Scour and burial mechanics of conical frustums on a sandy bed under combined flow conditions

The scour and burial of conical frustums placed on a sandy bed under waves alone (WA) and combined flows (CF) conditions was investigated. The observations indicate that equilibrium burial depth is smaller than burial of other objects such as short cylinders laying on a sand bed under equivalent hydrodynamic conditions. Truncated cone offers less resistance to the flow field due to its more round shape when compared to a horizontally placed short cylinder characterized by sharp edges. A smaller disruption to the flow field translates to less turbulent intensity and to smaller sediment transport capacity of the flow around the object and less burial. The equilibrium burial depth shows a significantly weaker dependency on the Shields parameter than on the Keulegan-Carpenter number, contrary to the case of finite short cylinders. A new empirical predictor based on the relative strength of the wave to the wave plus current velocity, the Keulegan-Carpenter number, and the Shields parameter is proposed for estimating the equilibrium burial of truncated cones under combined flows. Both the Keulegan-Carpenter number and the Shields parameter determine the width of the scour hole around the cone. The former however, is the most dominant parameter influencing the length of the scour hole.     

Measured and Predicted Burial of Cylinders During the Indian Rocks Beach Experiment

Burial of instrumented mine-like cylinders as a result of wave-induced scour was measured during experiments conducted in shallow water (15-16 m) with fine-sand (133-mum) and coarse-sand (566-mum) sediments off Indian rocks beach (IRB), FL. scour pits developed around the instrumented cylinders in the fine-sand site when significant waveheights exceeded 2 m, causing the cylinders to pitch, then roll into the developing scour pits, often changing heading to align parallel with the wave crest. Final cylinder burial was nearly 40 cm (about 70%-80% mine diameter) relative to the sediment-water interface, but only 20%-50% relative to surface area covered. The difference was caused by the lack of complete infilling of scour pits. Little development of scour pits and burial was noted on the coarse-sand site and the cylinders buried to only 20%-40% of the cylinder diameter below the sediment surface. Burial results, although variable, are in general agreement with the wave-induced scour model developed by Trembanis et al. (2007) for the fine sand, but not for the coarse sand where measured burial was much less than predicted.     

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies.     

Burial and scour around short cylinder under progressive shoaling waves

The results of a laboratory experimental program aimed at better understanding the scour around and burial of heavy cylindrical objects under oscillating flow on a sandy bed are described. This study was motivated by its application to the dynamics of isolated cobbles/mines on a sandy floor under nonlinear progressive waves, such as that occur in shallow coastal waters beyond the wave-breaking region. In the experiments, nonlinear progressive waves were generated in a long wave tank of rectangular cross-section with a bottom slope. Model mines (short cylinders) were placed on the sandy bottom and the temporal evolution of the bed profile and the velocity field in the near field of the object were observed. Experiments were conducted at relatively high Reynolds numbers for a range of flow conditions, which can be characterized by the Keulegan–Carpenter number and Shields parameter. Depending on the values of these parameters, four different scour regimes around the cylinder including periodical burial of cylinder under migrating sand ripples were observed; they were classified as: (i) no scour/burial, (ii) initial scour, (iii) expanded scour, and (iv) periodic burial cases. A scour regime diagram was developed and the demarcation criteria between different regimes were deduced. Semi-empirical formulae that permit estimation of the scour depth with time, the equilibrium maximum scour depth and length, and conditions necessary for the burial of the cylinder as a function of main external parameters are also proposed.     

Interaction of cnoidal waves with an array of vertical concentric porous cylinders

An array of large concentric porous cylinder arrays is mounted in shallow water exposed to cnoidal waves. The interactions between waves and cylinders are studied theoretically using an eigenfunction expansion approach. Semi-analytical solutions of hydrodynamic loads and wave run-up on each cylinder are obtained using first approximation to cnoidal waves. The square array configuration of four-legged identical concentric porous cylinder is investigated in present study. Numerical results reveal the variation of dimensionless wave force and wave run-up on individual cylinder with angle of incidence, porosity parameter, spacing between outer and inner cylinders, spacing between concentric porous cylinders and wave parameter. Different mechanism of wave force is found under different range of scattering parameter.     

