Sloshing Response Research Articles

Experimental investigation on the three-dimensional liquid sloshing behavior in an offshore circular cylindrical container

A series of experimental cases are conducted to explore the three-dimensional sloshing response in a cylindrical container under lateral excitation. When the forcing frequency is in the vicinity of the resonance frequency of the lowest asymmetric mode (1, 1), three different wave regimes are observed: planar, irregular and swirling. The results of the wave regimes at the second asymmetric mode (1, 2) exhibit a number of similarities to those at the mode (1, 1), such as the generation of irregular mode and swirling mode at the forcing frequency close to the resonance frequency of mode (1, 2). The present experiments also exhibit some spectacular phenomena that are unique to the resonant sloshing at the mode (1, 2). In particular, when the sloshing wave builds up sufficient energy, the energy will be transferred to adjacent natural modes, i.e., (3, 1) and (2, 2). As a consequence, the motion of the sloshing wave is dominated by three natural modes and exhibits very complicated wave patterns.

An improved macroscopic model for sloshing flow-combined porous structure interaction

The design of the aquaculture tank system is important for fish survival, as it directly affects the behavior of farmed fish. To avoid violent liquid sloshing, this study proposes a side-mounted bracket-shaped perforated baffle and a special porous layer to explore their anti-sloshing performance. A macroscopic computational fluid dynamics (CFD) method, applicable to the combined porous structure, is developed by introducing the volume-averaged porous media theory, with corresponding experimental tests conducted. In this study, the macroscopic CFD method is first achieved to solve the fluid force on the perforated baffle by reasonably predicting the momentum flux through the porous surface. The microscopic model is also established to further verify the reliability of our proposed macroscopic model. The amplitudes of the free water surface and sloshing loads are adopted to assess the sloshing response. In addition, an index referred to as area-weighted-average velocity is introduced to quantify the kinetic energy. Results reveal that the established macroscopic model reliably replicates the free water surface and sloshing loads and greatly improves computational efficiency. Moreover, the high-frequency component of the wave energy is more easily dissipated, thus the transfer of energy from low frequency to high frequency resulting from the porous structure enhances its anti-sloshing performance, while conversely, the performance is weakened; the suppressing performance of the porous structure is closely related to the filling depth and excitation frequency, which dominate the frequency components of the sloshing behavior.

The Effect of Nonlinear Sloshing Response of Water on Seismic Behavior of Reinforced Concrete Elevated Water Tanks

In this study, the fluid-structure interactive behavior by using the Westergaard approach and the Smoothed Particle Hydrodynamics (SPH) method of a 1000 m3 reinforced concrete (RC) elevated water tank under different seismic activities i.e., Kocaeli, Van, Kahramanmaraş and Kobe earthquakes was investigated. In the SPH method, the resulting hydrodynamic pressures were applied to the interior of the wall of the structure as an external force which is made as mass additions to the tank walls in Westergaard approach. With the help of software developed, the load carrying system of the elevated water tank was modeled using the MATLAB Partial Differential Equation Toolbox (PDE) software, based on the finite element method, and its verification was made by comparing with ANSYS software model. Dynamic condensation method was used to perform time history analyses for the cited earthquakes. The time-dependent solutions of partial differential equations are solved with the help of ODE45 functions based on Runge-Kutta method, by arranging the equation of motion in state-space format. The cited tank was analyzed linearly under different seismic activities for empty, half-filled (50%) and full-filled (100%) cases and the obtained results were compared with each other. It has been concluded that considering nonlinear behavior of the fluid during the earthquake with the SPH method provided consistency with the real behavior of RC elevated water tanks and gave more realistic results than the traditional Westergaard approach.

