Sloshing Response Research Articles

Finite element method for analyzing effects of porous baffle on liquid sloshing in the two-dimensional tanks

Purpose The purpose of this paper is to analyze the liquid sloshing behaviors in two-dimensional tanks with various porous baffles under the external excitation. Design/methodology/approach Adopting the finite element method (FEM) and control variable method to study the impacts of the height, length, number, location, shape, porous-effect parameter of the porous baffle, the external load frequency and the shape of the tank on the liquid sloshing response. Findings The amplitude of the free surface can be reduced effectively when the baffle opening is appropriate. The anti-sway ability of the system increases in pace with the baffle’s height growing. Under the same conditions, the shapes of the baffles have an important effect on improving the anti-sway ability of the system. Originality/value As there exist the differences of the velocity potential between each side of the porous baffle, which means that there are two different velocity potentials at a point on the porous baffle, the conventional finite element modeling technologies are not suitable to be applied here. To deal with this problem, the points on the porous baffle are regarded as two nodes with the same coordinate to model and calculate.

Influence of the vibroimpact interaction on sloshing dynamics in a rectangular tank

The paper studies a sloshing phenomenon occurring as a result of a vibroimpact motion of a rectangular tank subjected to an external harmonic excitation. This presented model is a result of an idealization of realistic scenario in which an impact interaction between a ship and floating ice can occur. The behavior of a liquid inside the tank is modeled by the five mass-spring-damper subsystems mimicking a response of the liquid at different sloshing response modes. Two-sided motionless barriers are introduced to model the vibroimpact motion of the tank. The paper studies the influence of the vibroimpact motion onto the sloshing intensity and proposes a sloshing mitigation strategy, which employs a flexible vertically oriented baffle. The results of the numerical simulations indicate that the sloshing intensity is higher in the case of a classical rigid baffle and can be significantly reduced by the flexible baffle.

Liquid Sloshing in a Cylindrical Tank with Multiple Baffles Under Horizontal and Pitching Motions

The sloshing response of fluid in a rigid circular cylindrical tank with multiple rigid annular baffles and subjected to horizontal and pitching excitations is investigated. The subdomain method for fluid sloshing is utilized to obtain exact solutions to the convective velocity potential of liquid. By substituting the velocity potential of liquid into free surface sloshing equation, the response equation under the horizontal excitation is constructed. According to producing the similar lateral force and moment as analytical solutions undergoing horizontal motion, an equivalent mass-spring model is developed to replace continuous liquid. Based on the model, dynamic response of liquid sloshing in the tank under the horizontal and pitching excitations is obtained. Compared with the reported results, the lateral force is in excellent agreement with literature solutions and the overturning moment shows good agreement with available solutions under the excitation with low frequency. The proposed model can be employed to simplify dynamics of complicated liquid-structure systems undergoing pitching motion without tedious derivation and great amount of calculation. The effects of the liquid height, the positions and sizes of the baffles on the influence coefficient factor of pitching motion and the steady-state response are revealed in detail.

Sloshing Motion in a Real-Scale Water Storage Tank under Nonlinear Ground Motion

Water storage tanks in cities are usually large and are occasionally affected by earthquakes. A sudden earthquake can cause pressure pulses that damage water containers severely. In this study, the sloshing motion in a high filling level tank caused by seismic excitation is investigated by the numerical method in a 2D model. Two well-studied strong earthquakes are used to analyze the broadband frequency nonlinear displacement of the tank both in the longitudinal and vertical directions. Based on careful experimental verification, the free surface motion and the elevations at the side wall are captured, and the sloshing pressure response is examined. The results show that the 2D section of the cylindrical tank can be used to estimate the maximum response of the 3D sloshing, and the water motions under the seismic excitations are consistent with the modal characteristics of the sloshing. The time histories response of the water motion reflected that the sloshing response is hysteretic compared with the seismic excitation. The anti-seismic ability of the damping baffle shows that its effect on sloshing pressure suppression is limited, and further study on the seismic design of water tanks in earthquake-prone regions is needed.

