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.     

Higher-order boundary element method for the interaction of a floating body with both waves and slow current

A hybrid boundary element method is suggested to solve the problem of the interaction of floating structures with both waves and slow current. A pulsating source and its mirror image referring to the sea bottom are adopted as the Green's function. The velocity potentials are expanded into an eigenfunction expansion in the outer region of the fluid domain while higher order elements are used to discretize the boundary surface surrounding the inner region. The method is validated by comparing calculated results for a circular cylinder with the semi-analytical solutions. The method is then applied to ellipsoids of various breadth and draft to investigate the influence of body shape on the wave drift damping.     

Slow drift damping force acting on a horizontal cylinder

The hydrodynamic forces acting on a circular cylinder and a rectangular cylinder undergoing slow drift oscillation in regular waves were investigated experimentally and numerically. Forced oscillation tests with low frequency and large amplitude in regular waves and forced two-harmonic oscillation with combined low and high frequencies were carried out in the experimental study. In the numerical study a finite-difference method was used to simulate viscous flow around a two-dimensional oscillating cylinder. The results of experiments showed that a horizontal rectangular cylinder oscillating slowly in waves has much higher damping coefficients than one oscillating in two-harmonic mode, while the numerical study indicated that such differences in the damping coefficient arise partly from the different effects of one-direction harmonic flow and rotating flow on the vortex shedding caused by the slow drift oscillation.     

采用THOBEM方法研究波流与结构物相互作用的数值模拟(英文)

To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method (HOBEM). By assuming small flow velocities, the velocity potential could be expressed for linear and higher order components by perturbation expansion. A 4th-order Runge-Kutta method was applied for time marching. An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves. Validation of the numerical method was carried out on run-up, wave exciting forces, and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder. The results were in close agreement with the results of a frequency-domain method and a published time-domain method. The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.     

两船在波浪载荷作用下的运动响应分析

基于波浪辐射/绕射理论,利用水动力分析软件AQWA研究两船在波浪作用下的运动响应特性,给出驳船受浮式生产储油船(FPSO)影响时的附加质量和辐射阻尼,分析了驳船的漂移力和运动响应。计算结果表明,当两船间距为5 m时驳船的附加质量比间距为10 m时的值大2倍多,驳船的附加质量和阻尼随着间距的减小逐渐增大;在间距30 m时,驳船的速度越小所受的漂移力就越大,并且驳船的横摇和首摇运动就越剧烈。     

Wave analysis of porous geometry with linear resistance law

The wave diffraction-radiation problem of a porous geometry of arbitrary shape located in the free surface of a fluid is formulated by a set of integral equations, assuming a linear resistance law at the geometry. The linear forces, the energy relation and the mean horizontal drift force are evaluated for non-porous and porous geometries. A geometry of large porosity has an almost vanishing added mass. The exciting forces are a factor of 5–20 smaller compared to a solid geometry. In the long wave regime, the porous geometry significantly enhances both the damping and the mean drift force, where the latter grows linearly with the wavenumber. The calculated mean drift force on a porous hemisphere and a vertical truncated cylinder, relevant to the construction of fish cages, is compared to available published results.     

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.     

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.     

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。     

二阶波浪力数值计算与试验方法研究

目前准确测量波浪中船舶与海洋结构物二阶波浪力是一个难点,本文提出采用半约束法和弹簧系统约束法两种试验方法测量二阶波浪力.首先介绍了半约束法和弹簧系统约束法两种试验方法,然后针对某散货船采用这两种方法开展了二阶平均波浪力试验测量研究,最后将试验结果与理论计算结果进行了对比,并对两种试验方法的优缺点进行了分析.研究结果表明:两种试验方法均能准确测量二阶平均波浪力.     

Steady streaming of viscous surface layer in waves

An investigation of the drift velocity induced by water waves of a contminated surface layer is carried out. The theoretical analysis is based on a thin boundary layer on the free surface. The results of the analysis reveal that the drift velocity of a viscous layer on the water surface is 7/4 times the Stokes prediction ofc(ak) ² wherec is the wave celerity andak the wave slope. The present experimental investigation confirms the validity of the theoretical prediction for the drift velocity for a lightly contaminated surface layer; however, for a heavily contaminated surface layer, the experimental results exceed the theoretical prediction. An investigation for a heavily contaminated layer is carried out assuming an inextensible surface layer. Thus, in the experiment, vinyl sheets are used to substitute the contaminated layers. By balancing the wave-induced mean thrust force with the mean drag force, the drift velocity is obtained and compared with the experimental results. Based on the theoretical and experimental analyses, formulae for predicting the drift velocities for laminar and turbulent flow conditions are proposed.     

