Numerical simulation of pollutant transport acted by wave for a shallow water sea bay

A numerical model of pollutant transport acted by water waves on a shallow‐water mild‐slope beach is established in this study. The numerical model is combined with a wave propagation model, a multiple wave‐breaking model, a wave‐induced current model and a pollutant convection–dispersion model. The wave propagation model is based on the higher‐order approximation of parabolic mild‐slope equation which can be used to simulate the wave refraction, diffraction and breaking in a large area of near‐shore zone combined with the wave‐breaking model. The wave‐induced current model is established using the concept of the radiation stress and considering the effect of bottom resistance caused by waves. The numerical model is verified by laboratory experiment results of regular and irregular waves over two mild beaches with different slopes. The numerical results agree well with experimental results. The numerical model has been applied in the near‐shore zone of Bohai bay in China. It is concluded that pollutant transport parallel to the shoreline due to the action of waves, which will induce serious pollution on the beach. Copyright © 2005 John Wiley & Sons, Ltd.     

Steep wave fronts on extrudates of polymer melts and solutions: lubrication layers and boundary lubrication

Steep wave fronts tend to develop in many regimes of lubricated, slipping flows in which waves appear. Problems of slip, spurt, fracture and extrudate distortion can be framed in terms of lubrication theory with paradigms arising from the lubrication of heavy oil with water for some problems and concepts from the theory of boundary lubrication for others. In water-lubricated pipelines, high pressures are produced at the front side of a wave on the oil when water is forced through the wavecrest and the wall, low pressures develop at the back of the wave where the gap opens. The steep waves which develop on cores of heavy oil lubricated by water are irregular and look like melt fracture. Direct numerical simulation of regular periodic waves give rise to sharkskin solutions in which the wave length decreases with the wave amplitude as the gap size decreases, preserving the steep wave front. Wave steepening seems always to occur in extrusion when the polymers slip, in the abrasion of rubber samples and in Schallamach's waves of detachment.     

直立码头前船波浪力耦合计算模型

建立了外域用Boussinesq方程、内域用刚体运动方程的直立码头前二维船剖面波浪力的时 域计算耦合模型,内域与外域在交界面的匹配条件是流量连续和压力相等. 进行了相关模型 实验,并把计算结果与实验结果进行了对比. 推导了船体与水底和直立码头之间间隙内流体 运动的自振频率,研究了间隙内流体运动的共振现象.     

基于相平均方法的折射绕射联合波浪模型

近岸带波浪运动的研究具有很重要的工程意义,近年来已获得了较丰硕的研 究成果并发展了许多波浪模型,而基于不同理论的波浪模型往往具有特定的适用性. 在海岸 工程中应用比较广泛的一类波浪模型以波能(波作用量)守恒为基本依据,如SWAN模型. 该 类模型在实际工程中已经得到了大量的应用,但该类模型未计及波浪绕射效应,成为其突出 的缺陷之一. 如何对模型做适当的改进,使之适用于波浪绕射的模拟,从而在原有基础上拓 广模型的应用范围是一项具有实际意义的研究工作. 该文采用波能(波作用量)守恒方程描 述近岸带波浪运动,通过引入绕射因子,得到折射、绕射联合波浪模型,从而拓广了模型的 应用范围. 通过实际算例验证,表明所建立的模型计及了波浪折射、绕射作用,对相平 均波浪模型在波浪绕射效应模拟方面的改进具有一定的意义.     

Finite element method for shallow water equation including open boundary condition

A method to deal with an open boundary condition in the analysis of water surface waves, the tide, etc. by means of the finite element method is proposed in this paper. The present method has two important features relating to the treatment of the open boundary condition. The first feature is to consider the non-reflective virtual boundary condition which has been developed in the numerical wave analysis method. The incident wave conditions without spurious reflected waves can be imposed at the open boundary. The second feature is to identify the amplitude of the components of incident waves in terms of observed water elevations in the field of standing waves. This can be done as a parameter identification based on an optimization problem by applying the conjugate gradient method. The applicability of this method to wave propagation problems is verified by several numerical computations.     

