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.

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.

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.

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.

Time-Independent Finite Difference and Ghost Cell Method to Study Sloshing Liquid in 2D and 3D Tanks with Internal Structures

A finite difference scheme with ghost cell technique is used to study viscous fluid sloshing in 2D and 3D tanks with internal structures.The Navier-Stokes equations in a moving coordinate system are derived and they are mapped onto a time-independent and stretched domain.The staggered grid is used and the revised SIMPLEC iteration algorithm is performed.The developed numerical model is rigorously validated by extensive comparisons with reported analytical,numerical and experimental results.The present numerical results were also validated through an experiment setup with a tank excited by an inclined horizontal excitation or a tank mounted by a vertical baffle.The method is then applied to a number of problems including sloshing fluid in a 2D tank with a bottom-mounted baffle and in a 3D tank with a vertical plate.The phenomena of diagonal sloshing waves affected by a vertical plate are investigated in detail in this work.The effects of internal structures on the resonant frequency of a tank with liquid are discussed and the present developed numerical method can successfully analyze the sloshing phenomenon in 2D or 3D tanks with internal structures.

Influences of the tank liquid lateral sloshing and mass time-varying on high clearance self-propelled sprayer ride comfort

To explore the influence of the lateral sloshing and the time-varying mass of the liquid in the tank on the ride comfort of the high-clearance sprayer,a spring-mass-damping equivalent mechanics that can describe the lateral sloshing of the liquid under different filling ratios was constructed based on the equivalent criterion.The Fluent was used to simulate the moment acting on the wall of the tank by the lateral sloshing of the liquid,and then the parameters of the equivalent mechanical model are obtained by fitting and solving.Comparative analysis of Fluent simulation and bench test on lateral sloshing of tank liquid under different filling ratios.The results show that the lateral sloshing trend of the tank liquid level obtained from the Fluent simulation and the bench test was consistent,which proved the accuracy of the Fluent fluid simulation process and the correctness of the required equivalent mechanical model parameters.Incorporating a liquid sloshing equivalent model,a four-degree-of-freedom vertical dynamic model of the sprayer half-car was established.Subsequently,the performance of the sprayer was systematically analyzed and compared under the excitation of a bump road and a random E-level road.This investigation took into account varying liquid filling ratios of 10%,50%,and 90%.The focus lay on evaluating the vertical acceleration of the sprayer body,dynamic deflection of the suspension,and dynamic load on the tires in response to these road conditions.This analysis is conducted independently of the liquid sloshing factor.The results show that the lateral sloshing of the liquid medicine significantly reduces the ride smoothness of the machine,and makes the vibration response of the machine produce a certain hysteresis effect.With the reduction of the quality of the liquid medicine in the spray tank,the vibration amplitude of the sprayer body gradually decreases,the hysteresis effect is also gradually weakened.The results presented in this study offer a theoretical foundation for the analysis of ride comfort and the optimization of chassis structure in high-clearance sprayers.

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.

Numerical Simulation of Sloshing with Large Deforming Free Surface by MPS-LES Method

Moving particle semi-implicit （MPS） method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation （LES） by coupling with a sub-particle-scale （SPS） turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is ＂neighbor particle＂. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no ＂neighbor particles＂ in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.

Finite Element Analysis to Two-Dimensional Nonlinear Sloshing Problems

A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domain second order theory of water waves. Liquid sloshing in a rectangular container Subjected to a horizontal excitation is simulated by the finite element method. Comparisons between the two theories are made based on their numerical results. It is found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur for large amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features of nonlinear wave and can be used instead of the fully nonlinear theory.

Nonlinear coupled dynamics of liquid-filled spherical container in microgravity

Nonlinear coupled dynamics of a liquid-filled spherical container in microgravity are investigated. The governing equations of the low-gravity liquid sloshing in a convex axisymmetrical container subjected to lateral excitation is obtained by the variational principle and solved with a modal analysis method. The variational formulas are transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method, in which admissible functions for the velocity potential and the liquid flee surface displacement are determined analytically in terms of the Gaussian hypergeometric series. The coupled dynamic equations of the liquid-filled container are derived using the Lagrange＇s method and are numerically solved. The time histories of the modal solutions are obtained in numerical simulations.

