Trapped Modes in a Three-Layer Fluid

In this work, trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities. The impermeable cylinder is fully immersed in either the bottom layer or the upper layer. The effect of surface tension at the surface of separation is neglected. In this set-up, there exist three wave numbers: the lowest one on the free surface and the other two on the internal interfaces. For each wave number, there exist two modes for which trapped waves exist. The existence of these trapped modes is shown by numerical evidence. We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth. We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity. The existence of trapped modes shows that in general, a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.     

三层流体中的捕获模态分析（英文）

In this work, trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities. The impermeable cylinder is fully immersed in either the bottom layer or the upper layer. The effect of surface tension at the surface of separation is neglected. In this set-up, there exist three wave numbers: the lowest one on the free surface and the other two on the internal interfaces. For each wave number, there exist two modes for which trapped waves exist. The existence of these trapped modes is shown by numerical evidence. We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth. We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity. The existence of trapped modes shows that in general, a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.     

Empirical model of the wake-induced lift force on a cylinder with low mass ratio

The vortex-induced vibrations (VIV) of two flexible circular cylinders in a tandem configuration were studied numerically for spacing ratios ranging from 6 to 18 and the reduced velocities ranging from 2.35 to 12.59. The VIV response amplitude, response frequency, fluid force, pressure distribution and vortex structure of the tandem cylinders with different spacing ratios under different reduced velocities were compared. The results indicate that there is a great difference between the lift forces on the downstream and upstream cylinders. The lift coefficient of the downstream cylinder undergoing the wake-induced vibrations (WIV) is larger than that of the upstream cylinder, and the dominant frequency curves of the lift coefficients of the upstream and downstream cylinders separate. It can be found that the length and intensity of the wake are quite different under different reduced velocities and spacing ratios, and the reattachment positions between the wake and the downstream cylinder are different, which leads to a great change in the flow around the downstream cylinder and have a great effect on the wake-induced lift force on the downstream cylinder. Considering these factors, an empirical model for the wake-induced lift force on a cylinder with low mass ratio was proposed and verified.     

直立圆柱体内孤立波载荷特性数值模拟

以三类内孤立波理论(KdV、eKdV和MCC)的适用性条件为依据,将内孤立波诱导上下层深度平均水平速度作为入口条件,采用Navier-Stokes方程为流场控制方程,建立了两层流体中内孤立波对直立圆柱体强非线性作用的数值模拟方法.结果表明,数值模拟所得内孤立波波形及其振幅与相应理论和实验结果一致,并且直立圆柱体内孤立波水平力、垂向力及其力矩数值模拟结果与实验结果吻合.直立圆柱体内孤立波载荷由波浪压差力、粘性压差力和摩擦力构成,其中摩擦力很小,可以忽略;对于水平力,其波浪压差力与粘性压差力量级相当,流体粘性的影响显著;对于垂向力,粘性压差力很小,流体粘性影响可以忽略.此外,直立圆柱体对内孤立波的波形及其诱导流场的影响很小,因此采用Morison公式和傅汝德—克雷洛夫力分别计算其内孤立波水平力和垂向力是可行的.     

Vortex-induced vibrations of piggyback pipelines near the horizontal plane wall in the upper transition regime

Slender subsea structures like pipelines, jumpers and umbilicals when exposed to currents may experience vortex-induced vibrations (VIV), which can shorten their fatigue life and increase the risk of structural failure. In the present study, flow around different configurations of a piggyback pipeline close to a flat seabed has been investigated using the two-dimensional (2D) Unsteady Reynolds-Averaged Navier Stokes (URANS) equations with the k − ω Shear Stress Transport (SST) turbulence model. The Reynolds number (based on the free stream velocity and large cylinder diameter) is equal 3.6 × 10⁶ corresponding to upper-transition regime. The drag forces acting on the cylinders and base pressure coefficient value are well predicted by the present simulations, while the other hydrodynamic quantities (root-mean-square lift coefficient, Strouhal number) are predicted reasonably well as compared to published experimental data. The piggyback pipeline in the present study is modeled as two circular cylinders with a diameter ratio d/D = 0.2 (D denoting diameter of the large cylinder, d is diameter of the small cylinder). These two cylinders are clamped together at a distance G/D = 0.2. The two rigidly coupled cylinders are elastically supported and free to vibrate in two degrees of freedom. The effects on the vibration amplitudes and hydrodynamic forces are analyzed. The flow structures around the cylinders are investigated to explain the variations in observed structural responses. Depending on the angular position (α) of the small cylinder, the lock-in regime is narrower (α = 0°) or significantly wider (α = 180°) when compared to that of a single cylinder.     

