The effect of fluid compressibility on the simulation of sloshing impacts

Resonant and near-resonant sway-induced sloshing flow in a rectangular container is used to compare various combinations of compressibility models for air and water. The numerical model is implemented in a commercial RANS computational fluid dynamics (CFD) code. A criterion based on wave propagation is developed to assess the importance of including fluid compressibility. For sloshing flows with low levels of fluid impact, this can be simulated with incompressible fluid models for both air and water. When modelling sloshing at low-filling levels with a travelling wave, which generates large air bubble entrainment, the choice of fluid compressibility model is shown to have a significant influence on pressure magnitude and frequency of oscillation required for structural assessment. Further comparisons with theoretical models show that a full thermal energy compressibility model is also required.     

Experimental and numerical investigation of sloshing using different free surface capturing methods

We investigated the use of numerical methods to predict liquid sloshing phenomena in a moving tank and compared our results to model test measurements. The numerical techniques for the free surface, based on the so-called finite Volume-of-Fluid (VoF) approach, comprised an incompressible VoF method, an incompressible coupled Level-Set and Volume-of-Fluid (clsVoF) method, and a compressible VoF method. We assessed the capability of these three numerical methods to achieve suitable numerical predictions of sloshing phenomena, specifically, air pockets and bubbles on the free surface inside a test tank. To observe the described sloshing phenomena, we simulated tank motions leading to well defined single impact wave motions. We performed repeated physical tests for validation purposes. Computed velocity and pressure time histories were compared to experimental data we obtained from Particle Image Velocimetry (PIV) and pressure sensor measurement. Grid sensitivity and turbulence model studies were performed. We demonstrated that the compressible VoF method was the most suitable method to obtain accurate predictions of sloshing phenomena.     

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.     

Numerical predictions of water–air wave slam using incompressible–compressible smoothed particle hydrodynamics

The high-speed impact between a body and water is an important practical problem, whether due to wave impact on a structural deck or wall, or due to a moving body such as a ship or aircraft hitting water. The very high pressures exerted are difficult to predict and the role of air may be significant. In this paper, numerical simulations are undertaken to investigate the impact of a rigid horizontal plate onto a wave crest and, in the limit, onto a flat water surface. A two-phase incompressible–compressible smoothed particle hydrodynamics (SPH) method for water and air, respectively, is applied where the water phase imposes kinematics on the air phase at the air–water interface and the air phase imposes pressures on the water at the interface. Results are compared with experimental measurements undertaken using a drop rig positioned over a wave flume so that a horizontal plate impacts the water surface in free flight. Numerical predictions of impact pressure are quite accurate; air is shown to have a significant cushioning effect for impact on to flat water and this reduces for waves as the ratio of wave height to wavelength increases.     

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.     

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.     

双浮板液舱晃荡特性的数值研究

基于黏性流理论,采用动网格技术和6自由度模型,以及动量源方法,建立了双浮板液舱晃荡的数值模型。分别采用3种不同空间步长的网格离散计算区域,进行了网格收敛性验证。通过光滑液舱晃荡的模型试验和解析得到的爬高最大值,验证了数值模型的精确性。在载液率为50%,激励幅值为2 mm条件下,对双浮板液舱晃荡进行了数值计算,与光滑液舱相比,双浮板液舱晃荡的最大爬高明显减小。通过一个激励周期内双浮板液舱晃荡的波面显示发现,液舱晃荡模式由光滑液舱的驻波模式变为U管模式,晃荡模式的改变起到了明显地抑制液舱晃荡的效果。     

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.     

