Experimental and numerical study on vortex-induced motions of a deep-draft semi-submersible

An experimental study on vortex-induced motions (VIM) of a deep-draft semi-submersible (DDS) was carried out in a towing tank, with the aim to investigate the VIM effects on the overall hydrodynamics of the structure. In order to study the fluid physics associated with VIM of the DDS, a comprehensive numerical simulation was conducted to examine the characteristics of vortex shedding processes and their interactions due to multiple cylindrical columns. The experimental measurements were obtained for horizontal plane motions including transverse, in-line and yaw motions as well as drag and lift forces on the structure. Spectral analysis was further carried out based on the recorded force time history. These data were subsequently used to validate the numerical model. Detailed numerical results on the vortex flow characteristics revealed that during the “lock-in”, the vortex shedding processes of the upstream columns enhance the vortex shedding processes of the downstream columns leading to the rapid increase of the magnitude of VIM. In addition to the experimental measurements, for the two uniform flow incidences (0° and 45°) investigated, comprehensive numerical data of the parametric study on the VIM characteristics at a wide range of current strength will also serve as quality benchmarks for future study and provide guidance for practical design.     

波浪作用下涵洞式直立堤水体交换特性研究

基于计算流体力学(CFD)数值模拟和物理模型试验结合的方式,开展涵洞式直立堤在波浪作用下的水体交换研究。CFD数值模拟采用VPM (volume-average/point-value method)-THINC (tangent of hyperbola for interface capturing)/QQ (quadratic surface representation and Gaussian quadrature)模型,并在此基础上提出一种能够标记涵洞内外水体变化的双液相流体体积模型(VOF)方法,定性及定量描述涵洞内外水体的交换特性;物理模型试验主要用来验证数值模型的准确性。研究表明,在波浪的作用下,涵洞内部会形成一股往复振荡的水流,对水体交换起到重要的作用。该振荡流主要受到涵洞高度、波浪周期以及波高的影响,涵洞深度对其影响不大。在波浪长时间的作用下,涵洞式直立堤能有效地增强港池内外水体交换。     

Benchmark computations of wave run-up on single cylinder and four cylinders by naoe-FOAM-SJTU solver

The benchmark simulations of wave run-up on a fixed single truncated circular cylinder and four circular cylinders are presented in this paper. Our in-house CFD solver naoe-FOAM-SJTU is adopted which is an unsteady two-phase CFD code based on the open source package OpenFOAM. The Navier-Stokes equations are employed as the governing equations, and the volume of fluid (VOF) method is applied for capturing the free surface. Monochromatic incident waves with the specified wave period and wave height are simulated and wave run-up heights around the cylinder are computed and recorded with numerical virtual wave probes. The relationship between the wave run-up heights and the incident wave parameters are analyzed. The numerical results indicate that the presented naoe-FOAM-SJTU solver can provide accurate predictions for the wave run-up on one fixed cylinder and four cylinders, which has been proved by the comparison of simulated results with experimental data.     

A model equation for the transverse forces on cylinders in oscillatory flows

A quasi-steady model is presented to predict the transverse force on cylinders in waves and oscillating flows. The model assumes that the Strouhal number, based on the instantaneous flow velocity, is constant, taking a value of 0.2. It is also assumed that the lift coefficient, based on the instantaneous dynamic pressure of the flow, is constant over a half cycle of the flow. The predictions of the model are compared with measurements taken on a circular cylinder in planar oscillatory flow over the Keulegan Carpenter number, KC, range from 5 to 53. The agreement between predicted and measured transverse forces is good at high KC but deteriorates at low KC. For high KC, it is shown that the model can be further improved if additional variables are introduced into the model equation.     

Loads on a 3D body due to second-order waves and a current

Non-linear loads on a fixed body due to waves and a current are investigated. Potential theory is used to describe the flow, and a three-dimensional (3D) boundary element method (BEM), combined with a time-stepping procedure, is used to solve the problem. The exact free-surface boundary conditions are expanded about the still-water level by Taylor series so that the solution is evaluated on a time-invariant geometry. A formulation correct to second order in the wave steepness and to first order in the current speed is used. Numerical results are obtained for the first-order and the second-order oscillatory forces and for the second-order mean force on a fixed vertical circular cylinder in waves and a current. The second-order oscillatory forces on the body in waves and current are new results, while the remaining force components are verified by comparison with established numerical and analytical models. It is shown that the current can have a significant influence on the forces, and especially on the amplitude of the second-order oscillatory component.     