Wave interaction with a concentric porous cylinder system

This is a theoretical investigation of wave interaction with a concentric surface-piercing two-cylinder system. The exterior cylinder is porous and considered to be thin in thickness and the interior cylinder is impermeable. Both cylinders are rigidly fixed at the sea bed. The fluid motion is idealized as a linearized potential flow. The free-surface elevation and the total net hydrodynamic forces acting on both cylinders are determined analytically. The wave-induced overturning moments are also evaluated. It is found that, with the existence of the exterior porous cylinder, the hydrodynamic force acting on the interior cylinder is reduced if compared to the force exerted on the interior cylinder by a direct wave impact. The reduction of the wave amplitude around the leeward side of the outer porous cylinder is shown from the free-surface computations. In this paper, results are also presented to illustrate the effects of wave parameter and structural porosity on this wave and cylinder interaction problem. The role played by the ratio of radii of the inner and outer cylinders is duscussed.     

A review of vortex shedding research and its application

This paper is a review of research work with cylinders in steady currents. The emphasis is mainly on cylinders in water, particularly the research undertaken at BHRA and its general application. Comparisons are made with the work of other authors for both water and air flow and over 60 references are reviewed. The mechanisms of flow-excited oscillations are discussed for isolated vertical and inclined cylinders. The effects of length/diameter ratio, cylinder surface roughness and channel blockage are presented. Wake interactions caused by cylinder-cylinder and cylinder-splitter arrangements are detailed. The results of tests with pane and three-dimensional frames are described and quantified in terms of isolated cylinder data.The paper closes with a section describing methods of avoiding oscillations by calculation at the design stage or by the use of clamp-on devices for completed structures in water flow.     

Numerical calculation of forces induced by short-crested waves on a vertical cylinder of arbitrary cross-section

Most off-shore oil platforms are supported by vertical cylinders extending to the ocean floor. An important problem in off-shore engineering is the calculation of the wave loading exerted on these vertical cylinders. Analytical solutions have been found for the case of plane incident waves incident on a circular cylinder by MacCamy and Fuchs [(1954), Wave forces on piles: a diffraction theory. U.S. Army Corps of Engineering, Beach Erosion Board, Technical Memorandum No. 69] and also for short-crested waves incident on a circular cylinder by Zhu [(1993), Diffraction of short-crested waves around a circular cylinder. Ocean Engng 20, 389–407]. However, for a cylinder of arbitrary cross-section, no analytic solutions currently exist. Au and Brebbia [(1983), Diffraction of water waves for vertical cylinders using boundary elements. Appl. Math. Modelling 7, 106–114] proposed an efficient numerical approach to calculate the wave loads induced by plane waves on vertical cylinders by using the boundary element method. However, wind-generated waves are better modelled by short-crested waves. Whether or not these short-crested waves can induce larger wave forces on a structure is of great concern to ocean engineers. In this paper wave loads, induced by short-crested incident waves, on a vertical cylinder of arbitrary cross-section are discussed. For a cylinder of certain cross-section, the wave loads induced by short-crested waves can be larger than those induced by plane waves with the same total wave number.     

五圆柱体结构群绕流特性及互扰效应研究

基于Fluent流体计算平台,运用大涡模拟方法对亚临界雷诺数Re=3900下“X”形排列五圆柱体结构群三维绕流特性进行研究,主要分析来流攻角α与间距比L/D两个关键参数对五圆柱体结构群的尾流区三维涡结构演化与流体力系数的影响,并揭示其内在流动互扰机理。研究表明:来流攻角和间距比的变化对五圆柱体结构群流动控制及互扰效应的影响显著。在小间距比工况下,观察到柱体群间隙区域内流体高速流动的现象,导致五圆柱体之间的互扰作用十分强烈。间隙流对中间圆柱体和下游圆柱体有较强的冲击作用,对其表面的流体力分布特性有显著的影响。另外,大间距比工况下,当α=0°与L/D≥5.0工况时,柱体群尾流效应强于其间隙流效应。当α=22.5°与L/D=7.0时,位于下游与中间处的圆柱体流体绕流特性存在较大差异。而当α=45°与L/D≥6.0时,位于上游与中间处的圆柱体尾流区均会产生正负交替的漩涡结构。     

Fully nonlinear simulations of wave resonance by an array of cylinders in vertical motions

The finite element method(FEM) is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions.The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions.The finite element linear system is solved by the conjugate gradient(CG) method with a symmetric successive overelaxlation(SSOR) preconditioner.The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation.Numerical examples are given by an array of floating wedgeshaped cylinders and rectangular cylinders.Results are provided for heave motions including wave elevations,profiles and hydrodynamic forces.Comparisons are made in several cases with the results obtained from the second order solution in the time domain.It is found that the wave amplitude in the middle region of the array is larger than those in other places,and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.     

