Comparisons of Wave Force Model Effects on the Structural Responses and Fatigue Loads of a Semi-Submersible Floating Wind Turbine

The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.

Wave Force on the Crown Wall of Rubble Mound Breakwaters at Intermediate Depths

Rubble mound breakwaters with a crown wall are a common coastal engineering structure.The wave force on crown walls is an important parameter for the practice engineering design.Particularly,the wave force on crown walls under intermediate depths has been studied through physical model tests and numerical simulations.In this study,a three-dimensional numerical wave flume was developed to investigate monochromatic wave interactions in a rubble mound breakwater with a crown wall.Armor blocks were modeled in detail.The Navier-Stokes equations for two-phase incompressible flows,combined with shear stress transport k-ωturbulence model and volume of fluid method for tracking the free surface,were solved.A set of laboratory experiments were performed to validate the adopted model.Subsequently,a series of numerical simulations were implemented to examine the impacts of different hydrodynamic parameters(including wave height,incident wave period,and water depth)and the berm width on the wave force of the crown wall.Finally,a comparison of the experimental results and Martin method shows that the latter method is not suitable for this experimental scope.New empirical formulas are proposed to predict the wave force on crown walls under intermediate depth.The results can provide a basis for the design of crown wall of rubble mound breakwaters at intermediate depths.

NUMERICAL MODEL OF WAVE FORCES ON CONTINUOUS CYLINDER STRUCTURES

A numerical model of wave force upon continuous cylinder structures with a large diameter using the boundary element method (BEM) is presented. A numerical model of reflecting wave upon continuous cylinders was established on the basis of linear wave theory.The fundamental solution to the Helmholtz equation within an infinite strip area that explicitly satisfies two infinite parallel boundaries is used together with Radiation condition rather than the solution of an infinite area.According to the proposed theory and method,the computer programs have been composed in Visual C ++ Development Studio.Several examples show that the technique and its program are feasible and efficient.And the wave forces upon continuous cylinders can be decreased by as much as 14%～24% under a ratio of D/L= 0.09～0.19 compared with the square caissons.

Wave Forces on Submerged Semi-Circular Breakwater and Similar Structures

The results of design and experiment of a submerged semi-circular breakwater at the Yangtze estuary show that the submerged structure will be unsafe when the general empirical wave force formula for semi-circular breakwater is used in design. Therefore, a new calculation method for the wave forces acting on a submerged semi-circular structure is given in this paper, in which the wave force acting on the inside circumference of semi-circular arch is included, and the phase modification coefficient in the general empirical formula is adjusted as well. The new wave force calculation method has been Verified by the results of seven related physical model tests and adopted in the design of the south esturary jetty of the first stage project of Deep Channel Improvement Project of the Yangtze River Estuary, the total jetty length being 17.5 km.

Viscous Effects on Wave Forces on A Submerged Horizontal Circular Cylinder

Numerical simulations are carried out for wave action on a submerged horizontal circular cylinder by means of a viscous fluid model, and it is focused on the examination of the discrepancies between the viscous fluid results and the potential flow solutions. It is found that the lift force resulted from rotational flow on the circular cylinder is always in anti-phase with the inertia force and induces the discrepancies between the results. The influence factors on the magnitude of the lift force, especially the correlation between the stagnation-point position and the wave amplitude, and the effect of the vortex shedding are investigated by further examination on the flow fields around the cylinder. The viscous numerical calculations at different wave frequencies showed that the wave frequency has also significant influence on the wave forces. Under higher frequency and larger amplitude wave action, vortex shedding from the circular cylinder will appear and influence the wave forces on the cylinder substantially.

A B-Spline Based BEM and Its Applicaion in Predicting Wave Forces on 3D Bodies

For the computation of wave forces on structures, a B-spline expansion is applied to discretize the body surface, and represent the velocity potentials on the body surface. The expansion coefficients for the body geometry are determined by the Least Square Method, and the coefficients for velocity potentials by the Galerkin method. The method can give continuous description of velocity potentials and their derivatives on the whole smooth body surface. The method has been implemented, and numerical results show that the method gives very accurate results and its convergence is fast.

Experimental study of reflection coefficient and wave forces acting on perforated caisson

The reflection coefficient and the total horizontal forces of regular waves acting on theperforated caisson are experimentally investigated. The empirical relationship between reflection coefficient and the ratio of the total horizontal forces acting on the perforated caisson to those on solid vertical walls with the relative chamber width, relative water depth and porosity of perforated wall, etc. are given. Moreover, the results of the ratio of the total horizontal forces are also compared with formulas given by Chinese Harbour Design Criteria and Takahashi, which may be useful for the practical engineering application.