Tuned Sloshing Dampers With Large Rectangular Core Penetrations

Abstract Space restrictions at the top of tall buildings may necessitate using tuned sloshing dampers (TSD) tanks with large rectangular penetrations to accommodate the structural core of the tower. A finite element model is employed to predict the natural sloshing frequencies and mode shapes of liquid sloshing in a rectangular tank with a rectangular core. Equivalent mechanical properties are determined to predict the sloshing response. Frequency response predictions of wave heights, sloshing forces, and energy-dissipation per cycle agree with results from shake table testing conducted on a rectangular tank with a rectangular core. Energy dissipation due to flow around the core adds considerable damping to the liquid and is proportional to the response velocity-squared. Nonlinear coupling among sloshing modes results in multiple peaks in the frequency response plots near the fundamental resonant frequency. An interior core with a broad dimension in one direction substantially reduces the fundamental sloshing frequency and equivalent mechanical mass in the perpendicular direction; however, the fundamental sloshing frequency and equivalent mechanical mass in the parallel direction are only influenced marginally. Large rectangular cores reduce the proportion of the total water mass that is effective in controlling tower motion. A TSD with a rectangular penetrating core may enable a TSD option to be considered for the control of a tall building in cases where a traditional rectangular TSD is infeasible.

A NURBS-based isogeometric boundary element method for analysis of liquid sloshing in axisymmetric tanks with various porous baffles

An isogeometric boundary element method (IGA-BEM) based on the non-uniform rational B-splines (NURBS) is firstly performed to investigate the liquid sloshing in axisymmetric tanks with the porous baffles. The proposed method can completely maintain the advantages of the BEM that only the boundary of a domain requires discretization. By applying the NURBS basis functions it can exactly describe the geometry of the boundary. Meanwhile, it can also be obtained better solution field approximation at the domain boundary. Furthermore, as to the axisymmetric geometries of the containers considered in this paper, the 3-D liquid sloshing problems can be effectively reduced to 2-D ones on half of the cross-sections of the containers, which can significantly increase the computational efficiency. Meanwhile, the zoning method is employed in this paper to treat the arbitrary mounted porous baffles, and the Laplace equation is utilized as the governing equation of the potential flow model by assuming the fluid motion to be inviscid, irrotational and incompressible. Additionally, the weighted residual method together with the Green’s theorem is applied to develop the BEM integral equation. The natural sloshing frequencies and dynamic sloshing forces solved by the proposed method are compared with the available literatures and the traditional boundary element method (BEM). Good agreements are observed in the comparisons between numerical results and those of the existing literatures. And higher accuracy and convergence can be achieved by the proposed IGA-BEM method with significantly fewer nodes than the traditional BEM. Moreover, spherical tanks with the coaxial hemispherical, wall-mounted conical or surface-piercing cylindrical porous baffle, ellipsoidal tanks with spheroidal or surface-piercing cylindrical porous baffle, and the toroidal tank with tubular porous baffle are considered to investigate the effects of the porous-effect parameter, radius, length, height, horizontal and vertical semi-axes of the porous baffle on the sloshing characteristics (i.e. dynamic sloshing forces and surface elevations). The results show that the surface-piercing cylindrical porous baffle offers more noticeable suppression on sloshing response than the hemispherical and spheroidal porous baffles. Changing the radius of the tubular porous baffle has almost negligible effect on the sloshing force acting on the toroidal tank. The excitation frequency corresponding to the maximal value of sloshing force can be altered evidently by changing the porous-effect parameter of the porous baffle. In addition, choosing reasonable porous-effect parameter, radius, horizontal semi-axes and relatively larger length, height as well as vertical semi-axes for the porous baffles yields considerable suppression on the sloshing response.

A Study on the Sloshing Problem of Vertical Storage Tanks under the Action of Near‐Fault Earthquakes

In this study, through a vibration table test, finite element simulation, and research on the rationality of the wave‐height fortification of national storage tank specifications, the sloshing response of vertical storage tanks under the action of near‐fault ground motion was analyzed. The test results showed that the sloshing wave height of a vertical storage tank was larger under near‐fault or long‐period ground motions, and the relationship between the sloshing wave height and the peak acceleration of input ground motions was approximately linear. The numerical simulations of the model tank showed that the simulation wave height and the test wave‐height data were well fitted. Therefore, it was feasible to simulate the sloshing of large vertical storage tanks using ADINA software. In addition, a large number of sloshing simulations of near‐fault ground motions on 10,000 m3 vertical storage tanks were performed. The simulated wave height had a high correlation with the predominant period or pulse period of near‐fault ground motions. Under the calculation with similar parameters, the wave height of the tank standard in several countries had a lower fortification of the near‐fault excitation wave height. Through the root mean‐square method using a small sample size, a wave‐height correction under a near‐fault effect was applied to the wave‐height formula for the Chinese tank seismic specification. Finally, the problem of a double‐damping correction was addressed by adjusting China’s GB50341 wave‐height formula. This work provides a reference value for practical engineering applications.