A probabilistic assessment of design sloshing pressure time histories in LNG tanks

The violent motion (sloshing) of liquefied natural gas (LNG) in cargo tanks has attracted significant attention. Transformations of the LNG market have led to the increased transport of LNG in partially filled tanks, but established technology is mainly based on engineering experience with completely filled containers. This paper investigates a large sample of sloshing pressure measurements. It focuses on the magnitude of individual sloshing impact events, and their associated temporal and spatial patterns. The durations of these impacts are comparable to the natural frequency of an LNG container wall, so the details of their time histories are important in determining the structural response. Experiments are performed on tanks with high (92.5%) and low (30%) filling levels, for various wave headings. The common post-processing approach of representing impact pressure histories by a triangular profile is studied, and an alternative approach is presented. Two statistical models are used to describe the distribution of maximal pressures in sloshing impacts: a three-parameter Weibull model and a generalized Pareto model. The latter is found to be of questionable utility due to small sample sizes. It is observed that for low filling levels the sloshing impacts are of greater magnitude, having longer durations, smaller ratios of rise time to duration, and larger spatial extents. All these factors should in principle increase the structural response.     

Comparison of laminar model,RANS, LES and VLES for simulation of liquid sloshing

Liquid sloshing in storage tank is a fundamental problem of great engineering importance. Sloshing motion can be laminar or turbulent. However, the necessity for inclusion of turbulence in CFD simulation of sloshing flows has not yet been established. In this paper, three roll–induced sloshing cases are studied to assess the merits and shortcomings of the laminar model and three most–commonly used turbulence models (RANS k–ε, LES and Very LES). To overcome the deficiencies in the RANS and LES, the new Very LES (VLES) model, which combines the RANS k–ε and LES, is developed in this paper. The free surface profiles are reconstructed by a coupled Level–Set and Volume–of–Fluid (CLSVOF) method. To the authors’ knowledge, the comprehensive and systematical assessment of the effect of turbulence on sloshing simulation has not been reported in the literature. The numerical results are evaluated using experimental measurements from Delorme and Souto−Iglesias. The present study indicates that the inclusion of an appropriate turbulence model has a profound influence on the simulations of violent and non–violent sloshing flows. The VLES and LES models can provide accurate predictions of free surface profiles and impact pressures, whereas the laminar flow assumption and the RANS model cannot adequately capture the energy dissipation in the sloshing simulation and lead to the inaccurate flow predictions.     

A combined wind and wave energy-converter concept in survival mode: Numerical and experimental study in regular waves with a focus on water entry and exit

A combined wind and wave energy converter concept, named STC concept was proposed. Model tests were performed in terms of operational and survival modes. Water entry and exit phenomena as well as green water on deck were observed during the survivability model tests. In this paper, a nonlinear numerical model based on a blended station-keeping potential-flow solver with a local impact solution for bottom slamming events and an approximated model for the water shipped on the deck is proposed to simulate these nonlinear phenomena. Physical investigation of the water entry and exit process was firstly carried out and uncertainty analysis of the model test results were performed. Numerical comparisons between the nonlinear solver and model test results are then performed in terms of mean, wave frequency and double wave frequency motion response components. The slamming and green water involved in the water entry process are specially investigated, in terms of the physical evolution and the effects on the dynamic motion responses. The validation work on the occurrence of slamming and water on deck as well as the slamming pressure are performed.     

Numerical Simulation on the Impact of A Liquid Square on Rigid Plate and Liquid Layer

Fluids and structures impact is one of the common phenomena in nature, and it widely exists in engineering practice,including ship hydrodynamic slamming, wave impact on offshore platforms, plunging wave on coastal structures,emergency landing of aircrafts at sea as well as impact of ultra-cold droplets and ice lumps under aviation conditions.In this paper, a two dimensional (2-D) solver for Navier-Stokes equations is developed and applied in the numerical simulation of the impact on a rigid plate by a liquid square. The computational domain is discretized by Finite Volume Method (FVM). The Volume of Fluid (VOF) technique is used to track the free surface and the PiecewiseLinear Interface Construction (PLIC) is used for reconstruction. The Continuum Surface Force (CSF) model is used to account for the surface tension. The convective term and the diffusive term are upwind and centrally differenced respectively. The Inner Doubly Iterative Efficient Algorithm for Linked Equations (IDEAL) is used to decouple the pressure and velocity. Based on the proposed techniques, collapse of water column is simulated and convergence study is performed for the validation of the numerical solver. Then the impact of a free falling liquid body is simulated, and the effect of volume and initial height of the liquid body is analyzed. In addition, the impact on a plate with a liquid layer is also simulated to study the effect of falling height on a liquid floor.     