Sloshing reduction with passive spring–mass baffles in partially filled containers

The potential for sloshing reduction of passive, moving baffles with translational motion constrained by springs is investigated numerically in partially filled containers. Simulations are based on the level-set formulation, considering water as the liquid under study and a baffle made of aluminum; this selection allows for direct validation of the model against experimental and analytical data. Depending on the filling ratio V∈(0,1), which simply measures the volume of liquid relative to the total container size, one can find an optimal spring stiffness K(V) that minimizes the kinetic energy and decay time of the sloshing response when subjected to a pulse-like acceleration. Results show that moving baffles significantly reduce sloshing compared to their fixed counterparts, with decreases up to 84.6% in decay time, τd. Frequency analyses for different V reveal one or two resonances in the range of 0.1–1.5Hz whose amplitudes are directly influenced (lowered) by K, analogous to the behavior of Tuned Mass Dampers. For potential applications, the selection of K should look for an adequate sloshing response over the entire range of V, and account for both quasi-static and harmonic excitation, conveniently weighted in accord with the expected operational loads.

Vibration response analysis of mobile liquid Pb-Bi micro-reactors under transportation with liquid sloshing

Mobile micro-reactors, which used the liquid lead–bismuth eutectic (LBE) as coolants, providing energy to remote regions had become a popular topic in nuclear energy due to their desirable characteristics, including inherent safety and modularity. However, the liquid sloshing effect in a reactor may exhibit fluid–structure interaction (FSI) coupling effects, which could have a significant impact on the relevant internal systems. And the ratio of coolant in liquid to solid form was correlated with the duration of heat dissipation. This paper aimed to investigate the liquid sloshing effect in a micro-reactor that was subject to vehicle vibrations, the objective was to provide recommendations for transportation scenarios involving various liquid sloshing. To achieve this, a full-vehicle dynamic model of the system was developed using multi-body dynamics. Additionally, MATLAB simulation software was utilized to simulate the road roughness loadings that the micro-reactor may encounter during transportation. Moreover, a finite element numerical model of the Mobile Micro-reactor had been developed in order to simulate the sloshing effect that occurred during transportation, the numerical models presented in this study were validated by comparing them with a previously-verified Housner model that involved a cylindrical tank. This study investigated the sloshing effects of the Mobile Micro-reactor under different liquid–solid ratios of coolant, internal component lengths, and liquid surface heights. The results indicated that the internal components within the reactor vessel can alleviate the sloshing effect. The solid ratios of liquid lead–bismuth coolant and the liquid surface height during transportation had an impact on the sloshing effect. These findings provided valuable insights for studying the sloshing response of on-board reactors during liquid sloshing transportation.

Effects of Higher Sloshing Modes on the Response of Rectangular Concrete Water Storage Tanks with Different Aspect Ratios to Near-Field Earthquakes

Near-field earthquakes have been shown to have different effects on structures than far-field events. This study examines the dynamic response of a rectangular concrete liquid storage tank with tapered walls to near-field ground motions, with particular emphasis on the effect of higher sloshing modes. The tank’s numerical modeling, calibrated using experimental results, was performed considering the tank’s wall flexibility. Seven selected near-field records were applied in each case, and the effects of the first five sloshing modes on the tank response at three different locations, including the corner, middle of the long wall, and middle of the short wall, were investigated. The effect of the earthquake incident angle on the tank’s response was also studied by applying major and minor horizontal earthquake components once along the longer and shorter tank walls, respectively, and vice versa. Results show that the tank corner may have a sloshing height up to 50% greater than the middle of the walls and that the maximum sloshing response is substantially influenced by the spectral acceleration value at the first sloshing period. Higher sloshing modes are found to affect the sloshing response, with a maximum R2 score of 0.95, depending on the excitation’s incidence angle.