四柱结构近场干涉的粘流分析（英文）

The hydrodynamic analysis of multi-floating bodies is important and widely used in marine engineering. In this study, we systematically simulated the wave diffraction problem of a fixed vertical four-cylinder structure in regular waves in the time domain in a viscous numerical wave tank. The hydrodynamic interaction of waves with a bottom-mounted structure consisting of four vertical cylinders arranged at the corners of a square shows a complicated interference phenomenon. In this paper, we illustrate and analyze the run-up around the structure and the corresponding wave forces. To investigate the viscous effect on the near-trapping phenomenon, we pay particular attention to investigating the waves near-trapped inside the four-cylinder structure,and make a comparative study of the viscous-and inviscid-flow solutions with the experimental measurements. The results show that the maximum wave elevation occurs on the inner side of the leeside cylinder, and that the wave elevations on the outer side of the cylinders are lower than those on the inner side. We can conclude that viscosity has an obvious damping effect on wave elevations inside the structure. The cylinders show a tendency to drift apart from each other when the near-trapping phenomenon occurs.     

Exciting forces for a wave energy device consisting of a pair of coaxial cylinders in water of finite depth

Two coaxial vertical cylinders-one is a riding hollow cylinder and the other a solid cylinder of greater radius at some distance above an impermeable horizontal bottom,were considered.This problem of diffraction by these two cylinders,which were considered as idealization of a buoy and a circular plate,can be considered as a wave energy device.The wave energy that is created and transferred by this device can be appropriately used in many applications in lieu of conventional energy.Method of separation of variables was used to obtain the analytical expressions for the diffracted potentials in four clearly identified regions.By applying the appropriate matching conditions along the three virtual boundaries between the regions,a system of linear equations was obtained,which was solved for the unknown coefficients.The potentials allowed us to obtain the exciting forces acting on both cylinders.Sets of exciting forces were obtained for different radii of the cylinders and for different gaps between the cylinders.It was observed that changes in radius and the gap had significant effect on the forces.It was found that mostly the exciting forces were significant only at lower frequencies.The exciting forces almost vanished at higher frequencies.The problem was also investigated for the base case of no plate arrangement,i.e.,the case having only the floating cylinder tethered to the sea-bed.Comparison of forces for both arrangements was carried out.In order to take care of the radiation of the cylinders due to surge motion,the corresponding added mass and the damping coefficients for both cylinders were also computed.All the results were depicted graphically and compared with available results.     

两圆柱体在波浪载荷作用下的运动响应分析

基于势流理论和波浪辐射/绕射理论,利用水动力分析软件(AQWA)研究两圆柱体在波浪作用下的运动响应特性,给出不同入射角与不同频率规则波作用下,小圆柱体单独运动时的六自由度响应幅值算子(RAOs)及运动响应,并与两个并排圆柱体六自由度响应幅值算子(RAOs)及运动响应作比较。结果表明:大圆柱体的干扰将使小圆柱体的纵摇、横摇、横荡、垂荡运动加剧,对小圆柱体漂移力也有较大影响,但对小圆柱体的纵荡与首摇运动影响不大。计算结果与传统方法计算值相近,证明此软件合理,可为两船在波浪中的干扰模拟计算提供参考。     

斜浪中二维潜体的二阶定常力

本文主要研究斜浪中作用于二维潜体（或看作为无限长的潜没柱体）上二阶定常波浪力的的力学机理和计算方法．研究表明．对圆柱而言，水平方向定常力在任意浪向中均可忽略．文中进而考察了潜没深度、浪向角和波浪频率对潜体垂向定常力的影响．同时，附带地证明了用于斜浪中二维绕射问题求解的格林函数在浪向角趋于横浪情况时可退化成横浪二维绕射问题中的格林函数．     

Numerical simulation with a macroscopic CFD method and experimental analysis of wave interaction with fixed porous cylinder structures