Numerical modeling of a wave energy converter based on U-shaped interior oscillating water column

The paper presents a concept of a wave energy converter and the numerical model to calculate the hydrodynamic responses in waves and the power produced by the power take off system. The system consists of an asymmetric floater with an interior U-tank partially filled with water and two lateral air chambers connected by a duct. The motion of the U-shaped oscillating water column, mainly induced by the rolling of the floater, forces the air through the duct where a Wells turbine is installed to absorb the wave energy.The wave-floater hydrodynamics is calculated with a Green's function panel method, while the oscillating water column motions hydro-mechanics are derived from the one-dimensional Euler's equation. The dynamics of the Wells turbine is realistically represented by one additional differential equation on the unknown air pressure fluctuation. This equation is derived assuming small amplitude motions of the water column and assuming the linear isentropic relation is valid for the air thermodynamics in the air chambers. The Wells turbine is characterized by a drastic drop of efficiency above a critical pressure value due to stalling on the blades. The effect of a by-pass valve to prevent stalling is introduced in the numerical model in a simplistic way. The numerical model is implemented and tested for a wave energy converter with a displacement of 1150 t, including 490 t for the interior water column, and an installed turbine with 2.3 m of diameter. An analysis of the influence of changing different design parameters on the system efficiency is also presented.     

Experimental hydrodynamic investigation of a fixed offshore Oscillating Water Column device

Oscillating Water Column (OWC) is one of the pioneer devices in harnessing wave energy; however, it is not fully commercialized perhaps due to the complicated hydrodynamic behavior. Previous studies are significantly devoted to OWC devices located in nearshore and coastal regions where incident wave energy would experience dissipation more than offshore. In this paper, a 1:15 scaled fixed offshore OWC model is tested in a large towing tank of National Iranian Marine Laboratory. Wave spectrum shape effect on the efficiency of the OWC model is addressed. Moreover, the paper investigates the effects of the geometric and hydrodynamic factors on OWC device efficiency and uncovers new points in nonlinear interaction occurring inside the chamber; i.e. sloshing. The results indicate that shape of the spectrum inside the chamber is affected by the type of incident wave spectrum, especially for long waves. Pierson–Moskowitz spectrum leaded to higher efficiency rather than JONSWAP spectrum at longer incident wave periods. According to efficiency analysis, increasing wave height may lead to air leakage from the chamber followed by vortex generation, which is a reason for decreasing the efficiency of the OWC device. Furthermore, no shift in the resonant period of the OWC model, due to wave height increase, was observed at the opening ratios equal or smaller than 1.28%. Spectral analysis of water fluctuation inside the OWC chamber illustrates two modes of sloshing. The first mode can be seen at short period waves while the second mode is visible at long period waves. The sloshing modes approximately vanish by increasing draft value.     

The numerical study of wave-induced pore water pressure response in highly permeable seabed

The coupling numerical model of wave interaction with porous medium is used to study waveinduced pore water pressure in high permeability seabed.In the model,the wave field solver is based on the two dimensional Reynolds-averaged Navier-Stokes(RANS) equations with a k-ε closure,and Forchheimer equations are adopted for flow within the porous media.By introducing a Velocity-Pressure Correction equation for the wave flow and porous flow,a highly efficient coupling between the two flows is implemented.The numerical tests are conducted to study the effects of seabed thickness,porosity,particle size and intrinsic permeability coefficient on regular wave and solitary wave-induced pore water pressure response.The results indicate that,as compared with regular wave-induced,solitary wave-induced pore water pressure has larger values and stronger action on seabed with different parameters.The results also clearly show the flow characteristics of pore water flow within seabed and water wave flow on seabed.The maximum pore water flow velocities within seabed under solitary wave action are higher than those under regular wave action.     

