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.     

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。     

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.     

Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank

A time-independent finite-difference method and a fifth-order Runge–Kutta–Felhberg scheme were used to analyze the dynamic responses of sea-wave-induced fully non-linear sloshing fluid in a floating tank. The interaction effect between the fully non-linear sloshing fluid and the floating tank associated with coupled surge, heave and pitch motions of the tank are analyzed for the first time in the present pilot study. For the analysis of fluid motion in the tank, the coordinate system is moving (translating and rotating) with tank motion. The time-dependent water surface of the sloshing fluid is transformed to a horizontal plane and the flow field is mapped on to a rectangular region. The Euler equations as well as the fully non-linear kinematic free surface condition were used in the analysis of the sloshing fluid. The strip theory for linearized harmonic sea-wave loading was adopted to evaluate the regular encounter wave force. In addition, the dynamic coefficients used in the dynamic equations of tank motion were also derived based on strip theory and a harmonic motion of the tank. The characteristics of free and forced tank motions with and without the sloshing effect are studied. By the damping effect, the response of free oscillation will damp out and that of forced oscillation will approach a steady state. Without sea-wave action, the contribution of the sloshing load would enlarge the angular response of tank motion as well as the rise of free surface and the sloshing effect will delay the damping effect on angular displacement. On the contrary, under sea-wave action, the sloshing effect will decrease the dynamic response of tank motion and rise of free surface. The interaction, sloshing and coupling effects are found to be significant and should be considered in the analysis and design of floating tanks.     

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.     

Motion responses of barge carrying liquid tank

The interaction between the liquid sloshing in a rectangular tank equipped inside the barge and the barge responses has been investigated through a comprehensive experimental program. The barge was subjected to both regular and random wave excitations under beam sea condition. Three relative fill levels (h_s/l) with liquid fill depth (h_s) to length of tank (l) ratio of 0.163, 0.325 and 0.488 were considered. In addition, the barge responses of equivalent dry weight condition corresponding to each fill level were measured to understand the influence of sloshing. While the excitation wave frequency equals to first mode natural sloshing frequency, a noticeable decrease in the sway response has been observed. However, the effect of sloshing oscillation on the heave response is insignificant. A split up of roll resonance was observed for the aspect ratio of 0.163 due to the coupling effect of roll motion and sloshing.     

Experimental Study on A Sloshing Mitigation Concept Using Floating Layers of Solid Foam Elements

A sloshing mitigation concept taking advantage of floating layers of solid foam elements is proposed in the present study. Physical experiments are carried out in a liquid tank to investigate the hydrodynamic mechanism of this concept. Effects of the foam-layer thickness, excitation amplitude, and excitation frequency on the sloshing properties are analyzed in detail. It is found that the floating layers of solid foam elements do not evidently affect the fundamental natural sloshing frequency of the liquid tank evidently among the considered cases. At the resonant condition, the maximum wave height and dynamic pressure are greatly reduced as the foam-layer thickness increases. Higher-order pressure components on the tank side gradually vanish with the increase of the foam-layer thickness. Cases with different excitation amplitudes are also analyzed. The phenomenon is observed when the wave breaking in the tank can be suppressed by solid foam elements.     

On the analysis of sloshing of water in rectangular containers: Numerical study and experimental validation

In this work the analysis of sloshing of water in rectangular open tanks has been extensively carried out. Two mathematical models are employed, respectively the Reynolds Averaged Navier Stokes Equations (RANSE) and the Shallow Water Equations (SWE). The RANSE are solved using a modified form of the well established MAC method (SIMAC) able to treat both the free surface motion and the viscous stresses over the rigid walls accurately. The Shallow Water Equations are solved by means of a simple and powerful algorithm (CE-SE) able to deal with large impacting waves over the tank walls.Successively, in order to validate the mentioned algorithms and for a better understanding of the sloshing phenomenon, experimental tests have been carried out using a 0.5 m breadth rectangular tank in periodic roll motion.It has been shown that RANSE provide more accurate solutions than SWE for small or moderate amplitudes of excitation. In particular in this paper it is proved that the shallow water approximation can be efficiently adopted within liquid depth to tank breadth RATIO = 0.15, when examining the sloshing problem. By increasing the water level inside the tank, results by SWE show large qualitative and quantitative disagreement with experiments. Nevertheless, in the case of large amplitude excitation, when sprays and large breaking waves are expected, SWE provide a fairly good estimate of the sloshing induced waves.Finally a simple baffle configuration inside the tank has been considered. By the analysis of numerical results, it has been observed that the presence of a vertical baffle at the middle of the tank dramatically changes the sloshing response compared to the unbaffled configuration. It produces a jump-like effect, resulting in a weak magnification of the dynamic loads on the vertical walls out of resonance, and a strong reduction of the dynamic loads in the resonance condition.     