Advantages and design of inerters for isolated storage tanks incorporating soil conditions

Inerter-based isolation systems are effective in providing seismic protection for storage tanks. However, the vibration control-oriented mechanism of inerter-based seismic isolation systems on the seismic response of liquid storage tanks remains unclear, with designs limited to rigid base assumptions. Moreover, the objective existence of the soil-structure interaction (SSI) is overlooked. This study contributes to a discovered advantage of the inerter-based isolation system, including the reduction of input energy and precise control of specific or multiple modes of sloshing heights. Furthermore, an advantageous feature-oriented optimal design for storage tanks with an inerter-based isolation system and with the incorporation of soil conditions is proposed in this study. Initially, an analytical model is developed, considering a storage tank with multi-mode sloshing responses and representing SSIs with frequency-dependent stiffness and damping coefficients. Stochastic response analysis is performed, leading to a novel formulation of multi-mode control and an empirical power equation that quantifies the input energy reduction effect. An advantageous feature-oriented optimal design framework, in which the SSI effect, tank geometric parameters, and inerter-based isolation system parameters are implemented, is established through comprehensive parametric analysis. The results demonstrate that the inerter-based isolation system can be intentionally designed to mitigate specific modes of sloshing height, with the inerter effectively reducing the input power of the entire tank. This study emphasizes the importance of incorporating the SSI effect in the seismic analysis and optimal design of inerter-based tanks. Particularly, the inerter-based isolation system designed assuming a rigid base cannot perform as expected due to the SSI effect, significantly resulting in larger seismic responses and energy dissipation burdens. The developed optimal design method guarantees a target base shear force and sloshing height regarding the considered soil condition.

Sloshing Response of an Aquaculture Vessel: An Experimental Study

The sloshing response is crucial to the design and operation of aquaculture vessels and affects the safety of the culture equipment and the efficiency of the culture operation. A 1/50 scaled model was utilized to investigate the coupled sloshing response characteristics of a novel aquaculture vessel in a wave basin. Two wave directions (beam and head wave) and two filling levels (81.5% and 47.4%) are taken into account. The time-domain and frequency-domain characteristics of the sloshing response under the linear regular wave and extreme operational sea state were investigated using regular wave tests and irregular wave tests, respectively. The sloshing mechanism in the aquaculture tanks is complicated, due to the coupling effect between external waves, ship motion, and internal sloshing. In linear regular waves, the wave frequency mode dominates the sloshing response, which is larger under beam wave conditions than under head wave conditions and larger under half load conditions than full load conditions. The irregular wave test results confirmed the regular wave test conclusions, but the sloshing response has stronger nonlinearity, higher natural modes appeared, and the amplitude of the higher natural modes is also relatively larger.

Numerical modelling of dual function tanks for fire suppression and tuned liquid damper applications

Exceeding serviceability limits due to wind-induced motions in tall buildings can cause discomfort for residents and adversely affect auxiliary building services, such as elevator operations. A tuned liquid damper (TLD) is an attractive type of dynamic absorber because of its simplicity and affordability. However, its dimensions and geometry can be limited by available floor space. Utilizing dual-purpose water tanks for both damping and fire suppression purposes can be a feasible resolution to fire code requirements and building motion control. Several design criteria need to be considered to accommodate the fire code requirements and the proper tuning of the TLD. Consequently, in this study, a TLD tank is fitted with a perforated floor to divide it into two compartments that allow water transmission to meet fire code requirements. However, the sloshing motion within the tank is complex and computationally expensive to capture when using traditional simulation models. This paper presents a 2D ISPH code equipped with a macro-level model to capture the effect of the perforated floor on the overall sloshing response of the tank. The model is first evaluated using existing results from previous studies on tanks with horizontal baffles. Next, the ISPH model is used to numerically model the perforated floor using the Ergun resistance (ER) macro-level model. In addition, the perforated floor is also explicitly micro-level modelled using rigid boundary particles to validate the proposed ER model. A numerical analysis is then conducted under different excitation amplitudes and frequencies, with both time history and frequency response results being presented. A structure-TLD model is subsequently used to capture the structure-TLD system response under random excitation. Results show that the ER model can efficiently model tanks with dual functions under both harmonic and random excitation and across a wide range of amplitudes and frequencies, with appreciable computational time savings. The proposed tank with a perforated floor is found to be effective in serving as a dual-purpose TLD and storage tank for fire suppression in buildings.