Flight Dynamic Analysis of Hypersonic Vehicle Considering Liquid-Solid Coupling

With the liquid propellant making up 60%—70% of the takeoff weight of the hypersonic vehicle,the dynamic load caused by great propellant sloshing interacts with the flexible structure of the aircraft.Therefore,the dynamic model displays characteristics of strong coupling with structure/control and nonlinearity.Based on the sloshing mass dynamic simplified as a spring-mass-damping model,a rigid-flexible-sloshing model is constructed.Moreover,the effect on the dynamic performance of the coupled model is analyzed with changing frequency and damping.The results show that propellant sloshing dynamics significantly affects the rigid body motion modes,especially flexible mode and short mode.The right half plane pole(RHP)moves far from the imaginary axis with the consumption of the propellant.The flexible mode attenuates with the increase of the sloshing damping,and the coupling becomes stronger when sloshing frequency is close to the short mode frequency or the flexible frequency of the beam.

BAFFLE EFFECT OF SLOSHING INDUCEDFLOWS IN RESPONSE TO AXIAL IMPULSE IN MICROGRAVITY

Sloshing dynamics for partially filled liquid of superfluid helium Ⅱ in a rotating dewar container in resPonse to axial impulse is investigated. The study includes howrotating bubble of suPerfluid he1ium Ⅱ reacts to the impulse in microgravity, how ampli-tudes of bubble mass center fluctuate with growth and decay of disturbances, how thesedisturbances in fluid system feed back to dewar in terms of force and moment through thedynamics of sloshing waves, and hwo the differences react on the container with andwithout the baffle.

MOTION ANALYSIS OF A SPINNING SATELLITE SYSTEM WITH OFF-CENTRE TANKS PARTIALLY FILLED WITH LIQUID

The sloshing problem for a spherical tank partially filled with liquid is analysed in this paper The study is based on the goveming equations of fluid dynamics and the Euler's equations of systems with the influences of tank off centering,fluid vortices and the Coriolis'acceleration on the motion states of the systems taken into consideration.In the study,we adopt the concept of uniform vortex motion of fluid gen- eralized by Pfeiffer and apply the boundary element method(BEM)to the calculation of the natural frequence and the velocity field of the liquid sloshing.The motion charateristics of the flow-solid spinning system is then analysed.

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.

FREE BENDING VIBRATION OF ANNULAR CYLINDRICAL TANK PARTIALLY FILLED WITH LIQUID IN THE CONSIDERATION OF SURFACE WAVE

This paper studies the problem of free bending vibration of annular cylindricaltank partially filled with liquid in the consideration of surface wave.The exactformulae of the mode shape functions and frequencies are deduced.Results can beobtained by means of computer.The analysis shows that the effect of liquid on vibration of annular cylindrical tank is equivalent to different generalized distributivemasses attached to inner and outer cylinders respectively.

Stability analysis of liquid filled spacecraft system with flexible attachment by using the energy–Casimir method

The stability of partly liquid filled spacecraft with flexible attachment was investigated in this paper. Liquid sloshing dynamics was simplified as the spring-mass model, and flexible attachment was modeled as the linear shearing beam. The dynamic equations and Hamiltonian of the coupled spacecraft system were given by analyzing the rigid body, liquid fuel, and flexible appendage. Nonlinear stability conditions of the coupled spacecraft system were derived by computing the variation of Casimir function which was added to the Hamiltonian. The stable region of the parameter space was given and validated by numerical computation. Related results suggest that the change of inertia matrix, the length of flexible attachment, spacecraft spinning rate, and filled ratio of liquid fuel tank have strong influence on the stability of the spacecraft system.

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.

DYNAMIC CHARACTERISTICS OF LIQUID FORCED SLOSHING IN A TURNING SPHERICAL TANK WITH A SPACER UNDER LOW GRAVITY

Under the condition of low gravity the characteristics of liquid forced sloshing in a turning spherical tank with a spacer were investigated. The static shape of the liquid surface was analyzed. By expanding the characteristic functions, the frequencies and velocity potential of liquid free-sloshing were derived. The governing equations and boundary conditions for the forced sloshing of liquid under the tank turning were established. The transverse force of liquid acting on the tank and the moment of force to the centre of the tank which is caused by the force of liquid acting on the spacer were given. Numerical results were compared with the ones of the spherical tank without a spacer. The results show that when a spacer is inserted in the tank, the sloshing frequency of liquid and the transverse force of liquid acting on the tank 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.

Attitude tracking control of flexible spacecraft with large amplitude slosh

This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli–Euler beam, and the assumed modal method is employed.A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics,liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking.

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.