Experimental studies on sloshing behavior due to horizontal movement of liquids in baffled tanks

A series of experiments have been carried out in a developed liquid sloshing setup to estimate the pressure developed on the tank walls and the free surface displacement of water from the mean static level. The square tank attached to a shaking table can be moved to and fro by a cam arrangement driven by a DC motor. Pressure and displacement studies are done on the basis of changing excitation frequency of the shaking table and fill level in the tank. Experiments were carried out without and with baffles, and the consequent changes in the parameters are observed.     

FLNG液舱晃荡压力影响因素及安全性评估研究

针对大型浮式液化天然气储卸生产装置FLNG的液舱晃荡压力变化特征,在深水试验池中开展带液舱模型的FLNG水池模型试验研究。通过试验,获得了FLNG在风浪流联合作用下的浮体六自由度运动,以及相应的液面高度变化数据。通过液舱的液面高度变化数据,提出平液面假设,并在此基础上,求得液舱晃荡引起的舱壁压力变化结果。研究中进一步讨论了液舱晃荡压力的影响因素,并将试验数据与CCS船级社规范计算结果进行对比,为FLNG液舱晃荡压力引起的结构安全性评估提供技术支持。     

A parametric sensitivity study on LNG tank sloshing loads by numerical simulations

A series of parametric sensitivity studies on unmatched dimensionless scale parameters is carried out on the liquified natural gas (LNG) tank sloshing loads by using a computational fluid dynamics (CFD) program. First, a brief dimensional analysis is conducted to identify the governing and non-matched non-dimensional parameters, assuming that Froude scaling law is adopted. Then the sensitivity of impact pressure is checked through numerical simulations against non-matched parameters, such as fluid viscosity, liquid-gas density ratio, and ullage pressure and compressibility. The CFD simulations are also verified against experimental results. It is concluded that the effects of viscosity and density ratio are insignificant, while the compressibility of ullage space plays an appreciable role, as was pointed out by Bass et al. [Bass, R.L., Bowles, E.B., Trudell, R.W., Navickas, J., Peck, J.C., Yoshimura, N., Endo, S., Pots, B.F.M., 1985. Modeling criteria for scaled LNG sloshing experiments. Transactions of the ASME 107, 272-280].     

Energy dissipation in sloshing waves in a rolling rectangular tank — III. Results and applications

The hydrodynamic aspects of the motion of a viscous fluid having a free surface in a rolling tank have been investigated. In a sequence of three papers, an analytical technique together with a numerical solution method will be presented to describe the sloshing phenomenon accurately and efficiently. This first paper introduces a linear theory of viscous liquid sloshing and formulates a boundary value problem subject to appropriate conditions. Viscosity is included in the problem formulation and its effects are properly accounted for. The second paper will describe a solution of the problem in function space by the truncation of infinite series. Boundary conditions are satisfied through the use of Fourier series expansions. However, the no-slip condition at the side walls can also be treated in a least-squares sense.Among the results that will be reported in the third paper are the effects of viscosity on liquid sloshing phenomenon and the dependence of viscous dissipation on the Reynolds and Froude numbers. Furthermore, the influence of the tank aspect ratio on viscous dissipation has been explored. These results demonstrate some unknown features of the functional relationships that exist between the dissipated energy and the Reynolds and Froude numbers. Similarly, the dependence of the dissipated energy on the aspect ratio has been analytically studied. The results obtained agree with the physical laws for the range of parameters investigated.     

Energy dissipation in sloshing waves in a rolling rectangular tank—I. Mathematical theory

The hydrodynamic aspects of the motion of a viscous fluid having a free surface in a rolling tank have been investigated. In a sequence of three papers, an analytical technique together with a numerical solution method will be presented to describe the sloshing phenomenon accurately and efficiently. This first paper introduces a linear theory of viscous liquid sloshing and formulates a boundary value problem subject to appropriate conditions. Viscosity is included in the problem formulation and its effects are properly accounted for. The second paper will describe a solution of the problem in function space by the truncation of infinite series. Boundary conditions are satisfied through the use of Fourier series expansions. However, the no-slip condition at the side walls can also be treated in a least-squares sense.Among the results that will be reported in the third paper are the effects of viscosity on liquid sloshing phenomenon and the dependence of viscous dissipation on the Reynolds and Froude numbers. Furthermore, the influence of the tank aspect ratio on viscous dissipation has been explored. These results demonstrate some unknown features of the functional relationships that exist between the dissipated energy and the Reynolds and Froude numbers. Similarly, the dependence of the dissipated energy on the aspect ratio has been analytically studied. The results obtained agree with the physical laws for the range of parameters investigated.     

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.     

