Motion Of Tank Research Articles

Heterogeneity's impact on the sloshing motion in excited tanks

AbstractThis paper aims to investigate the effect of liquid heterogeneity on sloshing in a two-dimensional rectangular tank. The container is excited horizontally, and the density of the liquid at equilibrium can almost be considered a linear dependence of the depth. The linearized equations representing the sloshing phenomenon are solved numerically using ANSYS 2020 R2 software and analytically using the separation method of variables in conjunction with the Fourier analysis. On the other hand, a comparison study has been carried out between the obtained results and other works related to the same phenomenon. Overall, the results exhibit considerable effects of variation in the Heterogeneity Coefficient β on the free surface's motion and the pressure distribution within the liquid. Furthermore, the free surface of liquid heterogeneity is also affected by the variation of Excitation Frequency Ω and the Filling Rate h of the liquid in the tank.

Wind-induced vibration control of tall buildings by designing the overhead fire water tanks as compliant deep tank dampers-inerter

Building codes often mandate the installation of overhead fire water tanks (OFWTs) on multi-storeyed buildings. The present study proposes a cost-effective solution by utilizing these OFWTs as tuned liquid dampers (TLDs) in tall buildings to improve serviceability under wind-induced excitation. However, designing OFWTs as TLDs is often hindered by the deep nature of the OFWTs and practical constraints in dimensioning the tank as per the tuning requirement. To alleviate these hindrances, the OFWT is designed as a compliant deep tank damper-inerter (CDTDI). A compliant damper system is achieved by connecting the tank with the building through spring and dashpot elements. This allows relative motion of the whole tank with respect to the building. Further, an inerter is employed to improve the efficiency of the compliant damper. Three example buildings, 20-, 30-, and 40-storeyed, are considered and modeled as multi-degrees-of-freedom (MDOF) systems. The CDTDI-MDOF structural system’s motion equations are formulated. An excitation-independent, genetic algorithm-based single-objective optimization is performed to estimate the optimum CDTDI parameters. Sequentially, the 2nd-order or H2 and infinity or H∞ norms of the transfer function of the roof displacement are chosen as objective function. The efficacy of the CDTDI is examined by subjecting the structure to 10 simulated wind excitations. The results reveal the proficiency of the CDTDI in controlling the multiple modes of the structure, alongside providing significant damping. The CDTDI induces up to 25 and 21 % reduction, respectively, in the peak roof displacement and peak roof acceleration of the example buildings. Further, CDTDI with parameters obtained through H∞ optimization is found to be relatively better performing.

The mechanism of switching direction of swirling sloshing waves

Swirling waves frequently occur in a three-dimensional tank under a nearly resonant excitation with oblique excitation angle. The oblique excitation produces two excitation components and the secondary component triggers rotational waves. The detailed mechanism of the switch in circular direction is clearly described in this study. The evolution of the hydrodynamic forces (Fz) on the tank walls presents a beating phenomenon and the switch direction always occurs at the peak and trough of the envelope of the Fz history. The external excitation moment changes the circulation intensity, and finally the swirling wave becomes a single-direction wave, but only for a short time. The profile of the single-direction wave was determined by the dominant sloshing mode and the instantaneous tank motion was found to be a key factor to determine the consequent swirling flow circulating direction.

Numerical simulation of half-full cylindrical and bi-lobed storage tanks against the sloshing phenomenon

This paper examines sloshing dynamics in cylindrical and bi-lobed liquid storage tanks including horizontal cylinders, vertical cylinders, horizontal bi-lobes, and vertical bi-lobes. The influence of baffle was evaluated, and the analysis presented accounts for sway induced hydrodynamic force as the criterion to compare different scenarios. To do this, the sloshing phenomenon was modeled by OpenFOAM based on coupled RANS solver and VOF method, and the RANS equations were discretized by the Finite Volume Method, and solved by using the PIMPLE algorithm. Finally, an engineering method suggesting the find the best dimension of the tank and baffle for the case of a cylindrical and bi-lobed tanks is presented to minimize the horizontal force exerted along the tank motion.