Boundary element analysis of liquid sloshing characteristics in axisymmetric tanks with various porous baffles

This paper aims to investigate the effects of the porous baffles on the suppression of sloshing for the tanks with axisymmetric geometries under lateral excitation. Based on the assumptions of inviscid, irrotational, incompressible liquid and small amplitude sloshing, an axisymmetric boundary element method (BEM) for 3D Laplace equation is derived by using the Green's theorem together with the weighted residual method. And a zoning method is employed to model fluid domain in the tanks with complex porous baffles. Meanwhile, the porous baffles are treated motioning together with the tanks, and the velocity across the porous baffle is assumed to be linearly proportional to the pressure gradient between each side of the porous baffle. And the mechanism of suppressing the sloshing response is mainly the energy dissipation of the fluid passing through the porous baffle. Moreover, the linear free surface boundary conditions are also used to solve the governing equations. Compared with other numerical methods, the most prominent advantage of the BEM in solving axisymmetric potential problem is that only the boundaries of half the cross-section instead of the entire problem domain should be discretized, which can cut down large amount of memory and time costs. The present method is verified by comparing the numerical results with the existing literatures, and excellent agreements are obtained. Meanwhile, the proposed models are applied to investigate the effects of the porous baffles on sloshing response in circular cylindrical, annular cylindrical and conical tanks. The effects of the porous baffle length, porous-effect parameter, installation angle and baffle height on the sloshing force, natural frequency and surface elevation are studied. Additionally, some typical sloshing pressure distributions, velocity potential contours and velocity fields are plotted. The results show that swirls at the tips of the baffles can be observed in many cases, and the top-mounted porous baffle makes more significant suppression effects on sloshing response than that of bottom-mounted porous baffle, while increasing the number of ring porous baffles can achieve better restraint effects on sloshing response. And increasing the baffle length of the horizontal wall-mounted ring porous baffle can significantly decrease the sloshing frequencies, as well as the first non-dimensional natural frequency decreases with decrease in porous-effect parameter of the coaxial porous baffle. In addition, remarkable effects on sloshing can be obtained when reasonable designed by selecting the optimal porous-effect parameter, installation angle and baffle height. And this paper can be a useful guide for the seismic design and analysis of many actual liquid storage tanks (such as the Advanced Passive PWR, large water cooling tower, etc.).

Method of fundamental solutions on simulating sloshing liquids in a 2D tank

A two dimensional numerical model for sloshing response of the partially filled container is developed by a meshless method in this study. Laplace equation is considered as the governing equation for potential flow, and fully non-linear free surface boundary conditions are implemented on the free surface. The numerical model is established in the moving coordinate system attached to the container. The present meshless method, method of fundamental solutions, only need to distribute nodes on the physical boundaries and the virtual boundaries outside the computational domain. Comparing with the traditional mesh-based numerical method, this method has the advantage of being easy to construct and flexible in dealing with the moving boundary problem. The program is written in Python. A simple method for tracking fully non-linear free surface is implemented, and the physical boundaries are updated with time. The numerical results agree very well with existing results in both resonance and off-resonance cases. The present numerical model is further applied to the sloshing response under coupled motions (horizontal and vertical). In order to study the stability of sloshing response (Benjamin and Ursell, 1954) under vertical motion, 25 cases are conducted in various sloshing parameters. In addition, the present numerical model has been successfully applied to investigating sloshing response under coupled motions.