Sloshing waves and resonance modes of fluid in a 3D tank by a time-independent finite difference method

A 3D time-independent finite difference method is developed to solve for wave sloshing in a three-dimensional tank excited by coupled surge and sway motions. The 3D equations of fluid motion are derived in a moving coordinate system. The three-dimensional tank, with an arbitrary depth and a square base, is subjected to a range of excitation frequencies with motions that exhibit multiple degrees of freedom. For demonstration purposes the numerical scheme is validated by a benchmark study. Five types of sloshing waves were observed when the tank is excited by various excitation frequencies. A spectral analysis identified the resonant frequencies of each type of wave and the results show a strong correlation between resonant modes and the occurrence of the sloshing wave types. The method can be used to simulate fluid sloshing in a 3D tank with six-degrees of freedom.     

The effects of LNG-tank sloshing on the global motions of LNG carriers

The coupling and interactions between ship motion and inner-tank sloshing are investigated by a time-domain simulation scheme. For the time-domain simulation, the hydrodynamic coefficients and wave forces are obtained by a potential-thoery-based three-dimensional (3D) diffraction/radiation panel program in frequency domain. Then, the corresponding simulations of motions in time domain are carried out using convolution integral. The liquid sloshing in a tank is simulated in time domain by a Navier–Stokes solver. A finite difference method with SURF scheme is applied for the direct simulation of liquid sloshing. The computed sloshing force and moment are then applied as external excitations to the ship motion. The calculated ship motion is in turn inputted as the excitation for liquid sloshing, which is repeated for the ensuing time steps. For comparison, we independently developed a coupling scheme in the frequency domain using a sloshing code based on the linear potential theory. The hydrodynamic coefficients of the inner tanks are also obtained by a 3D panel program. The developed schemes are applied to a barge-type FPSO hull equipped with two partially filled tanks. The time-domain simulation results show similar trend when compared with MARIN's experimental results. The most pronounced coupling effects are the shift or split of peak-motion frequencies. It is also found that the pattern of coupling effects between vessel motion and liquid sloshing appreciably changes with filling level. The independent frequency-domain coupled analysis also shows the observed phenomena.     

The air–water sloshing problem: Fundamental analysis and parametric studies on excitation and fill levels

The problem of liquid sloshing has gained recent attention with the proliferation of liquefied natural gas (LNG) carriers transporting liquids in partially filled tanks. Impact pressures caused by sloshing depend on the tank fill level, period and amplitude of oscillation of the tank. In this paper, we first present the rudiments of a linear potential theory for sloshing motions in a two-dimensional rectangular tank, due to small amplitude sway motions. Although this topic is fundamental, we clarify inconsistencies in the published literature and texts.Numerical investigations were carried out on the sloshing motions in a two-dimensional tank in the sway excitation. The fluid domain was modeled using a finite volume approximation, and the air–water interface was tracked using a volume-of-fluid (VOF) technique. Computational results for free surface elevation and impact pressure are found to be in good agreement with theory and published data. The fill levels were varied from 10% to 95%, and the excitation time periods were varied from 0.8 to 2.8 s for a constant sway amplitude of 0.25 m (peak–peak) at 1:30 scale. The results of the parametric study are compared with theoretical predictions and suggestions are made on incorporating sloshing effects in standard seakeeping analysis for LNG carriers.     

弹性液舱内液体晃荡实验研究

通过物理模型实验,对水平简谐激励下弹性矩形液舱内液体晃荡问题进行了研究。实验中给出了不同液深和不同激励振幅下弹性液舱内液体最低阶固有频率。采用影像采集与分析系统获得液舱内自由液面的形状和高度,通过压力采集系统得到舱壁上的压力分布。实验中分析了不同液深、不同激励频率下弹性和刚性液舱内自由液面高度和晃荡压力的变化特性。比较了弹性和刚性液舱内不同位置处自由液面高度随外界激励频率的变化规律,以及舱壁上不同位置处的压力峰值随外界激励频率的变化规律。结果表明:非共振情况下,弹性和刚性实验结果及理论值三者的波高和压力较为接近。共振情况下,弹性和刚性波高基本相等,在近舱壁处二者明显大于理论值,而在远离舱壁处二者与理论值存在一定差别;弹性压力较刚性压力略小,但二者与理论值差别较大。     

An approximation to energy dissipation in time domain simulation of sloshing waves based on linear potential theory

This paper proposes a new approximation to energy dissipation in time domain simulation of sloshing waves by use of a linear potential theory.The boundary value problem is solved by the NURBS(non-uniform rational B-spline) higher-order panel method,in which a time-domain Green function is employed.The energy dissipation is modeled by changing the boundary condition on solid boundaries.Model experiments are carried out in a partially filled rectangular tank with forced horizontal motion.Sloshing-induced internal pressures and horizontal force obtained numerically and experimentally are compared with each other.It is observed that the present energy dissipation approximation can help produce a fair agreement between experimental forces and those of numerical simulations.     

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.