Simulation of Fully Nonlinear 3-D Numerical Wave Tank

A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.

Development of A Fully Nonlinear Numerical Wave Tank

A fully nonlinear numerical wave tank based on the solution of the σ-transformed Navier-Stokes equation is developed in this study. The numerical wave is generated from the inflow boundary, where the surface elevation and/or velocity are specified by use of the analytical solution or the laboratory data. The Sommerfeld/Orlanski radiation condition in conjunction with an artificial damping zone is applied to reduce wave reflection from the outflow boundary. The whole numerical solution procedures are split into three steps, i.e., advection, diffusion and propagation, and a new method, the Lagrange-Euler Method, instead of the MAC or VOF method, is introduced to solve the free surface elevation at the new time step. Several typical wave cases, including solitary waves, regular waves and irregular waves, are simulated in the wave tank. The robustness and accuracy of the NWT are verified by the good agreement between the numerical results and the linear or nonlinear analytical solutions. This research will be further developed by study of wave-wave, wave-current, wave-structure or wave-jet interaction in the future.

Generation and Properties of Freak Waves in A Numerical Wave Tank

Freak waves are generated based on the mechanism of wave focusing in a 2D numerical wave tank. To set up the nonlinear numerical wave tank, the Boundary Element Method is used to solve potential flow equations incorporated with fully nonlinear free surface boundary conditions. The nonlinear properties of freak waves, such as high frequency components and wave profile asymmetry, are discussed. The kinematic data, which can be useful for the evaluation of the wave forces exerted on structures to avoid underestimation of linear predictions, are obtained, and discussed, from the simulated results of freak waves.

Determining the Onset and Strength of Unforced Wave Breaking in A Numerical Wave Tank

A numerical wave tank is used to investigate the onset and strength of unforced wave breaking, and the waves have three types of initial spectra： constant amplitude spectrum, constant steepness spectrum and Pierson-Moscowitz spectrum. Numerical tests are performed to validate the model results. Then, the onset of wave breaking is discussed with geometric, kinematic, and dynamic breaking criteria. The strength of wave breaking, which is always characterized by the fractional energy loss and breaking strength coefficient, is studied for different spectra. The results show how the energy growth rate is better than the initial wave steepness on estimating the fractional energy losses as well as breaking strength coefficient.

Generation of linear and nonlinear waves in numerical wave tank using clustering technique-volume of fluid method

A two-dimensional （2D） numerical model is developed for the wave sim- ulation and propagation in a wave flume. The fluid flow is assumed to be viscous and incompressible, and the Navier-Stokes and continuity equations are used as the governing equations. The standard k-e model is used to model the turbulent flow. The Navier- Stokes equations are discretized using the staggered grid finite difference method and solved by the simplified marker and cell （SMAC） method. Waves are generated and propagated using a piston type wave maker. An open boundary condition is used at the end of the numerical flume. Some standard tests, such as the lid-driven cavity, the constant unidirectional velocity field, the shearing flow, and the dam-break on the dry bed, are performed to valid the model. To demonstrate the capability and accuracy of the present method, the results of generated waves are compared with available wave theories. Finally, the clustering technique （CT） is used for the mesh generation, and the best condition is suggested.

Numerical Investigation on the Generation and Propagation of Irregular Waves in A Two-Dimensional Wave Tank

The modeling of generation and subsequent propagation of irregular waves in a numerical wave flume is performed by mean of the boundary element method. Random waves are generated by a piston-type wave generator at one end of the flume with the Mitsuyasu-Bretschneider spectrum used as the target spectrum for the generation. An artificial absorbing beach is placed at the other end of the flume to minimize wave reflection. Surface fluctuations are described by use of the Lagrangian description, and finite difference is adopted for the approximation of time derivative. To monitor the developments of the waves, a number of pseudo wave gauges are installed along the tank. Through comparison of the spectra from those gauges with the target spectrum, satisfactory results can be obtained from the present numerical scheme.

Evaluation of Hydrodynamic Coefficients of Ships Oscillating in A Numerical Wave Tank

A technique for the evaluation of the hydrodynamic coefficients of ships is outlined for ship oscillating in a numerical wave tank, which is established on Computational Fluid Dynamics （CFD） theories. The numerical simulation of ship sections and bodies forced oscillating in the tank are carried out. The added mass and damping coefficients are obtained by the decomposition of the computational results, which agree well with the corresponding ones of potential theories.

A Numerical Wave Tank for Nonlinear Waves with Passive Absorption

A numerical wave tank with passive absorption for irregular waves is considered in this paper. Waves with spectral shapes corresponding to that of the Mitsuyasu- Bretschneider type are used as the initial condition at one end of the flume, An absorbing boundary is imposed at the other end of the wave flume to minimize reflection. By use of a Lagrangian description for the Surface elevation, and finite difference for approximation of the time derivative, the problem is then solved by the boundary element method, The effects of the absorbing boundary are investigated by varying the values of the absorption coefficient mu, and studying the time histories of the Surface elevations 'recorded' on pre-selected locations.