The role of cavitation effects in the mechanisms of destruction and explosive processes

The paper presents a review of the experimental results, mathematical models and numerical investigations of wave processes and the dynamics of liquid media under impulse loading. The presence of micro-inhomogeneities can change substantially the state of the liquid, the structure of the applied wave field and the mechanisms of the physical processes that take place in the liquid. Some crucial research trends received proper attention: the cavitation fracture of liquid under explosive loading, different methods of describing the mechanisms of pressurized-liquid tank explosions, the effects of bubble cavitation and inhomogeneities on the sensitivity of high explosives (HE) to the initiation and propagation of detonation, the problem of focusing the shock waves, and destruction of stones in lithotriptors. Received 10 August 1995 / Accepted 18 June 1996     

Experimental and numerical analysis of solitary waves generated by bed and boundary movements

This paper is an experimental and numerical study about propagation and reflection of waves originated by natural hazards such as sea bottom movements, hill slope sliding and avalanches. One‐dimensional flume experiments were conducted to study the characteristics of such waves. The results of the experimental study can be used by other researchers to verify their numerical models. A finite volume numerical model, which solves the shallow water equations, was also verified using our own experimental results. In order to deal with reflection on sloping surfaces and overtopping walls, a new condition for the treatment of the coastline is suggested. The numerical simulation of wave generation is also studied considering the bed movement. A boundary condition is proposed for this case. Those situations when the shallow water equations are valid to simulate this type of phenomena have been studied, as well as their limitations. Copyright © 2004 John Wiley & Sons, Ltd.     

间隙对金属锡爆轰加载过程的影响

采用高能炸药透过钢板对锡样品开展爆轰加载实验,并通过数值模拟对实验结果进行验证,分析不同间隙对爆轰加载过程的影响。研究结果表明:亚毫米级别的样品间隙能对实验结果会产生显著影响;一方面锡样品与钢层间的间隙将导致冲击波在间隙表面发生强反射,反射稀疏波在钢层与炸药界面再次反射形成较强的后续压缩冲击波,进而导致锡样品的加载压力显著升高,另一方面,金属层间与炸药间的间隙将导致加载压力降低;相较于金属层间与炸药间的间隙,锡样品与钢层间的间隙对加载影响更严重,并且随着间隙尺寸变化,两种情况中间隙影响的变化趋势也有所差异。     

Nonlinear wave amplification in front of reflective structures

For the design of marine and coastal structures subject to nonlinear waves in deep to shallow water, it is crucial to take into account both wave/structure and wave/wave interactions. A critical phenomenon involving large wave amplifications on the weather side of reflective structures has been recently observed during experimental campaigns. It appears for a wide range of wavelengths, when compared to the size of the structure, and it is directly related to third order interactions in the wave steepness. This induces high free surface elevations, known as ‘run-ups’, associated with high local loads that can damage the structure. In this paper, we pursue theoretical and numerical calculations using two approaches: a steady-state spectral solution and time-domain simulations using a high-order Boussinesq model. Cases involving normal and oblique wave interaction with a vertical rigid plate are investigated.     

Numerical study of breaking waves by a two‐phase flow model

A two‐phase flow model, which solves the flow in the air and water simultaneously, is presented for modelling breaking waves in deep and shallow water, including wave pre‐breaking, overturning and post‐breaking processes. The model is based on the Reynolds‐averaged Navier–Stokes equations with the k ?ε turbulence model. The governing equations are solved by the finite volume method in a Cartesian staggered grid and the partial cell treatment is implemented to deal with complex geometries. The SIMPLE algorithm is utilised for the pressure‐velocity coupling and the air‐water interface is modelled by the interface capturing method via a high resolution volume of fluid scheme. The numerical model is validated by simulating overturning waves on a sloping beach and over a reef, and deep‐water breaking waves in a periodic domain, in which good agreement between numerical results and available experimental measurements for the water surface profiles during wave overturning is obtained. The overturning jet, air entrainment and splash‐up during wave breaking have been captured by the two‐phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems.Copyright © 2011 John Wiley & Sons, Ltd.     

可燃气体中激波与障碍物作用在下游形成爆轰波的数值研究

对平面激波和单个矩形障碍物作用的过程进行了数值模拟,研究了反射产生的上行爆轰波在下游可燃气体中形成爆轰波的过程。数值结果表明,下游爆轰波形成过程主要有2种模式:爆轰波直接绕射和绕射波在上壁面反射,这和已有的实验结果是一致的。通过研究下游爆轰波的形成过程受入射激波马赫数、混合气体的压力和管道尺度的影响,分析了上游爆轰波向下游传播的波动力学过程,讨论了2种形成过程的作用规律和控制因素,阐明了下游爆轰波的形成规律。     

Rotary motion of the parametric and planar pendulum under stochastic wave excitation

In this paper a rotary motion of a pendulum subjected to a parametric and planar excitation of its pivot mimicking random nature of sea waves has been studied. The vertical motion of the sea surface has been modelled and simulated as a stochastic process, based on the Shinozuka approach and using the spectral representation of the sea state proposed by Pierson–Moskowitz model. It has been investigated how the number of wave frequency components used in the simulation can be reduced without the loss of accuracy and how the model relates to the real data. The generated stochastic wave has been used as an excitation to the pendulum system in numerical and experimental studies. For the first time, the rotary response of a pendulum under stochastic wave excitation has been studied. The rotational number has been used for statistical analysis of the results in the numerical and experimental studies. It has been demonstrated how the forcing arrangement affects the probability of rotation of the parametric pendulum.     

