作用在双圆柱桩上波浪力准确解和有限差分解的比较

The wave force exerted on vertical piles of offshore structures is the main criterion in designing them.In structures with more than one large pile,the influence of piles on each other is one of the most important issues being concerned in past researches.An efficient method for determining the interaction of piles is introduced in present research.First the wave force is calculated by the exact method using the diffraction theory,then in the finite difference numerical method the force is calculated by adding the velocity potentials of each pile and integration of pressure on their surface.The results showed that the ratio of the wave force on each of the double piles to a single pile has a damped oscillation around unity in which the amplitude of oscillation decreases with the increase in the spacing parameter.Also different wave incident directions and diffraction parameters were used and the results showed that the numerical solution has acceptable accuracy when the diffraction parameter is larger than unity.     

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 B/D was shown to have significant influence on the non-dimensional transverse wave force.     

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.     

船体周围Stokes波浪流耦合VOF模型的数值模拟（英文）

The surface wave generated by flow around a ship hull moving near free surface of water is simulated numerically in this study. The three-dimensional implicit finite volume method(FVM) is applied to solve Reynolds averaged Navier-Stokes(RANS) equation. The realizable k-ε turbulence model has been implemented to capture turbulent flow around the ship hull in the free surface zone. The volume of fluid(VOF) method coupled with the Stokes wave theory has been used to determine the free surface effect of water. By using is a six degrees of freedom model, the ship hull's movement is numerically solved with the Stokes wave together. Under the action of Stokes waves on the sea, the interface between the air and water waves at the same regular pattern and so does the pressure and the vertical velocity. The ship hull moves in the same way as the wave. The amplitude of the ship hull's heave is less than the wave height because of the viscosity damping. This method could provide an important reference for the study of ships' movement, wave and hydrodynamics.     

风机塔架与叶片相互作用的数值模拟(英文)

Numerical simulations of wind turbine blade-tower interaction by using the open source OpenFOAM tools coupled with arbitrary mesh interface(AMI) method were presented.The governing equations were the unsteady Reynolds-averaged Navier-Stokes(RANS) which were solved by the pimpleDyMFoam solver,and the AMI method was employed to handle mesh movements.The National Renewable Energy Laboratory(NREL) phase VI wind turbine in upwind configuration was selected for numerical tests with different incoming wind speeds(5,10,15,and 25 m/s) at a fixed blade pitch and constant rotational speed.Detailed numerical results of vortex structure,time histories of thrust,and pressure distribution on the blade and tower were presented.The findings show that the wind turbine tower has little effect on the whole aerodynamic performance of an upwind wind turbine,while the rotating rotor will induce an obvious cyclic drop in the front pressure of the tower.Also,strong interaction of blade tip vortices with separation from the tower was observed.     

Numerical Simulation of the Stokes Wave for the Flow around a Ship Hull Coupled with the VOF Model

The surface wave generated by flow around a ship hull moving near free surface of water is simulated numerically in this study. The three-dimensional implicit finite volume method(FVM) is applied to solve Reynolds averaged Navier-Stokes(RANS) equation. The realizable k-ε turbulence model has been implemented to capture turbulent flow around the ship hull in the free surface zone. The volume of fluid(VOF) method coupled with the Stokes wave theory has been used to determine the free surface effect of water. By using is a six degrees of freedom model, the ship hull’s movement is numerically solved with the Stokes wave together. Under the action of Stokes waves on the sea, the interface between the air and water waves at the same regular pattern and so does the pressure and the vertical velocity. The ship hull moves in the same way as the wave. The amplitude of the ship hull’s heave is less than the wave height because of the viscosity damping. This method could provide an important reference for the study of ships’ movement, wave and hydrodynamics.     

Improving longitudinal motion prediction of hybrid monohulls with the viscous effect

A new method improves prediction of the motion of a hybrid monohull in regular waves. Stem section hydrodynamic coefficients of a hybrid monohull with harmonic oscillation were computed using the Reynolds Averaged Navier-Stokes Equations (RANSE). The governing equations were solved using the finite volume method. The VOF method was used for free surface treatment, and RNGК-ε turbulence model was employed in viscous flow calculation. The whole computational domain was divided into many blocks each with structured grids, and the dynamic process was treated with moving grids. Using a 2-D strip method and 2.5D theory with the correction hydrodynamic coefficients allows consideration of the viscous effect when predicting longitudinal motion of a hybrid monohull in regular waves. The method is effective at predicting motion of a hybrid monohull, showing that the viscous effect on a semi-submerged body cannot be ignored.     