On the experimental scaling and power dissipation of violent sloshing flows

Violent and vertical sloshing flows appear when the fuel tanks of aircraft wings are shaken by air gusts or turbulence. The liquid slosh inside of the tank significantly damps the wing vibrations and its behaviour is still not fully understood. In this paper a simplified version of the problem is tackled, presenting the results obtained in an experimental campaign that investigates the scaling effects and the influence of the most relevant non-dimensional numbers of the problem. Single degree of freedom (SDOF) Froude scaled decay tests are devised in order to study the vertical sloshing problem in an aerospace context establishing relations between the slosh induced damping ratio and three of the most relevant non-dimensional numbers, namely the filling level, density ratio and initial amplitude. The experimental results indicate a maximum damping for a 50% fill level and a positive relationship between the damping ratio with the density ratio. The initial amplitude also increases with the damping ratio up until a threshold amplitude after which the damping starts to decrease. A clear explanation of the liquid induced damping ratio behaviour, confirmed for the three selected scales, is given in terms of two magnitudes: the sloshing force intensity and the phase-shift between this force and the tank motion. These two magnitudes are the key elements behind the physical interpretation of the liquid dissipation in the problem.Finally, the power dissipated by the liquid is calculated and correlated with the liquid slosh damping ratio, the sloshing force intensity and the phase-shift. This correlation shows an equivalency of the damping ratio with the dissipated power.

Energy dissipation in violent three-dimensional sloshing flows induced by high-frequency vertical accelerations

The European H2020 project SLOWD is aimed to investigate the fuel sloshing damping effect to reduce the design loads on aircraft wings. Wings house the fuel tanks and are highly flexible structures that can significantly deform under gust loads. In the recent experiment by Martinez-Carrascal and González-Gutiérrez [“Experimental study of the liquid damping effects on a SDOF vertical sloshing tank,” J. Fluids Struct. 100, 103172 (2021)], the complex problem of the fuel sloshing inside a flexible wing structure was significantly simplified by considering a partially filled vertically heaving tank attached to a system of springs. In the present research, a smoothed particle hydrodynamic model was adopted to evaluate the energy dissipated in the three-dimensional sloshing flow obtained using the same tank motions. From a numerical point of view, the simulation of such a violent flow is rather challenging, the involved vertical accelerations being as large as 10 g. The resulting flow is extremely complex because of the severe turbulence developed, the violent impacts, and the considerable fragmentation of the air–liquid interface. The role of the viscosity is investigated by taking into account two different liquids. Finally, some comparisons between three-dimensional results and previous two-dimensional studies are also discussed.

IMPACT ANALYSIS of CYLINDRICAL STEEL WATER STORAGE TANKS UNDER the SEISMIC ACTION

Cylindrical steel liquid tanks are widely used to store various liquids such as water, oil and industrial chemicals. In recent years, they are used in nuclear power plants for cooling purposes. Petroleum or other hazardous chemicals in steel liquid tanks can cause large financial and environmental damage due to damages in tanks during the earthquake. The main goal of this paper is to reveal buckling shape of cylindrical steel tanks with nonlinear seismic analysis according to roof shapes. Roof shapes were determined as open-top, flat-closed, conical-closed and torispherical-closed tanks. For this aim, El-Centro earthquake recording of 0.22 seconds was used for determine the significant shell buckling events. In addition, this earthquake values are ideal for impact analysis because ANSYS Workbench “Explicit Dynamics” tool provides very good results in the dynamic analysis of structures under destructive and short-term forces. In order to provide the interaction between the water and the tank wall, the "Eulerian Body" mesh technique is preferred in “Explicit Dynamics” model. As a result of this study, many collapse events were determined due to seismic ground motion in cylindrical steel liquid storage tanks. If the tank was closed in the shape of a torispherical, less buckling could occur in the tank.

Effect of MetaFoundation on the Seismic Responses of Liquid Storage Tanks

Cylindrical liquid storage tanks are vital lifeline structures, playing a critical role in industry and human life. Damages to these structures during previous earthquakes indicate their vulnerability against seismic events. A novel strategy to reduce the seismic demands in the structures is the use of metamaterials, being periodically placed in the foundation, called MetaFoundation (MF). The periodic configuration of metamaterials can create a stop band, leading to a decrease in wave propagation in the foundation. The aim of this paper is to study the effect of MF on the dynamic behaviour of liquid storage tanks. To that end, the governing equations of motion of the liquid storage tank equipped with MF are derived and solved in the time domain to obtain the time history of the responses under a set of ground motions. Then, the peak responses of tanks, mounted on MF, are compared with the corresponding responses in the fixed base condition. Besides, a parametric study is performed to assess the effect of the predominant frequency of earthquakes, the number of layers of metamaterials, the thickness of soft material, and the damping ratios of soft material on the performance of the MF. The obtained results indicate that the MF improves the dynamic behaviour of the squat tank, in which the mean ratio of responses using MF to the ones in the fixed base conditions equals 0.551 for impulsive displacement, overturning moment, and base shear.

