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.     

Steady drift force on vertical cylinder - viscous vs. potential

The contribution of the steady drift force on a floating structure may arise from waves, wind and current. The component of the wave drift force may be due to the second-order diffraction theory or potential effect and may be due to the velocity squared force or viscous effect. The presence of current in waves increases the effect of the viscous force. The expressions for these terms for a vertical cylinder are derived and their relative importance is investigated. Plots are presented showing the regions where the viscous or potential drift force predominates. Experiments were conducted with both small and large diameter cylinders. The mean drift forces obtained in these tests are compared with the theory.     

Numerical study on the reverse drift force of floating BBDB wave energy absorbers

The motions and time-mean horizontal drift forces of floating backward-bent duct buoy wave energy absorbers in regular waves are calculated taking account of the oscillating surface-pressure due to the pressure drop in the air chamber above the oscillating water column within the scope of the linear wave theory. The present numerical results show that the time-mean drift forces of backward-bent duct buoys are in the reverse direction of propagation of the incident waves over specific frequency ranges as found by McCormick through his experimental work. The drift force has been calculated by the near-field method. A brief discussion on Maruo’s formula which shows that the time-mean drift force must be in the direction of propagation of the incident waves, has also been presented.     

Numerical study of the motions and drift force of a floating OWC device

The motion and the drift force of a floating OWC (oscillating water column) wave energy device in regular waves are studied taking account of the oscillating surface-pressure due to the pressure drop across the duct of the air chamber. The potential problem inside the chamber is formulated by making use of the Green integral equation associated with the Rankine-type Green function while the outer problem with the Kelvin-type Green function. The added mass, wave damping and excitation coefficients as well as the motion and drift force of the OWC device are calculated for various values of parameter related to the pressure drop.     

顺应式海洋平台慢漂运动物理模型试验研究

为研究顺应式海洋平台慢漂运动的影响因素,以截断圆柱和漂浮方箱为例进行了不规则波作用下的慢漂运动模型试验。测量了不同系泊刚度条件下的漂浮方箱以及相同系泊刚度条件下的截断圆柱和漂浮方箱在静水中自由衰减运动和在不规则波中的运动响应,并将运动响应分解成一阶波频运动响应和二阶低频运动响应,分析了系泊刚度和浮体形状对浮体运动的影响。通过物理模型试验发现了系泊刚度及浮体形状对顺应式系泊浮体一阶运动标准差和二阶低频运动平均漂移值和标准差的关系。结果表明由于顺应式浮体的固有周期远离波浪谱峰周期时,系泊刚度以及浮体形状对慢漂运动的一阶运动响应影响不大;二阶低频运动相对偏离平衡位置的平均值和标准差均随系泊刚度增大而减小,浮体形状同样对慢漂运动的二阶低频纵荡运动响应影响较大。试验结果为实际海洋工程的外形选择和系泊刚度选择提供数据支持。     

Interaction of cnoidal waves with an array of vertical concentric porous cylinders

An array of large concentric porous cylinder arrays is mounted in shallow water exposed to cnoidal waves. The interactions between waves and cylinders are studied theoretically using an eigenfunction expansion approach. Semi-analytical solutions of hydrodynamic loads and wave run-up on each cylinder are obtained using first approximation to cnoidal waves. The square array configuration of four-legged identical concentric porous cylinder is investigated in present study. Numerical results reveal the variation of dimensionless wave force and wave run-up on individual cylinder with angle of incidence, porosity parameter, spacing between outer and inner cylinders, spacing between concentric porous cylinders and wave parameter. Different mechanism of wave force is found under different range of scattering parameter.     

Numerical prediction of MODUs drift during Hurricane Katrina

Severe hurricanes, such as Katrina, broke the mooring lines of a number of mobile offshore drilling units (MODU) deployed in the Gulf of Mexico and some of those MODUs went adrift. A drifting MODU may damage other critical elements of the offshore oil and gas infrastructure by colliding with floating or fixed production systems and transportation hubs, or by rupturing pipelines owing to their dragging anchors over the seabed. To avoid or mitigate the damage caused by a drifting MODU, it is desirable to understand the mechanics of the drift of a MODU under the impact of severe wind, wave and current and have the capability of predicting the trajectory of the drift. To explore the feasibility and accuracy of predicting the trajectory of a drifting MODU based on hindcast met-ocean conditions and limited knowledge of the condition of the drifting MODU, this study employed a simplified equation describing only the horizontal (surge, sway and yaw) motions of a MODU under the impact of steady wind, current and wave forces. The simplified hydrodynamic model neglects the first- and second-order oscillatory wave forces, unsteady wind forces (owing to wind gustiness), wave drift damping, and the effects of the body oscillation on the steady wind and current forces. It was assumed that the net effects of the oscillatory forces on the steady motion are insignificant. To verify the accuracy and feasibility of our simplified approach, the predicted drifting trajectories of two MODUs were compared with the corresponding measurements recorded by the global positioning system (GPS).     