Dynamic interaction of parallel moving ships in close proximity

Nowadays,there are many studies conducted in the field of marine hydrodynamics which focus on two vessels traveling and floating in sufficiently close proximity to experience significant interactions.The hydrodynamic behavior of parallel moving ships in waves is an interesting and important topic of late.A numerical investigation has been carried out for the prediction of wave exciting forces and motion responses of parallel moving ships in regular waves.The numerical solution was based on 3D distribution technique and using the linear wave theory to determine the exciting forces and ship＇s motion.The speed effects have been considered in the Green function for more realistic results.The numerical computations of wave exciting forces and motion responses were carried out for a Mariner and Series 60 for the purpose of discovering different Froude numbers and different separation distances in head sea conditions.Based on the numerical computations,it was revealed that the sway,roll and yaw have a significant effect due to hydrodynamic interaction.     

Shock resistance of supercharged boilers through integration with ship structure

The non-linear finite element software ABAQUS was used to simulate the dynamic response of a marine supercharged boiler when subjected to impact loading. Shock resistance was analyzed by the time-domain simulation method. After exhaustive simulations,the effect of air pressure induced by different working conditions on the shock response of a supercharged boiler was reviewed,leading to conclusions about the variability of structural response with different loading parameters. In order to simulate the real impulsive environments of supercharged boilers,the integration of equipment and ship structure was then primarily used to analyze shock response. These distinctly different equipment shock test methods,run under equivalent work conditions,were compared and the causes of discrepancy were analyzed. The main purpose of this paper is to present references for the anti-shock design of marine supercharged boilers.     

Multigrid fictitious boundary method for incompressible viscous flows around moving airfoils

In this paper, an efficient multigrid fictitious boundary method (MFBM) coupled with the FEM solver package FEATFLOW was used for the detailed simulation of incompressible viscous flows around one or more moving NACA0012 airfoils. The calculations were carried on a fixed multigrid finite element mesh on which fluid equations were satisfied everywhere, and the airfoils were allowed to move freely through the mesh. The MFBM was employed to treat interactions between the fluid and the airfoils. The motion of the airfoils was modeled by Newton-Euler equations. Numerical results of experiments verify that this method provides an efficient way to simulate incompressible viscous flows around moving airfoils.     

高速滑行艇在规则波中运动的RANSE数值模拟(英文)

This paper presents a study on the numerical simulation of planing crafts sailing in regular waves. This allows an accurate estimate of the seas keeping performance of the high speed craft. The simulation set in six-degree of freedom motions is based on the Reynolds averaged Navier Stokes equations volume of fluid (RANSE VOF) solver. The trimming mesh technique and integral dynamic mesh method are used to guarantee the good accuracy of the hydrodynamic force and high efficiency of the numerical simulation. Incident head waves, oblique waves and beam waves are generated in the simulation with three different velocities (Fn =1.0, 1.5, 2.0). The motions and sea keeping performance of the planing craft with waves coming from different directions are indicated in the flow solver. The ship designer placed an emphasis on the effects of waves on sailing amplitude and pressure distribution of planing craft in the configuration of building high speed crafts.     

粘流方法的螺旋桨尾流场数值分析(英文)

The computational fluid dynamics(CFD) method is used to numerically simulate a propeller wake flow field in open water.A sub-domain hybrid mesh method was adopted in this paper.The computation domain was separated into two sub-domains,in which tetrahedral elements were used in the inner domain to match the complicated geometry of the propeller,while hexahedral elements were used in the outer domain.The mesh was locally refined on the propeller surface and near the wake flow field,and a size function was used to control the growth rate of the grid.Sections at different axial location were used to study the spatial evolution of the propeller wake in the region ranging from the disc to one propeller diameter(D) downstream.The numerical results show that the axial velocity fluctuates along the wake flow;radial velocity,which is closely related to vortices,attenuates strongly.The trailing vortices interact with the tip vortex at the blades’ trailing edge and then separate.The strength of the vortex shrinks rapidly,and the radius decreases 20% at one diameter downstream.     

A second order volume of fluid （VOF） scheme for numerical simulation of 2-D breaking waves

Among all environmental forces acting on ocean structures and marine vessels, those resulting from wave impacts are likely to yield the highest loads. Being highly nonlinear, transient and complex, a theoretical analysis of their impact would be impossible without numerical simulations. In this paper, a pressure-split two-stage numerical algorithm is proposed based on Volume Of Fluid (VOF) methodology. The algorithm is characterized by introduction of two pressures at each half and full cycle time step, and thus it is a second-order accurate algorithm in time. A simplified second-order Godunov-type solver is used for the continuity equations. The method is applied to simulation of breaking waves in a 2-D water tank, and a qualitative comparison with experimental photo observations is made. Quite consistent results are observed between simulations and experiments. Commercially available software and Boundary Integral Method (BIM) have also been used to simulate the same problem. The results from present code and BIM are in good agreement with respect to breaking location and timing, while the results obtained from the commercial software which is only first-order accurate in time has clearly showed a temporal and spatial lag, verifying the need to use a higher order numerical scheme.     

