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Owing to the increasing g lobal demand for natural gas, the construction of liquefied natural gas (LNG) carriers has become a key trend in the shipbuilding market. In the design of membrane-type LNG carriers, a sloshing analysis is crucial for cargo containment systems (CCSs). In this study, structural responses due to impulsive sloshing loads were observed, including the effects of hydroelasticity and the test medium. To this end, the structural responses were first observed with and without hydroelastic coupling between the liquid and structure. When fluid–structure coupling is considered, a finite element analysis is performed for the integrated structure of the hull and CCS. This method was then applied to evaluate the capacity and safety of the inner hull structures of actual LNG vessels in cases where different sloshing pressures occurred owing to the different liquid–gas media. The structural capacity was evaluated using the utilization factor (UT). The results confirm that the effects of the hydroelasticity, density ratio, and phase transition of the experimental medium are essential for the evaluation of the structural responses of LNG CCSs. [ABSTRACT FROM AUTHOR]

A coupled numerical calculation method combining smooth particle hydrodynamics (SPH) and the finite element method (FEM) was implemented to investigate the seismic response of horizontal storage tanks. A numerical model of a horizontal storage tank featuring a free liquid surface under seismic action was constructed using the SPH-FEM coupling method. The stored liquid was discretized using SPH particles, while the tank and supports were discretized using the FEM. The interaction between the stored liquid and the tank was simulated by using the meshless particle contact method. Then, the numerical simulation results were compared and analyzed against seismic simulation shaking table test data to validate the method. Subsequently, a series of numerical models, considering different liquid storage volumes and seismic effects, were constructed to obtain time history data of base shear and top center displacement, which revealed the seismic performance of horizontal storage tanks. Numerical simulation results and experimental data showed good agreement, with an error rate of less than 18.85%. And this conformity signifies the rationality of the SPH-FEM coupling method. The base shear and top center displacement values obtained by the coupled SPH-FEM method were only 53.3% to 69.1% of those calculated by the equivalent mass method employed in the current code. As the stored liquid volume increased, the seismic response of the horizontal storage tank exhibited a gradual upward trend, with the seismic response increasing from 73% to 388% for every 35% increase in stored liquid volume. The maximum von Mises stress of the tank and the supports remained below the steel yield strength during the earthquake. The coupled SPH-FEM method holds certain advantages in studying the seismic problems of tanks with complex structural forms, particularly due to the representation of the flow field distribution during earthquakes by involving reservoir fluid participation. [ABSTRACT FROM AUTHOR]

Sloshing refers to a certain kind of fluid movement that changes as it progresses. It possesses properties that are both nonlinear and exceedingly unpredictable, and these properties affect the tank wall. This effect may lead to structural wear, which in turn can cause the tank to fail. Benzene and gasoil liquids are used to test the effect of sloshing liquid and accompanying pressure on the wall tank caused by the baffles in partially full fluid tanks. To attain this, modeling of the interaction between fluid and structure is justified using the finite element analysis while the ANSYS Fluent is used to do the simulation. Specifically, the analysis enables us to anticipate the pressure that is being exerted on the shield, the influence of sloshing on the grounding point forces, and the size of the sloshing waves. The pressure distribution over time indicates a reduction of pressure on the tank wall as a result of utilising a vertical baffle if compared to the case of a tank wall without a baffle. The usage of vertical shields allows for around 20% of the greatest contact energy to be deflected, which is attributed to the potential of generating turbulence and vortices by the baffle. [ABSTRACT FROM AUTHOR]

Major problems can occur when liquid sloshes in a tank, such as in liquid storage tanks during an earthquake, and this is an important engineering problem to address. To analyze this phenomenon, the finite-element method is generally used but involves many degrees of freedom when the tank is large. In this paper, a nonlinear numerical model with relatively few degrees of freedom is established for vertical and horizontal two-dimensional nonlinear sloshing in a rectangular tank excited horizontally. In addition, a method is proposed for reducing the number of degrees of freedom in the two-dimensional model. The natural frequencies, modes, and frequency responses are then compared among the concentrated mass model, theoretical calculations, and experimental results. Good agreement was achieved among them, thus demonstrating the validity of the model. [ABSTRACT FROM AUTHOR]

Sloshing in fuel tanks is one of the major sources of noise in hybrid and high-end vehicles. During sloshing, the fluid causes impacts on tank walls resulting in their vibration, which further leads to noise, referred to as "hit noise." Therefore, hit noise generation is a multi-physics phenomenon involving fluid flow, structural response, and acoustic radiation. This paper presents a multi-physics approach to predict hit noise in a rectangular tank. The methodology involves the prediction of fluid loading on tank walls and their structural response using transient fluid and structural analyses which are weakly coupled. Radiated hit noise is predicted using acoustic finite element analysis. Longitudinal periodic excitation is applied to the fluid domain at different frequencies to simulate the sloshing regime which has dominant fluid-structure interactions. Parameters like tank wall pressures, the resulting dynamic acceleration, and radiated sound pressure levels are monitored and validated with the experimental results available in the literature. [ABSTRACT FROM AUTHOR]

A robust input command based on multiple steps for eliminating the residual vibrations of a multimode linear system is proposed. Only the system resonant frequencies are needed to determine the step magnitudes in the shaped command. The command duration is selectable to help in designing an optimum command that compensates between the reduction in the transient vibration, the enhancement in the command robustness, and the increase in the total maneuver time. The induced transient and residual sloshing oscillations of a suspended water-filled container are suppressed using the proposed command. The dynamics of the sloshing is numerically simulated using finite element method that accommodates the interactions between the fluid, structural, and multi-body dynamics. A short move time penalty is incurred with the price of significant reduction in the liquid sloshing. The performance of the shaped command to the system parameters and the robustness to their uncertainty are investigated. An improved robust input command in the presence of uncertainties in the cable length and water depth is also introduced. The effectiveness and excellence of the proposed command is demonstrated through a comparison with multimode zero-vibration input shaper and time-optimal flexible-body control. [ABSTRACT FROM AUTHOR]

