Numerical analysis of vortex-induced motion of two-dimensional circular cylinder by lattice Boltzmann method

Vortex-induced motion of two-dimensional circular cylinder was numerically analyzed by using the lattice Boltzmann method. Unlike conventional methods, in which the computational grids are fit to the solid body, the present method adopts rectangular grids and the movement of the solid body was treated by the boundary condition for the simplicity of computation. The hydrodynamic force acting on the cylinder was estimated by integrating the momentum of the fluid over the cylinder surface. The quantitative validation of the simulation results was confirmed for the fixed cylinder at Re = 500. When the cylinder is allowed to move only in the spanwise direction, the resonance between the vortex-shedding frequency and the natural frequency of damping force by spring was confirmed. When the natural frequency is larger than the vortex-shedding frequency, secondary mode appears which may be resulted from the nonlinear effect. Finally, the motion in the streamwise direction is considered as well as the spanwise direction and the characteristic of the cylinder motion in the horizontal direction was demonstrated in relation to the damping force by the mooring. Although the target of the present study is limited to two-dimensional and low Re, the applicability of the lattice Boltzmann method to vortex-induced motion was confirmed.     

On the slack phenomena and snap force in tethers of submerged floating tunnels under wave conditions

Under severe sea wave conditions, the mooring tethers of submerged floating tunnel (SFT) might go slack. It may cause the structure failure during the service lifetime of SFT. The paper investigated SFT dynamics when going through tether slacking and the related snap force under wave conditions. Besides the nonlinearity of fluid drag and of structural geometry for a relative large structure displacement, the problem is characterized by the nonlinearity due to the discontinuity in axial stiffness of the tethers. To include these nonlinearities, the method of Lagrange energy is used to build the governing equations of SFT motion, and a bilinear oscillator is introduced to simulate the mooring tether operating in an alternating slack-taut state. The sensitivities of the occurrence of tether slacking to wave height and wave period are investigated. Results show that at a large wave height SFT tether will go slack and snap force occurs. SFT responses are categorized into three types of state according to the dynamic response characteristics of tether tension. Effects of two fundamental structure parameters, buoyancy-weight ratio (BWR) and inclined mooring angle (IMA), on the dynamic responses of SFT are analyzed. A slack-taut map of SFT tethers is built. It intuitively describes the occurrences of slack and snap force with different combinations of the two parameters. An analytical approach for slack prediction by deriving the slack criterion is provided to reveal the mechanism of the presented slack-taut map. By present research, the authors tried to make their effort to provide an alternative philosophy for SFT structural design on concerning preventing the occurrence of tether slacking and snap force.     

弹性支撑低质量比圆柱涡激振动数值模拟

近年来,随着深海石油工业的发展,立管的涡激振动现象越来越受学者们关注.使用RANS方程求解器,并结合SST κ-ω湍流模型,对横向和流向自然频率比为1的低质量比弹性支撑圆柱体的两自由度运动进行了数值模拟,计算雷诺数范围为5 300至32 000.采用四阶Runge-Kutta方法求解柱体的振动方程.并结合近期物理实验结果对升力系数、阻力系数、位移和尾涡模式进行了详细比较和讨论.较好地再现了试验观察到的锁定、迟滞、差拍等现象.     

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.     

Local joint flexibility of tubular X-joints stiffened with external ring or external plates

In the present paper, the Local Joint Flexibility (LJF) of the ring-stiffened X-joints and plate-stiffened X-joints under compressive load is investigated. In the first phase, a finite element (FE) model was generated and verified with the results of available experimental tests and equations. In the next phase, a set number of 234 FE models were created to evaluate the role of the external ring size (β_r and τ_r), the external plate size (β_p and τ_p), and the connection geometry (γ, τ, and β) on the LJF factor (f_LJF). In these FE models, the weld connecting the chord and brace members was generated. The results indicated that the f_LJF of a plate stiffened joint can be down to 76% of the f_LJF of the corresponding un-stiffened joint. Also, the effect of the ring size on the f_LJF was more than the effect of the plate size on the f_LJF, because of the stiffener position. Despite the notable effect of the ring and the plate on the f_LJF, there is not any study or formula on tubular connections stiffened with ring or plate. Therefore, the FE results were used to propose two parametric formulas for determining the f_LJF in X-joints with external ring or external plate under brace compressive load. Moreover, the derived formulas were checked based on the UK DoE acceptance criteria.     