不同运动自由度组合串列双圆柱涡激振动数值模拟

基于自主研发的紧致插值曲线CIP (Constrained Interpolation Profile)方法数学模型,对均匀来流条件时不同运动自由度组合下的串列双圆柱涡激振动问题开展二维数值模拟。模型针对雷诺数Re=100,质量比m*=2的串列双圆柱涡激振动问题,选取上、下游圆柱不同运动自由度组合工况进行模拟。重点分析圆柱的升阻力系数、运动位移随折合速度Ur变化的响应。研究表明:当上游圆柱双自由度运动时,随着下游圆柱运动自由度的增加,下游圆柱对上游圆柱涡激振动响应的影响减弱;当下游圆柱双自由度运动时,随着上游圆柱运动自由度的增加,上游圆柱对下游圆柱涡激振动响应的影响变强。研究结果表明圆柱运动自由度组合形式对串列双圆柱涡激振动的影响不可忽略。     

Fully Nonlinear Simulations of Wave Resonance by An Array of Cylinders in Vertical Motions

The finite element method (FEM) is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions. The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions. The finite element linear system is solved by the conjugate gradient (CG) method with a symmetric successive overelaxlation (SSOR) preconditioner. The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation. Numerical examples are given by an array of floating wedge- shaped cylinders and rectangular cylinders. Results are provided for heave motions including wave elevations, profiles and hydrodynamic forces. Comparisons are made in several cases with the results obtained from the second order solution in the time domain. It is found that the wave amplitude in the middle region of the array is larger than those in other places, and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.     

Solitary wave interactions with an array of two vertical cylinders

This paper addresses a numerical investigation of nonlinear waves interactions with an array of two surface-piercing vertical cylinders and the corresponding nonlinear hydrodynamic loads on each individual cylinder. The primary interest of this study is concentrated on the problem of three-dimensional scattering of solitary waves by cylinder arrays and the nonlinear interactions between scattered waves. The theoretical model adopted for simulation is the generalized Boussinesq two-equation model. The boundary-fitted coordinate transformation and multiple-grid technique are utilized here to simplify the computation domain and to facilitate the applications of the boundary conditions on the cylinder surfaces. The velocity potential, free-surface elevation and subsequent evolution of the scattered wave field are numerically evaluated. The hydrodynamic forces on each cylinder during wave impact are also determined. A study of the sheltering effect by the neighboring structures on wave loads is conducted. It is found that the presence of the neighboring cylinder has shown significant influence on the wave loads and the scattering of the primary incident waves. For two transversely arranged cylinders, the transverse force coefficient increases as the separation distance decreases.     

Analysis of single and tandem cylinder data using an orthogonal Volterra model approach

The development of a definitive predictive model that accurately accounts for the nonlinear hydrodynamics and structural response behavior observed in arrays of closely spaced risers on deep water structures will require a more detailed understanding of this fluid–structure interaction. Through the analysis and interpretation of data from model basin tests on single and paired tandem cylinder configurations this study is directed at uncovering the nature of some aspects of this nonlinear response behavior using an orthogonal third-order Volterra technique that can delineate between linear, quadratic and cubic nonlinear frequency dependent behavior. As part of the analysis procedure the data was organized in input–output pairs that would provide logical groupings of the measured quantities. The data pairs presented in this study include wave excitation and inline cylinder displacement, wave excitation and transverse cylinder displacement, wave excitation and inline reaction force, and, upstream cylinder and downstream cylinder response. This information is presented in terms of spectral and coherence plots. The single cylinder data is presented as a means to contrast the behavior of the tandem cylinders. Both configurations were analyzed at two different pretensions adding another dimension to this investigation. It is shown that although a primary variable such as displacement may be more easily measured, pretension and force measurements provide an important key to our understanding of this difficult problem.     