A note on variational formalism for sloshing with rotational flows in a rigid tank with an unprescribed motion

UDC 517.9 The Bateman – Luke-type variational formulation of the free-boundary ‘sloshing’ problem is generalized to irrotational flows and unprescribed tank motions, i.e., to the case where both the tank and liquid motions should be found simultaneously for a given set of external forces applied to fixed points of the rigid tank body. We prove that the variational equation, which corresponds to the formulated problem, implies both the dynamic (force and moment) equations of the rigid body and the free-boundary problem, which describes sloshing in terms of the Clebsch potentials.

Drifting of a dead ship in wind

ABSTRACT The drift characteristics in wind of a dead ship that cannot sail on its own are investigated experimentally and theoretically. First, a free-drift test of a bulk carrier model in wind is conducted. Next, a time-domain simulation method is developed for predicting the drift motion of the dead ship in wind. Tank tests and motion simulations show that the dead ship drifts with a large hull drift angle over in wind, and the converged drift angle is independent of wind speed and initial ship heading angle. To explain why the dead ship drifts with a large drift angle in wind, a theoretical formula is derived for investigating the motion stability of the dead ship in wind. It is theoretically confirmed that the ship drifts stably with a large drift angle over in wind, whereas drift angles of and result in unstable motion. Thus the reason for the drift behaviour of the dead ship is clarified.

Sloshing induced damping across Froude numbers in a harmonically vertically excited system

An investigation was performed to measure sloshing motion and damping during harmonic forced vertical motion of a rectangular tank containing fluid, with a particular focus on the amplitude dependent transition between lateral sloshing and turbulent, vertical slamming. Qualitative and quantitative explanations are provided for the damping saturation point and dissipation effects, together with metrics to distinguish the different sloshing regimes, and a ballistic-harmonic analytical model is presented capable of reproducing the physical trends. Image processing tools were used to analyse experimental high-speed video footage, illustrating potential routes to increased damping in vertically oscillating structures, and correlating well with measured fluid forces and flow regimes.

Properties of the pressure field in highly nonlinear free surface flows with critical jet

In this note we examine fluid violent kinematics in a plunging breaker. The fluid motion is computed in the frame of the potential flow theory. The fluid kinematics is basically generated by forcing the motion of a rectangular tank, starting from rest. When a sufficient level of energy is injected in the fluid, the free surface has highly nonlinear behavior, here a plunging breaker. In the vicinity of the main tip crest, a sharp corner (cusp) appears along the surface of the barrel. The appearance of this critical jet is described and discussed in terms of the spatial and temporal variations of the pressure field. In the present case a local pressure maximum is captured that follows a continuous decreasing pressure gradient in a region of positive Gaussian curvature of the pressure. It is also shown that, at the free surface before the appearance of the critical jet, there is a strong correlation between the change of sign of the Gaussian curvature of the pressure on the one hand and the radius of curvature of the free surface profile on the other hand.

Coupling between resonant sloshing and lateral motions of a two-dimensional rectangular tank

Abstract

Analytical Study of Elevated Service Reservoir with Water Baffles Under Seismic Loading

Around the world earthquakes occur often causing some serious damages to property and life. Earthquakes weaken the structure and cause it to fail suddenly. Elevated Water tanks are such structures which have heavier mass suspended at a height supported on slender staging. When earthquake is induced in the tanks, it generates wave sloshing, the motion of the water induced due to seismic excitation. This sloshing of the water inside the tank will move in relative direction the seismic excitation causing structural instability. The water inside the tank will also act as tuned liquid mass damper and absorbs most of the energy created during seismic excitation. In this paper we have analysed various arrangement of baffle walls inside the tank in order to determine the stresses and displacements induced by the sloshing motion of the water tank. The water inside the tank will also act as tuned liquid mass damper where it will reduce the energy generated due to seismic excitation. During sloshing motion, there is an increase in lateral pressure applied over the tank walls which has adverse effect on the displacement of the system. The displacement of the system increases due to sloshing activity. By providing baffle walls we can reduce this displacement induced due to sloshing and thereby reduce the stresses generated on the supporting structure. From this analytical work the latter said was very evident.

