopic scales. The numerical calculations indicate that the results obtained with macroscopic and microscopic modeling both fit the measurements fairly well in terms of the free surface elevations and velocity fields. Specifically, the microscopic modeling better simulates detailed phenomena such as flow injection from the porous medium and the initial stage of the formation of the main vortex in the leeward face of the obstacle. After the solitary wave completely propagates over the permeable object, the discrepancies between macroscopic and microscopic model results are insignificant. More accurate 3D results are used to determine the trajectories of fluid particles around the porous object to help understand the possible sediment movements in suspensions.     

Wave reflection from vertical breakwater with porous structure

This paper presents numerical solutions for the wave reflection from submerged porous structures in front of the impermeable vertical breakwater. A new time-dependent mild-slope equation involves the parameters of the porous medium including the porosity, the friction factor and the inertia coefficient, etc. is derived for solving the boundary value problem. A comprehensive comparison between the present model and the existing analytical solution for the case of simple rectangular geometries of the submerged structure is performed first. Then, more complicated cases such as the inclined and trapezoidal submerged porous structures in front of the vertical breakwater with sloping bottom are considered. This study also examines the effects of the permeable properties and the geometric configurations of the porous structure to the wave reflection. It is found that the submerged porous structure with trapezoidal shape has more efficiency to reduce the wave reflection than that of triangular shape. The numerical results show that the minimum wave reflection is occurred when the breakwater is located at the intermediate water depth.     

A model for obliquely incident wave interacting with a multi-layered object

This paper presents an analytical solution for scattering of oblique incident, small amplitude, monochromatic wave trains by a stationary rigid multi-layered objects with rectangular cross-section. The object is infinite long and consists of multilayers, which can be either solid or permeable. This paper extends the previous work by Hu and Liu [1] from normal incident wave condition with a special object configuration to oblique incident waves with multi-layered object. The present model is validated with several existing solutions for normal/oblique waves interacting with a single object; excellent agreement is observed. New numerical results are presented to investigate the effects of incidence angle on reflection, transmission and energy loss coefficients for a combined floating and bottom-mounted permeable breakwater. A new floating board-cage breakwater is developed from the present model and its solutions are discussed in detail. A computer program, AWAS-P, has been updated so that it is applicable for both oblique and normal incident waves, while the object is multi-layered.     

多消浪室局部开孔沉箱防波堤反射特性的迭代解析研究

基于势流理论，对多消浪室局部开孔沉箱防波堤的反射特性进行解析研究。研究中采用开孔墙处的二次压力损失边界条件，可以直接考虑波高对于开孔墙处能量损失的影响。利用匹配特征函数展开法和迭代方法得到当前问题的解析解。收敛性验证表明，迭代计算和级数解均具有良好的收敛性。该解析解的计算结果与分区边界元的数值计算结果一致，并且与已有的试验结果符合良好。通过算例分析，研究开孔沉箱防波堤反射系数的主要影响因素。结果表明：与单消浪室开孔沉箱防波堤相比，多消浪室开孔沉箱防波堤可以在更宽的波浪频率范围内保持低反射；增大开孔墙的开孔率，有利于降低多消浪室开孔沉箱防波堤的反射系数；当开孔墙的开孔率沿着入射波方向依次递减时，多消浪室开孔沉箱防波堤的反射系数较小。本文所建立的解析模型简单可靠，可用于工程初步设计中分析开孔沉箱防波堤的水动力性能。     

Numerical modeling of dynamic responses and mooring forces of submerged floating breakwater

Using the volume of fluid (VOF) method, a numerical model is developed to estimate the nonlinear dynamics of a pontoon type moored submerged breakwater under wave action and the forces acting on the mooring lines, for both the vertical and inclined mooring alignments. The model is developed for a two-dimensional wave field in a vertical plane. The finite displacements of the breakwater such as sway, heave and roll in a very small time step are considered and the numerical grid cells intersected by the breakwater surfaces for changing its position due to wave action are treated using the concept of porous body model. Also, two-dimensional experimental studies are carried out to investigate the performance of the proposed model. The comparison of the computed and measured results reveals that the developed numerical model can reproduce well the dynamics of the floating body and the mooring line forces.     