Porous structures have been widely applied in the coastal and ocean engineering due to their wave energy dissipation mechanism. The macroscopic computational fluid dynamics (CFD) approach where the quadratic pressure drop condition of porous surface is introduced to model the wave interaction with porous cylinders. A series of CFD simulations of waves interacting with a single porous cylinder and the combined structure of a porous cylinder with a concentric inner solid column are performed, with corresponding tank tests conducted. The CFD method is compared with experiments, linear potential model, and the quadratic BEM (boundary element method) model. The effects of porosity and porous cylinder radius on wave force and wave heights inside porous cylinder are analyzed to evaluate the performance of porous shell reducing wave loads and wave surface elevation, and the wave force variation with incident wave amplitudes are also investigated. The results demonstrate that the established CFD model is reliable for engineering analysis and thereby being of great significance for reference purpose in the CFD simulations of waves interacting with porous structures.     

The hydrodynamic forces acting on a cylinder array oscillating in waves and current

The problem of the interaction of multiple cylinders oscillating in waves and slow current is considered. The interaction is represented by waves emitted from adjacent cylinders towards the cylinder under consideration. Wave drift forces and moment in the horizontal plane are calculated by the far-field method based on the conservation of momentum or angular momentum. A semianalytical formula for the calculation of the wave drift damping is then deduced. The conservation of the integrals in these formulae is proved. Special treatments to improve the accuracy of results are discussed. Comparisons between calculated results and experimental measurements are made, showing satisfactory agreement. Effects of various combinations of current direction and incident wave angle on the wave drift damping and damping moment are also examined.     

Experimental investigation of TARMAX model for modeling of hydrodynamic forces on cylinder-like structures

A new approach that models lift and drag hydrodynamic force signals operating over cylindrical structures was developed and validated. This approach is based on stochastic auto regressive moving average with exogenous (ARMAX) input and its time-varying form, TARMAX. Model structure selection and parameter estimation were discussed while considering the validation stage. In this paper, the cylindrical structure was considered as a dynamic system with an incoming water wave and resulting forces as the input and outputs, respectively. The experimental data, used in this study, were collected from a full-scale rough vertical cylinder at the Delft Hydraulics Laboratory. The practicality of the proposed method and also its efficiency in structural modeling were demonstrated through applying two hydrodynamic force components. For this purpose, an ARMAX model is first used to capture the dynamics of the process, relating in-line forces provided by water waves;secondly, the TARMAX model was applied to modeling and analysis of the lift forces on the cylinder. The evaluation of the lift force by the TARMAX model shows the model is successful in modeling the force from the surface elevation.     

Trapped waves within the blocking frequency under compressed sea ice and two-dimensional current

The existence of trapped modes due to a horizontal submerged rigid cylinder placed below a compressed ice-covered surface is shown to exist within the frequency band of wave blocking by employing linearized water wave theory and with the inclusion of the effects of a two-dimensional current and the obliqueness of the propagating wave. A new modified multipole expansion method catering to the multiple propagating modes is proposed. The impact of different choices of propagating modes at a fixed frequency within the above-mentioned band on the trapped modes is detailed. Multiple trapped modes whose number depends on the direction and magnitude of the current exist within the frequency band. Out of the three choices of current types considered, while two of them result in the generation of trapped modes for all three possible choices of the propagating wave, the remaining one shows that only one propagating mode can generate a trapped wave. A break in the continuous spectrum of the trapped mode frequency due to the wave blocking and at the point of inflexion is presented. There exists a region of angle of propagation within which an abundance of the trapped mode is shown. The surface profiles for different angles of propagation and choices of propagating modes are illustrated graphically. The trapped modes associated with a higher angle of propagation decay at a faster rate.     

球体波能转换装置捕获能量的理论研究

球体波能转换装置在波浪的激励下可以同时在水平和竖直两个模式振荡。基于线性微幅波浪和势流理论,将波浪与球体相互作用简化为球体固定不动,波浪绕过球体和球体在静止流体中运动。线性叠加以后得到总的速度势,计算出球体波能转换装置的平均功率和能量俘获宽度因子的解析表达式。理论研究表明:装置与波浪运动的相位差是影响波能的最重要的参数,最优相位差为-π/2,并且给出了最优相位差调节的理论表达式。另外,对波长、波幅、球体半径、水深和球心距静水面的距离等因素也进行了分析。     

Second-order wave run-up on a vertical cylinder adjacent to a plane wall based on the application of quadratic transfer function in bi-directional waves