Base shear and sloshing response control in ground-supported circular cylindrical liquid storage tank is achieved by oblate spheroid base isolation (OSBI) system used along with floating surface diaphragm on the contained liquid. The new base isolation system, OSBI proposed herein is based on rolling-friction mechanism in ellipsoidal-shaped isolators in both the horizontal axes. The surface diaphragm is proposed to float on the free liquid surface to control the sloshing amplitude. The tank is analyzed using the coupled acoustic-structural (CAS) approach in finite element method (FEM). In order to have conformity of the present FE model, the FEM results are compared with the mechanical lumped-mass model of the tank (without surface diaphragm). The seismic response is investigated for the tank subjected to harmonic and real-earthquake excitations. The parameters considered for the analysis are the aspect ratio of the tank, eccentricity of the isolator, and thickness of the diaphragm. The seismic response quantities evaluated are base shear, sloshing displacement, and impulsive hydrodynamic pressure in the tank. Further, to study the effectiveness of the OSBI, the seismic responses of the tank subjected tri-directional components are compared with the two horizontal bi-directional components of the earthquakes. Also, the sloshing displacement with and without surface diaphragm in the non-isolated and base-isolated tanks are compared. From the results, it is observed that the OSBI system is efficient in mitigating the seismic responses in the tanks and the surface diaphragm is efficient in controlling the sloshing displacement. The superior performance of the proposed isolator depends on the design parameters, namely, eccentricity, and coefficient of rolling friction selected. The effectiveness of the surface diaphragm depends on the choice of material and thickness adopted. [ABSTRACT FROM AUTHOR]

The sloshing phenomenon is an important field of fluid dynamics in liquid storage tanks under earthquake excitation. When the sloshing frequency gets close to the liquid tank's natural frequency, the resulting resonance could lead to instability and even damage to structures, followed by catastrophic economic losses and environmental damages. As passive control devices, baffles are a place for liquid energy dissipation. This study uses annular and horizontal baffles to evaluate the baffles' relative effectiveness on the elevated storage tanks' dynamic response. The analysis results are compared with those of elevated storage tanks with no baffles. The flexible and rigid storage tank analysis is examined here, where half of the tank height is filled with liquid. The structural interaction between the liquid, the (horizontal and annular) baffle, and the elevated storage tank affected by seismic action are investigated using Abaqus software. The results confirm that using the baffles, the maximum base shear force in flexible and rigid elevated storage tanks decreases as much as 26.43% and 31.90%, respectively, and the maximum hydrodynamic pressure reduction in the tank is 50.1%. [ABSTRACT FROM AUTHOR]

Sloshing flows of liquid natural gas (LNG) with multi-phase flow characteristics consisting of liquids and gases can affect the load conditions and structural response of cargo containment systems (CCS). The compressible properties of the sloshing flow can limit the maximum pressure, so a multi-phase fluid model is required to represent the sloshing physics. In this study, we identified a suitable numerical model to simulate the sloshing flow and structural strength evaluation based on the inhomogeneous fluid model. The computational fluid dynamics (CFD) is based on a Eulerian domain model, which is in turn based on the constant volume based finite element method (CVFEM) in a commercial Reynolds-averaged Navier–Stokes CFD code (ANSYS CFX). It includes the interphase momentum transfer between the liquids and gasses. The physics for the sloshing assessment were considered to identify the main aspects of the inhomogeneous multiphase model. For numerical analysis of the sloshing, we conducted a sloshing simulation on the experimental data of the model scale to examine the validity of the results. The velocity of the sloshing flow was extended to the real scale and applied to a local two-way fluid structure interaction (FSI) analysis model. Structural strength evaluation of the LNG CCS by sloshing flow was performed by FSI analysis. Through the example of structural response analysis of Mark III type CCS, the results were discussed and effectiveness of the proposed structural response assessment model by sloshing was reviewed. [ABSTRACT FROM AUTHOR]

Due to the complexity of fluid–structure interactions (FSI), the majority of studies in the literature dealing with the sloshing problem are restricted to rigid tanks. This paper is devoted to a numerical investigation of the liquid sloshing behavior in a flexible tank subjected to external loading. A numerical methodology is proposed, taking into account the FSI problem by coupling two open-source codes: OpenFOAM for the fluid and FEniCS for the solid, using the preCICE library, a free library for fluid–structure interaction. The Arbitrary Lagrangian–Eulerian formulation is used for the two-phase flow system to solve the Navier–Stokes equations in the fluid domain using the finite volume method. Simultaneously, the linear-elastic equation of the structure is solved using the finite element method. An implicit coupling scheme is considered at the fluid–structure interface. The numerical methodology is validated by the results given in literature for harmonic excitation at different frequencies. Subsequently, an analysis of complex external loading, such as Gabor wavelets and earthquake ground motion, is conducted to highlight the significant impact of the wall flexibility on sloshing, as well as the influence of hydrodynamic forces on the structure's deformation. The proposed coupling methodology is robust and effective, it can be applied to all types of liquids and materials. A dataset of one of the studied cases is given as a supplement to the paper (Kha et al., 2024). [ABSTRACT FROM AUTHOR]

The sloshing phenomenon is an important field of fluid dynamics in liquid storage tanks under earthquake excitation. When the sloshing frequency gets close to the liquid tank’s natural frequency, the resulting resonance could lead to instability and even damage to structures, followed by catastrophic economic losses and environmental damages. As passive control devices, baffles are a place for liquid energy dissipation. This study uses annular and horizontal baffles to evaluate the baffles’ relative effectiveness on the elevated storage tanks’ dynamic response. The analysis results are compared with those of elevated storage tanks with no baffles. The flexible and rigid storage tank analysis is examined here, where half of the tank height is filled with liquid. The structural interaction between the liquid, the (horizontal and annular) baffle, and the elevated storage tank affected by seismic action are investigated using Abaqus software. The results confirm that using the baffles, the maximum base shear force in flexible and rigid elevated storage tanks decreases as much as 26.43% and 31.90%, respectively, and the maximum hydrodynamic pressure reduction in the tank is 50.1%.