Minimization of drift force on a floating cylinder by optimizing the flexural rigidity of a concentric annular plate

The deployment of suitable configurations of mutually interacting floating bodies for efficiently controlling their hydrodynamic interactions towards the reduction of the wave drift forces and, thus, of the mooring lines’ loads, has, nowadays, gained a great scientific interest. In this paper, the hydrodynamic behaviour of a floating cylinder and a concentric annular flexible plate is analysed in the frequency domain aiming at the minimization of the drift forces acting on the cylinder by optimizing the flexural rigidity of the plate. The diffraction/radiation problem is solved using a higher-order boundary element method. The analysis is implemented assuming that both floating bodies oscillate freely in heave, while for the plate, flexible modes are, additionally, considered for describing its structural deformations. The required modes shapes are determined in vacuum (“dry” mode superposition approach) through analytical expressions. The flexural rigidity of the plate, D, is optimized at a specific wave number using a real-coded genetic algorithm. Initially, results are compared with numerical results of other investigators for the case of two rigid concentric floating cylinders. Next, extended results are presented, focusing on the effect of D, including its optimum value, on various physical quantities describing the behaviour of both the cylinder and the plate. Contrary to the isolated cylinder, the presence of the plate introduces sharp peaks in the variation pattern of the drift force of the cylinder, bounded at specific wave numbers, where resonance of the seiche mode of water motion in the annular cavity or of specific flexible modes of the plate occurs. However, by reducing D to its optimum value, the cylinder’s drift force obtains practically zero values at the target wave number, due to an efficient improvement of the wave field in the annular cavity around the cylinder. Moreover, a great reduction of the drift force compared to the isolated cylinder is achieved in the subsequent high frequency range.     

An analytical approach for the calculation of random wave forces on submerged tunnels

This paper deals with the random forces produced by high ocean waves on submerged horizontal circular cylinders. Arena [Arena F, Interaction between long-crested random waves and a submerged horizontal cylinder. Phys Fluids 2006;18(7):1–9 (paper 076602)] obtained the analytical solution of the random wave field for two dimensional waves by extending the classical Ogilvie solution [Ogilvie TF, First- and second-order forces on a cylinder submerged under a free surface. J Fluid Mech 1963;16:451–472; Arena F, Note on a paper by Ogilvie: The interaction between waves and a submerged horizontal cylinder. J Fluid Mech 1999;394:355–356] to the case of random waves. In this paper, the wave force acting on the cylinder is investigated and the Froude Krylov force [Sarpkaya T, Isaacson M, Mechanics of wave forces on offshore structures, Van Nostrand Reinhold Co.; 1981], on the ideal water cylinder, is calculated from the random incident wave field. Both forces represent a Gaussian random process of time. The diffraction coefficient of the wave force is obtained as quotient between the standard deviations of the force on the solid cylinder and of the Froude Krylov force. It is found that the diffraction coefficient of the horizontal force C_do is equal to the C_dv of the vertical force. Finally, it is shown that, since a very large wave force occurs on the cylinder, it may be calculated, in time domain, starting from the Froude Krylov force. It is then shown that this result is due to the fact that the frequency spectrum of the force acting on the cylinder is nearly identical to that of the Froude–Krylov force.     

On the effects of wave drift on the dispersion of floating pollutants

The movement of floating pollutants such as oil slicks on the surface of the sea is due to a number different factors, among which wave drift is certainly significant.In principle, it has been known since Stokes' time that a floating particle is subject to the movement caused by the orbital motion of water particles and that an average drift velocity results because the trajectories are not closed. In the past, however, this effect was often either disregarded or simply included with the surface wind induced current. In recent times the difference between the two effects has been conceptually clarified, so that the average wave drift in random one-dimensional seas has been the object of research and the results are now included in most handbooks and models for oil slick forecasting.Due to the chaotic nature of the wave field, however, the drift also causes floating substances to disperse, and this phenomenon is a much more neglected area of research. Recent work by Bovolin et al. [IAHR Congress, 1997] and Sobey and Barker [J. Coast. Res. 13 (1997)] has brought the subject to attention, and computational tools can now be made to quantify the effect and to verify when and how it should be taken into consideration in oil slick accident practise.The work presented in this paper is based on random simulation of the wave induced Eulerian velocity field in a directional sea, by making use of standard offshore wave directional models and on the ensemble averaging of floating particles trajectories in order to compute the spatial dispersion.     

