Investigation of the Effects of Baffles on the Shallow Water Sloshing in A Rectangular Tank Using A 2D Turbulent ISPH Method

Liquid sloshing is a common phenomenon in the liquid tanks transportation. Liquid waves lead to fluctuating forces on the tank wall. Uncontrolled fluctuations lead to large forces and momentums. Baffles can control these fluctuations. A numerical method, which has been widely used to model this phenomenon, is Smoothed Particle Hydrodynamics(SPH). The Lagrangian nature of this method makes it suitable for simulating free surface flows. In the present study, an accurate Incompressible Smoothed Particle Hydrodynamics(ISPH) method is developed and improved using the kernel gradient correction tensors, particle shifting algorithms, k–ε turbulence model, and free surface particle detectors. Comparisons with the experimental data approve the ability of the present algorithm for simulating shallow water sloshing. The main aim of this study is to investigate the effects of the vertical baffle on the damping of liquid sloshing. Results show that baffles number has a major role in sloshing fluctuation damping.     

A set of canonical problems in sloshing, Part I: Pressure field in forced roll—comparison between experimental results and SPH

In this article, impact pressure in the case of shallow water sloshing is investigated experimentally and numerically for forced rolling motion. The maximum values of impact pressures have been found for a frequency lower than the first sloshing frequency. Experimental results are compared with numerical ones obtained using smoothed particle hydrodynamics (SPH). The influence of viscosity and of density re-initialization on the SPH results are discussed. A new method for calculating the pressure on walls with SPH is presented.     

Investigation on a damaged ship model sinking into water based on three dimensional SPH method

Damaged ship at sea will be a direct threat to lives and property, and it has a great significance of studying ship's remaining buoyancy, stability, sinking time and other important parameters. The process of a damaged ship sinking into water is a complex motion involving ship hull, inner and outer fluid coupled with waves and many other factors. It is featured by high nonlinearity and hard to establish a precise theoretical model to study. Yet SPH (smoothed particle hydrodynamics) as a meshfree method has a great advantage in solving such problems because of the nature of self-adaptive and Lagrangian. Firstly, the experiments of two scaled ship models with different openings sinking into water are carried out, through the sinking processes of broadside opening and bottom opening models, the conclusion is drawn that although the serious loss of stability of broadside opening model, the sinking time and other parameters are more conducive to rescue after maritime distress. Secondly, the parallel program of three dimensional SPH is developed to simulate the above more complex model, broadside opening model. The coupled process of sloshing is compared with that of experiment, and the results show good agreement with each other which verify the accuracy and feasibility of three dimensional parallel program.     

Comparative Study of Different SPH Schemes on Simulating Violent Water Wave Impact Flows

Free surface flows are of significant interest in Computational Fluid Dynamics（CFD）. However, violent water wave impact simulation especially when free surface breaks or impacts on solid wall can be a big challenge for many CFD techniques. Smoothed Particle Hydrodynamics（SPH） has been reported as a robust and reliable method for simulating violent free surface flows. Weakly compressible SPH（WCSPH） uses an equation of state with a large sound speed, and the results of the WCSPH can induce a noisy pressure field and spurious oscillation of pressure in time history for wave impact problem simulation. As a remedy, the truly incompressible SPH（ISPH） technique was introduced, which uses a pressure Poisson equation to calculate the pressure. Although the pressure distribution in the whole field obtained by ISPH is smooth, the stability of the techniques is still an open discussion. In this paper, a new free surface identification scheme and solid boundary handling method are introduced to improve the accuracy of ISPH. This modified ISPH is used to study dam breaking flow and violent tank sloshing flows. On the comparative study of WCSPH and ISPH, the accuracy and efficiency are assessed and the results are compared with the experimental data.     

Towards the modeling of the ditching of a ground-effect wing ship within the framework of the SPH method

Ditching often takes place for a ground-effect wing (WIG) ship. During the ditching, the extreme load developed by water impacts may cause damages to structures, posing a great threat to the safety of crew and passengers. In the paper, a weakly compressible smoothed particle hydrodynamics (SPH) model combined with enhanced numerical techniques has been adopted to tackle the ditching problems. In order to handle the motion of a rigid body in the three-dimensional ditching problems, the six degrees-of-freedom (6-DOF) equations of motion are incorporated into the SPH scheme. The accuracy of the SPH model is validated through two benchmarks, respectively, the two-dimensional wedge water entry and the three-dimensional stone-skipping. The former is aimed to validate the prediction of pressures during the free surface impact while the latter is a good case for testing the coupling motions of the rigid body. Furthermore, the ditching of the real scale WIG ship under different conditions is simulated with the established SPH model, through which some useful conclusions are drawn.     