The sloshing phenomenon of liquid in a partially filled tank mounted rigidly within a barge exposed to regular wave field has been considered for numerical investigation. This paper details the numerical scheme developed in time domain to study the interaction of wave induced barge motion with sloshing oscillations in a partially filled container. The sloshing time history results obtained from the numerical scheme adopted are validated with experimental measurements of Nasar et al. (2008) The harmonics present in the sloshing oscillation for the liquid fill levels (25%, 50% and 75%) have been analyzed. [ABSTRACT FROM AUTHOR]

We report in this work a numerical analysis of the sloshing of a squared tank partially filled with a domestic vegetable oil. The tank is subject to controlled motions with a shake table. The free-surface evolution is captured using ultrasonic sensors and an image capturing method. Only confirmed data within the error range is reported. Filling depth, imposed amplitude and frequency effects on the sloshing wave pattern are specifically evaluated. The experiments also reveal the nonlinear wave behavior. The numerical model is based on a stabilized finite element method of the variational multi-scale type. The free-surface is captured using a level set technique developed to be used with adaptive meshes in Arbitrary Lagrangian–Eulerian framework. The numerical results are compared with the experiments for different sloshing conditions near the first sloshing mode. The simulations satisfactorily match the experiments, providing a reliable tool for the analysis of this kind of problems. [ABSTRACT FROM AUTHOR]

Abstract Numerical studies on the seismic behavior of a typical spherical liquid storage tank, equipped with conventional braces or retrofitted with passive energy dissipation devices, are presented. Three energy dissipation systems, in the form of diagonal braces, are investigated: non-linear viscous dampers and buckling-restrained and friction struts. All numerical analyses are performed by means of a detailed finite element model, considering the exact geometry of the elevated steel tank structure, the fluid-structure interaction effects for an arbitrary level of fluid filling, as well as the non-linearities introduced by the various bracing systems. Representative results for base shear forces, vertical displacements of the fluid content due to sloshing and displacements at characteristic locations of the retrofitted spherical tank are presented. The benefits introduced by each of the dissipative bracing systems used in this study are identified and discussed in comparison to the dynamic characteristics and the seismic response of the original spherical tank, fitted with a conventional bracing system. Highlights • Energy dissipation devices are used for the seismic retrofit of a spherical liquid storage tank. • The seismic behavior of the structure improved by reducing the stress levels by about 80%. • Sloshing affects substantially the dynamic characteristics of the structure-fluid system. [ABSTRACT FROM AUTHOR]

Abstract A numerical study of the base-isolated ground-supported cylindrical liquid storage tank is carried out using finite element method (FEM). The coupled acoustic-structural (CAS) approach in the FEM is used for the analysis of the base-isolated tanks with rigid and flexible walls with varying parameters. Base isolation systems used in the present study are laminated rubber bearing (LRB) and friction pendulum system (FPS). The effects of aspect ratio (liquid height to radius) of the tank, and the isolation time period on the seismic response of the base-isolated tank is considered for investigation. For this study, the broad and slender tanks with three different isolation time periods are considered, which exhibit their relative flexibility. The sloshing displacement, base shear, hydrodynamic pressure, and bearing displacement responses are evaluated for three-dimensional (3-D) rigid and flexible tanks subjected to bi-directional components of earthquake ground motions. Moreover, the FE results are compared with the commonly used mechanical lumped-mass model of the base-isolated tank. The results show that as the time period of the isolator increases, i.e. increased flexibility, the base shear response is considerably reduced in both the rigid and flexible, broad and slender tanks. The reduction in the impulsive component causing base shear is more as compared to the convective (sloshing) component in the base-isolated tanks. The sloshing displacement increases with increase in the time period of the base isolation systems in both the rigid and flexible tanks. The impulsive hydrodynamic pressure along the tank wall is reduced with introduction of the isolation systems and the reduction is significantly more in case of the flexible isolators. The bearing displacement increases with increase in the time period of the isolation system adopted. Highlights • Finite element (FE)-based simulations using the coupled acoustic-structural (CAS) approach for fluid-structure interaction (FSI) in tank. • Sloshing, base shear, and hydrodynamic pressures induced in 3-D ground-supported cylindrical rigid and flexible base-isolated tanks. • Bi-directional earthquake ground motion components affecting seismically base-isolated and non-isolated tanks. [ABSTRACT FROM AUTHOR]

Spherical storage tanks are widely used for various types of liquids, including hazardous contents, thus requiring suitable and careful design for seismic actions. On this topic, a significant case study is described in this paper, dealing with the dynamic analysis of a spherical storage tank containing butane. The analyses are based on a detailed finite element (FE) model; moreover, a simplified single-degree-of-freedom idealization is also set up and used for verification of the FE results. Particular attention is paid to the influence of sloshing effects and of the soil-structure interaction for which no special provisions are contained in technical codes for this reference case. Sloshing effects are investigated according to the current literature state of the art. An efficient methodology based on an "impulsive-convective" decomposition of the container-fluid motion is adopted for the calculation of the seismic force. With regard to the second point, considering that the tank is founded on piles, soil-structure interaction is taken into account by computing the dynamic impedances. Comparison between seismic action effects, obtained with and without consideration of sloshing and soil-structure interaction, shows a rather important influence of these parameters on the final results. Sloshing effects and soil-structure interaction can produce, for the case at hand, beneficial effects. For soil-structure interaction, this depends on the increase of the fundamental period and of the effective damping of the overall system, which leads to reduced design spectral values. [ABSTRACT FROM AUTHOR]