On the numerical assessment of the resonant sloshing responses in 3D multi baffled partially liquid-filled steel cylindrical tanks shaken by long-period ground motions

This study displays a coupled numerical process to scrutinize the sloshing response for multi baffled flexible cylindrical container subjected to lateral excitations. The developed algorithm is based on a coupled three-dimensional boundary element-finite element approach which allows computing sloshing natural frequencies, as well as seismic responses. The intricate liquid region is divided into several simple sub-regions so that in each liquid sector the Laplace equation is solved by introducing interface influence matrix and, finite element route is employed to model the tank shell. This process has a substantial influence on lessening computational cost and a good precision in evaluating the response of the whole system. The time variations of sloshing responses, base forces, the maximum hydrodynamic pressure and shell radial displacement in relation to various system parameters such as the liquid-fill depth, tank geometry and baffles arrangement are deliberated in detail. From these examinations, it may be concluded that with the installation of baffle rings inside the liquid tank, the dynamic response of such structures during severe earthquake ground shakings can be significantly diminished. Furthermore, in the exceptional case of long-period ground excitations, the seismic response of multi baffled containers may be controlled by the baffle rings only at particular statuses of shallow structures. For the case of slender containers, special considerations would be required to be assigned to the design of baffle plates believed to experience long-period seismic excitations. The proposed coupled numerical procedure can serve as a basis for future analysis of multi baffled cylindrical tanks in conjunction with fluid due to severe long-period earthquakes.

Evaluation of breaking wave effects in liquid sloshing problems: ANCF/SPH comparative study

This paper is focused on evaluating the effect of breaking waves in liquid sloshing problems. Two fundamentally different approaches, namely the smoothed particle hydrodynamics (SPH) and the finite element (FE) absolute nodal coordinate formulation (ANCF), are used to describe the liquid sloshing response in several sloshing scenarios. The SPH method is a mesh-free numerical technique often used to capture very large displacements in fluid and solid mechanics problems. ANCF finite elements, on the other hand, can be used to develop a non-incremental solution procedure, suited for the nonlinear analysis of flexible bodies undergoing large rotation and large deformation. The fundamental differences between the two approaches and the advantages and limitations of each are discussed. Two benchmark problems, the dam break and sloshing tank, are used to perform a detailed SPH/ANCF quantitative comparative study in different sloshing scenarios. While a good agreement is found between the ANCF and SPH converged solutions for the dam break problem, in the sloshing tank problem the SPH solution underpredicts the amplitude of oscillation of the fluid center of mass and the wave height at a selected probe point. Because one ANCF element can capture complex shapes, nearly 40 times fewer degrees of freedom than the SPH model are needed in both problems. The use of the ANCF models leads to a CPU saving of 70% and 25% in the broken dam and sloshing tank problems, respectively. In the case of the tank problem, the effect of light, moderate, and severe turbulence is examined. The position of the fluid center of mass is computed using the two approaches, and the results obtained are verified using a reference analytical solution. The power spectral density of the center of mass is evaluated using the fast Fourier transform (FFT) to study the effect of breaking waves. The results show that in the case of light and moderate turbulence, the ANCF model allows for accurately averaging the fluid inertia properties, and the obtained solutions are in good agreement with the SPH solutions. In the case of severe turbulence, on the other hand, the mechanical energy dissipation due to fluid mixing and wave breaking, which can only be captured using the SPH method, damps out the sloshing oscillations.

Nonlinear sloshing response of liquid-filled rectangular concrete tanks under seismic excitation

The current study is mainly focused on nonlinear sloshing analysis of rectangular liquid storage tanks. The main response quantity of interest is free surface sloshing height. There are some key factors to be investigated in order to make a better understanding of the performance of liquid tanks under seismic loading. These include three-dimensional geometry, corner sloshing, tank aspect ratio, bidirectional loading, and earthquake frequency content. The main focus of this work is to investigate these important parameters through a comprehensive parametric study using a rigorous finite element technique capable of accounting for nonlinear fluid-structure interaction effects. The validity of current code provisions in seismic analysis of such structures is then investigated by comparing the obtained numerical results with those recommended by current practice and important conclusions are drawn. The present paper suggests that the sloshing nonlinearity could have a significant effect on the seismic performance of liquid containing structures and failing to account for it properly could introduce a major concern with respect to their satisfactory performance for a certain group of tanks in particular shallow tanks.