Dynamic behavior of offshore spar platforms under regular sea waves

Many innovative floating offshore structures have been proposed for cost effectiveness of oil and gas exploration and production in water depths exceeding one thousand meters in recent years. One such type of platform is the offshore floating Spar platform. The Spar platform is modelled as a rigid body with six degrees-of-freedom, connected to the sea floor by multi-component catenary mooring lines, which are attached to the Spar platform at the fairleads. The response dependent stiffness matrix consists of two parts (a) the hydrostatics provide restoring force in heave, roll and pitch, (b) the mooring lines provide the restoring force which are represented here by nonlinear horizontal springs. A unidirectional regular wave model is used for computing the incident wave kinematics by Airy’s wave theory and force by Morison’s equation. The response analysis is performed in time domain to solve the dynamic behavior of the moored Spar platform as an integrated system using the iterative incremental Newmark’s Beta approach. Numerical studies are conducted for sea state conditions with and without coupling of degrees-of-freedom.     

Nonlinear coupled dynamic response of offshore Spar platforms under regular sea waves

Many innovative floating offshore structures have been proposed for cost effectiveness of oil and gas exploration and production in water depths exceeding one thousand meters in recent years. One such type of platform is the offshore floating Spar platform. The Spar platform is modelled as a rigid body with six degrees-of-freedom, connected to the sea floor by multi-component catenary mooring lines, which are attached to the Spar platform at the fairleads. The response dependent stiffness matrix consists of two parts (a) the hydrostatics provide restoring force in heave, roll and pitch, (b) the mooring lines provide the restoring force which are represented here by nonlinear horizontal springs. A unidirectional regular wave model is used for computing the incident wave kinematics by Airy’s wave theory and force by Morison’s equation. The response analysis is performed in time domain to solve the dynamic behavior of the moored Spar platform as an integrated system using the iterative incremental Newmark’s Beta approach. Numerical studies are conducted for sea state conditions with and without coupling of degrees-of-freedom.     

A general method for calculating hydrodynamic forces

This paper presents the derivation of a general method for calculating wave forces on the cylindrical members of offshore structures. By means of the proposed method one can calculate the wave loading on cylindrical members of fixed or floating offshore structures orientated randomly in waves. This method of calculating wave forces is based on the linear Airy wave theory. Calculation procedure of wave force components is presented in great detail on the basis of wave particle kinematic properties obtained from the linear Airy wave theory. In the procedure of calculating wave forces presented, definitions of the wave reference system for propagating wave, the structure reference system for the platform and the member reference system for the tubular members of the structure are first established, and then the calculation of wave forces is given in terms of its components, which are pressure, acceleration and velocity forces, including current forces. At the end of the paper, expressions of total heave, sway and surge forces and total roll, pitch and yaw moments acting on the platform are given as a sum of these forces acting on each member of the platform. The calculation procedure derived in this paper provides a very efficient means of calculating wave forces and moments during the time-domain simulations of a floating platform experiencing large amplitude motion in intact, progressive flooding and damaged conditions. Comparisons of the predictions with the measurements which will be presented elsewhere reveal that the calculation procedure developed can predict large amplitude oscillatory and steady motion characteristics of an intact and damaged platform in waves with an acceptable degree of accuracy.     

Third order wave force on axisymmetric bodies

The third order triple-frequency wave load on fixed axisymmetric bodies by monochromatic waves is considered within the frame of potential theory. Waves are assumed to be weak non-linearity and a perturbation method is used to expand velocity potentials and wave loadings into series according to a wave steepness of kA. Integral equation method is used to compute velocity potentials up to second order in wave steepness. The third order triple-frequency wave loads are computed by an indirect method and an efficient method is applied to form the third order forcing term on the free surface quickly. The method can be used to compute third order triple-frequency surge force, heave force and pitch moment on any revolution bodies with vertical axes. The comparison with Malenica and Molin's results is made on surge force on a uniform cylinder, and comparison with experimental results is made on third order surge force, heave force and pitch moment on a truncated cylinder. More numerical computations are carried out for third order forces and moments on a uniform cylinder, truncated cylinders and a hemisphere.     