Numerical investigation of structural models equipped with tuned liquid damper

Tuned liquid dampers (TLDs) are introduced in structural systems to suppress vibration of the structure due to dynamic actions. Using a grid-based Finite Volume Method-Finite Element Method (FVM/FEM), efficiency of TLDs of cylindrical and rectangular geometries was evaluated by performing a two-way Fluid-Structure Interaction (FSI) analysis. The nonlinear sloshing response of fluid was simulated by employing a three-dimensional Navier–Stokes equation as the governing equation and occurrence of wave breaking was accounted by using Volume of Fluid (VOF) method for free surface tracking. Utilizing the developed numerical model, a series of three-dimensional transient analysis were conducted on a structure with and without TLDs aiming to investigate effect of base excitation amplitude. The result show that maximum performance of TLDs at resonance is obtained when the forcing ratio is limited to 0.1, and for this case, both cylindrical and rectangular TLDs displayed comparable efficiency. Effect of excitation frequency fe was also investigated under a wide range of the forcing ratio showing that as fe increases, the natural frequency of coupled TLD-structural system approaches the natural frequency of un-damped structural system.

Characteristics of seismically-induced resonant sloshing waves and the effects of bed topography

The seismically-induced resonant sloshing wave (SIRSW) is a crucial concern in the design of storage tanks and reservoirs. To uncover the generative mechanism and characteristics of SIRSW and the effects of bed topography, a numerical study using a Navier-Stokes solver with the Virtual-Boundary-Force (VBF) approach for modelling structures is conducted. Various seismic excitations with low to high frequency contents are used to excite nonlinear sloshing. Simplified bed topographies, i.e. the uniformly bottom-mounted rectangular barriers, are considered. Special attention is paid to the correlation between the sloshing response and the seismic characteristics through two groups of parametric studies: 1) changing the peak ground velocity (PGV) under fixed peak ground acceleration (PGA); 2) changing the frequency band under fixed PGV. Results indicate that the seismic PGV, frequency content and frequency band are three significant parameters dominating the sloshing wave; the bed topography can enhance or suppress SIRSW depending on the predominant frequencies of the seismic excitation and their durations.

Liquid sloshing in a baffled rectangular tank under irregular excitations

Sloshing responses in vertical and horizontal baffled tanks under irregular external excitations are investigated by employing a viscous fluid flow model with the Navier–Stokes solver. After the extensive validation of the present numerical model, the numerical experiment reveals many new understandings of the problem. A three-phase variation is suggested to describe the sloshing response under irregular excitations, that is, the first-order natural period controlling stage, the second-order natural period controlling stage, and the transitional stage between them. The sloshing periods are always around the corresponding natural periods with small standard deviations at the first- and second-order natural period controlling stages; while the decreased sloshing periods with large standard deviations can be observed at the transitional stage between them. The sloshing energy concentrated at a single natural frequency or multiple natural frequencies is the major reason for the phenomena. Compared to the results under regular excitations, smaller and larger sloshing amplitudes can be observed in the results of irregular excitations around the resonant and non-resonant frequency ranges, respectively. The normalized sloshing amplitudes calculated from the samplings of the large free surface amplitudes are always smaller than the samplings of the small free surface amplitudes.

Effects of Uncertain Soil Parameters on Seismic Responses of Fixed Base and Base-Isolated Liquid Storage Tanks

ABSTRACT Effects of soil-structure interaction (SSI) on the seismic performance of cylindrical ground-supported liquid storage tanks are studied. The present study attempts to investigate the effects of uncertainties, associated with the critical soil parameters, on the seismic behavior of liquid storage tanks. Random multi-layered soil models coupled with the fixed base liquid storage tank are developed and analyzed. Further, the tank structure is considered base-isolated with lead rubber bearing and analyzed with the same set of soil models, to investigate the seismic behavior of base-isolated tank under uncertain soil condition. A set of three ground motions are selected from a large suite through a mean spectral matching scheme for investigating the effect of soil uncertainties on the seismic response. Distributions of the peak seismic response quantities observed herein show that the uncertainties in soil parameters critically affect the seismic responses of fixed base and base-isolated liquid storage tanks. Sloshing displacement of fixed base and base-isolated tanks is affected by both uncertainty in the soil parameters and ground motion characteristics. Nevertheless, for ground-supported tank, relatively larger dispersion or variability of base shear and overturning moment, as compared to that of the sloshing response, is observed.

