Coupling Frequency of the Liquid Sloshing in a Cylindrical Tank with a Flexible Baffle

The coupling oscillation of a liquid in a cylindrical tank with an elastic slosh baffle is investigated. Free surface conditions are considered in the study. The complexity of the coupled boundary-value problem for the liquid and elastic damping spacer results in significant analytical difficulties. Two different velocity potential functions are respectively used in the liquid domain above, or below the damping spacer. A coupled frequency equation is obtained by using the pair of velocity potential functions. The numerical and theoretical analysis show that the natural frequency changes according to the location and stiffness of the spacer. Results indicate that the frequency coupling between damping spacer and sloshing liquid is obvious near the free liquid surface. It is shown that the coupling frequency increases with the increase of damping baffle rigidity.

A Numerical Study of Liquid Sloshing in a Two-dimensional Tank under External Excitations

在这研究，在 2-D 的液体 sloshing 行为矩形的坦克用 ANSYS 流畅的软件题目被模仿到单个或多重夫妇的外部刺激(例如结合的摇摆，转动和结合的转动胀起) 。液体(VOF ) 的体积方法被用来追踪 sloshing 的免费表面。外部刺激被使用动态网孔技术通过坦克的运动强加。学习证明如果坦克受到多重联合刺激和反响的刺激频率，液体 sloshing 将变得强烈， sloshing 装载，包括最高的墙上的影响，将被加强。

Numerical simulation of viscous liquid sloshing by moving-particle semi-implicit method

网孔更少数字模拟法，动人粒子的半含蓄的方法(MPS ) 在这篇论文被介绍在海洋和海军的工程学习 sloshing 现象。作为一个网孔更少的方法，在传统的方法代替网孔的 MPS 使用粒子，管理方程是由粒子，和压力的泊松方程的关系的优点的 discretized 被不完全的 Cholesky 解决结合坡度方法( ICCG )，免费表面被数字密度的变化追踪。一个数字实验粘滞液体 sloshing 坦克被介绍并且与差别方法与 VOF，和另外的修正得到的结果相比走被增加使模拟更稳定。结果证明 MPS 方法对模拟合适粘滞与在容易安排粒子的优点，液体 sloshing 特别在弄弯的某建筑群上出现。

Review on the Progress and Issues in Liquid Tank Sloshing of Ships

With the development of large liquid cargo ships,liquid tank sloshing has gradually become a hot research topic in the area of shipping and ocean Engineering.Liquid tank sloshing,characterized by strong nonlinearity and randomness,not only affects the stability of the ship but also generates a huge impact force on the wall of the tank.To further investigate liquid tank sloshing,a comprehensive review is given on the research process of the most focused subjects of liquid sloshing.Summarizing the existing research will help to identify issues in the current field and provide useful references.The methods for investigating sloshing,the research progress and the situations worldwide are discussed.The advantages and defects of experiments and numerical simulations are also explored.The problems which need to be explored in the future are subsequently proposed.

Influence of baffle position on liquid sloshing during braking and turning of a tank truck

The influence of baffle position on liquid sloshing during the braking and turning of a tank truck was studied using a volume of fluid (VOF) model. The forces,their positions and weight distribution during braking and the forces and rolling moment during turning were calculated. The reliability of the calculation method was validated by comparisons with experimental results. The results showed that during braking,liquid splashes in the tank and the maximum forces and G (the ratio of weight acting on the front axle to the rear axle) are large when A (the ratio of the arch area above the baffle to the area of cross section)≤0.1. When A≥0.2,as the position of the baffle is lowered,the maximum of Fx (the force in direction x) first decreases then increases,and the maximum of Fy (the force in direction y) and G increase. During turning,liquid splashes in the tank and the maximum forces and M (the rolling moment) are large when D (the ratio of the arch area above the baffle to the area of cross section)≤0.2. When D≥0.3,as the position of the baffle is lowered,the maximums of Fy,Fz (the force in direction z) and M increase.