Local joint flexibility of tubular T/Y-joints retrofitted with GFRP under in-plane bending moment

In the present paper, the Local Joint Flexibility (LJF) of tubular T/Y-joints retrofitted with Glass Fiber Reinforced Polymer (GFRP) under IPB moment is studied and discussed. For this aim, a finite element (FE) model was generated and verified with the results of available experimental data and parametric formulas. Afterward, a set of 158 finite element (FE) models was created to evaluate the efficacy of the FRP sheets (number, length, and orientation), the brace inclination angle (θ), and the non-dimensional parameters (β, τ, and γ) on the LJF coefficient (f_LJF) and the f_LJF ratio of the retrofitted to the associated un-retrofitted joint. In the FE models, the efficacy of the weld profile and the contact between the FRP and the steel members (chord, weld, and brace) was considered. Also, analysis of variance (ANOVA) is used to identify the most dominant parameters which affect the f_LJF ratios. Results showed that in the retrofitted joints, the increment of the FRP sheet number results in the notable drop of the f_LJF. But, the efficacy of the FRP sheet orientation on the f_LJF can be ignored. Despite the considerable efficacy of the FRP sheets on the behavior of the tubular joints, there was not any study on the LJF in the joints retrofitted with FRP. Hence, after an extensive parametric study, the results were used to derive a parametric equation for determining the f_LJF of T/Y-joints retrofitted with FRP. Moreover, the derived equation was checked according to the UK DoE acceptance criteria.     

Hydrodynamic characteristics of slotted breakwaters under regular waves

The performance of a slotted breakwater consisting of one row of vertical slots was investigated theoretically and experimentally under normal regular waves. A simple theoretical model based on an eigenfunction was developed. The wave transmission, reflection, energy loss, and hydrodynamic force exerted on the breakwater were calculated for different values of the wave and structure parameters. The validity of the theoretical model was examined by comparing its results with theoretical and experimental results obtained from different studies. It was found that the transmission coefficient decreases with increasing dimensionless wavenumber (kh), increasing wave steepness (H _i/L), and decreasing breakwater porosity (ε). The reflection coefficient showed the opposite trend to the transmission coefficient. Also, about 20–50% of incident wave energy was lost due to the effect of the breakwater. In addition, the proposed theoretical model can be used for predicting the performance of slotted breakwaters and the hydrodynamic forces exerted on these structures using the friction coefficient f = 1.5.     

A study on the estimation of the seaquake response of a floating structure considering the characteristics of seismic wave propagation in the ground and the water

 Seaquakes, which are characterized by the propagation of vertical earthquake motion at the sea bottom as a compression (longitudinal) wave, are reported to cause damage to ships, and their effect on floating structures is a matter of great concern. To comprehend the basic properties of seaquakes, we first discuss a method to calculate the displacement of the seabed when it is subjected to hydrodynamic pressure. To investigate the interrelationship between the vibration of a floating structure and the deformation of the seabed, a new boundary integral equation is derived which assumes that the seabed is a semiinfinite homogeneous elastic solid in order to analyze the seaquake-induced hydrodynamic pressure acting on the floating structure. By considering the propagation of the seismic wave in the ground and in the water, the incident wave potential in seaquake problems is also deduced and its characteristics are discussed. Finally, the response of a very large floating structure in a seaquake is investigated using a fluid force analysis method, and considering the interrelationship between the vibration of the floating structure and the deformation of the seabed. Received: August 19, 2002 / Accepted: November 11, 2002 Address correspondence to: H. Takamura (hiroaki_takamura@nishimatsu.co.jp) Updated from the Japanese original, which won the 2002 SNAJ prize (J Soc Nav Archit Jpn 2001;189:87–92,93–100 and 190:381–386)     