Numerical and experimental investigation of wave dynamic processes in high-speed train/tunnels

Numerical and experimental investigation on wave dynamic processes induced by high-speed trains entering railway tunnels are presented. Experiments were conducted by using a 1:250 scaled train-tunnel simulator. Numerical simulations were carried out by solving the axisymmetric Euler equations with the dispersion-controlled scheme implemented with moving boundary conditions. Pressure histories at various positions inside the train-tunnel simulator at different distance measured from the entrance of the simulator are recorded both numerically and experimentally, and then compared with each other for two train speeds. After the validation of nonlinear wave phenomena, detailed numerical simulations were then conducted to account for the generation of compression waves near the entrance, the propagation of these waves along the train tunnel, and their gradual development into a weak shock wave. Four wave dynamic processes observed are interpreted by combining numerical results with experiments. They are: high-speed trains moving over a free terrain before entering railway tunnels; the abrupt-entering of high-speed trains into railway tunnels; the abrupt-entering of the tail of high-speed trains into railway tunnels; and the interaction of compression and expansion waves ahead of high-speed trains. The effects of train-tunnel configuration, such as the train length and the train-tunnel blockage ratio, on these wave processes have been investigated as well.     

A non-hydrostatic numerical scheme for dispersive waves generated by bottom motion

A numerical scheme based on the staggered finite volume method is presented at the aim of studying surface waves generated by a bottom motion. We address the 2D Euler equations in which the vertical domain is resolved only by one layer. The resulting non-hydrostatic scheme is used to simulate surface waves generated by bottom motion in a water tank. Here we mimic Hammack experiments numerically, in which a bed section is moved upwards or downwards, resulting in transient dispersive waves. For an impulsive downward bottom thrust, free surface responds in terms of a negative leading wave, followed with dispersive train of waves. For an upward bottom thrust, amplitude of the leading wave decays as the wave propagates, and no wave of permanent form evolves— instead, there appears a train of solitons. In this article, we show that our numerical scheme can produce the correct wave profiles, comparable with the analytical and experimental results of Hammack. Simulations using intermediate and slow bottom motions are also presented. In addition, we perform a simulation of a wave generated by submerged landslide, that compares well against previous numerical simulations. Via this simulation, we demonstrate that our scheme can incorporate a moving wet–dry boundary algorithm in the run-up simulation.     

Quantification of phase shift in the simulation of shallow water waves

Numerical simulation of nonlinear waves to reproduce the laboratory measurements has been a topic of great interest in the recent past. The results reported in the literature are mainly focused on qualitative comparison or on the relative errors between the numerical simulation and measurements in laboratory and hence lack in revealing the existence of phase shift in nonlinear wave simulation. In this paper, the simulation of nonlinear waves in mixed Eulerian and Lagrangian framework using finite element method (FEM) is investigated by applying two different velocity calculation methods viz, cubic spline and least squares (LS). The simulated wave surface elevation has been compared with the experimental measurements. The coherence analysis has been carried out using the wavelet transformation, which gives a better understanding between the numerical and the experimental results with respect to the time–frequency space, compared with the conventional Fourier transformation. It is observed that the application of cubic spline approach leads to a higher phase difference for steeper waves. The present study has shown that the phase difference exists at the higher modes rather than at the primary period. For waves with steepness (wave height/wave length) higher than 0.04, LS approach is found to be effective in capturing the higher‐order frequency components in the event of nonlinearity. In addition, the comparison of numerical simulations with that from PIV measurements for the tests with solitary waves is also reported. Copyright © 2009 John Wiley & Sons, Ltd.     

