The Effects of Fluid Sloshing on Different Baffle Configurations in Storage Tanks Transported on Trucks during an Emergency Braking

Different Baffle designs usable in cylindrical and elliptical storage tanks carried by trucks often used for transporting inflammable liquid materials in Cameroon are investigated to evaluate their safest fluid sloshing damping response during emergency braking where the magnitude of sloshing waves are the greatest. The uncontrolled fluid sloshing creates thrust on the walls of the tanks usually felt externally on the truck carrying the tank and capable of hindering driver’s effort to maintain steer ability and improve on safety during critical braking moments. The study first passes through COMSOL, to expose the safest margin of each Baffle type at instantaneous fluid pressure wave propagation initiated at a single phase to reflect sloshing in the storage tank during an emergency braking by the truck carrying the tank. The vivid results can be seen in the domain of Acoustic Iso-surface Pressure response;but also acoustic Pressure and Sound pressure response are seen automatically. Secondly, through an experimental finding in which fluid is forced to pass through each Baffle and the resistance to fluid flow is a measured as it’s the Baffle’s damping ability. Either, the fluid is lost through the Baffle and by determination of the surface load exerted on each Baffle due to the reaction of the residual fluid acting on the surface of each Baffle after some of it is Lost, the individual sloshing damping abilities are exposed. By comparing the Experimental outcome with the computational response obtained, an ideal Baffle design is proposed for cylindrical and elliptical tanks and considered to respond to abrupt braking more effciently. The application of the Baffle designs with an average multiple holes rather than the usual face centered proved to be more effcient in fluid sloshing as they provide a more uniformly distributed damping pressure during fluid sloshing in the tank thereby reducing the magnitude of forward thrust that can be created by the conventional Baffle type during emergency braking hence contributing to improving safety. Mindful of the human, material and environmental damages that an accident involving mobile petroleum storage tanks can course, this study is therefore of great significance for design optimization by petroleum storage tank manufacturing companies in Cameroon.

Nonlinear semi-analytical modeling of liquid sloshing in rectangular container with horizontal baffles

A nonlinear semi-analytical scheme is proposed for investigating the finiteamplitude nonlinear sloshing in a horizontally baffled rectangular liquid container under the seismic excitation.The sub-domain method is developed to analytically derive the modal behaviors of the baffled linear sloshing.The viscosity dissipation effects from the interior liquid and boundary layers are considered.With the introduction of the generalized time-dependent coordinates,the surface wave elevation and velocity potential are represented by a series of linear modal eigenfunctions.The infinite-dimensional modal system of the nonlinear sloshing is formulated based on the Bateman-Luke variational principle,which is further reduced to the finite-dimensional modal system by using the NarimanovMoiseev asymptotic ordering.The base force and overturning moment induced by the nonlinear sloshing are derived as the functions of the generalized time-dependent coordinates.The present results match well with the available analytical,numerical,and experimental results.The paper examines the surface wave elevation,base force,and overturning moment versus the baffle parameters and excitation amplitude in detail.

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.

Numerical simulations of sloshing and suppressing sloshing using the optimization technology method

Sloshing is a common phenomenon in nature and industry, and it is important in many fields, such as marine engineering and aerospace engineering. To reduce the sloshing load on the side walls, the topology optimization and optimal control methods are used to design the shape of the board, which is fixed in the middle of the tank. The results show that the new board shape, which is designed via topology optimization, can significantly reduce the sloshing load on the side wall.

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.

Experimental Studies on Sloshing Mitigation Using Dual Perforated Floating Plates in A Rectangular Tank

The performance of dual perforated floating plates in a rectangular tank is investigated based on the model tests under different external excitations for different filling rates.It is found that dual perforated floating plates in the tank can remarkably mitigate violent resonant sloshing responses compared with the clean tank,especially when the external excitation frequency is in the vicinity of the first-order resonant frequency.Next,the parametric studies based on different filling rates and external excitation amplitudes are performed for the first-order resonant frequencies.The presence of dual perforated floating plates seldom shifts the sloshing natural frequencies.Further,dual perforated floating plates change the sloshing modes from the standing-wave mode in the clean tank to the Utube mode,which can arise from the sloshing reduction to some extent.