Seismic performance of a base-isolated flexible liquid storage tank equipped with a novel rate-independent damping device

Conventional base-isolation systems can significantly reduce the hydrodynamic pressure on the walls of large liquid storage tanks, but they have limited or even adverse effects on the sloshing response of liquids because the sloshing period is comparable to the isolation period. In this study, a combined base-isolation system consisting of natural rubber bearings and a novel rate-independent damping device was developed to achieve a simultaneous reduction in the hydrodynamic pressures and sloshing heights of liquid storage tanks. Using an analytical flexible tank model considering higher sloshing modes, the seismic responses of liquid storage tanks equipped with the proposed combined base-isolation system under strong ground motions were investigated. The influence of tank flexibility, higher sloshing modes, and liquid heights on the seismic responses of the controlled storage tank were evaluated quantitatively. The effectiveness of the proposed combined base-isolation system was verified, and its advantages over conventional base-isolation systems were identified. The proposed system can achieve a larger reduction in base shear, overturning moment, and sloshing height than conventional systems without increasing the isolator displacements.

Effect of Frequency Content of Seismic Excitation on Slosh Response of Liquid Tank with Baffle Plate

The violent dynamic behavior of liquid under horizontal excitation is a key factor that needs to be addressed in the seismic-resistant design of liquid tanks. Therefore, this study focuses on the slosh response of the liquid medium in a rectangular tank under Imperial Valley 1979, El Centro 1940 and Kobe 1995 ground motions of different frequency ranges. The ground motions records are selected based on the PGA/PGV ratio. For slosh control, a single vertical perforated baffle plate is used as an anti-slosh element with different configurations of perforations. Considering the free surface elevation as the major response parameter, the effect of percentage of perforation of the baffle plate, clear spacing of perforations and offset distance of the perforated plate are investigated by carrying out the pressure-based transient analysis using computational fluid dynamic (CFD). The optimum perforation varies from 10% to 17%, corresponding to the frequency of ground motion in the range of far-resonant to near-resonant conditions. Additionally, “rapid zone” ([Formula: see text]-zone) and “moderate zone” ([Formula: see text]-zone) are identified to pilot the positioning of the perforated baffle plate in liquid tanks. The perforated baffle plate with an optimum range of moderately spaced perforations positioned at the moderate zone of the tank effectively reduces the free surface elevation. Furthermore, the perforated baffle plate is more advantageous during violent sloshing under near-resonant conditions.

Slosh Damping in Rectangular Liquid Tank With Additional Blockage Effects Under Pitch Excitation

Abstract The quantification and damping of slosh responses are significant due to the increasing demand for safety of the liquid-based applications under severe external excitation. Recently, the solid or perforated baffle plates have been used to damp the slosh response of the liquid. However, there is uncertainty in the selection of an effective configuration of the baffle plates. In addition, most of the studies reported the slosh response under surge excitation. Therefore, this study focuses on the slosh response of the rectangular tank fitted with perforated baffle plates of different configurations under pitch excitation. For this, the liquid sloshing is simulated using the concepts of computational fluid dynamics (CFD) using pressure-based solver in the time domain. A detailed parametric study is carried out to develop an effective configuration of the perforated baffle plates considering the area of perforations, interperforation distance, size of perforations, distance between the perforated baffle plates, alignment of perforations, and the vertical position of perforated baffle plate as the parameters. The slosh responses are observed in terms of free surface elevation, hydrodynamic pressure, turbulence kinetic energy, velocity streamlines, power spectral density corresponding to the free surface elevation and the free surface deformation. The study developed a “zig-zag blocking alignment” of perforations for effective slosh damping, with the solid area between the perforations being 50%–60% of the area of perforations. In addition, “single-acting range” and “damping range” are identified to pilot the positioning of the multiple baffle plates in a rectangular tank under pitch excitation.