A numerical model was developed in this study to simulate the wave diffraction caused by an arbitrarily shaped structure in the presence of bi-directional incident waves based on a higher-order boundary element method (HOBEM). Based on the developed model, the wave elevation quadratic transfer function (QTF) in bi-directional waves, which is defined as the second-order wave elevation caused by two incident waves of unit amplitude from two directions, can be determined. The developed model was subsequently used to investigate the wave interaction with a cylinder situated near a vertical wall. The image principle was applied to transform the original problem into an equivalent one of wave diffraction caused by two symmetrical cylinders in open seas exposed to bi-directional incident waves. The second-order wave run-up on the cylinder can then be determined using the wave elevation QTF obtained from an analysis of the equivalent problem. A detailed numerical analysis was then conducted. Numerical results revealed that the presence of the vertical wall can apparently disturb the wave diffraction process from the cylinder, and lead to significantly amplified second-order wave elevation within the region between the wall and cylinder. In addition, the respective contribution from the first- and second-order components to the overall wave elevation around the cylinder was discussed.     

鹰式波浪能发电装置水动力学性能分析及优化

根据牛顿第二定律,对鹰式波浪能装置多个浮体进行了力学分析,基于微波理论,通过每个浮体之间三种模态的运动耦合,建立了流体力、阻尼力、铰接力、静水回复力等内外力之间的力学方程组。通过以运动浮体为边界条件求解多个浮体的水动力学参数,代入方程组中计算求得最优外加阻尼和最优俘获宽度比,从而优化设计方案,得到此时各浮体在纵荡、垂荡和纵摇三种运动模态下的位移幅值,以及阻尼力、铰接力、液压缸运动速度等相关参数。研究成果为鹰式波浪能装置的设计及制造提供了理论参考和依据。     

Estimation of wind loads on VLFS of semisubmersible type

This paper presents the results of investigation of wind lift force on VLFS of semisubmersible type. In the present study, wind–wave tank experiments on the scale model were also conducted in regular progressive waves. Lift forces and wind pressure were measured as a function of column diameter, unit number, superstructure and wave condition, and divided into time-averaged mean and fluctuating components. The importance of lift force, especially at the leading edge of deck, was verified in the experimental results. The results showed that fluctuation in lift force which was caused by interaction between the wind and wave was significantly large in typhoon conditions. Measured lift forces were linearly related to fluctuation of wind velocity. A lift force model is further proposed for the estimation of lift forces on VLFS of semisubmersible type and the effectiveness of this model was confirmed by the present experimental data.     

1/4 圆弧面沉箱防波堤设计分项系数研究(英文)

The quarter-circular caisson breakwater (QCB) is a new type of breakwater, and it can be applied in deepwater. The stability of QCB under wave force action can be enhanced, and the rubble mound engineering can be less than that of semi-circular breakwaters in deepwater. In order to study the wave force distribution acting on the QCB, to find wave force formula for this type of breakwater, firstly in this paper, the distribution characteristics of the horizontal force, the downward vertical force and the uplift force on the breakwater were gotten based on physical model wave flume experiments and on the analysis of the wave pressure experimental data. Based on a series of physical model tests acted by irregular waves, a kind of calculation method, which was modified by Goda formula, was proposed to carry out the wave force on the QCB. Secondly, the reliability method with correlated variables was adopted to analyze the QCB, considering the high correlation between wave forces or moments. Utilizing the observed wave data in engineering field, the reliability index and failure probability of QCB were obtained. Finally, a factor Q=0.9 is given to modify the zero pressure height above SWL of QCB, and wave force partial coefficient 1.34 to the design expressions of QCB for anti-sliding, as well as 1.67 for anti-overturning, were presented.     

串列双圆柱流致振动数值模拟

基于开源程序OpenFOAM和动网格技术,利用切应力平衡法建立水流作用下的海上风电基础局部冲刷数学模型。通过模拟结果与实验数据的对比发现,所建立的冲刷数学模型能够合理反映圆柱型单桩基础周围的水流结构,冲刷深度与实验结果吻合较好。     

块体形状对水流拖曳力的影响

在计算块体受到的水流拖曳力时,常借鉴针对球体所提出的公式,然而它并不能客观地反映出块体形状对拖曳力产生的影响。文中将块体形状概化为长方体,通过水槽试验测量了水流作用下不同尺度的大颗粒块体受到的水平拖曳力,研究了块体形状对水流拖曳力的影响,并提出了考虑块体形状影响的拖曳力计算公式。