Two Dimensional Fully Nonlinear Numerical Wave Tank Based on the BEM

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 comer 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.

Numerical Wave Tank Based on A Conserved Wave-Absorbing Method

Recently the numerical wave tank has become a widely-used tool to study waves as well as wave-structure interactions, and the wave-absorbing method is very important as its effect on the quality of waves generated. The relaxation method and the derived momentum source method are often utilized, however, the damping weight is constant during calculation and repeated trials are required to obtain an acceptable wave-absorbing effect. To address the abovementioned issues, a conserved wave-absorbing method is developed. The damping weight is determined by solving the mass conservation equation of the absorbing region at every time step. Based on this method, a two-dimensional numerical wave tank is established by using the VB language to simulate various waves by which the validation of this method is evaluated.

Air Gap Prediction for Floating Bodies Using a 3D Numerical Wave Tank Approach

Computations for air gap response of a semisubmersible platform based on a 3D numerical wave tank approach are presented.The developed method is in time domain and can consider nonlinearities associated with incident wave and hydrostatic forces exactly in determining the body response, but the interaction hydrodynamics of radiation and diffraction are based on simplified linearization assumptions. The incident wave can be defined by any suitable wave theory and here defined by a fully nonlinear numerical wave model. After verifying the present computations results in its degenerated linearized version against the usual linear 3D Green function–based frequency-domain results for air gap predictions, systematic comparative studies are undertaken between linear and the approximate nonlinear solutions. It is found that nonlinear computations can yield considerably conservative predictions as compared to fully linear calculations, amounting to a difference of up to 30%–40% in the minimum air gap in steep ambient incident waves at high and moderate frequencies.

Performance analysis of a tuned point absorber using SPH calm water and wave tank simulations

In this paper,two smoothed particle hydrodynamics(SPH)models,namely SPH-W and SPH-C were used to evaluate the motion response of a point absorber wave energy converter(WEC).In the SPH-W model,a long wave flume was constructed and a long simulation was performed to obtain the motion response of the WEC.In the SPH-C model,the SPH method is only used to find the hydrodynamic coefficients of the device by analysing a few seconds of free-decaying motion of WEC in calm water in a much smaller numerical flume.Then,these coefficients were inserted in the equation of motion of a heaving WEC that was solved using a 4th order Runge-Kutta(ODE45)solver in MATLAB.First,the energy conservation property of the WCSPH model was examined through a standing wave benchmark test.Then,the wavepoint absorber interaction was simulated.While the simulation time for SPH-C model is much smaller than that of SPH-W,it gave almost similar results for the motion response of WEC.These two models were used to evaluate the effects of the control force and the draft of a cone-cylinder point absorber on its hydrodynamic responses.The results showed that compared to the effect of the supplementary inertia,changes in the draft of the WEC have a small influence on its hydrodynamic responses.The buoy draft has an inverse relationship with both added mass and damping coefficients.However,increasing the supplementary mass increases the added mass and decreases the hydrodynamic damping coefficients.

A 2-D NUMERICAL IRREGULAR WAVE TANK AND ITS VERIFICATION

A two-dimensional numerical irregular wave tank based on the potential wave theory was developed. A source term was used inside the domain to generate waves, and outgoing waves were dissipated by sponge layers and transmitted by radiation boundary. The σ-coordinate transformation was introduced to map the time-dependent irregular physical domain to a fixed regular computational domain, and thus the free surface and bottom boundary conditions could be implemented precisely. The model was verified by simulating the nonlinear regular and irregular wave propagation on constant-depth water, as well as regular waves reflected from a vertical wall, and satisfactory agreement between numerical results and analytical solutions was obtained. The present numerical model is proved to be an effective tool for a long-duration simulation of coastal wave dynamics where the wave reflection is significant.

Development of two-dimensional numerical wave tank based on lattice Boltzmann method

A 2-D numerical wave tank(NWT)is developed using the lattice Boltzmann method(LBM)and a multi-relaxation-time(MRT)collision model coupled with an algebraic volume of fluid(VOF)scheme for free surface tracking.An external force based on the momentum source function is used to generate the waves,and a zone of porous media is used to absorb the waves.Numerical simulations of the progressive and standing waves show that the NWT can generate stable wave trains in agreement with the analytical solutions and eliminate the re-reflection waves.The NWT is used to simulate two problems encountered in practice,namely:the wave transformation over a submerged breakwater and the wave runup on a sea dike.The numerical predictions are in good agreement with the measured data.

A third-order KdV solution for internal solitary waves and its application in the numerical wave tank

A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system.The solution corrects an error by Mirie and Su(1984).A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam.Various analytical solutions,including the first-order to third-order KdV solutions,the eKdV solution and the MCC solution,have been used to initialise the flow fields in the CFD simulations of internal solitary waves.Two groups including 11 numerical cases have been carried out.In the same group,the initial wave amplitudes are the same but the implemented analytical solutions are different.The simulated wave profiles at different moments have been presented.The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively.It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases.The finding is significant for the further simulations involving internal solitary waves.

