Second-order sum-frequency wave diffraction by a truncated surface-piercing cylinder in bichromatic waves

This work considers the second-order sum-frequency diffraction problem for a stationary truncated surface-piercing circular cylinder in bichromatic waves. The solution method was based on a semianalytical formulation of the second-order sum-frequency diffraction potential. The boundary conditions were properly satisfied by introducing the “locked” and the “free” wave components of the nonlinear velocity potential. The method was validated by comparing the calculated results with numerical data previously reported by other authors. Particular attention was paid to the second-order sum-frequency heave forces and the change in the wave run-up configuration due to the existence of the lower fluid domain underneath the truncated cylinder.     

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．     

Three-dimensional numerical wave tank simulations on fully nonlinear wave–current–body interactions

A finite-difference scheme and a marker-and-cell (MAC) method are used for numerical wave tank (NWT) simulations to investigate the characteristics of nonlinear wave motions and their interactions with a stationary three-dimensional body in the presence of steady uniform currents. The Navier–Stokes (NS) equation is solved in the computational domain, and the boundary values are updated at each time-step by a finite-difference time-marching scheme in the frame of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is satisfied by the marker–density function technique developed for two fluid layers. The incident waves are generated from the inflow boundary by prescribing a velocity profile resembling the motions of a flexible flap wavemaker, and the outgoing waves are numerically dissipated inside an artificial damping zone located at the end of the tank. Using the NS–MAC NWT, nonlinear wave and current interactions around a stationary vertical truncated circular cylinder are studied, and the results are compared with the experimental results of Mercier and Niedzwecki, a time-domain NWT based on linear potential theory, a fully nonlinear NWT, and a second-order diffraction computation. Received: July 3, 2001 / Accepted: September 25, 2001     

Accelerated second-order hydrodynamic load calculation on semi-submersible floaters

A rapid method for calculation of second-order hydrodynamic wave loads on semi-submersible platforms is developed and validated against radiation–diffraction theory. The method is based on slender-body theory and builds on modal truncation of the quadratic transfer function (QTF). The semi-submersible floater is split into individual members and the existing theory for vertical cylindrical columns is extended to include the heave force. Further expressions for the surge, heave and pitch load on the horizontal pontoons are derived and implemented. The accuracy of the method is assessed by comparison to radiation–diffraction results using the Pinkster approximation. We find that the slender-body approximation for the column surge force is most accurate for small values of the diameter-to-draft ratio. For the three sea states considered, this error is below 10% for diameter-to-draft ratios less than 0.2.Error analysis is provided for the column heave and pitch and the pontoon loads. For all members, application of 128 modes in the QTF approximation is found sufficient to accurately represent the full slender-body QTF solution.Next, the first- and second-order loads on the full floater under different sea state conditions are compared to radiation–diffraction theory. With 128 modes, the second-order loads are obtained 2500 times faster than with conventional approaches with error levels of 22% for surge, 10% for pitch and zero error for heave. The surge error is discussed and linked to the small draft of the columns. The numerical efficiency of the method allows the consideration of second-order loads in the first stages of the design and optimisation of semi-submersible floaters.     

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.     

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.     

波浪入射角度对立柱周围波面扰动特性的影响研究

基于N-S方程和连续性方程建立了三维数值波浪水池,并在该水池内对固定直立柱在不同浪向下的波浪爬升和绕射问题进行了数值模拟。为了验证数值计算的准确性,对立柱近壁面处的波浪爬升效应展开了模型试验研究,计算值与试验值吻合较好,证明了该方法的可行性。研究了入射角度的变化对立柱周围波浪爬升幅度和非线性特征的影响,同时从垂直浪向的投影面积和相对浪向的投影面形状这两个因素出发,探讨了不同浪向角下立柱周围的波浪叠加、波面放大率以及二次波峰效应,并对自由面漩涡生成特性进行了较为深入的机理性研究,可为今后进一步研究不同的入射角度下,复杂的海洋结构物周围的波浪非线性效应提供有价值的参考。     