Launch and impact of free-fall lifeboats. Part II. Implementation and applications

There is a great interest in a practical method of predicting the behaviour of a free-fall lifeboat, when dropped from an offshore platform or from a ship, in order to assess the risk of injury to the occupants. In particular, for those environmental conditions in which full-scale experiments are very difficult, one can benefit from numerical prediction. The hydrodynamic impact of the boat at water entry is a complex problem and makes the establishment of an analytical prediction method a challenging task.This paper is the second of two articles outlining a practical method for simulating the water entry of a free-fall lifeboat. The first article (Part I: impact theory) [Boef, W. J. C. (1992), Ocean Engng19, 119–138] reviewed the relevant literature on hydrodynamic impact and outlined the theoretical model for the water entry of a lifeboat. This paper discusses the implementation of the lifeboat launch model and a method for evaluating the effects of impacts on the occupants. The results of a comparison with full-scale tests and of a case study are also included.     

双矩形浮子波能装置辐射问题的解析方法

在有限水深下1个漂浮在水中的矩形浮子和1个淹没在水下的浮子构成双矩形波能装置模型。基于特征函数展开法求解了线性入射波作用下双矩形浮子波能装置的辐射问题,得出了双矩形浮子辐射速度势的1种新解析式,然后根据Haskind关系由入射势和辐射势来计算波浪激励力,并且采用数值方法对相同算例进行了计算,得到了完全一致的结果,从而证明这种方法是正确的。研究了在不同工况下的波浪激励力和系统的水动力学系数变化的规律。     

大尺度海工圆柱的非线性波浪载荷

引入Stokes二阶水波理论,建立了对海洋工程中大尺度综合型圆柱式结构波浪载荷的二阶修正统一积分算式。通过对波势特征解法的推广及引入干扰波叠加法、最小二乘法,使原仅适合于轴对称单柱的二阶散射波浪载荷快速积分算法可完全适用于类型广泛的任意型实用圆柱的计算。几则实例(圆台,单、双柱)的计算检验了该方法的有效性。     

Wave drift enhancement effects in multi column structures

A theoretical assessment is made of mean wave drift forces on groups of vertical circular cylinders, such as the columns of a floating offshore platform. A complete analytical solution is obtained for two cylinders extending from seabed to free surface, and a long wave approximation is found to provide reliable predictions of the drift force in line with the waves at low frequencies. For moderate separation between the two cylinders, this force is found to tend at low frequencies to a value four times the force on an isolated cylinder.A numerical method is employed to study two surface piercing cylinders truncated below the free surface, and an arrangement of four vertical cylinders characteristic of a floating offshore platform. The mean vertical drift force is found to be reasonably well approximated, over the frequency range of practical interest, by the force on an individual cylinder considered in isolation multiplied by the number of cylinders in the group. Interaction effects, however, have a profound influence on the total horizontal drift force. At low frequencies this force is found to tend to the force on an isolated cylinder multiplied by the squate of the number of cylinders in the group.     

Effect of shallow and narrow water on added mass of cylinders with various cross-sectional shapes

The sway, heave and roll added masses of three uniform cylinders with semi-circular, rectangular and triangular cross-sectional shapes in shallow and narrow water are numerically analysed. The method is based on simulation of the potential flow induced by the cylinder's mode of motion. The effects of shallow and narrow water on added mass are analysed and presented. It is concluded that the shallow and narrow water effects on added mass depend on the different cross-section shapes of the cylinders. In particular, the water depth effect on sway added mass is stronger than that on heave added mass while the narrow water effect on sway is weaker than that on heave. The shallow water effect on added mass tends to weaken the narrow water effect. Lastly the effect of shallow and narrow water on added mass on a rectangular cylinder is the strongest while that on a triangular cylinder is the weakest.     

软土地基中插入式大直径薄壁圆筒结构的一种简化数值计算方法

简述了对插入式大直径薄壁圆筒进行数值分析采用的力学机制，用弹簧元模拟薄壁圆筒与地基土体接触面间的连接所形成一种简化的数值计算模型，运用大型通用有限元软件ANSYS进行二次开发后对其进行数值计算与分析，比较了对筒内外淤泥粘土采用不同加固处理方法以及考虑相邻圆筒间采用不同边界约束条件时，对圆筒的应力和稳定性的影响。通过实例计算，验证了该数值模型的有效性与可行性，并得出一些有益结论。