Research on Numerical Wave Tank Based on the Improved Moving-Particle Semi-Implicit Method with Large Eddy Simulation

Moving-particle semi-implicit(MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numerical wave, we combine the MPS method with large eddy simulation(LES) which can simulate the turbulence in the flow. The intense pressure fluctuation is a significant shortcoming in MPS method. So, we improve the original MPS method by using a new pressure Poisson equation to ease the pressure fluctuation. Divergencefree condition representing fluid incompressible is used to calculate pressure smoothly. Then, area-time average technique is used to deal with the calculation. With these improvements, the modified MPS-LES method is applied to the simulation of numerical wave. As a contrast, we also use the original MPS-LES method to simulate the wave in a numerical wave tank. The result shows that the new method is better than the original MPS-LES method.

DYNAMIC MODEL FOR OIL SLICK DISPERSION INTO A WATER COLUMN- A WINDDRIVEN WAVETANK EXPERIMENT

A dynamic experiment for oil dispersion into a water column was performed with a 21 m long, 0.5 m wide, and 1 m high wind-driven wave tank. At wind velocity between 6-12 m/s and with the oil slide kept constant (about 1 um), the rate of the oil content increase in the water column could be approximated from the difference between the dispersion rate (R) of the oil slick and the coagulation rate (R’) of the dispersed oil slick. Assuming the coagulation rate is directly proportional to the concentration of the water dispersed oil slick (i. e. R’ =KC),, the integral form of the dynamic model can be expressed as C=R*[1-exp(-K*t)]/K and parameters R and K can be regressed with a computer. The relative deviation of model results from the experimental data was mainly less than 10%. The oil slick dispersion rate (R) had exponential relationship with the wind velocity (V), and can be fitted with a formula R=A*(U+1)B.The fitted constant of the coagulation rate, K(0.8-3.0* 10-3 min-1) did not have significant

Linear and Nonlinear Stokes Waves Theory: Numerical Hydrodynamic and Energy Studies

The increase of wave energy in electricity production is an objective shared by many countries to meet growing demand and global warming. To analyze devices capable of converting the energy of sea waves into electrical energy, it is important to master the various theories of gravity waves and generation. We will in our work consider a numerical waves tank for an amplitude A=0.5, a wavelength λ=0.25 , an average height He=10 and a Froude number fixed at 1 × 105. Numerical wave channel analysis is used to reproduce the natural phenomenon of wave propagation in an experimental model. Wave makers are usually used to generate waves in the channel. In theory, the influence of an incident wave can be considered, as in the case of our study. In this study, the evolution of the hydrodynamic parameters and the energy transported in one wavelength can be determined by calculation. A change of variable will be done in this work to facilitate the writing of the boundary conditions at the free surface and at the bottom. The nonlinear Stokes theory will be studied in this case in order to provide hydrodynamic solutions through the Navier-Stokes equations to finally deduce the energetic results. To do this, the finite difference method will be used for the hydrodynamic results such as the velocity potential and the free surface elevation and the trapezium method of Newton for the energetic results. Thus, we will determine the energetic potential according to the decrease in the slope of the tank. To do this, we will take as values of beta representing the inverse of the slope of the tank, β=100, β=105, β=110 and β=105. .

基于流固耦合的卡车油箱振动特性研究

卡车油箱在使用过程中,存在因振动产生本体及焊缝开裂的问题。针对某400 L卡车柴油油箱,基于流固耦合理论,运用ANSYS软件分析油箱的振动特性。锤击法模态试验和仿真模态分析结果,仿真与试验测得的结构模态参数数据误差最大为13%,仿真的准确性得到验证。油箱结构自由状态下计算得到的前6阶固有频率略大于油箱安装状态下的固有频率,油箱固有频率会随着液体含量的增加而降低。油箱的固有频率在液体量从0到100 L以及300到400 L这两阶段变化明显。油箱充液比低于1/2时,油箱结构的各阶固有频率均高于危险区域的频率,不会产生共振。充液量大于3/4时固有频率接近于30 Hz的标准规定值,存在共振风险。油箱设计时,应优化油箱的结构,使其在充满液量时也能避开30 Hz标准值,更为安全。

双浮体直驱波浪发电装置建模分析与基于模型预测控制的能量提取算法研究

基于振荡浮体结构的直驱波浪发电装置具有损耗低、控制灵活等优点,近年来,逐渐成为波浪发电领域的研究热点。双浮体直驱波浪发电装置不需要海上固定平台,能够通过锚系结构在海水中工作,是一种工程可行的直驱波浪发电方案,但其动力学模型更为复杂,相关控制算法缺少实际装置测试。该文通过等效电路的方法对双浮体装置进行建模分析,指出采用张力锚结构可将双浮体装置等效为单浮体装置进行分析,简化控制器的分析与设计,从而建立基于模型预测控制的高效波浪能提取问题。提出一种结合波浪激励力辨识、预测与快速模型预测求解的控制算法,并且设计了双浮体直驱波浪发电装置,在不同波浪条件下进行了相关实验测试。实验结果表明,所提控制算法能够在有效降低运算复杂度的前提下提高装置的波浪能提取效率。