立柱直径比对四立柱平台涡激运动性能影响的数值研究

与单立柱平台(Spar)类似,四立柱平台在洋流作用下也容易发生涡激运动,对锚泊和立管系统的疲劳寿命产生不利影响。一种非对称半潜式平台具有两种不同尺寸的立柱,立柱直径比对非对称平台涡激运动性能的影响尚需深入研究。采用计算流体力学(CFD)方法,对直径比分别为1.0、1.5和2.0的立柱组合在两种不同角度水流作用下的运动响应进行了二维数值模拟,分析发现:立柱直径比不为1时四立柱平台也具有明显的涡激运动,其横荡运动具有显著的锁定现象;在广义折合速度定义下,与相同直径的四立柱平台相比,立柱直径比不为1时其横荡运动锁定区间变宽且滞后,横荡响应幅值的峰值具有明显差异;在所研究的直径比范围内,大直径立柱在上游时涡激运动响应比其在下游时更显著,且这种差异随着直径比变大而变大。     

The effect of fluid compressibility on the simulation of sloshing impacts

Resonant and near-resonant sway-induced sloshing flow in a rectangular container is used to compare various combinations of compressibility models for air and water. The numerical model is implemented in a commercial RANS computational fluid dynamics (CFD) code. A criterion based on wave propagation is developed to assess the importance of including fluid compressibility. For sloshing flows with low levels of fluid impact, this can be simulated with incompressible fluid models for both air and water. When modelling sloshing at low-filling levels with a travelling wave, which generates large air bubble entrainment, the choice of fluid compressibility model is shown to have a significant influence on pressure magnitude and frequency of oscillation required for structural assessment. Further comparisons with theoretical models show that a full thermal energy compressibility model is also required.     

The instability of viscous two-layer oscillatory flows

The instability of oscillatory flows in a two-layer fluid where the two layers differ in density and viscosity has been analysed using a perturbation method for long waves with special interest on effects of viscosity, time scale, density and depth of the fluid. The flow of a fluid with homogeneous density can be unstable, when the kinematic viscosity of the upper fluid layer is different from that of the lower one. Viscosity stratification results in unstable oscillatory flows. Two limiting cases of single-layer flow are also considered.     

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.     

A Numerical Investigation of Vortex-Induced Vibration Response and Fatigue Damage for Flexible Cylinders Under Combined Uniform and Oscillatory Flow

Vortex-induced vibration(VIV) for flexible cylinders under combined uniform and oscillatory flow is a challenging and practical issue in ocean engineering. In this paper, a time domain numerical model is adopted to investigate the characteristics of cross-flow VIV response and fatigue damage under different combined flow cases. Firstly, the adopted VIV model and fatigue analysis procedure are validated well against the published experimental results of a4-m cylinder model under pure oscillatory flows. Then, forty-five combined flow cases of the same cylinder model are designed to reveal the VIV response characteristics with different non-dimensional oscillation period T* and combined ratio r. The combined flow cases are classified into three categories to investigate the effect of r on cylinder's dynamic response, and the effect of T* is described under long and short period cases. Finally, fatigue analysis is carried out to investigate how the structural fatigue damage varies with the variations of r and T*. The captured characteristics of structural response and fatigue damage are explained through the VIV mechanism analysis.     

Time domain simulation of side-by-side floating bodies using a 3D numerical wave tank approach

The coupled system of two side-by-side fixed and/or floating bodies interacting with a large amplitude nonlinear wave is studied using a direct time domain solution method. The numerical model is based on a three-dimensional mixed Eulerian–Lagrangian (MEL) method under certain simplifying approximations permitting Rankine panel scheme to be implemented over a time-invariant boundary surface to solve the boundary value problem for the unknown velocity potentials. A 4th order Adams–Bashforth–Moulton scheme is used for time marching of rigid-body motion histories of the individual bodies and evolution of the free-surface including the gap region in which large resonant fluid motions occur. A systematic study has been carried out to evaluate the performance of the developed time domain method in simulating the forces and motions as well as the fluid motion in the gap region for the two body system under various arrangements and in different wave-headings. At first, the computed numerical results have been validated and verified with computational and experimental results available in literature for standard geometries such as vertical truncated cylinders and rectangular boxes. Secondly, effectiveness of the damping lid model which is introduced to suppress wave resonance in the gap region is investigated including its influence on maximum sway forces on fixed and floating rectangular barges in side-by-side configurations. Thirdly, comparative studies on absolute and relative motion response for two cases (two rectangular barges, and a FLNG-FPSO + shuttle tanker) in side-by-side arrangement are detailed to bring out the importance of nonlinearities arising due to steep nonlinear incident waves. Finally, coupled motions of the two-body system of an FPSO and a shuttle tanker floating in side-by-side configuration in a steep nonlinear wave field are studied in which the two bodies are connected through hawsers, and also the FPSO is moored to the ground. Additionally there is a fender between the two bodies.     

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

A numerical study on dynamic properties of the gravity cage in combined wave-current flow

Recent work in the area of open-ocean aquaculture-system dynamics has focused either on the response of fish cages in waves or the steady drag response from ocean currents, not on them combined. In reality, however, the forces bearing on these open-ocean structures are a nonlinear, multidirectional combination of both waves and current profiles. In this paper, a numerical model has been developed to simulate the dynamic response of the gravity cage to waves combined with currents. When current flows are combined with regular waves, gravity-cage motion response (including heave, surge, and pitch) and mooring-line forces have been calculated. To examine the validity of simulated results, a series of physical model tests have been carried out. The results of our numerical simulation are all in close agreement with the experimental data.     