A practical prescreening method for sloshing severity evaluation

This paper aims at finding a proper way to estimate sloshing severity.First,the concept of sloshing severity RAO(SSR) is introduced,and the wave elevation on the liquid free surface is chosen as an initial index for the rough prediction of sloshing severity.Then,compared with experimental data from a 3 D regular model test,this index is adjusted and a new index is generated.One step further,sloshing severity under irregular sea states can be achieved by nonlinear combinations of the new index.For validation,the same model tank is tested under a set of irregular sea conditions,and peak pressures and impulse areas are taken as comparison standards.It is found that both numerical and experimental results show a similar tendency of sloshing severity.As a real ship application on the new index,the sloshing severity of a liquefied natural gas floating production storage and offloading(LNG-FPSO) is predicted under a low filling condition.Besides,the ship motion responses with and without sloshing effects are considered for the calculation of severity.From the present observation,this proposed methodology and generated new index is expected to be applicable to the selection of severe sea states for sloshing loads analysis.

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.

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.

Optimization of Baffled Rectangular and Prismatic Storage Tank Against the Sloshing Phenomenon

The fluid motion in partially filled tanks with internal baffles has wide engineering applications. The installation of baffles is expected to reduce the effect of sloshing as well as the consequent environmental damages. In the present study, a series of experimental tests are performed to investigate the sloshing phenomenon in a baffled rectangular storage tank. In addition, the sloshing phenomenon is also modeled by using Open Foam. Based on the experimental and numerical studies, optimization of the geometric parameters of the tank is performed based on some criteria such as tank area, entropy generation, and the horizontal force exerted on the tank area due to the sloshing phenomenon.The optimization is also carried out based on the entropy generation minimization analysis. It is noted that the optimum baffle height is in the range of h_b/h_w=0.5-0.75 in the present study(where h_b and h_w are the baffle height and water depth, respectively). Based on the results, the optimal design of the tank is achieved with R_A= 0.9-1.0(where R_A=L/W, L and W are the length and width of the tank, respectively). The results also show that the increase of h_b can lead to a decrease of the maximum pressure and horizontal force exerted on the tank. It is also noted that the horizontal force exerted on the tank firstly continues to increase as the sway motion amplitude increases.However, as the normalized motion amplitude parameter, a/L(The parameter a is the motion amplitude), exceeds0.067, the effect of motion amplitude on the force is not obvious. The same optimization is also performed in the multiple-variable-baffled tank and prismatic storage tank.

A SPH simulation on large-amplitude sloshing for fluids in a two-dimensional tank

Smoothed particle hydrodynamics（SPH） is a mesh-free adaptive Lagrangian particle method with attractive features for dealing with the free surface flow.This paper applies the SPH method to simulate the large-amplitude lateral sloshing both with and without a floating body,and the vertical parametrically-excited sloshing in a two-dimensional tank.The numerical results show that the SPH approach has an obvious advantage over conventional mesh-based methods in handling nonlinear sloshing problems such as violent fluid-solid interaction,and flow separation and wave-breaking on the free fluid surface.The SPH method provides a new alternative and an effective way to solve these special strong nonlinear sloshing problems.

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.

Experimental Study on Sloshing Characteristics in the Elastic Tank Based on Morlet Wavelet Transform

Hydroelastic effect of sloshing is studied through an experimental investigation. Different excitation frequencies are considered with low-fill-depth and large amplitude. Morlet wavelet transform is introduced to analyze the free surface elevations and sloshing pressures. It focuses on variations and distributions of the wavelet energy in elastic tanks. The evolutions of theoretical and experimental wavelet spectra are discussed and the corresponding Fourier spectrums are compared. Afterwards, average values of the wavelet spectra are extracted to do a quantitative study at various points. From the wavelet analysis, sloshing energies are mainly distributed around the external excitation frequency and expanded to high frequencies under violent condition. In resonance, experimental wavelet energy of the elevation in elastic tanks is obviously less than that in the rigid one; for sloshing pressures, the elastic wavelet energy close to the rigid one and conspicuous impulse is observed. It recommends engineers to concern the primary natural frequency and impulsive peak pressures.

Damping computation of liquid sloshing with small amplitude in rigid container using FEM

An FEM （Finite Element Method） based damping estimation method of liquid sloshing with small amplitude in rigid container is proposed. Damping of the sloshing is affected by many factors and some of them are very complicated. Therefore, this paper aims to provide an estimation range, instead of computing the exact value of damping. This method will consider the dissipation at wall, in the interior, and at the contaminated free surface. Owing to the complexity of viscous damping at the free surface, damping of two extreme conditions are computed to estimate the range of actual damping. An iterative algorithm is designed to solve a special general eigenvalue problem. Comparing the computation results with experimental results, it is found that most of the experimental results are within the range of the numerical estimation. Therefore, the method is effective in estimating the range of the damping of liquid sloshing with small amplitude in rigid container.