Coupled SPHS–BEM method for transient fluid–structure interaction and applications in underwater impacts

Coupled SPHS–BEM method is proposed for transient fluid–structure interaction problems: SPH shell (SPHS) is selected to discretize shell structures, the second-order doubly asymptotic approximations (DAA₂) of boundary element method (BEM) is chosen to analyze flow-field. BEM can remedy the expensive costs for three-dimensional SPH (smoothed particle hydrodynamics), yet SPHS provides a structural solver for BEM. The coupled method is attractive, since only a layer of SPHS particles and a piece of flow-field boundary elements are needed to be modeled; the compatibility conditions of the coupled surface are performed with moving least square (MLS) function. The final two benchmarks on underwater impacts prove the feasibility, stability and accuracy of the proposed method.     

MPS方法数值模拟液舱晃荡问题

基于无网格粒子法MPS方法(moving particle semi-implicit method)研究了液舱晃荡问题。针对二维矩形液舱晃荡问题进行了数值验证,结果表明MPS方法能够很好地计算晃荡产生的拍击压力。同时将MPS方法应用到带隔板的液舱晃荡问题计算中,分析了二维和三维带隔板液舱晃荡问题。计算结果表明:隔板的存在很大程度地限制了流体的水平运动,隔板附近出现了自由面的翻卷、破碎和融合现象,MPS方法能够很好地模拟这些流动现象。计算得到的波高与实验测得的波高吻合较好,表明MPS方法模拟带隔板的晃荡问题具有一定的可靠性。     

Liquid moment amplitude assessment in sloshing type problems with smooth particle hydrodynamics

Sloshing moment amplitudes in a rectangular tank for a wide range of rolling frequencies are investigated both experimentally and numerically. In a previous paper, Souto et al. [2004. Simulation of anti-roll tanks and sloshing type problems with smoothed particle hydrodynamics. Ocean Eng. 31 (8–9), 1169–1192] numerical results obtained with a 3-D Smooth Particle Hydrodynamics (SPH) formulation were presented. These only corresponded to the phase lag between the tank motion and the liquid response moment. This paper is aimed at improving those results by obtaining accurate values for the moment amplitudes. We present the corrections with respect to the aforementioned implementation that focus on the time integration scheme and on the treatment of the boundary conditions. In addition better quality experimental results are presented.     

基于SPH方法的开孔沉箱比尺效应研究

由于在前壁上设置了尺寸较小的孔,开孔沉箱受流体黏性力作用显著,依照弗劳德数相似准则设计模型存在比尺效应。为揭示比尺效应,建立了模拟波浪与开孔沉箱相互作用的光滑粒子流体动力学(SPH)模型。其中流体运动由连续性方程和Navier-Stokes方程控制,固壁边界由改进的动力边界粒子施加。模型收敛性通过分析不同粒子分辨率下的波浪反射系数得到,模型精度通过比较计算与理论波浪反射系数证明。使用经过验证的SPH模型,计算并比较了不同几何比尺和开孔率下开孔沉箱附近的涡量场、箱体外侧的波面时程曲线和波浪反射系数。结果表明,随着模型几何比尺的减小,开孔沉箱受到偏大的流体黏性力,致使更多波能在湍流运动中耗散,进而减小了波浪反射系数并降低了箱体外侧的波面高度。     

Moving particle method for modeling wave interaction with porous structures

This paper presents a numerical model for simulating wave interaction with porous structures. Incompressible smoothed particle hydrodynamics in porous media (ISPHP) method is introduced in this study as a mesh free particle approach that is capable of efficiently tracking the large deformation of free surfaces in a Lagrangian coordinate system. The developed model solves two porous and pure fluid flows simultaneously by means of one equation that is equivalent to the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the extended Forchheimer equation for the flows inside the porous media. Interface boundary between pure fluid and porous media is effectively modeled by the SPH integration technique. A two-step semi-implicit scheme is also used to solve the fluid pressure satisfying the fluid incompressibility criterion.The developed ISPHP model is then validated via different experimental and numerical data. Fluid flow pattern through porous dam with different porosities is studied and regular wave attenuation over porous seabed is investigated. As a practical case, wave running up and overtopping on a caisson breakwater protected by a porous armor layer are modeled. The results show good agreements between numerical and laboratory data in terms of free surface displacement, overtopping rate and pressure distribution. Based on this study, ISPHP model is an efficient method for simulating the coastal applications with porous structures.     