Strip method for a laterally drifting ship in waves

Lateral drift occurs due to the effects of wind forces, wave drifting forces, or both on ships sailing in actual seas. It is important therefore to investigate the influence of lateral drift on seakeeping performance for improved ship operation. The velocity potential was expanded as an asymptotic power series in terms of the lateral speed parameter, τ, defined as ω _e V ₀/g, where ω _e is the frequency of wave encounter; V ₀ denotes the lateral velocity, which is assumed to be sufficiently small; and g is the acceleration due to gravity. By combining this technique with the strip method, two sets of motion equations of all the hydrodynamic force coefficients for ship seakeeping were derived. The first set is for ships without lateral drift and is the same as the equations in the new strip method, and the second set is for the additional motions induced by lateral drift. It was found that all ship motion modes except surge are coupled when a ship drifts laterally in waves.     

Risk zone of wrack hitting marine structure simulated by 2D hydraulic model

The wrack or the ship out of control will drift with flow.One of the most important factors that drive the ship is flow current which moves circularly in tidal area.The wrack from same place always drifts in different ways if the start time is different.So,during the ship drifting period,the drift trace is also determined by both wave and wind forces.The drift direction is limited by water depth which must be deeper than ship draft. These marine structures that can not afford the hit of wrack or will destroy the wrack must be well considered when they are placed near harbor and waterway or other water area with ship running.The risk zone should be consulted according to tide and weather conditions to protect structures and ships in necessary.A method is presented here to simulate the risk zone by 2D numerical hydraulic model with tidal current,wave,wind and water depth considered.This model can be used to built early-warning and protect system for special marine structure.     

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。     

系泊船舶在不规则波中慢漂振荡的马尔可夫模型

一艘在非高斯慢漂波浪力激励下的系泊船舶的响应被用一个连续的马尔可夫过程来建模.提出了一个数值路径积分解法来计算该艘船舶的响应统计.该数值路径积分法是基于Gauss-Legendre插值方案,响应概率密度值是在子区间内的高斯分点上获得的.显示该数值路径积分解法有独特的能力在很低概率水平时生成精确解,这在系统可靠性分析时有重要意义.     

基于AQWA的波浪能发电装置主浮体水动力特性研究

利用水动力计算软件AQWA对双浮体式振荡浮子波浪能发电装置主浮体进行仿真分析,对不同尺寸垂荡板的主浮体进行建模仿真,并就各自RAOs、激振力、附加阻尼和附加质量进行频域分析。结果表明,在波浪频率低于0.3 Hz时,垂荡板尺寸对其影响尤为明显;当波浪频率分别大于0.2 Hz、0.36 Hz和0.35 Hz时,垂荡板尺寸分别对RAOs、激振力和附加阻尼失去影响;对于同一吃水线、不同垂荡板尺寸的主浮体,波浪频率对其附加质量有较大影响,且垂荡板尺寸越大影响越严重。     

Internal Resonances for the Heave Roll and Pitch Modes of a Spar Platform Considering Wave and Vortex Exciting Loads in Heave Main Resonance

The objective of this paper is to study the nonlinear coupling internal resonance of the heave, roll, and pitch response performance of a spar platform when their frequencies are in the ratio of 2:1:1 under wave and vortex exciting loads. The three degree-of-freedom (DOF) nonlinear coupled equations are established by considering a time-varying wet surface with a first-order wave force in heave and pitch and a vortex-induced force in roll. The first-order steady-state response is solved using the multi-scale method in heave main resonance. The multiple solutions of the motion equations are discussed using the analytic method and a numerical simulation. A sensitivity analysis is conducted to test the influence of the damping and internal detuning parameter. The regions of multiple solutions are found, and the jump phenomenon exists with the changes of the wave excitation. The regions of multiple solutions depend on the values of damping and detuning parameter.     

Optimization of bottom-hinged flap-type wave energy converter for a specific wave rose

In this paper, we conducted a numerical analysis on the bottom-hinged flap-type Wave Energy Convertor (WEC). The basic model, implemented through the study using ANSYS-AQWA, has been validated by a three-dimensional physical model of a pitching vertical cylinder. Then, a systematic parametric assessment has been performed on stiffness, damping, and WEC direction against an incoming wave rose, resulting in an optimized flap-type WEC for a specific spot in the Persian Gulf. Here, stiffness is tuned to have a near-resonance condition considering the wave rose, while damping is modified to capture the highest energy for each device direction. Moreover, such sets of specifications have been checked at different directions to present the best combination of stiffness, damping, and device heading. It has been shown that for a real condition, including different wave heights, periods, and directions, it is very important to implement the methodology introduced here to guarantee device performance.     

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.