具有阶梯状海底的表面穿透柔性多孔屏障结构斜波捕获（英文）

This study presents a simple numerical method that can be used to evaluate the hydrodynamic performances of antifouling paints.Steady Reynolds-averaged Navier-Stokes equations were solved through a finite volume technique, whereas roughness was modeled with experimentally determined roughness functions. First, the methodology was validated with previous experimental studies with a flat plate. Second, flow around the Kriso Container Ship was examined. Lastly, full-scale results were predicted using Granville's similarity law. Results indicated that roughness has a similar effect on the viscous pressure resistance and frictional resistance around a Reynolds number of 107. Moreover, the increase in frictional resistance due to roughness was calculated to be approximately 3%–5% at the ship scale depending on the paint.     

K2_SPH方法及其在二维水波模拟中的应用(英文)

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian meshless particle method. However, its low accuracy of kernel approximation when particles are distributed disorderly or located near the boundary is an obstacle standing in the way of its wide application. Adopting the Taylor series expansion method and solving the integral equation matrix, the second order kernel approximation method can be obtained, namely K2_SPH, which is discussed in this paper. This method is similar to the Finite Particle Method. With the improvement of kernel approximation, some numerical techniques should be adopted for different types of boundaries, such as a free surface boundary and solid boundary, which are two key numerical techniques of K2_SPH for water wave simulation. This paper gives some numerical results of two dimensional water wave simulations involving standing wave and sloshing tank problems by using K2_SPH. From the comparison of simulation results, the K2_SPH method is more reliable than standard SPH.     

等效波的散货船舱口角疲劳评估应力组合方法(英文)

The stress combination method for the fatigue assessment of the hatch corner of a bulk carrier was investigated based on equivalent waves.The principles of the equivalent waves of ship structures were given,including the determination of the dominant load parameter,heading,frequency,and amplitude of the equivalent regular waves.The dominant load parameters of the hatch corner of a bulk carrier were identified by the structural stress response analysis,and then a series of equivalent regular waves were defined based on these parameters.A combination method of the structural stress ranges under the different equivalent waves was developed for the fatigue analysis.The combination factors were obtained by least square regression analysis with the stress ranges derived from spectral fatigue analysis as the target value.The proposed method was applied to the hatch corner of another bulk carrier as an example.This shows that the results from the equivalent wave approach agree well with those from the spectral fatigue analysis.The workload is reduced substantially.This method can be referenced in the fatigue assessment of the hatch corner of a bulk carrier.     

Interaction of two three-dimensional explosion bubbles

The interaction of two underwater explosion bubbles was mathematically analyzed in this paper. Based on the assumption of potential flow, high-order curved elements were used to discretize the boundary integral equation and solve it. Assuming that gas inside the bubble follows the isentropic rule, the Euler-Lagrange method was used to trace the evolution of the bubble, and when calculating the singular integral, the singularity of the double-layer singular integral was eliminated by reconstructing a principal-value integral of double-layer potential so that a more precise result could be obtained. Elastic mesh technique (EMT) was also used when tracing the evolution of the bubble interface, and numerical smoothing wasn't needed. A comparison of calculations using this three-dimensional model with results of the Reyleigh-Plesset bubble model shows that the three-dimensional model and calculation method in this paper is practical. This three-dimensional model was applied to simulate the interaction of two bubbles under the action of gravity, and the dynamic characteristics of two bubbles near the surface was also analyzed. Bubbles influenced by surface effects and gravity present severe non-linearity. This paper provides a reference for research into the dynamics of multi-bubbles.     

基于边界元方法的二维全非线性数值波浪水槽(英文)

The development of a two dimensional numerical wave tank (NWT) with a rocker or piston type wavemaker based on the high order boundary element method (BEM) and mixed Eulerian-Lagrangian (MEL) is examined. The cauchy principle value (CPV) integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the corner problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.     

海水风机与不同类型基座耦合的非稳态流动分析（英文）

Environmental effects have an important influence on Offshore Wind Turbine(OWT) power generation efficiency and the structural stability of such turbines. In this study, we use an in-house Boundary Element(BEM)—pan MARE code—to simulate the unsteady flow behavior of a full OWT with various combinations of aerodynamic and hydrodynamic loads in the time domain. This code is implemented to simulate potential flows for different applications and is based on a three-dimensional first-order panel method. Three different OWT configurations consisting of a generic 5 MW NREL rotor with three different types of foundations(Monopile, Tripod, and Jacket) are investigated. These three configurations are analyzed using the RANSE solver which is carried out using ANSYS CFX for validating the corresponding results. The simulations are performed under the same environmental atmospheric wind shear and rotor angular velocity, and the wave properties are wave height of 4 m and wave period of 7.16 s. In the present work, wave environmental effects were investigated firstly for the two solvers, and good agreement is achieved. Moreover, pressure distribution in each OWT case is presented, including detailed information about local flow fields. The time history of the forces at inflow direction and its moments around the mudline at each OWT part are presented in a dimensionless form with respect to the mean value of the last three loads and the moment amplitudes obtained from the BEM code, where the contribution of rotor force is lower in the tripod case and higher in the jacket case and the calculated hydrodynamic load that effect on jacket foundation type is lower than other two cases.