Hydrodynamic performance of multiple-row slotted breakwaters

This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients (C _R , C _T , and C _E ) for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the C _R increases with increasing wave number, kd, and with a decreasing permeable wall part, dm. The C _T follows the opposite trend. The C _E slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the C _R , while increasing the C _T . At lower values of kd, a decreasing porosity increases the C _E , but for high values of kd, a decreasing porosity reduces the C _E . The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd<0.5. Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd>0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.     

Resistance analysis of a semi-SWATH design concept in shallow water

Resistance analysis is an important analytical method used to evaluate the hydrodynamic performance of High Speed Craft (HSC). Analysis of multihull resistance in shallow water is essential to the performance evaluation of any type of HSC. Ships operating in shallow water experience increases in resistance because of changes in pressure distribution and wave pattern. In this paper, the shallow water performance of an HSC design concept, the semi-Small Waterplane Area Twin Hull (semi-SWATH) form, is studied. The hull is installed with fin stabilizers to reduce dynamic motion effects, and the resistance components of the hull, hull trim condition, and maximum wave amplitude around the hull are determined via calm water resistance tests in shallow water. These criteria are important in analyzing semi-SWATH resistance in shallow water and its relation to flow around hull. The fore fin angle is fixed to zero degrees, while the aft fin angle is varied to 0°, 5°, 10°, and 15°. For each configuration, investigations are conducted with depth Froude numbers (Fr _H ) ranging from 0.65 to 1.2, and the resistance tests are performed in shallow water at the towing tank of UTM. Analysis results indicate that the resistance, wave pattern, and trim of the semi-SWATH hull form are affected by the fin angle. The resistance is amplified whereas the trim and sinkage are reduced as the fin angle increases. Increases in fin angle contribute to seakeeping and stability but affect the hull resistance of HSCs.     

Temporal and spectral characteristics of seismic ground motions: Offshore versus onshore

To distinguish offshore and onshore seismic ground motions, conventional analyses in terms of peak ground acceleration (PGA) and earthquake response spectrum (ERS) have been carried out in a recent work by authors and other papers in literature. In the present study, distinct temporal and spectral characteristics between onshore and offshore earthquake ground motions are further investigated in time-domain and frequency-domain. The data used is 69 pairs of concurrent onshore and offshore ground motions collected from the Kyoshin Network (K-NET). Each pair of data are of approximately identical epicenter distances. Comparisons are made on zero-up-crossing period (T_z), peak-to-trough acceleration range (A_pt) and period (T_pt), duration of ground motion (T_d), predominant frequency (f_p) and the spectral bandwidth parameter (ε). The results indicate that for offshore horizontal and vertical seismic signals, statistics of T_z, T_pt, T_d and predominant period T_p tend to be larger than the onshore counterparts. Meanwhile, ε of the offshore vertical ground motions is also greater. Through the proposed energy ratio (ER) analysis, the spectral energy of offshore ground motion is found to shift to moderate and low frequency bands. The time-frequency analysis conducted by Hilbert-Huang transform (HHT) shows that the Hilbert spectra of offshore accelerations contain larger spectral energy than the onshore counterpart but the corresponding instantaneous frequencies at peak energy are smaller, especially for horizontal recordings. Therefore, larger dynamic response of offshore structures is prone to be induced by the offshore ground excitation. This is further validated through the dynamic analysis of a marine pipeline in case study.     