Effects of Free Heave Motion on Wave Forces on Two Side-by-Side Boxes in Close Proximity Under Wave Actions

Wave forces on two side-by-side boxes in close proximity under wave actions were analyzed using the OpenFOAM package.The upstream box heaved freely under wave actions,whereas the downstream box remained fixed.For comparison,a configuration in which both boxes were fixed was also considered.The effects of the heave motion of the upstream box on the wave loads,including the horizontal wave forces,vertical wave forces,and moments on the boxes,were the focus of this study.Numerical analyses showed that all frequencies at which the maximum horizontal wave forces,maximum vertical wave forces,and maximum moment appeared are dependent on the heave motion of the upstream box and that the effects of the heave motion on these frequencies are different.Furthermore,these frequencies were observed to deviate from the corresponding fluid resonant frequency.Moreover,the heave motion of the upstream box reduced the wave forces acting on both boxes and altered the variation trends of the wave forces with the incident wave frequency.

Numerical Simulation of Nonlinear Wave Force on a Quasi-ellipse Caisson

A three dimensional numerical model of nonlinear wave action on a quasi-ellipse caisson in a time domain was developed in this paper. Navier-Stokes equations were solved by the finite difference method, and the volume of fluid （VOF） method was employed to trace the free surface. The partial cell method was used to deal with the irregular boundary typical of this type of problem during first-time wave interaction with the structure, and a satisfactory result was obtained. The numerical model was verified and used to investigate the effects of the relative wave height H/d, relative caisson width kD, and relative length-width ratio B/D on the wave forces of the quasi-ellipse caisson. It was shown that the relative wave height H/d has a significant effect on the wave forces of the caisson. Compared with the non-dimensional inline wave force, the relative length-width ratio BID was shown to have significant influence on the non-dimensional transverse wave force.

A Finite Element Solution of Wave Forces on Submerged Horizontal Circular Cylinders

In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two dimensional Navier Stokes equations is solved numerically with a finite element method. In order to track the moving non linear wave surface boundary, the Navier Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data. Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder. The effects of the KC number and the cylinder depth on the wave forces are studied.

A Time-Domain Coupled Model for Nonlinear Wave Forces on A Fixed Box-Shaped Ship in A Harbor

A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor. The domain is divided into an inner domain and an outer domain. The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations. The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions. Along the interface boundaries between the inner domain and the outer domain, the volume flux is assumed to be continuous and the wave pressures are equal. Relevant physical experiment is conducted to validate the present model. It is shown that the numerical results agree with the experimental data. Compared with the coupled model with the flow in the inner domain governed by the Laplace equation, the present coupled model is more efficient and its solution procedure is more simple, which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.

An Experimental Study of Irregular Wave Forces on Multiple Quasi-ellipse Caissons

An experimental investigation of irregular wave forces on quasi-ellipse caisson structures is presented. Irregular waves were generated based on the Jonswap spectrum with two significant wave heights, and the spectrum peak periods range from 1.19 s to 1.81 s. Incident wave directions relative to the centre line of the multiple caissons are from 0＆#176; to 22.5＆#176;. The spacing between caissons ranges from 2 to 3 times that of the width of the caisson. The effects of these parameters on the wave forces of both the perforated and non-perforated caissons were compared and analyzed. It was found that the perforated caisson can reduce wave forces, especially in the transverse direction. Furthermore, the relative interval and incident wave direction have significant effects on the wave forces in the case of multiple caissons.

Numerical Simulation of Wave Forces on Seabed Pipelines

A three-step finite element method (FEM) together with Large Eddy Simulation (LES) is applied to incompressible turbulent flow around seabed pipelines at relatively high Reynolds numbers. Both two dimensional and three-dimensional numerical simulation is carried out to determine the three-dimensional effect. The results of numerical simulation agree quite well with the wave forces acting on pipeline models measured in physical model test.

An Engineering Computational Method of Calculating Wave Forces on the Mat and Platform's Sit-on-Bottom Stability

- In this paper, an engineering method is employed to calculate the horizontal and vertical wave forces on the mat of the submersible platform under Froude-Krylov hypothesis. According to some model tests, appropriate diffraction coefficients are selected. And the results of the formulae given in the paper agree satisfactorily with those experimental data now available. The proposed computational method is effective and convenient to use in evaluating the horizontal and vertical wave forces on the mat. An exmaple is also given in this paper. Finally, the effects of the vertical wave force on the platorm's sit-on-bottom stability are analyzed.

Application of the state space model to the system of wave energy conversion Analytical method for wave forces on singleoscillating rectangular buoy

A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves.In the method a new analytical expression for the diffraction velocity potential is obtained first by use of theeigenfunction expansion method and then the wave excitation force is calculated by use of the known incident wavepotential and the diffraction potential. Compared with the classical analytical method, it can be seen that the presentmethod is simpler for a two-dimensional problem due to the comparable effort needed for the computation ofdiffraction potential and for that of radiated potential. To verify the correctness of the method, a classical example inthe reference is recomputed and the obtained results are in good accordance with those by use of other methods,which shows that the present method is correct.