Laboratory investigation of the hydroelastic effect on liquid sloshing in rectangular tanks

A sloshing experiment is conducted to study the hydroelastic effect in an elastic tank. For this purpose, a translational harmonic excitation is applied to a 2-D rectangular tank model. The lowest-order natural frequencies of the liquid in the tank are determined through the sweep test. The wave elevation and the sloshing pressure are obtained by changing the excitation frequency and the liquid depth. Then the characteristics and the variation of the elevation and the pressure are discussed. The results are compared with the experimental results and the theoretical calculations in a rigid tank. Our analysis indicates that, in the non- resonant cases, the elastic results, the rigid experimental results and the theoretical values are all close to each other. In contrast, under the resonant condition, the elastic experimental result is slightly smaller than the rigid one. Also, the theoretical values are smaller than the experimental results at the resonant frequency.

Numerical simulations of multi-layer-liquid sloshing by multiphase MPS method

In this paper,a multiphase moving particle semi-implicit(MPS)method is developed by introduction of various multiphase models into the original MPS method for single-phase flows,and is then applied to the numerical simulations of two-layer-liquid and three-layer-liquid sloshing in a 2-D rectangular tank under different external excitations.To validate the accuracy of the present multiphase MPS method,the qualitative and quantitative results,including wave profiles,interface elevations and impact pressures,are compared with experimental data and other numerical results,which show a good agreement.In particular,the evolutions of free surface and phase interfaces are compared and an obvious discrepancy is found,indicating that the phase interfaces may suffer from complex deformations while the free surface keeps relatively quiet.Moreover,the different modes of phase interface are observed under different excitation frequencies.Then,the violent sloshing of a three-layer-liquid system is simulated and the phenomenon of internal wave breaking is well captured,which mainly benefitted from the Lagrangian basis of MPS method and its advantage in multiphase flows with complex interfaces.Finally,the three-layer-liquid sloshing with a vertical baffle are simulated to investigate the suppressing effect of baffle on multi-layer-liquid sloshing.

THE EQUIVALENT MECHANICAL MODELS OF LIQUID SLOSHING IN A SPHERICAL TANK WITH SPACER UNDER LOW GRAVITY

The dynamics of liquid sloshing in a spherical tank with spacer under low gravity was investigated. By extending the characteristic functions, the frequencies of liquid free sloshing, reaction force and moments on the wall of tank were obtained. By mechanical equivalent principle, the equivalent models of spring vibrator damper of liquid sloshing were given. The numerical results obtained show when a spacer is inserted in the tank, the sloshing frequency of liquid and the sloshing mass of liquid will decrease.

DYNAMIC CHARACTERISTICS OF LIQUID SLOSHING IN A RECTANGULAR TANK UNDER LOW GRAVITY

In this paper, the dynamics of liquid sloshing in a rectangular tank under low gravity was investigated. The basic frequencies and the velocity potentials of sloshing of liquid were obtained by expansion of the Fourier series. The characteristics of force and moment of the liquid acting on a rectangular tank were analyzed. The equivalent mechanical models of spring-vibrator-damper of sloshing of liquid were established with mechanical equivalent principle and numerical results were given. The numerical results show that the equivalent sloshing mass increases with the increase of gravity, and that the basic frequency and the equivalent sloshing mass increase with the increase of the liquid depth.

FORCES AND MOMENTS OF THE LIQUID FINITE AMPLITUDE SLOSHING IN A LIQUID-SOLID COUPLED SYSTEM

Nonlinear coupling dynamics between a spring-mass system and a finite amplitude sloshing system with liquid in a cylindrical tank is investigated. Based on a group of nonlinear coupling equations of six degrees of freedoms, analytical formulae of forces and moments of the liquid large amplitude sloshing were obtained. Nonlinearity of the forces and moments of the sloshing was induced by integrating on final configuration of liquid sloshing and the nonlinear terms in the liquid pressure formula. The symmetry between the formula of Ox and Oy direction proves that the derivation is correct. According to the coupled mechanism, the formulae are available in other liquid-solid coupled systems. Simulations and corresponding experimental results arecompared. It is shown that the forces and moments formulae by integrating on the final sloshing configuration are more reasonable. The omitted high-dimensional modal bases and high-order nonlinear terms and the complexity of sloshing damping are main sources of errors.