Coupling vibration analysis of the elastics structure with liquid

The equations of the structure motions are accomplished in terms of the displacement form, and the liquid formulations are expressed by pressure, with or without considering the effect of sloshing. The unknown coefficients in the two domains are expanded into velocity potential and vibration functions by Galerkin's method. The coupled vibration of the elastic baffle with two sides' fluid, in a rigid tank, is also carried out by finite element method, which regards the structure and fluid element global degrees of freedoms as row index and column index, and the coupled matrix is assembled to the global matrix. Finally, the coupled frequencies of a simple supported beam and liquid are computed, which are in good agreement with the FEM results. The effects of the liquid filling height and beam flexibility on the slosh response are also investigated. The baffles with two sides' fluid vibration numerical results by the proposed FEM are compared with the test example, which agree well.

High performance analysis of lateral sloshing response in vertical cylinders with dual circular or arc-shaped porous structures

This study presents a semi-analytical solution with the scaled boundary finite element method (SBFEM) for the sloshing of liquid in vertical cylinders with the coaxial dual circular or arc-shaped porous structures in the context of the linear potential theory. Firstly, the whole flow domain can be divided into three sub-domains with the porous structures and the wall of tank, in which the arc-shaped porous structure should be extended to the whole circle and the perforated coefficient of the extension section is set to infinite. Then the velocity potential of flow in each sub-domain is determined by utilizing the SBFEM for solving the Helmholtz equation or the modified Helmholtz equations, and the fundamental equations and the solution process of the SBFEM for this sloshing problem have been derived in detail. In the SBFEM, one of the superior features is that only the circumferential boundary of the computational domain needs to be discretized with the same form of the finite element. As a result, the spatial dimension of the problem can be reduced by one. As a key point, although there are the dual circular or arc-shaped porous structures, only the wall of tank should be discretized. Meanwhile, the governing equations can be solved analytically in the radial direction by using the Bessel functions or the modified Bessel functions. Numerical examples show that only a small quantity of the discretized elements over the cylindrical boundary can achieve an excellent agreement between the numerical results obtained by the proposed method and the analytical solutions, which demonstrate the accuracy and efficiency of this formulation. Finally, several numerical examples are further studied to investigate the effects of the radius of the porous structures, the porous-effect parameter, the nondimensional wave number, and the opening degree together with the distribution of the centre of the arc-shaped porous structures on the sloshing characteristics of liquid in the cylindrical container with the porous structures.

Experimental and numerical investigation of sloshing behavior in annular region separated by several cylinders related to fast reactor design

Abstract The liquid sloshing behavior analysis of reactor vessel is an important topic of sodium-cooled fast reactor design. It is known that there are two pumps and four heat exchangers immersed in sodium liquid. Although lots of research work has been performed on the liquid sloshing inside simple cylindrical tank and coaxial circular cylinders, few about sloshing inside annular region separated by several cylinders (ARSSC), this paper deals with the analysis of the liquid sloshing inside the ARSSC geometry. A simplified cylindrical tank of fast reactor was designed, in which there are six internal cylinders used to model pumps and heat exchangers. By shaking table experiments, the number of internal cylinders was gradually increased, and the natural frequency and wave height of liquid sloshing were measured under each case. In numerical investigation, the VOF models were built to record wave height using the CFD simulation approach, the conditions were consistent with experiments. Much different with previous research, the characteristics of sloshing inside ARSSC geometry were strongly dependent on the number of internal cylinders. Experiment results showed that the natural frequency and wave height all decrease with the increase of internal cylinders gradually. The wave height response obtained by numerical simulation was in good agreement with the experimental results. In addition, as the increase of internal cylinders gradually, the maximum sloshing response occurred when the forcing frequency matched high order natural frequency of sloshing. Moreover, a correction factor was obtained by experiments for the natural frequency theoretical calculation formula. The conclusions can provide favorable reference for the seismic design of the sodium-cooled fast reactor.