A Corrected Solid Boundary Treatment Method for Smoothed Particle Hydrodynamics

Smoothed Particle Hydrodynamics method (SPH) has a good adaptability for simulating of free surface flow problems. However, there are some shortcomings of SPH which are still in open discussion. This paper presents a corrected solid boundary handling method for weakly compressible SPH. This improved method is very helpful for numerical stability and pressure distribution. Compared with other solid boundary handling methods, this corrected method is simpler for virtual ghost particle interpolation and the ghost particle evaluation relationship is clearer. Several numerical tests are given, like dam breaking, solitary wave impact and sloshing tank waves. The results show that the corrected solid boundary processing method can recover the spurious oscillations of pressure distribution when simulating the problems with complex geometry boundary.     

Coupled analysis of nonlinear sloshing and ship motions

A coupled numerical model considering nonlinear sloshing flows and the linear ship motions has been developed based on a boundary element method. Hydrodynamic performances of a tank containing internal fluid under regular wave excitations in sway are investigated by the present time-domain simulation model and comparative model tests. The numerical model features well the hydrodynamic performance of a tank and its internal sloshing flows obtained from the experiments. In particular, the numerical simulations of the strong nonlinear sloshing flows at the natural frequency have been validated. The influence of the excitation wave height and wave frequency on ship motions and internal sloshing has been investigated. The magnitude of the internal sloshing increases nonlinearly as the wave excitation increases. It is observed that the asymmetry of the internal sloshing relative to still water surface becomes more pronounced at higher wave excitation. The internal sloshing-induced wave elevation is found to be amplitude-modulated. The frequency of the amplitude modulation envelope is determined by the difference between the incident wave frequency and the natural frequency of the internal sloshing. Furthermore, the coupling mechanism between ship motions and internal sloshing is discussed.     

Boundary element analysis of liquid sloshing characteristics in axisymmetric tanks with various porous baffles

This paper aims to investigate the effects of the porous baffles on the suppression of sloshing for the tanks with axisymmetric geometries under lateral excitation. Based on the assumptions of inviscid, irrotational, incompressible liquid and small amplitude sloshing, an axisymmetric boundary element method (BEM) for 3D Laplace equation is derived by using the Green's theorem together with the weighted residual method. And a zoning method is employed to model fluid domain in the tanks with complex porous baffles. Meanwhile, the porous baffles are treated motioning together with the tanks, and the velocity across the porous baffle is assumed to be linearly proportional to the pressure gradient between each side of the porous baffle. And the mechanism of suppressing the sloshing response is mainly the energy dissipation of the fluid passing through the porous baffle. Moreover, the linear free surface boundary conditions are also used to solve the governing equations. Compared with other numerical methods, the most prominent advantage of the BEM in solving axisymmetric potential problem is that only the boundaries of half the cross-section instead of the entire problem domain should be discretized, which can cut down large amount of memory and time costs. The present method is verified by comparing the numerical results with the existing literatures, and excellent agreements are obtained. Meanwhile, the proposed models are applied to investigate the effects of the porous baffles on sloshing response in circular cylindrical, annular cylindrical and conical tanks. The effects of the porous baffle length, porous-effect parameter, installation angle and baffle height on the sloshing force, natural frequency and surface elevation are studied. Additionally, some typical sloshing pressure distributions, velocity potential contours and velocity fields are plotted. The results show that swirls at the tips of the baffles can be observed in many cases, and the top-mounted porous baffle makes more significant suppression effects on sloshing response than that of bottom-mounted porous baffle, while increasing the number of ring porous baffles can achieve better restraint effects on sloshing response. And increasing the baffle length of the horizontal wall-mounted ring porous baffle can significantly decrease the sloshing frequencies, as well as the first non-dimensional natural frequency decreases with decrease in porous-effect parameter of the coaxial porous baffle. In addition, remarkable effects on sloshing can be obtained when reasonable designed by selecting the optimal porous-effect parameter, installation angle and baffle height. And this paper can be a useful guide for the seismic design and analysis of many actual liquid storage tanks (such as the Advanced Passive PWR, large water cooling tower, etc.).     