3D Numerical Modeling of Wave Forces on Tandem Fixed Cylinders Using the BEM

In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders.The fluid was considered to be inviscid and irrotational.Therefore,the Helmholtz equation was used as a governing equation.The boundary element method（BEM） was adopted to discretize the relevant equations.Open boundaries were used in far fields of the study domain.Linear waves were generated and propagated towards tandem fixed cylinders to estimate the forces applied on them.Special attention was paid to consideration of the effect on varying non-dimensional cylinder radius and distance between cylinders,ka and kd on forces and trapped modes.The middle cylinder wave forces and trapped modes in a set of nine tandem cylinders were validated utilizing analytical data.The comparisons confirm the accuracy of the model.The results of the inline wave force estimation on n tandem cylinders show that the critical cylinder in the row is the middle one for odd numbers of cylinders.Furthermore the results show that the critical trapped mode effect occurs for normalized cylinder radiuses close to 0.5 and 1.0.Finally the force estimation for n tandem cylinders confirms that force amplitude of the middle cylinder versus normalized separation distance fluctuates about that of a single cylinder.

Reliability Analysis of Numerical Simulation of Sea-Crossing Bridge Deformation Under Wave Forces

To study on the numerical simulation calculation reliability of sea-crossing bridge under complex wave forces,the paper applied GPS deformation monitoring and numerical simulation calculation by researching Qingdao Jiaozhou Bay Sea-Crossing Bridge.The db3 wavelet three-layer decomposition was used on the horizontal movement of the sea-crossing bridge and the wind speed of the waves to analyze their correlation.The complex wave forces value of Qingdao Jiaozhou Bay Sea-Crossing Bridge was loaded on FLAC3D software successfully to make numerical simulation calculation of bridge deformation.Since the accuracy of the GPS deformation monitoring reaches millimeter level,it was used to monitor the exact value of the bridge deformation to judge the reliability of numerical simulation.The relative errors of displacement in X,Y and Z directions were between 33%and 41%through comparison.It could be seen that the numerical simulation error was relatively large,which was mainly due to various environmental factors and the deviation of applied wave forces.However,numerical simulation generally reflects the deformation law of the sea-crossing bridge under complex wave forces,providing an effectively technical support for the safe operation assessment of the sea-crossing bridge.

Feasibility Study on Common Methods for Wave Force Estimation of Deep Water Combined Breakwaters

China's newly enacted Breakwater Design Specifications(JTS154-2011) explicitly state that breakwaters with water depths greater than 20 m are categorized as deep-water breakwaters, and emphasize that design principles, methods and construction requirements are different from those of common shallow water breakwaters. However, the specifications do not make any mention of how to choose wave force calculation methods of deep-water breakwaters. To study the feasibility of different formulae for wave force estimation of deep water combined breakwaters, the wave force calculated by the Sainflou's, Goda's, modified Goda's and specifications' methods are compared for various water depths and wave heights in this paper. The calculated results are also compared with experimental data. The total horizontal forcing and the pattern of pressure distributions are presented. Comparisons show that the wave pressure distributions by the four methods are similar, but the total horizontal forces are different. The results obtained by the Goda's method and the specified formulae are much closer to the experimental data. As for the wave force estimation for the deepwater mixed embankment foundation bed parapet, the Goda's formula is applied in the case with a water depth of less than 42 m. The Specifications method is suitable for standing waves. In the wave force estimates of breastworks, Sainflou's and the modified Gaoda's formulae are no longer applicable for the foundation bed of mixed embankment.

Nonlinear Wave Force on Pier Group in Shallow Water

Based on the 1st order cnoidal wave theory, the wave diffraction around the pier group inshallow water is studied in this paper. The formulas for calculating the nonlinear wave forces are also presented here. In order to verify the theoretical results, model tests are conducted in the wave flume in The State Key Laboratory of Coastal and Offshore Engineering located in Dalian University of Technology. The range of the wave parameters in the experiments is characteristic wave period T g/d^(1/2) = 8.08- 22.86, characteristic wave height H/ d= 0.1 ~ 0.45. The results obtained from the experiments agree with the theoretical results quite well. It is shown that, in shallow water the nonlinear wave forces acting on a pier group are greater than those calculated by linear wave theory, the value of increment in wave force increases with the increases of the nonlinearity of the wave. In the wave range studied in this paper, the nonlinear wave force can reach over 4 times the force calculatecd by linear wave theory. Thus, it is suggested that, when Tg / d^(1/2)> 8, the wave force on the piers in the pier group in shallow water should be calculated by using the cnoidal wave theory.

Study on Current-Random Wave Forces Acting on a Framework

The forces of random wave plus current acting on a simplified offshore platform (jacket) model have been studied numerically and experimentally. The numerical results are in good agreement with experiments. The mean force can be approximated as a function of equivalent velocity parameter and the root-mean-square force as a function of equivalent significant wave height parameter.