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.

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.

DYNAMIC SIMULATION OF FLUID-STRUCTURE INTERACTION PROBLEMS INVOLVING LARGE-AMPLITUDE SLOSHING

An effective computational method is developed for dynamic analysis offluid-structure interaction problems involving large-amplitude sloshing of the fluid andlarge-displacement motion of the structure. The structure is modeled as a rigid container supportedby a system consisting of springs and dashpots. The motion of the fluid is decomposed into twoparts: the large-displacement motion with the container and the large-amplitude sloshing relative tothe container. The former is conveniently dealt with by defining a container-fixed noninertiallocal frame, while the latter is easily handled by adopting an ALE kinematical description. Thisleads to an easy and accurate treatment of both the fluid-structure interface and the fluid freesurface without producing excessive distortion of the computational mesh. The coupling between thefluid and the structure is accomplished through the coupling matrices that can be easilyestablished. Two numerical examples, including a TLD-structure system and a simplified liquid-loadedvehicle system, are presented to demonstrate the effectiveness and reliability of the proposedmethod. The present work can also be applied to simulate fluid-structure problems incorporatingmultibody systems and several fluid domains.

Sloshing-Coupled Ship Motion Algorithm for Estimation of Slosh-Induced Pressures

The effect of coupling between sloshing and ship motions in the evaluation of slosh-induced interior pressures is studied. The coupling between sloshing loads and ship motions is modelled through a hybrid algorithm which combines a potential flow solution based on transient Green function for the external ship hydrodynamics with a viscous flow solution based on a multiphase interface capturing volume of fluid(VOF) technique for the interior sloshing motion. The coupled algorithm accounts for full nonlinear slosh forces while the external forces on the hull are determined through a blended scheme of linear radiationdiffraction with nonlinear Froude-Krylov and restoring forces. Consideration of this level of nonlinearities in ship motions is found to have non-negligible effects on the slosh-coupled responses and slosh-induced loads. A scheme is devised to evaluate the statistical measure of the pressures through long-duration simulation studies in extreme irregular waves. It is found that coupling significantly influences the tank interior pressures, and the differences in the pressures between coupled and uncoupled cases can be as much as 100% or more. To determine the RAO over the frequency range needed for the simulation studies in irregular waves, two alternative schemes are proposed, both of which require far less computational time compared to the conventional method of finding RAO at each frequency, and the merits of these are discussed.

Analytical Modeling of Fluid Sloshing in A 2D Rectangular Container with A Bottom-Mounted T-Shaped Baffle

An analytical procedure is presented to evaluate the fluid sloshing characteristics in a two-dimensional(2D)rectangular container with a bottom-mounted T-shaped baffle.The fluid region is divided into several sub-domains with hypothetical interfaces and the velocities and pressures of the fluid on adjacent interfaces should be identical.The separation of variables in conjunction with the superposition principle is employed to formulate the velocity potential of each sub-domain.The Fourier series expansion is used to derive the eigenvalue equation by substituting the velocity potential solutions into the free surface conditions and the continuity conditions on adjacent interfaces.Under the horizontal base excitation,the total velocity potential of fluid is decomposed of the impulsive and perturbed velocity potentials.The orthogonality of the sloshing modes is demonstrated by implementing Gauss formula.The dynamic response equation is established by incorporating the total velocity potential solution into the surface wave equation.Excellent agreements are achieved between the present results and those from the reported literature and finite element code.Numerical results are exhibited to reveal the effect of the baffle parameters and excitation frequency on sloshing characteristics and responses of liquid.

Stable response of low-gravity liquid non-linear sloshing in a circle cylindrical tank

Under pitch excitation, the sloshing of liquid in circular cylindrical tank includes planar motion, rotary motion and rotary motion inside planar motion. The boundaries between stable motion and unstable motion depend on the radius of the tank, the liquid height, the gravitational intension, the surface tensor and the sloshing damping. In this article, the differential equations of nonlinear sloshing are built first. And by variational principle, the Lagrange function of liquid pressure is constructed in volume intergration form. Then the velocity potential function is expanded in series by wave height function at the free surface. The nonlinear equations with kinematics and dynamics free surface boundary conditions through variation are derived. At last, these equations are solved by multiple-scales method. The influence of Bond number on the global stable response of nonlinear liquid sloshing in circular cylinder tank is analyzed in detail. The result indicates that variation of amplitude frequency response characteristics of the system with Bond, jump, lag and other nonlinear phenomena of liquid sloshing are investigated.