Mathematical modelling of response amplitude operator for roll motion of a floating body: Analysis in frequency domain with numerical validation

This paper investigates mathematical modelling of response amplitude operator （RAO） or transfer function using the frequency-based analysis for uncoupled roll motion of a floating body under the influence of small amplitude regular waves. The hydrodynamic coefficients are computed using strip theory formulation by integrating over the length of the floating body. Considering sinusoidal wave with frequency （ω ） varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed, analytical expressions of RAO in frequency domain is obtained. Using the normalization procedure and frequency based analysis, group based classifications are obtained and accordingly governing equations are formulated for each case. After applying the fourth order Runge-Kutta method numerical solutions are obtained and relative importance of the hydrodynamic coefficients is analyzed. To illustrate the roll amplitude effects numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave with a fixed wave height. The effect of viscous damping on RAO is evaluated and the model is validated using convergence, consistency and stability analysis. This modelling approach could be useful to model floating body dynamics for higher degrees of freedom and to validate the result.     

Effects of roughness on hydrodynamic characteristics of a submerged floating tunnel subject to steady currents

The effects of surface roughness as induced by marine fouling on the hydrodynamic forces on a submerged floating tunnel (SFT) are experimentally and numerically investigated in detail at Reynolds numbers Re = 8.125 × 10³–5.25 × 10⁴. A sensitivity analysis to different roughness parameters including roughness height, skewness, coverage ratio, and spatial arrangement is performed. In addition, an optimized parametric cross-section for an SFT is proposed, and the hydrodynamic performance of the parametric shape and circular SFT cross-section shape with roughness elements is compared. The pressure distribution along the SFT, flow separation and wake characteristics are analyzed to provide a systematic insight into the fundamental mechanism relating the roughness parameters and flow around an SFT. In order to better understand the nonlinear relationships among structural geometry, roughness parameters, flow states, and structural response, an artificial intelligence method using Random Forest (RF) for feature importance ranking is applied. The results show that with the parametric shape, the hydrodynamic forces on the fouled SFT can be effectively mitigated. The roughness height and coverage ratio affect the equivalent blockage and hence, change flow separation and recirculation length in the wake. Lower skewness of the roughness elements can increase the critical Re by changing the relative roughness parameter. Horizontal arrangement of the roughness elements on an SFT generally results in the largest hydrodynamic forces, compared to staggered and vertical distributions. Throughout the feature importance ranking, the flow regime is found to be the most important feature of the hydrodynamics of the SFT. In addition, the SFT cross-section shape and roughness coverage ratio play a dominant role.     

CFD simulation of fixed and variable pitch vertical axis tidal turbine

In this paper, hydrodynamic analysis of vertical axis tidal turbine (both fixed pitch & variable pitch) is numerically analyzed. Two-dimensional numerical modeling & simulation of the unsteady flow through the blades of the turbine is performed using ANSYS CFX, hereafter CFX, which is based on a Reynolds-Averaged Navier-Stokes (RANS) model. A transient simulation is done for fixed pitch and variable pitch vertical axis tidal turbine using a Shear Stress Transport turbulence (SST) scheme. Main hydrodynamic parameters like torque T, combined moment C _M , coefficients of performance C _P and coefficient of torque C _T , etc. are investigated. The modeling and meshing of turbine rotor is performed in ICEM-CFD. Moreover, the difference in meshing schemes between fixed pitch and variable pitch is also mentioned. Mesh motion option is employed for variable pitch turbine. This article is one part of the ongoing research on turbine design and developments. The numerical simulation results are validated with well reputed analytical results performed by Edinburgh Design Ltd. The article concludes with a parametric study of turbine performance, comparison between fixed and variable pitch operation for a four-bladed turbine. It is found that for variable pitch we get maximum C _P and peak power at smaller revolution per minute N and tip sped ratio λ.     