A numerical investigation of western boundary currents in subtropical and subpolar gyres with a barotropic model

Dynamics of western boundary currents in the subtropical and subpolar gyres are studied as a source-sink flow of barotropic fluid by means of numerical integration of the time-dependent non-linear vorticity equation. The bottom topography consists of a continental shelf of uniform slope (120 km wide) parallel to the straight western coast and a flat bottom of uniform depth. The steady solution in the case of low Reynolds number (Re≦100) shows the vorticity balance of the western boundary current between theβ-, diffusion-, and bottom relief terms. The cuspidated flow of the western boundary current in the subpolar gyre is observed as a compensating flow for the subtropical western boundary current separating from the western coast. In the case of Re=350, the zonal current separating from the coast meanders with the wave length of the stationary Rossby waves. It is shown that in the present model the separation of the boundary current is controlled by the planetary vorticity (f) of the fluid particle in the boundary flow, with which the same particle flows out the eastern wall at the corresponding latitude. The decrease of the efflux width increases the intensity of the non-linear overshooting of the boundary current separating from the western coast.     

细长输流管内外流耦合振动特性研究

管内流动会影响输流管的振动响应,目前关于输流弹性管涡激振动方面的研究较少。基于计算流体力学(CFD)方法,开展内外流对细长输流弹性管振动特性影响的研究。首先在不考虑内流的情况下将弹性管涡激振动数值预报结果与模型试验数据进行对比,验证了数值方法的可靠性。再者考虑内外流耦合作用情况下,对不同内流流速下细长输流弹性管振动位移时—空分布、顺流向最大平均偏移、振动轨迹、内部横向涡的形成与分布等进行了对比分析。结果发现,与外流流速相比,内流流速的增加虽然难以改变弹性管的主振模态,但对沿管体的振动强度影响显著。顺流向最大偏移处管体运动轨迹发生明显的变形和跳跃。在剪切外流和均匀内流对弹性管的联合作用下,沿管跨方向模态间能量转换频繁,伴随着间歇性出现或消失的沿弹性管传播的行波组分,这主要归因于复杂的双重流固耦合系统(外流—管体,内流—管体)。在内流以附加质量力、离心力和科氏力形式的激励下,弹性管内二次流现象明显。在振动过程中,内部横向涡沿管壁生成、脱落并逐渐散布于整个横截面。     

Investigation of unrestrained cylinders rolling in steady uniform flows

The goal of this study is to understand the movement of unexploded ordnance that may become unburied and forced by currents. Symmetrical, smooth, finite-length, unrestrained cylinders were studied in steady, uniform flows over a range of Reynolds numbers in a smooth-bottomed, horizontal flume. The study uses PIV tracking methods in the laboratory to identify the movement of ordnance simulated by unrestrained cylinders. The PIV is supported with a numerical analysis using a RANS flow solver. The simulations showed that at low Reynolds numbers the cylinders should roll at speeds near 70% of the free-stream flow.     

The effect of currents on the generation of internal waves by a barotropic tide near an underwater ridge

In the frame of the linear theory for long waves, the paper studies long waves generated by a barotropic tide running at an arbitrary angle over a bottom ridge. The ocean is assumed to be two-layered. In the area of a ridge with a rectangular cross section, geostrophic flows are considered, coupled with the inclinations of the free surface and interface. Wave amplitudes are shown to depend on the angle of an onrunning tide and this allows us to reach a conclusion about the influence of a geostrophic current on the generation of internal waves. Translated by Vladimir A. Puchkin.     

Wave Action on Structures of Combined Cylinders

1.Introduction Owingtoitssignificanteffectofreductionofwaveloadsandwaverun up,theperforatedwallon anarrayofcylindricalstructureshasreceivedconsiderableattentioninrecentyears.Manyresearches havebeencarriedoutinthisfield.Anexactsolutionforthediffractionoflinearwaterwaveswithan arrayofimpermeablecylinderswasfirstgivenbySpringandMonkmeyer(1974)usinganeigenfunction expansionapproach.Subsequently,LintonandEvans(1990)madeamajorsimplificationtothetheo ry,whichallowedthenear fieldquantitiessuchasload…     

Diffraction of oblique waves by thick rectangular barriers

A complete analytical solution is presented for the linear diffraction of oblique waves by horizontal rectangular cylinders either fixed at the free surface or mounted on the sea bed in a finite-depth of water. Helmholtz equation is employed as the governing differential equation obtained by reducing the 3-D oblique wave scattering problem to a 2-D case. According to the method proposed, the fluid region is divided into three sub-regions in which the governing differential equation is solved by the separation of variables. The solutions for each region are then matched on the common boundaries of sub-regions to determine the unknowns of the eigen series expansions and Fourier series. Thus transmitted and reflected waves are obtained in the far-field, and forces and moments acting on the rectangular cylinder fixed at the free surface are also given. Comparisons are made in order to check the accuracy of the method.