基于Laguerre函数对圆柱面绕射势的数值逼近

无限深圆柱表面绕射势沿水深方向的变化是连续的、不断衰减的。基于无穷区间Laguerre多项式并引入的伸缩系数s定义了Laguerre函数,既保证了函数在无穷区间的正交性,又使函数具有灵活性。绕射势的变化,可以用一系列Laguerre函数表示成级数形式。文中对该方法的收敛性进行了证明,并以一条FPSO为例对其在圆柱面的绕射势进行了逼近。求解级数展开式的系数时会遇到无穷积分问题,采用多次使用Gauss-Legendre积分和Gauss-Laguerre积分相结合的方法代替传统的Gauss-Laguerre积分方法,获得更高的积分精度。利用Laguerre函数可以对Rankine源法或者Rankine-Kelvin法的控制面上速度势进行逼近。     

系泊浮体运动响应分析的非线性水动力学方法（英文）

Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.     

存在底部起伏影响的近壁面处双层多孔栅栏陷波研究（英文）

Trapping of oblique surface gravity waves by dual porous barriers near a wall is studied in the presence of step type varying bottom bed that is connected on both sides by water of uniform depths. The porous barriers are assumed to be fixed at a certain distance in front of a vertical rigid wall. Using linear water wave theory and Darcy's law for flow past porous structure, the physical problem is converted into a boundary value problem. Using eigenfunction expansion in the uniform bottom bed region and modified mild-slope equation in the varying bottom bed region, the mathematical problem is handled for solution. Moreover, certain jump conditions are used to account for mass conservation at slope discontinuities in the bottom bed profile. To understand the effect of dual porous barriers in creating tranquility zone and minimum load on the sea wall, reflection coefficient, wave forces acting on the barrier and the wall, and surface wave elevation are computed and analyzed for different values of depth ratio, porous-effect parameter, incident wave angle, gap between the barriers and wall and slope length of undulated bottom. The study reveals that with moderate porosity and suitable gap between barriers and sea wall, using dual barriers an effective wave trapping system can be developed which will exert less wave force on the barriers and the rigid wall. The proposed wave trapping system is likely to be of immense help for protecting various facilities/infrastructures in coastal environment.     

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.     

Second-order hydrodynamic effects on an arrangement of two concentric truncated vertical cylinders

The second-order diffraction problem by a piston-like arrangement that consists of two concentric surface piercing cylinders is considered. The developed matched axisymmetric eigenfunction expansion solution methodology in cylindrical co-ordinates is based on the semi-analytical formulation of the velocity potentials in the various fluid regions which are defined by the geometry of the two-body arrangement. The main difficulty associated with the specific configuration originates from the fact that the geometry defines two fluid regions that extend up to the free surface in which the inhomogeneous second-order free surface boundary condition has to be fulfilled. To this end the associated velocity potentials in these regions are decomposed into a number of components defining the so-called ‘free’ and ‘locked’ waves. The latter are calculated by solving the resulting Sturm–Liouville problems. The seek second-order velocity potential in the whole fluid domain is then derived by enforcing matching conditions for the radial velocities and the fluid pressures at the cylindrical boundaries of adjacent fluid domains. Numerical results concerning the second-order hydrodynamic loading and the wave run-up on the cylinders are given, whereas special attention is given at incident wave frequency regions where the first-order exciting wave forces attain maximum values due to the resonant fluid motions in the moonpool.     

孤立波作用于V形薄壁防波堤的绕射波浪力

在一定条件下浅水波可能以孤立波形态作用于离岸结构。基于波浪绕射理论,推导V形薄壁防波堤的一阶孤立波绕射理论解。通过对孤立波作用于防波堤的波浪力进行计算,研究孤立波对V形防波堤的作用规律。通过对180°张角的有限长薄壁V形堤足够长时的绕射波浪力计算,与无限长直立薄壁堤的孤立波反射波浪力进行有效的相似性比较。结果表明:孤立波的最大无量纲波浪力明显大于相同浅水条件下Airy微幅波理论的对应结果,由此反映浅水波的非线性效应;孤立波入射角、V形堤张角、防波堤臂长与水深比以及孤立波特征参数等因素的变化均将对波浪荷载产生一定的影响。     

The estimation of wave elevation and wave disturbance caused by the wave orbital motion of a fully submerged hydrofoil craft

The current control system of a fully submerged hydrofoil craft has manual input of fore-foil depth and control mode selection to improve the performance of the control system. However, the manual input needs skillful human operation and observation of waves the encountered to work well over a wide range of waves. In order to use information about the waves encountered in the control system, we considered the estimation of wave elevation and wave disturbance which was caused by the orbital motion of the waves in irregular waves. First, we investigated the wave disturbance by a fully submerged hydrofoil craft, in a state-space model of wave disturbance, and in hydrofoil craft motion, etc. We than considered estimations of the wave elevation and wave disturbance using a shaping filter, a Kalman filter, an autoregressive (AR) model, etc. Finally, we confirmed through simulations that the estimation results and estimation error of wave elevation and wave disturbance were valid.     