三阶Stokes型随机波浪载荷谱研究

应用非线性谱分析理论，对三阶Stokes型随机波浪载荷谱进行了分析，将波面方程及海水质点的水平速度用一阶波面的非线性组表示，导出了随机波浪谱的表达式。为了便于求解随机波浪的载荷谱，将阻力项展开为幂级数式，并应用非线性谱分析理论，确定了幂级数的系数，进而将波浪载荷表示为一阶波面及其导数的非线性组合，最后得出波浪载荷谱密度的表达式，并应用数值分析方法，得出单位桩柱波浪力及总波浪力谱密度。     

Fully nonlinear simulations of wave resonance by an array of cylinders in vertical motions

The finite element method(FEM) is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions.The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions.The finite element linear system is solved by the conjugate gradient(CG) method with a symmetric successive overelaxlation(SSOR) preconditioner.The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation.Numerical examples are given by an array of floating wedgeshaped cylinders and rectangular cylinders.Results are provided for heave motions including wave elevations,profiles and hydrodynamic forces.Comparisons are made in several cases with the results obtained from the second order solution in the time domain.It is found that the wave amplitude in the middle region of the array is larger than those in other places,and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.     

Calculating the Wave Force on Partially Immersed Large-Scale Horizontal Cylinders

Large-scale interceptors constitute the main structure of offshore self-driven floating marine litter collection devices,and the structural stability of such interceptors under the action of waves directly influences the overall safety of the device.When the ratio of the diameter of a horizontal cylinder in such interceptors to the incident wavelength is larger than 0.25,the wave force can be calculated by using the diffraction theory,by considering the problem as that of the interaction between the waves and a partially immersed large-scale horizontal cylinder.In this study,an analytical approach to calculate the wave force on a partially immersed large-scale horizontal cylinder was formulated by using the stepwise approximation method.Physical model tests were conducted to investigate the effects of different factors(wave height,period,and immersion depth)on the wave force on a large-scale horizontal cylinder under conditions involving short-period waves.The results show that both horizontal and vertical wave forces on the cylinder increase as the wave height(immersion depth)increases in most cases.The vertical wave force decreases with the decrease of the period.For the horizontal wave force,it increases with the decrease of the period when the wavelength is larger than the diameter of the cylinder and decreases with the decrease of the period when the wavelength is smaller than the diameter of the cylinder.     

Application of smoothed particle hydrodynamics for modeling the wave-moored floating breakwater interaction

The application of a Smoothed Particle Hydrodynamics (SPH) model to simulate the nonlinear interaction between waves and a moored floating breakwater is presented. The main aim is to predict and validate the response of the moored floating structure under the action of periodic waves. The Euler equations together with an artificial viscosity are used as the governing equations to describe the flow field. The motion of the moored floating body is described using the Newton’s second law of motion. The interactions between the waves and structures are modeled by setting a series of SPH particles on the boundary of the structure. The hydrodynamic forces acting on the floating body are evaluated by summing up the interacting forces on the boundary particles from the neighboring fluid particles. The water surface elevations, the movements of the floating body and the moored forces are all calculated and compared with the available experimental data. Good agreements are obtained for the dynamic response and hydrodynamic performance of the floating body. The numerical results of different immersion depths of the floating body are compared with that of the corresponding fixed body. The effects of the relative length and the density of the structure on the performance of the floating body are analyzed.     

Interaction of regular waves with a group of dual porous circular cylinders

Diffraction of linear waves around a group of dual porous cylinders consisting of a thin and porous outer cylinder with an impermeable inner cylinder is investigated analytically based on the eigenfunction expansion method proposed by Spring and Monkmeyer [Spring BH, Monkmeyer PL. Interaction of plane waves with vertical cylinders. In: Proceedings 14th international coastal engineering conference. 1974. p. 1828–47] and further modified by Linton and Evans [Linton CM, Evans DV. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 1990;215:549–69]. The present formulation is an extension of the work of Wang and Ren [Wang KH, Ren X. Wave interaction with a concentric porous cylinder system. Ocean Engineering 1994;21(4):343–60], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. This paper aims at investigating the influence of multiple interactions between the cylinders in the group on the hydrodynamic wave forces, wave run-up and free-surface elevation in their vicinity. Further, the study focuses on the variation of the forces and run-up on the individual cylinders within the group compared to that on isolated cylinders.