Numerical Simulations of Wave Impact Forces on the Open-Type Sea Access Road Using A Two-Phase SPH Model

A numerical study based on a two-dimensional two-phase SPH(Smoothed Particle Hydrodynamics)model to analyze the action of water waves on open-type sea access roads is presented.The study is a continuation of the analyses presented by Chen et al.(2022),in which the sea access roads are semi-immersed.In this new configuration,the sea access roads are placed above the still water level,therefore the presence of the air phase becomes a relevant issue in the determination of the wave forces acting on the structures.Indeed,the comparison of wave forces on the open-type sea access roads obtained from the single and two-phase SPH models with the experimental results shows that the latter are in much better agreement.So in the numerical simulations,a two-phaseδ-SPH model is adopted to investigate the dynamical problems.Based on the numerical results,the maximum horizontal and uplifting wave forces acting on the sea access roads are analyzed by considering different wave conditions and geometries of the structures.In particular,the presence of the girder is analyzed and the differences in the wave forces due to the air cushion effects which are created below the structure are highlighted.

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.

Effects of Second-Order Sum-and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.

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.

Wave-Current Forces on Small Square Cylinders (Part II)

Based on model tests, the lift and resultant forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in this paper. The lift and resultant force coefficients CL and Cf related to KC number and the effect of direction of wave propagation are also given, which may be useful for practical engineering application.

Depression and elevation internal solitary waves in a two-layer fluid and their forces on cylindrical piles

Both large amplitude depression and elevation internal solitary waves （ISWs） were observed on the continental shelf of the northwest South China Sea （SCS） during the Wenchang Intemal Wave Experiment. In this study, we investigate the characteristics of depression and elevation ISWs based on comparisons between observational results and internal wave theories. It is suggested that the large amplitude depression wave is better represented by the extended Korteweg-de Vries （EKdV） theory than by the KdV model, whereas the large amplitude elevation wave is in better agreement with the KdV equation than with the EKdV theory. Wave-induced forces on a supposed small-diameter cylindrical pile by depression and elevation waves are also estimated using the internal wave theory and Morison formula. The wave-induced force by elevation ISWs is rarely reported in the literature. It is found that the force induced by the elevation wave differs significantly fi＇om that by the depression wave, and the elevation wave generally produces greater force on the pile in the lower water column than the depression wave. These results show that ISWs in the study area can present a serious threat to ocean engineering structures, and should not be ignored in the design of oil platforms and ocean operations.

Wave-Current Forces on Small Square Cylinders (Part I)

-Based on the extended Morison Equation and model tests, the in-line forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in detail in this paper. The hydrodynamic coefficient CD and Cu related to KC number and the effect of direction of wave incidence are also given, which can be used in engineering practice.

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.

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.

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.

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.

Study on Nonlinear Characteristics of Freak-Wave Forces with Different Wave Steepness

The nonlinear wave forces on vertical cylinders induced by freak wave trains were experimentally investigated. A series of freak wave trains with different wave steepness were modeled in a wave flume. The corresponding wave forces on vertical cylinders of different diameters were measured. The experimental wave forces were also compared with the predicted results based on Morison formula. Particular attentions were paid to the effects of wave steepness on the dimensionless peak forces, asymmetry characteristics of the impact forces and high-frequency force components. Wavelet-based analysis methods were employed in revealing the local energy structures and quadratic phase coupling in the freak wave forces.

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.

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.

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.

Wave Drift Forces on Two Floating Bodies Arranged Side by Side

An innovative hydrodynamic theory and numerical model were developed to help improve the efficiency, accuracy, and convergence of the numerical prediction of wave drift forces on two side-by-side deepwater floating bodies. The wave drift forces were expressed by the double integration of source strength and the corresponding Green function on the body surface, which is consistent with the far field formula based on momentum conservation and sharing the advantage of near field calculations providing the drift force on each body. Numerical results were validated through comparing the general far field model and pressure integral model, as well as the middle field model developed usin^z the software HydroStar.