A coupled numerical model of wave interaction with porous medium

A new coupling model of wave interaction with porous medium is established in which the wave field solver is based on the two dimensional Reynolds Averaged Navier-Stokes (RANS) equations with a kε closure. Incident waves, which could be linear waves, cnoidal waves or solitary waves, are produced by a piston-type wave maker in the computational domain and the free surface is traced through the Piecewise Linear Interface Construction-Volume of Fluid (PLIC-VOF) method. Nonlinear Forchheimer equations are adopted to calculate the flow field within the porous media. By introducing a velocity–pressure correction equation, the wave field and the porous flow field are highly and efficiently coupled. The two fields are solved simultaneously and no boundary condition is needed at the interface of the internal porous flow and the external wave. The newly developed numerical model is used to simulate wave interaction with porous seabed and the numerical results agree well with the experimental data. The additional numerical tests are also conducted to study the effects of seabed thickness, porosity and permeability coefficient on wave damping and the pore water pressure responses.     

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.     

Three-dimensional liquid sloshing in a tank with baffles

A numerical model has been developed to study three-dimensional (3D) liquid sloshing in a tank with baffles. The numerical model solves the spatially averaged Navier-Stokes equations, which are constructed on a non-inertial reference frame having six degree-of-freedom (DOF) of motions. The large-eddy-simulation (LES) approach is employed to model turbulence by using the Smagorinsky sub-grid scale (SGS) closure model. The two-step projection method is employed in the numerical solutions, aided by the Bi-CGSTAB technique to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate volume-of-fluid (VOF) method is used to track the distorted and broken free surface. The baffles in the tank are modeled by the concept of virtual boundary force (VBF) method. The numerical model is first validated against the available analytical solution and experimental data for two-dimensional (2D) liquid sloshing in a tank without baffles. The 2D liquid sloshing in tanks with baffles is then investigated. The numerical results are compared with other results from available literatures. Good agreement is obtained. Finally, the model is used to study 3D liquid sloshing in a tank with vertical baffles. The effect of the baffle is investigated and discussed.     

Numerical simulations of sloshing flows with an elastic baffle using a SPH-SPIM coupled method

In this work, sloshing flows were successfully simulated by using a coupled numerical scheme between smoothed particle hydrodynamics (SPH) and smoothed point interpolation method (S-PIM) (SPH-SPIM coupled method). SPH is a Lagrangian particle method to solve flow fields while S-PIM is developed to deal with the structure dynamics. A coupling scheme is proposed, the key of which is that the fluid and solid fields are not necessary to be discretized by the same resolution. The stability, accuracy, convergence and conservation of the SPH-SPIM coupled method were validated by the case of hydrostatic water column on an elastic plate. Then, a wave impact problem was simulated to verify that the present SPH method worked well for sloshing flows. Finally, two sloshing problems with an elastic baffle were simulated, which validated the accuracy and stability of the method in predicting the fluid-structure interaction (FSI) features during the process of sloshing. It has been found that both the shape of the free surface and the large deformation of the elastic baffle can be well captured by the present method, which shows the potential of the present method to be a good candidate for simulating sloshing problems.     

半球形多向波聚合波道振荡水柱气室优化设计

为了解决振动水柱式波浪能转换装置收集多向波浪问题,本文设计了半球形多向聚合波道振荡水柱气室结构,以适合远海单点波浪能采集和发电。在规则波正向入射条件下,基于流体仿真分析软件(FLUENT)、流体动力学连续性假设和粘性不可压缩流体动量守恒的运动方程(Navier-Stokes方程)建立半球形振荡气室和三维数值波浪水槽模型。仿真结果表明:增设气室后壁,合理设计波道开口角度实现多向迎波捕获波浪能,优化前壁形状可降低波浪触底反射带来的能量耗散,同时提高了气室内空气压强和出气口速度,有效提升波浪能俘获效率,为后续发电的二次能量转换提供高效的空气动力。