Cylindrical storage tanks are widely used for various types of liquids, including hazardous contents, thus requiring suitable and careful design for seismic actions. The study herein presented deals with the dynamic analysis of a ground-based horizontal cylindrical tank containing butane and with its safety verification. The analyses are based on a detailed finite element (FE) model; a simplified one-degree-of-freedom idealization is also set up and used for verification of the FE results. Particular attention is paid to sloshing and asynchronous seismic input effects. Sloshing effects are investigated according to the current literature state of the art. An efficient methodology based on an "impulsive-convective" decomposition of the container-fluid motion is adopted for the calculation of the seismic force. The effects of asynchronous ground motion are studied by suitable pseudo-static analyses. Comparison between seismic action effects, obtained with and without consideration of sloshing and asynchronous seismic input, shows a rather important influence of these conditions on the final results. [ABSTRACT FROM AUTHOR]

As more and more liquid carriers with huge size are manufactured to support the transportation demand of natural resources, risks such as local deformation or even damage of cargo containment systems resulting from sloshing phenomenon subsequently increase, and it's necessary to take the elasticity of tank walls into account in the researches of sloshing phenomenon. In present paper, we numerically studied the interaction between liquid sloshing flow and elastic bulkheads of liquid carrier by fully Lagrangian particle method, MLParticle-SJTU solver, which is an in-house solver developed based on the moving particle semi-implicit (MPS) method. Coupled with the finite element method (FEM), the MLParticle-SJTU solver is extended to numerical analysis of elastic structural response due to the impact loads of sloshing flows. To validate the feasibility of the MPS-FEM coupled solver in dealing with fluid structure interaction (FSI) problems, a benchmark of dam-breaking flow interacting with elastic lateral wall is studied firstly and results show good agreement with published data. Then, the sloshing phenomenon in an elastic tank is numerically investigated. By varying the Young's modulus of tank walls, interesting characteristics regarding evolutions of free surface, variation of impact pressures, dynamic responses of the structures in both time and frequency domains are presented. [ABSTRACT FROM AUTHOR]

A computational model is described and implemented in this work to analyze the performance of a ferrofluid based electromagnetic energy harvester. The energy harvester converts ambient vibratory energy into an electromotive force through a sloshing motion of a ferrofluid. The computational model solves the coupled Maxwell’s equations and Navier-Stokes equations for the dynamic behavior of the magnetic field and fluid motion. The model is validated against experimental results for eight different configurations of the system. The validated model is then employed to study the underlying mechanisms that determine the electromotive force of the energy harvester. Furthermore, computational analysis is performed to test the effect of several modeling aspects, such as three-dimensional effect, surface tension, and type of the ferrofluid-magnetic field coupling on the accuracy of the model prediction. [ABSTRACT FROM AUTHOR]

A technique to study effect of various baffles on liquid oscillations in partially filled rigid toroidal tanks is first developed by extending the semi-analytical scaled boundary finite element method (SBFEM), which utilizes the advantages of both the boundary element (BEM) and finite element methods (FEM). As found in the BEM, only the boundary is discretized to reduce the space by one, and no fundamental solution is needed unlike the BEM. The calculated liquid domain is divided into several simple sub-domains so that the liquid velocity potential in each liquid sub-domain becomes the class C 1 with continuity boundary conditions. Based on the linear potential theory and weighted residual method, the semi-analytical solutions of the liquid velocity potential corresponding to each sub-domain are obtained by means of SBFEM, where the geometry of each sub-domain is transformed into scaled boundary coordinates, including the radial and circumferential coordinates by using a scaling centre, and the finite-element approximation of the circumferential coordinate yields the analytical equation in the radial coordinate. By discretizing the flow boundaries, the integral equation governed on the boundary is formulated into a general matrix eigenvalue problem. Based on the eigenvalue problem and multimodal method, an efficient methodology is adopted to computer the sloshing masses and sloshing force. Accuracy, simple and fast numerical computations are observed by the convergence study, and excellent agreements have been achieved in the comparison of results obtained by the proposed approach with other methods. Meanwhile, several baffle configurations are considered including the horizontal bottom-mounted and surface-piercing ring baffles as well as their combination form, bottom-mounted and surface-piercing ring baffles as well as their combination, and free surface-touching baffles. The effects of baffled arrangement, the ratio b / a of elliptical cross section, liquid fill level, and baffles' length upon the sloshing frequencies, the associated sloshing mode shapes and sloshing forces are investigated in detail and some conclusions are outlined. The results show that the present method allows for the simulation of complex 3D sloshing phenomena using a relative small number of degrees of freedom while the mesh consists of two-dimensional elements only. [ABSTRACT FROM AUTHOR]

Scaled models are important in marine engineering since it is prohibitive testing of actual ship size. However, the crashworthiness analysis on marine structures in reduced scale is not an ordinary research topic given the scientific and technical limitations surrounding this type of practice. It is reported here a series of collision tests of marine structures in reduced scale. These experiments are used to validate the subsequent finite element analysis. The scaled shiplike specimens were built from metallic thin-walled structures in a reduced scale of 1:100 taken into account shipbuilding processes analogous to that used in real scale marine structures. The experiments include scaled collision tests of a T cross-section beam, head-on collision of an oil tanker against a rigid wall, ship grounding and collision between two oil tankers. It is discussed the influence of different numerical and experimental aspects inherent to experimental impact tests of marine structures. This includes the mechanical properties of the materials, slight misalignments in test arrangements, failure criteria, weld joints and sloshing effect of ship cargo. These aspects are thoroughly analyzed and discussed here so bringing new insights in the modeling of marine structures subjected to collision events using reduced scale experiments. [ABSTRACT FROM AUTHOR]