Numerical simulation of solitary wave scattering by a circular cylinder array

The interaction of a solitary wave with an array of surface-piercing vertical circular cylinders is investigated numerically. The wave motion is modeled by a set of generalized Boussinesq equations. The governing equations are discretized using a finite element method. The numerical model is validated against the experimental data of solitary wave reflection from a vertical wall and solitary wave scattering by a vertical circular cylinder respectively. The predicted wave surface elevation and the wave forces on the cylinder agree well with the experimental data. The numerical model is then employed to study solitary wave scattering by arrays of two circular cylinders and four circular cylinders respectively. The effect of wave direction on the wave forces and the wave runup on the cylinders is quantified.     

不同间距大直径圆筒防波堤波压力试验研究

通过开展物理模型试验,进行不规则波作用下不同间距大直径圆筒防波堤的波峰压力分布规律研究,分析了圆筒相对间距、相对水深、波陡等主要影响因素对圆筒波压力的影响规律,并通过波压力试验值与各家理论公式计算值的比较,进行不同间距圆筒波压力的计算方法研究。基于直立墙结构和大尺度孤立墩柱结构波压力公式给出修正系数以及横向衰减函数的拟合公式,用以计算圆筒周身不同位置处的波压力,从而为工程设计和理论研究提供参考。     

Wave radiation by a uniform cylinder in front of a vertical wall

In this paper, an exact analytical method is developed for the problem of wave radiation by a uniform cylinder in front of a vertical wall. Based on the image principle, the hydrodynamic problem of a cylinder in front of a vertical wall is transformed into the equivalent problem of double cylinders in unbounded fluid domain. Consequently, an analytical method of eigenfunction expansion is adopted to calculate the radiation of the cylinder due to the motion in surge, sway, roll and pitch, respectively. Moreover, numerical analysis has been carried out in detail in order to discuss the influences of the distance between the cylinder and the vertical wall and water depth on the added mass and radiation damping of the cylinder. It is shown that added mass and damping of the cylinder in front of a vertical wall are evidently different from those in case of the cylinder in unbounded fluid domain from the numerical results. It is also found that the added mass and radiation damping oscillate with wave number, and the oscillating frequency increases with the increasing of the distance between the cylinder and the wall.     

Solitary wave propagation influenced by submerged breakwater

The form of Boussinesq equation derived by Nwogu （1993） using velocity at an arbitrary distance and surface elevation as variables is used to simulate wave surface elevation changes. In the numerical experiment, water depth was divided into five layers with six layer interfaces to simulate velocity at each layer interface. Besides, a physical experiment was carried out to validate numerical model and study solitary wave propagation.“Water column collapsing”method （WCCM） was used to generate solitary wave. A series of wave gauges around an impervious breakwater were set-up in the flume to measure the solitary wave shoaling, run-up, and breaking processes. The results show that the measured data and simulated data are in good agreement. Moreover, simulated and measured surface elevations were analyzed by the wavelet transform method. It shows that different wave frequencies stratified in the wavelet amplitude spectrum. Finally, horizontal and vertical velocities of each layer interface were analyzed in the process of solitary wave propagation through submerged breakwater.     

Numerical Simulation of Random Wave Overtopping of Rubble Mound Breakwater with Armor Units

Based on the open source code OpenFOAM,a three-dimensional model is presented for simulation of the interaction between waves and rubble mound breakwater with armor units.The armor units with their real geometries are depicted through computational grids.The volume-averaged RANS equation and the seepage equation containing nonlinear term are used to describe the percolation in the core and underlayer of the breakwater.Grids independence analysis are carried out,the horizontal and vertical grid size are recommended to take as one-fifteenth of the mean nominal diameter D₅₀ of the armor units and one-fifteenth of the wave height respectively.Random wave overtopping of rubble mound breakwater with armor units is simulated through the proposed model.The results show good agreement between the simulated and measured overtopping discharge rates for different types of armor units.The developed numerical model can be used to evaluate the random wave overtopping in design of rubble mound breakwater with artificial armor blocs.