Numerical Simulation on Partially Liquid-Filled Sloshing with Baffle Under Different Density Ratios by the CLSVOF/IB Method

The density and viscosity ratios on partially liquid-filled sloshing with baffle have been investigated numerically in this study.As the key to success in the present simulation,the Coupled Level Set and the Volume of Fluid(CLSVOF)method and the Immersed Boundary(IB)method are used to capture gas/liquid and fluid/structure interfaces,respectively.Within the CLSVOF method,surface normal in weighting factors is calculated by the level set function,resulting in a more accurate solution.Furthermore,the Tangent of Hyperbola for INterface Capturing(THINC)coupled with the Weighted Linear Interface Calculation(WLIC)scheme is used for capturing moving interface.As a standard practice,we first validate the code by comparing it with experimental results of liquid sloshing,which involves large deformation of interface.In addition to the validation study of the present method,the problems of liquid sloshing with baffle are investigated to understand kinematics and dynamics behaviors under different density and viscosity ratios.

Viscous liquid sloshing damping in cylindrical container using a volume of fluid method

Liquid sloshing is a kind of very complicated free surface flow and exists widely in many fields.In order to calculate liquid sloshing damping precisely a volume of fluid method based on finite volume scheme is used to simulate free surface flows in partly filled cylindrical containers.A numerical method is pre-sented to simulate the movement of the free surface flow,in which a piecewise linear interface con-struction scheme and an unsplit Lagrangian advection scheme instead of Eulerian advection scheme are used.The damping performance of liquid sloshing in cylindrical containers under fundamental sloshing mode is investigated.There are four factors determining the surface-wave damping:free surface,boundary-layer,interior fluid and contact line.In order to study different contributions from these four factors to whole damping,several examples are simulated.No-slip and slip wall boundary conditions on both side wall and bottom wall of the cylindrical containers are studied to compare with the published results obtained by solving Stokes equations.In the present method the first three main factors can be considered.The simulation results show that the boundary-layer damping contribution increases while the interior fluid damping contribution decreases with increase of Reynolds number.

Large-scale amplitude liquid sloshing in container under pitching excitation

Large-scale amplitude liquid sloshing in container under pitching excitation is numerically studied in this paper.Firstly,the kinematics of the ALE description is introduced and the fluid dynamics equations are revised in the ALE form.Secondly,the boundary condition about free-surface tension is represented in the form of weak integration that can be computed by the differential geometry method derived in the present paper and the normal vector on free surface is calculated using accurate formulas presented in this paper.Then the numerical discretized equations of fractional step finite element method are developed by Galerkin weighted residual method.Furthermore,the numerical simulation of large-scale amplitude sloshing of the liquid both in rectangular container and cylindrical container is carried out.The computed time evolution of the wave height,and free surface profiles at different time are obtained.Comparisons among the present numerical results with other published numerical results and experimental data confirm the effectiveness and validity of the method developed in this paper.

DYNAMIC CHARACTERISTICS OF LIQUID SLOSHING IN A TRANSVERSELY VIBRATING SPHERICAL TANK WITH A SPACER UNDER LOW GRAVITY

The dynamic characteristics of liquid sloshing in a transversely vibrating spherical tank with spacer under low gravity were investigated. By expanding the characteristic functions, the frequencies and velocity potentials of liquid free-sloshing were obtained. The dynamic equations and boundary conditions of liquid sloshing in the traverse vibrational spherical tank with spacer under low gravity were derived. By modifying the velocity potentials of liquid free-sloshing, the velocity potentials of liquid sloshing in the traverse vibrating spherical tank with a spacer were obtained. Furthermore, the forces and the moments acting on tank wall were given. The numerical results show when a spacer is inserted in the tank, the sloshing frequencies of liquid and the forces acting on tank wall will decrease, but the moment of force to the centre of the tank which is caused by the force of liquid acting on the spacer will occur.