Liquid Sloshing Suppression for Three-Phase Separators Installed on Floating Production Unit

In this study, a computational fluid dynamics model based on the volume of fluid (VOF) method is developed to simulate the dynamic sloshing response to external excitations. The modal analysis model based on the linear potential theory is established to predict natural sloshing frequencies and the corresponding mode shapes in three-phase separators. In addition, the effects of separator location, length-to-diameter ratio, oil/water level, porosity, and spacing of perforated baffles on the sloshing response are evaluated quantitatively. Furthermore, comprehensive approaches are proposed to mitigate the sloshing, like enhancing viscous damping effect, reducing the intensity of external excitation sources, and keeping away from the resonant frequencies. Finally, a practical application is carried out to display the optimal design of a three-phase separator. The results show that three-phase separators should be located as close as possible to the center of rotation (COR) of the floating production units (FPU). The length-to-diameter ratio is recommended to be no greater than three. Once the fluids can be separated to reach their respective interfaces, the liquid level should be increased as high as possible, whereas the water level should be lowered as far as possible. There is an almost inversely linear relationship between the antisloshing performance of a perforated baffle and its porosity. The antisloshing performance is attenuated rapidly when the spacing distance of a pair of baffles exceeds a specific range. This research extends the existing scope of sloshing suppression approaches and provides useful guidance in the design of FPU-based three-phase separators.

Sloshing reduction in a swaying rectangular tank by an horizontal porous baffle

Sloshing occurs in a tank containing liquid with free surface. It may result in resonant liquid motions causing carrier-vessel instability or structural damage of tank walls. The horizontal porous baffle is capable of dissipating the sloshing energy and reducing the sloshing pressures acting on tank walls. In the context of linear potential theory, the MEEM (matched eigenfunction expansion method) is applied to obtain the analytic solution for the sloshing with porous horizontal baffle. A BEM (boundary element method) with the porous boundary conditions is also independently developed for double checking and the application to more general cases. Two baffle positions at the center and at both walls of a rectangular tank are considered for various porosities, lengths, and submergence depths. The theoretical prediction is then compared with a series of experiments conducted by authors using harmonically oscillated rectangular tank with various baffle porosities and submergence depths. The measured data reasonably correlate with the predicted values. It is found that horizontal porous baffles installed at both tank walls significantly suppress violent resonant sloshing responses compared to one installed at the tank center. Through parametric study using the developed numerical tools, the optimal porosity, length, and submergence depth can also be determined.

Nonlinearity of Finite-Amplitude Sloshing in Rectangular Containers

This paper investigates the influence exerted by small surface tension on the nonlinear normal sloshing modes of a two-dimensional irrotational, incompressible fluid in a rectangular container. To this end, the influence of surface tension on the modal frequencies is investigated by assuming pure slipping at the contact line and a 90 deg contact angle between the fluid surface and the walls. The regions of possible nonlinear internal resonances up to the fifth mode are highlighted. Away from the highlighted regions, the influence of surface tension on the effective nonlinearity of the lowest four modes is studied and used to shed light onto its effect on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, the response of the sloshing waves near two-to-one internal resonances is studied. It is shown that, in the vicinity of such internal resonance, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the high-frequency mode (high-frequency uncoupled mode response). The regions where the coupled mode uniquely exists are shown to depend on the surface tension. Moreover, it is demonstrated that such regions may be underestimated considerably when neglecting the influence of the cubic nonlinearities.

Liquid sloshing in partly-filled laterally-excited cylindrical tanks equipped with multi baffles

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 C1. 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.

Small scale experiments of sloshing considering the seismic safety of MYRRHA

Sloshing can be a great concern for the seismic safety of heavy liquid metal cooled nuclear reactors, such as the Gen IV prototype MYRRHA, currently under development by the Belgian Nuclear Research Center (SCK•CEN). Sloshing is studied using reduced scale laboratory experiments on the SHAKESPEARE shaking table facility of the von Karman Institute. Scaling of the experimental model is discussed through dimensional analysis, identifying the appropriate scaling factors which are then applied to the seismic excitation signals. Qualitative results of the liquid sloshing motions inside the model are obtained with flow visualization, while moments are measured on an instrumented rod that is partially immersed in the liquid. A two component moment-balance is constructed to measure the bending moments on the element about the horizontal axes. The results demonstrate that sloshing, as a non-linear phenomenon, is highly dependent on the frequency of forcing relative to the natural frequency of the liquid in the specific container. In the resonance case the sloshing response reaches the highest amplitude and maximum moments are measured, representing a worst case scenario for the reactor safety. Experiments with internal components in the sloshing model indicate that obstructions reduce the sloshing loads and prevent resonance type sloshing. The proposed methodology with small scale experiments can provide a useful tool for the prediction of the sloshing effects for the MYRRHA design and safety analysis.