A hybrid Lagrangian-Eulerian numerical model for sea-ice dynamics

A hybrid Lagrangian-Eulerian(HLE) method is developed for sea ice dynamics,which combines the high computational efficiency of finite difference method(FDM) with the high numerical accuracy of smoothed particle hydrodynamics(SPH).In this HLE model,the sea ice cover is represented by a group of Lagrangian ice particles with their own thicknesses and concentrations.These ice variables are interpolated to the Eularian gird nodes using the Gaussian interpolation function.The FDM is used to determine the ice velocities at Eulerian grid nodes,and the velocities of Lagrangian ice particles are interpolated from these grid velocities with the Gaussian function also.The thicknesses and concentrations of ice particles are determined based on their new locations.With the HLE numerical model,the ice ridging process in a rectangular basin is simulated,and the simulated results are validated with the analytical solution.This method is also applied to the simulation of sea ice dynamics in a vortex wind field.At last,this HLE model is applied to the Bohai Sea,and the simulated concentration,thickness and velocity match the satellite images and the field observed data well.     

Numerical simulation of wave interaction with porous structures using an improved smoothed particle hydrodynamic method

A smoothed particle hydrodynamic (SPH) model is developed to simulate wave interaction with porous structures. The mean flow outside the porous structures is obtained by solving Reynolds Averaged Navier–Stokes (RANS) equations and the turbulence field is calculated by a large eddy simulation (LES) model. The porous flow is described by the spatially averaged Navier–Stokes type equations with the resistance effect of the porous media being represented by an empirical frictional source term. The interface boundaries between the porous flow and the outside flow are modeled by means of specifying a transition zone along the interface. The model is validated against other available numerical results and experimental data for wave damping over porous seabed with different levels of permeability. The validated model is then employed to investigate wave breaking over a submerged porous breakwater and good agreements between the SPH model results and the experimental data are obtained in terms of free surface displacement. In addition the predicted velocity, vorticity and pressure fields near the porous breakwater and in the breaking wave zone are also analyzed.     

基于Level-set法和通度概念液体晃荡特性研究

液体晃荡现象在诸多工程领域具有深刻的研究意义,并引起了广泛的关注。基于Level-set方法,借助流场通度的概念,模拟了流场内具有障碍物的液体晃荡现象。选取不同形式的防晃结构分析研究对晃荡的抑制效果,得到几点关于防晃结构的设计与选择的重要结论。计算结果表明,通度系数法与Level-set方法的结合使用,能够有效地处理流场内带有障碍物的液体晃荡问题,该方法具有一定的可行性和应用前景。     

Numerical Simulation of Sloshing Using the MPS-FSI Method with Large Eddy Simulation

A numerical model has been developed to study sloshing of turbulent flow in a tank with elastic baffles. The Moving-Particle Semi-implicit method(MPS) is a kind of meshless Lagrangian calculation method. The large eddy simulation(LES) approach is employed to model the turbulence by using the Smagorinsky Sub-Particle Scale(SPS)closure model. This paper uses MPS-FSI method with LES to simulate the interaction between free surface flow and a thin elastic baffle in sloshing. Then, the numerical model is validated, and the numerical solution has good agreement with experimental data for sloshing in a tank with elastic baffles. Furthermore, under external excitations,the MPS is applied to viscous laminar flow and turbulent flow, with both the deformation of elastic baffles and the wave height of the free surface are compared with each other. Besides, the impact pressure with/without baffles and wave height of free surface are investigated and discussed in detail. Finally, preliminary simulations are carried out in the damage problem of elastic baffles, taking the advantage of the MPS-FSI method in computations of the fluid–structure interaction with large deformation.     

Simulation of wave overtopping by an incompressible SPH model

The paper presents an incompressible Smoothed Particle Hydrodynamics (SPH) model to investigate the wave overtopping of coastal structures. The SPH method is a grid-less Lagrangian approach which is capable of tracking the large deformations of the free surface with good accuracy. The incompressible algorithm of the model is implemented by enforcing the constant particle density in the pressure projection. The SPH model is employed to reproduce a transient wave overtopping over a fixed horizontal deck and the regular/irregular waves overtopping of a sloping seawall. The computations are validated against the experimental and numerical data and a good agreement is observed. The SPH modelling is shown to provide a promising tool to predict the overtopping characteristics of different waves. The present model is expected to be of practical purpose if further improvement in the spatial resolution and CPU time can be adequately made.     

Effects of perforated baffle on reducing sloshing in rectangular tank: Experimental and numerical study

A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional （3D） rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.