A dynamic mesh-adaptation algorithm based on an unstructured mesh was used to solve sloshing problems by a finite element method. The free surface evolution of sloshing with a low filling ratio is so violent that a local mesh coarsening/refinement (LCR) technique can be effectively used to resolve the flow field near the interface of two immiscible fluids. Since an implicit discretization method was employed to solve the incompressible Navier-Stokes equations, an assembled global matrix was generated using a dynamic compressed sparse row (CSR) method. The proposed algorithm was validated by comparing the simulation results with those of a non-adaptive method with respect to wall impact pressures and mass conservation. Numerical results showed that relative mass error strongly depends on mesh resolution near the interface. Results of adaptive simulations were found to be comparable with those of non-adaptive simulations only if a similar mesh resolution was used near the interface. Moreover, adaptive simulations were about two times faster than the non-adaptive ones. The effect of the adaptive zone and smoothing zone on the impact pressure was also examined for the proposed algorithm. [ABSTRACT FROM AUTHOR]

Fluid-structure interaction (FSI) problems caused by fluid impact loads are commonly existent in naval architectures and ocean engineering fields. For instance, the impact loads due to non-linear fluid motion in a liquid sloshing tank potentially affect the structural safety of cargo tanks or vessels. The challenges of numerical study on FSI problems involve not only multidisciplinary features. but also accurate description of non-linear free surface. A fully Lagrangian particle-based method , the moving particle semi-implicit and finite element coupled method (MPS-FEM), is developed to numerically study the FSI problems. Taking into account the advantage of the Lagrangian method for large deformations of both fluid and solid boundaries, the MPS method is used to simulate the fluid field while the finite element method (FEM) to calculate the structure field. Besides, the partitioning strategy is employed to couple the MPS and FEM modules. To validate accuracy of the proposed algorithm, a benchmark case is numerically investigated. Both the patterns of free surface and the deflections of the elastic structures are in good agreement with the experimental data. Then, the present FSI solver is applied to the comparative study of the mitigating effects of rigid baffles and elastic baffles on the sloshing motions and impact loads. [ABSTRACT FROM AUTHOR]

Reliable strength assessment of the Liquefied Natural Gas (LNG) cargo containment system under the sloshing impact load is very difficult task due to the complexity of the physics involved in, both in terms of the hydrodynamics and structural mechanics. Out of all those complexities, the proper selection of the design sloshing load which is applied to the structural model of the LNG cargo containment system, is one of the most challenging one due to its inherent randomness as well as the statistical analysis which is tightly linked to the design sloshing load selection. In this study, the response based strength assessment procedure of LNG cargo containment system has been developed and proposed as an alternative design methodology. Sloshing pressure time history, measured from the model test, is decomposed into wavelet basis function targeting the minimization of the number of the basis function together with the maximization of the numerical efficiency. Then the response of the structure is obtained using the finite element method under each wavelet basis function of different scale. Finally, the response of the structure under entire sloshing impact time history is rapidly calculated by synthesizing the structural response under wavelet basis function. Through this analysis, more realistic response of the system under sloshing impact pressure can be obtained without missing the details of pressure time history such as rising pattern, oscillation due to air entrapment and decay pattern and so on. The strength assessment of the cargo containment system is then performed based on the statistical analysis of the stress peaks selected out of the obtained stress time history.

The aim of this work is to carry out numerical simulations in the time domain of seakeeping problems taking into account internal flow in tanks, including sloshing. To this aim, a Smooth Particle Hydrodynamics (SPH) solver for simulating internal flows in tanks is coupled in the time domain to a Finite Element Method (FEM) diffraction–radiation solver developed for seakeeping problems. Validations are carried out comparing against available experimental data. Good agreement between obtained numerical results and experimental data is found. [ABSTRACT FROM AUTHOR]

Baffles are used effectively to reduce the sloshing response of liquid in the liquid storage containers. This study is aimed at analysis of transient lateral sloshing in a partially-filled cylindrical tank with multi baffles including floating circular baffle, wall-mounted ring baffle, floating ring baffle and their combination form, and those baffles with inclination using a coupled multimodal method and scaled boundary finite element method (SBFEM). Slosh frequencies and mode shapes are initially estimated using the extending semi-analytical SBFEM by applying the linearized free surface boundary condition using the zoning method, where the liquid domain is firstly divided into several simple sub-domains so that the liquid velocity potential in each sub-domain has continuous boundary conditions of class C 1 . As a key point, a new type of local co-ordinate system for SBFEM with axisymmetric geometry is presented for each sub-domain. Based on the multimodal method, significant improvement in computational time is achieved by reducing the generalized eigenvalue problem to a standard one involving only the velocity potentials on the two-dimensional half free-surface length. The generalized coordinates of the free-surface oscillations under a lateral excitation are then obtained from superposition of the natural slosh modes. The sloshing mass and lateral slosh force are also formulated in terms of the generalized coordinates and hydrodynamic coefficients. The validity of the model is examined through comparisons with available other solutions, and the results show that the present method has higher accuracy and efficiency with a very small number of degrees of freedom for the simulation of the complex sloshing problem partly-filled laterally-excited cylindrical tanks. It is also shown that consideration of only the first sloshing mass is adequate to represent the dynamic behavior of the liquid container quite accurately. The effects of liquid fill level, baffled arrangement and length of those baffles upon the sloshing masses and sloshing forces are discussed in detail. [ABSTRACT FROM AUTHOR]

A hierarchical finite element is developed for the free vibration analysis of a liquid in a rigid cylindrical tank with or without a free surface. It is a hierarchical quadrilateral element and has the advantage that the hierarchical mode number is allowed to vary independently of direction. Liquid behavior in tanks with large aspect ratios can therefore be solved very accurately by using a higher hierarchical mode number in the longer direction than in the shorter one. Furthermore, it is possible to idealize the liquid by using only one element. The solution can therefore be obtained to any desired degree of accuracy simply by increasing the hierarchical mode number. In this method, the liquid behavior is described by the displacements alone. The pressure and velocity potential are not considered as unknowns. The results are compared with other methods and show good agreement. [ABSTRACT FROM AUTHOR]

