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.

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.

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.

Wave Forces Acting on Vertical Walls

Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical model, and satisfactory agreements are obtained. The variation of wave forces with incident angles and the shape of simultaneous pressure distribution are investigated, and the comparisons between numerical results and Goda＇ s predictions are also carried out. It is concluded that the maximum wave forces acting on the unit length of vertical wall is often induced by the obliquely incident waves instead of normally incident waves, while Goda＇ s formula may be inapplicable for oblique wave incidence. The shape of simultaneous pressure distribution is not significantly influenced by incident angles, and it can be favorably predicted by Goda＇ s formula. When regular wave heights are taken as the same as irregular wave height H1%, the irregular wave forces Ph. 1% are slightly larger than regular wave forces in most cases.

Numerical Analysis of Wave Forces on Arbitrarily Shaped Multi-Pillars Over Varying Topography

The modified hybrid element method (MHEM) is utilized to predict and analyze wave forces on arbitrarily shaped multiple bodies. This method can be applied to waves of all water depths, i. e. shallow, intermediate, and deep waters, on slowly varying seabed. The MHEM employs the ICCG method to save CPU and storage, thus the computation of wave forces for large multi-body systems can be carried out on microcomputers. Numerical results of the present method are compared with experimental data and other solutions. It is shown that the MHEM provides more accurate solutions of the wave forces than other numerical methods do. Therefore, the methodology presented herein can be used in the design of coastal and ocean structures.

Nonlinear effect on inertia component of wave forces on a cylinder

A series of experiments on wave forces on a cylinder have been carried out when inertia component isdominant for a small she cylinder. The influence of nonlinear effect on the inertia component of wave forces on a cylinder is analyzed. The applicable range of nonlinear wave theories, such as Stokes and cnoidal wave theories, in calculating wave forces on a cylinder is discussed. A correction method is suggested for linear wave theory in calculated waveforces on a cylinder under the nonlinear condition.

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.

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.

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 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.

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.

Numerical Simulation of Solitary Wave Forces on A Vertical Cylinder on A Slope Beach

Wave forces acting on a vertical cylinder at different locations on a slope beach in the near-shore region are investigated considering solitary waves as incoming waves.Based on the Reynolds-averaged Navier-Stokes equations and the k-ε turbulence model,wave forces due to the interaction between the solitary wave and cylinder are simulated and analyzed with different incident wave heights and cylinder locations.The numerical results are first compared with previous theoretical and experimental results to validate the model accuracy.Then,the wave forces and characteristics around the cylinder are studied,including the velocity field,wave surface elevation and pressure.The effects of relative wave height,Keulegan-Carpenter(KC)number and cylinder locations on the wave forces are also discussed.The results show that the wave forces exerted on a cylinder exponentially increase with the increasing incident wave height and KC number.Before the wave force peaks,the growth rate of the wave force shows an increasing trend as the cylinder moves onshore.The cylinder location has a notable effect on the wave force on the cylinder in the near-shore region.As the cylinder moves onshore,the wave force on the cylinder initially increases and then decreases.For the cases considered here,the maximum wave force appears when the cylinder is located one cylinder diameter below the still-water shoreline.Furthermore,the fluid velocity peaks when the maximum wave force appears at the same location.

Simulation of Wave Forces on A Semi-Circular Breakwater Using Multilayer Feed Forward Network

In this paper, the Artificial Neural Network (ANN) is used to study the wave forces on a semi-circular breakwater. The process of establishing the network model for a specific physical problem is presented. Networks with double implicit layers have been studied by numerical experiments. 117 sets of experimental data are used to train and test the ANN. According to the results of ANN simulation, this method is proved to have good precision compared with experimental and numerical results.

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-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.

THE IRREGULAR BREAKING WAVE FORCES ON VERTICAL WALL

A method for the calculation of total horizontal wave forces by irregular breaking waves on vertical wall was developed by authors, which was based on physical model test, dimensionless analysis and assessment of real construction. The methods for the determination of pressure distribution of horizontal forces on vertical wall as well as u-plift forces on the bottom of wall are also given. The comparison between calculated results by this method and samples of real construction are very well.

PROBABILITY DISTRIBUTION OF IN-LINE WAVE FORCES ON A PILE IN IRREGULAR WAVES

The probability distribution of in-line wave forces on a pile can be mathematically summed up to that of a theory and the assumption of wave period being constant are used and the above probability distribution is simplified to that of a single dimentsion function.The probability density functions of the peak values of total wave forces on a whole vertical pile in irregular waves are derived from that of wave height which is the Rayleigh distribution(deep water wave)or the Kerohovski distribution(shallow water waves)on the base of the Morison Equation.The identification with experimental data shows that such simplification is successful.These distributions are compared with Weibull distribution and Rayleigh distribution and the result shows that the shallow water distribution of wave forces obtained here is the best one and can be used in practice.