海堤越浪的数值模拟

基于RANS方程和两方程湍流模型,采用有限体积法,将人射波波场作为人工的分布源项加人动量方程,提出了适用于VOF方法的源造波一消波技术。通过对行波及驻波的计算,分别考察了数值波浪水槽前端及末端消波段的有效性。在本文建立的数值波浪水槽内对规则波在海堤上爬高和越浪过程进行了数值模拟,并将计算结果与现有实验结果进行了比较。验证计算结果表明,数值模拟结果较好地复演了海堤越浪过程。为了研究模型尺度对越浪量的影响,文中设计了一组满足重力相似但具有不同几何比尺的数值实验模型。系列数值实验结果表明,若按重力相似换算越浪量,计算结果与实验预报值间的偏差随模型比尺的增大和堤前波浪破碎强度的增强而增大,建议在进行越浪物理模型实验时需进一步考虑模型比尺对原型预报值的影响。     

锥形长药柱水下爆炸冲击波参数计算方法

为了计算锥形长药柱水下爆炸冲击波压力,以及研究长脉宽冲击波的传输特性,基于叠加原理建立了冲击波压力-时间曲线的计算方法,通过实验验证了该方法的有效性,在此基础上分析了锥形长药柱不同方位冲击波压力的分布规律。研究结果表明:锥形长药柱产生的冲击波压力具有各向异性,在起爆端一侧形成的是具有厚波头特征的低幅值长脉宽冲击波,在装药径向形成的是接近指数衰减的高幅值冲击波,而在远离起爆端的冲击波压力幅值和脉宽则介于前两者之间。锥形长药柱与球形装药冲击波分布的差异是由于装药形状和起爆方式的改变所导致的,由于装药不同部位起爆的时间差,导致水下爆炸冲击波在不同位置的叠加效果存在明显差异,药柱周围流场中形成的冲击波压力具有方向性。利用提出的计算方法得到的计算结果与实验结果和数值模拟结果吻合较好,研究结果可为锥形长药柱水下爆炸冲击波威力场和毁伤评估提供参考和依据。     

退役单基药的冲击起爆特性

为了研究退役单基药的冲击起爆特性,参照GJB772A-97中卡片式隔板法实验方法,分别开展了退役单基药的连续爆速实验、冲击波感度实验及锰铜压力计实验,观测了其冲击起爆的爆轰建立过程,得到了临界隔板值以及临界起爆压力。在连续爆速实验中,隔板厚度为50 mm时,观察到了退役单基药反应冲击波不断增长的过程,并在90mm处转变为爆轰; 在冲击波感度以及锰铜压力计实验中,测得其临界隔板厚度为50~52 mm,临界起爆压力为1.35~1.49 GPa。对退役单基药的冲击起爆过程进行了数值模拟,结合三种实验的实验结果,标定了其点火增长模型反应速率方程参数。     

浅水区海底管道周围海床渗透压力计算研究

我国海上油田开采起步较晚,大部分油田处于浅水区,因此,在设计管道时,应充分考虑由浅水区波浪引起的管道周围海床渗流力。根据浅水波相关假设,考虑自由水面非线性影响,推导出椭圆余弦波的波面方程,在此基础上进一步得到一个关于速度势的表达式,并根据该表达式得出作用于海床表面的波压公式。考虑海床土的压缩性,推导出一阶近似椭圆余弦波作用下浅水区埋置管道周围海床的渗流压力解析解,最后将计算结果与大型水槽试验及以往研究成果作对比。结果表明,在椭圆余弦波的作用下,由一阶椭圆余弦波理论得到的计算结果与试验结果规律基本一致,与相似工况下的现有理论成果数值基本相同,具有一定的可行性和工程价值。     

Viscous waves and wave-structure interaction in a tank using adapting quadtree grids

Viscous waves and waves over a submerged cylinder in a stationary tank are simulated using a volume-of-fluid numerical scheme on adaptive hierarchical grids. A high resolution interface-capturing method is used to advect the free surface interface and the Navier–Stokes equations are discretised using finite volumes with collocated primitive variables and solved using a Pressure Implicit with Splitting of Operators (PISO) algorithm. The cylinder is modelled by using the technique of Cartesian cut cells. Results of flow of a single fluid past a cylinder at Reynolds number Re=100 are presented and found to agree well with experimental and other numerical data. Viscous free surface waves in a tank are simulated using uniform and quadtree grids for Reynolds numbers in the range from 2 to 2000, and the results compared against analytical solutions where available. The quadtree-based results are of the same accuracy as those on the equivalent uniform grids, and retain a sharp interface at the free surface while leading to considerable savings in both storage and CPU requirements. The nonlinearity in the wave is investigated for a selection of initial wave amplitudes. A submerged cylinder is positioned in the tank and its influence on the waves as well as the hydrodynamic loading on the cylinder is investigated.