A numerical model is developed for investigation of coupled dynamics of fuel contained elastic launch vehicles in planar atmospheric flight. Finite element method along with the linear quasi-steady piston aerodynamic theory is used for developing an aeroelastic model. A reduced order boundary element model is used for modeling the liquid sloshing in tanks. The interaction of sloshing and aeroelasticity is studied using stability analysis of the coupled system. Results show that the slosh–aeroelastic coupling in an elastic launch vehicle occurs for low tank filling ratios and may lead to decreasing the system damping. Due to more interactions between the slosh and rigid body modes, larger damping values of the rigid body mode and lower slosh frequencies are found for an elastic vehicle compared with a rigid vehicle. It is also shown that the slosh–aeroelastic interaction is increased as the slosh inherent damping decreases. [ABSTRACT FROM AUTHOR]

We aim to provide a finite element analysis for the elastoacoustic vibration problem. We use a dual-mixed variational formulation for the elasticity system and combine the lowest order Lagrange finite element in the fluid domain with the reduced symmetry element known as PEERS and introduced for linear elasticity in [1]. We show that the resulting global nonconforming scheme provides a correct spectral approximation and we prove quasi-optimal error estimates. Finally, we confirm the asymptotic rates of convergence by numerical experiments. [ABSTRACT FROM AUTHOR]

The aim of this paper is the examination of the dynamic of fluid in tank. Dynamic fluid analysis will be performed by finite element method (FEM). As a tool for FEM analysis will serve the commercial software ANSYS Workbench FLUENT, which is often used in technical practice because of its fast and effective means of FEM model creation. A case study of a fuel tank partially filled with fluid was simulated in this paper using Volume of Fluid (VOF) multiphase model. In this paper, a part of the project which aims to develop a computer aided methodology for developing/designing of the fuel tanks based on static and dynamic analysis is presented. Further research can be undertaken in improving the optimum configuration and dimensions of the baffles in order to further reduce the sloshing in the fuel tank. [ABSTRACT FROM AUTHOR]

A semi-analytical scaled boundary finite-element method (SBFEM) is firstly extended to study the effects of the T-shaped baffle on liquid sloshing in horizontal elliptical tanks. The proposed method is based on the finite-element technology and gains the advantages of the boundary element method as well. Only the boundary is discretized reducing the spatial discretization by one, no fundamental solution is required and singularity problems can be modeled rigorously. Based on linear potential theory, the formulations (using new variational principle formulation) and the solutions of SBFEM equations for the sloshing problems are derived in details. As a key point, the solution for the inclusion of flow velocity along the baffles, which is called the side-faces of bounded domain in SBFEM, is also expressed in details. The accuracy, simplicity and convergence of the present method are demonstrated via numerical examples, and excellent agreement with the other method is observed. Meanwhile, three T-shaped baffled configurations are considered including surface-piercing baffle, bottom-mounted baffle and their combination form, and Y-shaped baffled configuration evolved from that of T-shaped baffle has been taken into consideration as well. The effects of liquid fill level, baffled arrangement and length of those baffles upon the sloshing frequencies, the associated sloshing mode shapes and sloshing wave height are investigated in details. The results also show that the present method has strong ability to resolve singularity problems analytically by choosing the scaling center at the tip of the baffles and allows for the simulation of complex sloshing phenomena using a very small number of degrees of freedom while the mesh consists of one-dimensional elements only. [ABSTRACT FROM AUTHOR]

Floating roofs are used on large cylindrical storage tanks to prevent evaporation of oil. The single-deck floating roof considered herein consists of a thin circular plate, referred to as a "deck", attached to a buoyant ring with a hollow rectangular cross section referred to as a "pontoon". The deck plate is deformed to be created waves and is subjected to cyclic bending due to the wind load. Since this leads to the initiation of fatigue cracks at the welded joints, it is important to understand the wave characteristics in the deck plate. The authors have previously reported a computational fluid dynamics (CFD) analysis of a cylindrical storage tank under a wind load. The present paper describes an axisymmetric finite element analysis of the sloshing response of a single-deck floating roof on a cylindrical storage tank using the previous CFD results as the load conditions. It is assumed that the liquid is incompressible and inviscid, the roof exhibits linear elastic behavior, and the sidewalls and bottom of the tank are rigid. The effect of the wind velocity on the frequency and amplitude of vibrations in the deck plate is investigated. As a result, the relation between the amplitude of vibration and the wind velocity is shown. The predominant period of bending stress vibration of the deck plate is shorter than that of the waves.

A viscous fluid model based on non-inertial reference system is developed for the problem of liquid sloshing in rectangular tank with/without baffles. The accuracy of the numerical model is validated against available theoretical solutions, experimental data and numerical predictions by linear and nonlinear potential flow models and different Navier–Stokes solvers. The numerical examinations indicate that the dissipative effects have significant influence on the sloshing responses in both non-baffled and baffled tanks. The sloshing responses that are associated with the natural frequencies can be finally damped out due to the physical dissipations, while they are entirely retained in the potential solutions, which accounts for the general over-predictions of sloshing amplitudes by the potential flow theory. The sloshing in baffled tank involves more dissipation due to the stronger vortical flow. The resonant frequency and amplitude are highly dependent on the baffle width and position. The relative sloshing amplitudes around the resonant condition are found to decrease with the excitation amplitude in a power law. The necessity of using viscous fluid model for sloshing predictions is addressed. The extremely long numerical computations have to be carried out in order to obtain convincing stable solutions, especially for the weakly damped sloshing motion. [ABSTRACT FROM AUTHOR]

The article investigates the seismic response of a cylindrical liquid storage tank under tri-directional components of earthquake ground motions using coupled-structural finite element simulation. The study describes the tank modeling of the interaction, examines the time history responses of sloshing displacement and base shear and compares these with the bi-directional horizontal components of the earthquake ground motions. It also observes the hydrodynamic pressure distribution.