The Effect of Porous Media on Wave-Induced Sloshing in a Floating Tank

Placing porous media in a water tank can change the dynamic characteristics of the sloshing fluid. Its extra damping effect can mitigate sloshing and, thereby, protect the integrity of a liquefied natural gas tank. In addition, the out-of-phase sloshing force enables the water tank to serve as a dynamic vibration absorber for floating structures in the ocean environment. The influence of porous media on wave-induced sloshing fluid in a floating tank and the associated interaction with the substructure in the ambient wave field are the focus of this study. The numerical coupling algorithm includes the potential-based Eulerian–Lagrangian method for fluid simulation and the Newmark time-integration method for rigid-body dynamics. An equivalent mechanical model for the sloshing fluid in a rectangular tank subject to pitch motion is proposed and validated. In this approach, the degrees of freedom modeling of the sloshing fluid can be reduced so the numerical computation is fast and inexpensive. The results of the linear mechanical model and the nonlinear Eulerian–Lagrangian method are correlated. The dynamic interaction between the sloshing fluid and floating body is characterized. The effectiveness of the added porous media in controlling the vibration and mitigating the sloshing response is confirmed through frequency response analysis.

Seismic characteristics of isolated plate-shell integrated concrete LSS

Plate-shell integrated concrete liquid-storage structure (PSICLSS) has been widely applied with the development of water treatment technology. However, there are few anti-seismic performance and base-isolation design researches on it. The seismic performance of PSICLSS was studied, and the accuracy of finite element analysis was verified by experimental study. A calculation method of damping coefficient is proposed and used in a PSICLSS study. Based on 5 natural accelerations and 2 artificial accelerations, the dynamic responses of the isolation liquid storage structure under different peak ground acceleration are analyzed. The analysis results show that, non-isolated PSICLSS is easy to damage when subject to earthquake. The principal stress of the structure is maximum at the upper beam, and the maximum liquid hydrodynamic pressure appears at the connection position of the upper and lower conical shell. When the base isolation measure is used, the stress of the structure can be effectively reduced, but the liquid sloshing response will be magnified. With the increase of peak ground acceleration, the structural dynamic response and liquid sloshing response will increase.

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 U-tube mode, which can arise from the sloshing reduction to some extent.

Earthquake-induced nonlinear sloshing response of above-ground steel tanks with damped or undamped floating roof

Liquid storage tanks are widely used in the industry and can contain not only harmless substances but also various ones that can be explosive and toxic or pollutant, thus implying that both the structure and the content must remain safe and operational under different types of loading. The same applies to any tank-connected plant system/item. Yet, past earthquakes repeatedly demonstrated that even if structural damage is prevented in the shell, severe occurrences may still be observed due to sloshing phenomena, which drive the tank-fluid system response with high impacts in case of accidental release of chemicals. Therefore, this paper studies an energy dissipation system consisting of floating roof and external dampers that are utilized to control liquid vibration by augmenting the level of damping. In order to evaluate its effectiveness at the design-level earthquakes, a series of explicit nonlinear dynamic analyses have been performed, and comparisons are provided between floating roofed steel cylindrical tanks equipped with supplemental devices and counterparts without them. Changes in seismic performance because of geometrical variations in the tank (i.e. aspect ratio) and seismic input (i.e. far and near field earthquakes) have been quantified by means of experimentally validated numerical models that account for material and geometrical nonlinearities, as well as for fluid-structure interaction in an explicit manner. Shake-table tests available in the literature have been simulated, and the proposed modelling criteria show a good fit with experimental data on two tank specimens. Analysis data sets involving three tank geometries reveal that even if the dissipation system targets mainly large-capacity tanks, it can be effectively used to enhance the performance of any system, reducing the sloshing wave height which can be excessive especially when the tank is subjected to severe near field ground motions.