Hydrodynamic forces acting on a circular cylinder oscillating in waves and a small current

A complete theory to obtain semianalytical solutions of the wave drift damping for a circular cylinder freely oscillating in waves is developed. The wave drift damping can be significantly increased by heave and pitch motions. Effects of the draft of the cylinder and effects of the water depth are shown. The effective evaluation of the free-surface integral and the corner problem are also discussed, and the computed results of the far and near field formulations are compared. These semianalytical solutions may prove to be important in providing validation of results obtained by numerical techniques such as the higher-order boundary element method.     

不同沉箱结构形式防波堤对港内泊稳影响的试验研究

通过对韩国某港北防波堤工程波浪整体物理模型试验研究,分别对比了普通直立式和开孔直立式2种沉箱结构的防波堤对港内泊稳条件的掩护效果。试验采用SSE、SE两个代表波向,采集并分析港内及防波堤周围水域的波高及分布。试验结果表明,采用相同入射波条件时,2种结构防波堤均可对港内形成一定程度的掩护。但由于工程海域波高较大,次生波的出现影响了泊稳条件。两方案相比,开孔沉箱结构的防波堤对拟建港区的掩护效果略好,综合比较最后推荐开孔沉箱结构的防波堤方案。     

基于泰勒展开边界元耦合镜像格林函数法的浮体水动力学池壁效应（英文）

A novel numerical model based on the image Green function and first-order Taylor expansion boundary element method(TEBEM), which can improve the accuracy of the hydrodynamic simulation for the non-smooth body, was developed to calculate the side wall effects on first-order motion responses and second-order drift loads upon offshore structures in the wave tank. This model was confirmed by comparing it to the results from experiments on hydrodynamic coefficients, namely the first-order motion response and second-order drift load upon a hemisphere, prolate spheroid, and box-shaped barge in the wave tank. Then,the hydrodynamics of the KVLCC2 model were also calculated in two wave tanks with different widths. It was concluded that this model can predict the hydrodynamics for offshore structures effectively, and the side wall has a significant impact on the firstorder quantities and second-order drift loads, which satisfied the resonant rule.     

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.     

Shallow water effects on high order statistics and probability distributions of wave run-ups along FPSO broadside

Ship hydrodynamics in shallow water becomes especially complicated since the nonlinearities in both the incident waves and the wave–hull interactions will be affected by the water depth. For a ship-shaped Floating Production, Storage and Offloading unit (FPSO) operating in shallow water, the broadside often suffers from the wave run-up and green water incidents in non-collinear harsh ocean environments. By applying the methods of ordinary moments and L-moments and the empirical Weibull distribution on the data measured in a series of model experiments, the high order statistics and the exceedance probability distribution of the run-ups along the FPSO broadside are evaluated and the effects of the shallow water depth and the incident environments are analyzed in this paper. It is seen that both the incident waves and the wave run-ups are non-Gaussian in shallow water and that the wave run-up characteristics are significantly influenced by the water depth and the incident environments, while the contribution due to the vessel vertical motions is negligible for the FPSO used in this study. The exceedance probabilities of the wave run-ups show that the broadside will be more likely to suffer from serious wave run-up and green water incidents in shallower water, in a higher incident wave and a non-collinear environment, especially so at locations around the FPSO midship within a range of 3/8L_pp ∼ 5/8L_pp. The dependency of the shape and scale parameters of the wave run-up probability distributions on the locations and the environment is quantified by model tests. The present study leads to the conclusion that the wave run-up characteristics and the shallow water effects should be considered carefully in determining the wave loads and the freeboard of a large FPSO in non-collinear environment conditions.