The aim of this paper is to analyze an elastoacoustic vibration problem employing a dual-mixed formulation in the solid domain. The Cauchy stress tensor and the rotation are the primary variables in the elastic structure while the standard pressure formulation is considered in the acoustic fluid. The resulting mixed eigenvalue problem is approximated by a conforming Galerkin scheme based on the lowest order Lagrange and Arnold–Falk–Winther finite element subspaces in the fluid and solid domains, respectively. We show that the scheme provides a correct approximation of the spectrum and prove quasi-optimal error estimates. Finally, we report some numerical experiments. [ABSTRACT FROM AUTHOR]

This study presents a new model for predicting the response of a two-dimensional tuned liquid damper (TLD) tank with a variable fluid depth. A simple finite element method is presented, which is used to calculate the sloshing mode shapes. From the mode shapes, the equivalent mechanical properties of the sloshing fluid are estimated. Three tanks (flat-bottom, triangular-bottom, and circular-bottom), which have closed-form expressions for their equivalent mechanical properties are used to evaluate the model. The proposed model is in agreement with the closed-form expressions. Subsequently, a parametric study is conducted on tanks with a chamfered-bottom, boxed-bottom, and ramped-bottom to assess how their properties change as the shape of the tank bottom is altered. The model provides TLD designers with greater flexibility when selecting a tank shape. Moreover, the model could be used to optimize the shape of a TLD tank to maximize its performance for a given liquid mass, allowing construction cost savings to be realized. [ABSTRACT FROM AUTHOR]

Finite element computation and experimental validation of sloshing in rectangular tanks near the primary and secondary resonance modes are presented. In particular, 2D free-surface evolution is studied. The computational analysis is based on solving the Navier-Stokes equations of incompressible flows with a monolithic solver that includes a stabilized formulation and a Lagrangian tracking technique for updating the free surface. The time-dependent behavior of the numerical and experimental wave heights at different control points are compared, where the experimental data is collected using ultrasonic sensors and a shake table that controls the motion of the rectangular container. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model is developed based on coupled boundary element-finite element methods (BEM-FEM) to minimize liquid sloshing pressure in trapezoidal tank with different sidewall angles. Different geometric shapes such as rectangular, cylindri-cal, elliptical, spherical and circular conical have already been studied for ship storage tanks by other researchers. In this paper, a new arrangement, i.e., trapezoidal containers is suggested for liquid storage tanks. The tank shape is optimized based on sloshing pressures and forces for a range of frequencies and amplitudes of sway motion and tank configuration. Fluid is considered to be incompressible and inviscid. Therefore, Laplace equation and nonlinear free surface boundary conditions are used to model the sloshing phenomenon. The results validated using available data showed that a new arrangement of trapezoidal storage panels has a better efficiency against sloshing phenomenon than the conventional rectangular tanks. [ABSTRACT FROM AUTHOR]

The seismic behavior of partially filled rigid rectangular tank with bottom-mounted submerged block is numerically simulated. Six different ground motions characterized on the basis of low-, intermediate-, and high-frequency contents are used to investigate the dynamic behavior of tank-liquid-submerged block system. A velocity potential-based Galerkin finite element model is developed for the analysis. The effect of submerged block on impulsive and convective response components of hydrodynamic behavior manifested in terms of base shear, overturning base moment, and pressure distribution along the tank wall as well as the block wall has been quantified. [ABSTRACT FROM AUTHOR]

ABSTRACT A hybrid analytical and FEM is proposed to investigate the nonlinear sloshing in a floating-roofed oil storage tank under long-period seismic ground motion. The tank is composed of a rigid cylindrical wall and a flat bottom, whereas the floating roof is treated as an elastic plate undergoing large deflection. The contained liquid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The method of analysis is based on representation of the liquid motion by superposing the analytical modes that satisfy the Laplace equation and the rigid wall and bottom boundary conditions. The FEM is then applied to solve the remaining kinematic and dynamic boundary conditions at the moving liquid surface coupled with the nonlinear equation of motion of the floating roof. This requires only the discretization of the liquid surface and the floating roof into finite elements, thus leading to a computationally efficient and accurate method compared with full numerical analysis. As numerical examples to illustrate the applicability of the proposed method, two oil storage tanks with single-deck type floating roofs damaged during the 2003 Tokachioki earthquake are studied. It is shown that the nonlinear oscillation modes with the circumferential wave numbers 0, 2 and 3 caused by the finite liquid surface elevation as well as the membrane action due to large deflection of the deck produce excessively large stresses in the pontoon, which may cause the catastrophic failure of pontoon followed by the submergence of the roof. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the dynamic behavior of cylindrical open top ground-supported water tanks is investigated. The main focus of this study is to identify the major parameters affecting the dynamic response of such structures and to address the interaction between these parameters. Examined parameters include sloshing of liquid free surface, tank wall flexibility, vertical ground acceleration, tank aspect ratio, and base fixity. In addition, the dynamic results obtained from the rigorous finite element (FE) method are compared with those recommended by current practice and thereby the adequacy of current code provisions in estimating the dynamic response of liquid-filled cylindrical containers is investigated. The validity of the proposed FE method is verified by comparing the results with those calculated from well-proved analytical methods available in the literature. Both time history and free vibration analyses are carried out on concrete tank models with different aspect ratios. Time history response of both rigid and flexible tanks having different conditions at the base; fixed and hinged under both horizontal and vertical components of earthquake is obtained using the direct integration method. Based on the computed results, recommendations on seismic design of cylindrical liquid containers are made. It is concluded that the current design procedure in estimating the hydrodynamic pressure is too conservative. [Copyright &y& Elsevier]