波浪中母船干扰下潜水员梯的运动及水动力特性分析

潜水员梯是通过销轴连接在母船舷侧为潜水员执行潜水作业时上下船的平台,为保证在波浪中使用时的安全性,对其波浪作用力、运动响应及销轴处的动作用载荷设计有较高要求。为研究母船干扰下潜水员梯的动态响应特性,采用基于深水格林函数为积分内核的边界元方法,先计算母船及潜水梯这一整体的运动响应及其平均湿表面的辐射和绕射压力分布,依据刚体运动合成原理求解得到潜水梯重心处的运动。再以潜水员梯为研究对象,采用压力积分方法获得潜水员梯的波浪力作用,并将其运动、波浪力和销轴处的作用力联立构成动力学平衡方程,逆向求解出销轴处的动作用力。基于上述思路,系统研究了波长、航速及潜水员梯与母船相对位置变化时潜水员梯的运动、波浪作用力及销轴处作用力的变化规律,为潜水员梯的布置、销轴的选型及潜水作业时母船的操纵可提供指导意义。     

考虑粘滞阻尼的Truss Spar频域响应分析

联合势流理论与修改的Morison方程,建立波浪作用下的Truss Spar平台运动响应计算模型。波浪激振力与相关水动力信息采用高阶边界元计算方法获得。通过数值模拟得到Truss Spar平台纵荡、垂荡和纵摇RAO,针对Morison阻力系数对响应的影响进行参数分析。计算结果显示,纵荡和纵摇仅在低频部分对阻力系数敏感。因此平台在遭受二阶波浪慢漂力作用时,粘滞阻尼将起到重要作用。对于垂荡方向,由于Truss Spar安装的垂荡板提供了较大的竖向粘滞阻尼,因此垂荡RAO受阻力系数的影响较大。     

Characteristics of VIV in multi-degree-of-freedom tensioned beams using a numerical method

The object of this study is to analyze the characteristics of vortex-induced vibration of a slender marine structure with the numerical method. Applying a dynamic analysis method for a slender marine structure based on the 3D finite difference method, we carried out case studies for a tensioned beam model at a constant flow speed. The hydrodynamic forces, in the direction of inline and cross-flow, created by vortex shedding are simultaneously considered based on Morison equation. The frequency of force in the inline direction corresponding to the unstable zone is evaluated. An eigenvalue analysis for different flow speeds of a tensioned beam considering the effect of the tension increase due to the inline and cross-flow drag forces is performed. We found that a revision of the eigenvalue should be considered if the tension along a riser or beam is significantly affected by an environmental or functional load. From a trajectory on the XY plane it was shown that the riser did not move in an exact 8 shape for all flow conditions due to the phase angle difference between inline and cross-flow displacement. It is believed that the phase angles between inline and cross-flow displacements in high modes are different among the nodes.     

带有月池的非对称结构物水波辐射和激励力（英文）

A highly efficient "hybrid integral-equation method" for computing hydrodynamic added-mass, wave-damping, and wave-exciting force of general body geometries with a vertical axis of symmetry is presented. The hybrid method utilizes a numerical inner domain and a semi-infinite analytical outer domain separated by a vertical cylindrical matching boundary.Eigenfunction representation of velocity potential is used in the outer domain; the three-dimensional potential in the inner domain is solved using a "two-dimensional" boundary element method with ring sources and ring dipoles to exploit the body symmetry for efficiency. With proper solution matching at the common boundary, both radiation and diffraction potentials can be solved efficiently while satisfying the far-field radiation condition exactly. This method is applied to compute the hydrodynamic properties of two different body geometries: a vertical-walled moonpool with a bottom plate that restricts the opening and a spar-like structure with a diverging bottom opening inspired by designs of floating Oscillating Water Columns. The effects of the size of the bottom opening on the hydrodynamic properties of the body are investigated for both geometries. The heave motion of the floater as well as the motion of the internal free surface under incident wave excitation are computed and studied for the spar-like 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。     

船舶码头系泊的耦合动力响应分析

以码头系泊船舶为研究对象,利用水动力软件 AQWA,分析不同浪向角对其运动响应幅值算子和一阶波激力的影响,并在时域耦合分析的过程中,对系泊系统进行优化,从船舶运动响应和系泊缆张力2个方面,对沿型深方向优化和尾横缆优化的结果进行分析。计算结果表明,不同的优化方案对船舶的运动响应和系泊缆张力的影响不同。