HYDROELASTIC VIBRATIONS AND LIQUID SLOSHING SUPPRESSION IN A RECTANGULAR TANK WITH ELASTIC SPACER

In this paper, the couple vibration of liquid and elastic spacer in arectangular tank is investigated. Two different velocity potential functions correspondingrespectively to the liquid above and below the elastic spacer are assumed. Complicated boundaryconditions corresponding to two velocity potential functions and vibrations of elastic spacer aregiven. Using the method of energy, the equation of couple frequency is obtained. Through numericalcomputation the natural frequencies that change according to the location and stiffness of thespacer are shown.

Angle Compensation and Asymmetry Effect of Light Diffracted by Millimeter Liquid Surface Slosh Wave

The angle compensation method is adopted to detect sloshing waves by laser diffraction, in the case that the wavelength of the sloshing waves is much greater than that of the incident light. The clear diffraction pattern is observed to be of asymmetry, involving orders, position and interval of the diffraction spots that are discovered during the light grazing incidence. It is found that the larger the angle of incidence is, the more obvious the asymmetry is. The higher the negative diffraction orders are, the smaller the intervals between spots are. On the contrary~ in the positive region, the higher the diffraction orders are, the larger the spot intervals are. The positive interval is larger than that of the same negative diffraction order. If the incident angle reaches 1.558 rad in the experiment, all positive diffraction orders completely vanish. Based on the mechanism of phase modulation and with the Fourier transform method, the relations between the incident angle and position, interval spaces, and orders of diffraction spots are derived theoretically. The theoretical calculations are compared with the experimental data, and the comparison shows that the theoretical calculations are in good agreement with the experimental measurement.

ACTUATION OF SLOSHING MODULATED FORCE AND MOMENT ON LIQUID CONTAINER DRIVEN BY JITTER ACCELERATIONS ASSOCIATED WITH SIEW MOTION IN MICROGRAVITY

The mathematical formulation of sloshing dynamics for a partially liquid filleddewar container driven by the gravity jitter acceleration associated with slew motion isstudied.Explicit mathematical expressions to manage jitter accelerption associated withslew motion which is acting on the fluid systems in microgravity are derived. Thenumerical computation of sloshing dymamics is based on the non-inertia framecontainer bound coordinate and the solution of time-dependent three-dimensionalformulations of partial differential equations subject to initial and boundary conditions.The numerical computation of fluid viscous stress forces and moment fluctuationsexerted on the dewar container driven by jitter acceleration associated with slew motion is investigated.

ASYMMETRIC SLOSH WAVE EXCITATION IN A LIQUID-VAPOR INTERFACE UNDER MICROGRAVITY

The dynamical behavior of fluids affected by the asymmetric gravity jitter oscillations, in particular, the effect of surface tension on partially-filled rotating fluids in a Dewar tank imposed by time-dependent directions of background reduced gravity accelerations is investigated. Results show that the greater the components of background reduced gravity in radial and circumferential directions, the greater will be the tendency toward increasing amplitude and degrees of asymmetry of the liquid-vapor interface profiles.

Bifurcation of elastic tank-liquid coupled sloshing system

The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established.By means of the multi-scale method and the singularity theory,the bifurcation behaviors of the system are investigated and analyzed.The various nonlinear dynamical behaviors of the coupling system are obtained,which can further explain the relationship between the physical parameters and the bifurcation solutions.The results provide a theoretical basis to the realization of the parameter optimal control.

液罐车防波板对液体纵向晃动及车辆动力学的影响

为研究液罐车防波板对液体纵向晃动及车辆动力学的影响,进行液罐车的液体纵向晃动受力预测及动力学分析。首先基于计算流体力学(CFD)软件FLUENT对罐体施加纵向加速度激励,获得不同充液率下有无防波板的液体纵向晃动力和晃动力矩。利用仿真数据,训练得到有无防波板的罐内液体纵向晃动Elman神经网络预测模型,以此建立一个简化的双轴液罐车整车纵向动力学模型。通过模型直线制动工况的仿真,考察防波板不同布置方式下制动距离的响应。结果表明:Elman神经网络预测模型可以有效地预测有无防波板的罐体受力;罐体内设置防波板可以减小车辆制动距离,且防波板两头小(等间距)中间大的布置方式的制动距离较小,有利于液罐车的纵向制动稳定性。