In the present study a novel modeling approach is presented to solve the combined internal sloshing and sea-keeping problem. The model deals with interesting effects arising due to the coupled interaction between the sloshing in partially filled containers of several geometries and the ship motion. The study is very important for the liquid cargo carrier operating in rough sea or under different environmental conditions. The resulting slosh characteristics that include transient pressure variation, free surface profiles and hydrodynamic pressure over the container walls have been reported in this study. In addition, the effects of coupled ship response and sloshing on ship motion parameters have also been investigated. The equations of motion of fluid, considered inviscid, irrotational, and partially compressible, are expressed in terms of the pressure variable alone. A finite difference-based iterative time-stepping technique is employed to advance the coupled solution in the time domain. Several parameters of interest, including the container parameters, level of liquid, thrusters modeling and some important environmental factors are investigated. [ABSTRACT FROM AUTHOR]

Increasing computing power has made it not only possible but also highly practical to apply the Monte Carlo technique to a large variety of engineering problems. In this paper, the Monte-Carlo technique is used for calculating the statistical properties of inviscid incompressible fluid partially filled in a rectangular tank. First, uncertainty in the slosh and acoustic modes is estimated considering the gravitational forces and bulk modulus of the fluid as random variables. Second, uncertainty in the vibration frequencies in the rectangular tank with a baffle fixed inside it is studied. Later, linear slosh wave response analysis is carried out considering uncertainty in the external forcing function. Numerical results of the dynamic analyses show that the local minima and maxima of the slosh wave heights shift in time due to uncertainties in the frequency, whereas the local minima and maxima of the slosh wave heights change in magnitude only at a given time due to uncertainties in the amplitude. It is also found that the baffle, which is typically used to create desirable mode shifts, can also lead to increase in dispersion of the slosh and acoustic frequencies due to uncertainty. [ABSTRACT FROM PUBLISHER]

Abstract: This study investigates the coupling effects of six degrees of freedom in ship motion with fluid oscillation inside a three-dimensional rectangular container using a novel time domain simulation scheme. During the time marching, the tank-sloshing algorithm is coupled with the vessel-motion algorithm so that the influence of tank sloshing on vessel motions and vice versa can be assessed. Several factors influencing the dynamic behavior of tank–liquid system due to moving ship are also investigated. These factors include container parameters, environmental settings such as the significant wave height, current velocity as well as the direction of wind, wave and flow current acting on the ship. The nonlinear sloshing is studied using a finite element model whereas nonlinear ship motion is simulated using a hybrid marine control system. Computed roll response is compared with the existing results, showing fair agreement. Although the two hull forms and the sea states are not identical, the numerical result shows the same trend of the roll motion when the anti-rolling tanks are considered. Thus, the numerical approach presented in this paper is expected to be very useful and realistic in evaluating the coupling effects of nonlinear sloshing and 6-DOF ship motion. [Copyright &y& Elsevier]

Abstract: A three-dimensional soil–structure–liquid interaction is numerically simulated using the finite element method in order to analyze the seismic behavior of partially filled concrete rectangular tanks subjected to different ground motions. In this paper, the effect of earthquake frequency content on the seismic behavior of fluid rectangular tank system is investigated using four different seismic motions. A simple model with viscous boundary is used to include deformable foundation effects as a linear elastic medium. This method is capable of considering both impulsive and convective responses of liquid-tank system. Six different soil types defined in the well-recognized seismic codes are considered. The sloshing behavior is simulated using linear free surface boundary condition. Two different finite element models corresponding with flexible shallow and tall tank configurations are studied under the effects of longitudinal, transversal and vertical ground motions. By means of changing the soil properties, comparisons are made on base shear, base moment and sloshing responses under different ground motions. It is concluded that the dynamic behavior of the fluid–tank–soil system is highly sensitive to frequency characteristics of the earthquake record. [Copyright &y& Elsevier]

Sloshing in LNG membrane tanks may cause large pressures on the tank structure. To keep the cargo at the required low temperature, the tank structure is covered with an insulation, which has a much less strength than steel. The containment system is a very complex structure, which consists of different materials and requires a careful analysis with due consideration of the load process and dynamic effects in the response. The structural response of the membrane tank wall is investigated in this paper by finite element analyses. First, a modal composition of the structural response is studied. It is shown that many modes contribute to the response, which makes it difficult to establish the simplified DLF approach. The dynamic structural response to a typical sloshing impact is investigated in detail. An important observation is that, although the containment system has traditionally been modeled with a rigid support, the steel plate that supports the insulation may be flexible under the relevant load conditions. It is shown that the flexibility of the steel plate causes significant stress variation in the insulation. Different response patterns of the Mark III containment system are presented, and mechanisms that cause large stress concentrations and different response patterns in the static and dynamic cases are discussed. The scaling issue in view of the response is also investigated. Various scaling formulations may apply in post-processing sloshing experiments. While the Froude law yields conservative scaling for pressure magnitude, its conservatism for scaling the time needs to be investigated in view of the relevant dynamic response. By analyzing the structural response to the differently scaled loads, it is found that the Froude approach is conservative, but the scatter of results may be very large. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the treatment of methods for a preliminary safety assessment of next generation nuclear power plant (of Liquid Metal cooled Fast Reactor types) structures. As an example, it was considered the European Lead-cooled System (ELSY) international project response under a reference design basis earthquake (Safe Shutdown Earthquake-SSE) excitation, taking into account also the main isolating device effects in order to increase the reactor safety. This study is intended to analyze the structural effects of a reference SSE by means of an appropriate dynamic FEM code, for possible geometries of both not isolated and isolated ELSY containment building foundation cases. A great attention should be focused too on the arisen hydrodynamic forces and coupling effects between fluid and structures (sloshing phenomenon) that may impair the structures resistance and/or operating capabilities. The obtained numerical results were critically analysed with the intent also to contribute to a step of the safety optimization of the mentioned systems. [Copyright &y& Elsevier]