Про демпфовані усталені резонансні коливання рідини в контейнері кругового перерізу для довільних періодичних непараметричних збурень

Nonlinear modal Narimanov-Moiseev—type equations are investigated to study resonant sloshing in a vertical cylindrical tank. The tank moves periodically in the space with the forcing frequency close to the lowest natural sloshing frequency. We show that the considered sloshing problem can to within the higher-order asymptotic terms be reduced to the case of orbital tank motions in the horizontal plane. Analytical solutions of the secular system which couples the dominant amplitudes of the steady-state sloshing are analytically solved. Effect of viscous damping is accounted. The results are compared with experimental measurements conducted by diverse authors for longitudinal and circular orbital tank excitations. A parametric analysis of the amplitude curves is done to clarify how the steady-state wave regimes and their stability change versus the forcing frequency and the semi-axes ratio of the elliptic orbit. The main result consists of confirming the experimental disappearance of the counter-directed swirling wave mode (relative to the elliptic orbit direction) when passaging to the circular orbit.

Dry-friction-induced self-excitation of a rectangular liquid-filled tank

The self-excitation of spring–mass system subjected to dry friction has been studied for decades because of its interesting and complex nonlinear dynamics behaviors. In this paper, a fluid–structure interaction problem, which describes the dry-friction-induced self-excitation of a rectangular liquid-filled tank, is proposed here about how the liquid sloshing affects the tank’s motion. To study responses of both the tank and liquid in depth, an equivalent pendulum model is developed to consider the coupling effects of structure elasticity, liquid sloshing, and dry friction. Another model based on smoothed particle hydrodynamics (SPH) method is also built for studying the liquid behavior while sloshing. The multidimensional-mode convergence is first analyzed, and then, the parameter analysis on the mode and frequency of the tank–spring–liquid–belt coupled system is analytically and numerically conducted. With the increasing liquid, the first two modes of the system approach the structure frequency and liquid frequency, respectively, at first, and then, the tendency converts for the intersection of the structure frequency and liquid frequency. Based on Lyapunov stability theorem, the periodic motion of the liquid-filled tank, including the stick–slip phase and slip phase, is both caused by Hopf bifurcation of equilibrium point. The sloshing effect results in a comparatively smaller bifurcation point. When there is no liquid or a little liquid in tank, the system experiences a subcritical Hopf bifurcation. If the liquid mass is heavy enough, the subcritical Hopf bifurcation converts to the supercritical Hopf bifurcation. During the self-excitation motion, liquid in tank sometimes sloshes linearly with small-amplitude free-surface deformation based on SPH simulation and sometimes sloshes violently with impacting, turning, breaking, and merging. Results by equivalent model show that the swing range of the equivalent pendulum can even reach ± 25.0° at this time. Hence, the dry-friction-induced self-excitation of the liquid-filled tank with lots of interesting nonlinear dynamics behaviors is tightly parameter-related. Results show that the equivalent pendulum model and SPH model match each other well and have different advantages on handling the nonlinear dynamical behaviors of such systems.

Study on Sloshing Effect of Vertical Storage Tank With Displacement Seismic Excitation

Abstract A 1:4 scale seismic simulation shaking table experiment was designed and performed to study the sloshing wave height response of a storage tank under displacement due to seismic excitation, wherein a 1000 m3 vertical storage tank was used to compare the sloshing wave height for different tanks with different foundations. Under different foundation forms, the tank motion includes sway and roll. Meanwhile, the design code and finite element method were used to compare with the experiment for mutual verification. The results show that the peak value of the sloshing wave height is at its minimum at the center, and the maximum is near the tank wall when the model tank was excited to the ground motion with the predominant frequency range from 0.29 and 0.32 Hz, and the floating roof can significantly reduce the sloshing wave height. For different input conditions with equivalent seismic magnitude, the wave heights were notably different, so the design should use multiple seismic waves as inputs. The acceleration values were different when different foundations were used, but there was little effect on the sloshing wave height. Besides, the sloshing wave heights measured in the experiment were close to those calculated using standard equations and finite element results, which proves that the three can verify each other.

Analysis of the influence of parametric resonance on the motion of a tractor tank when transporting liquid cargoes

The process of transportation of a liquid cargo in a tank or cistern is simulated in the presence of an interface between liquid and gas. Oscillations of the walls lead to overflow along the free surface and redistribution of the mass of liquid in the tank. It is shown that, under unfavorable conditions, coupled vertical and horizontal oscillations of the liquid lead to the appearance of parametric resonance. Principles are formulated and stages are assigned for the development of a new mathematical model capable of investigating the process of transporting a liquid cargo, taking into account the main linear and nonlinear relationships between the motion parameters, as well as the possibility of resonances. When describing fluid oscillations, a discrete model of partial oscillators is used, into which a number of permissible simplifications have been introduced. The outlined simplifications are based on the principle of equivalent replacement of the real shape of the container with the shape of a rectangular parallelepiped. The principle of reduction is to preserve the size of the free surface of the liquid and the mass of the liquid in the tank. It is established that for problems with ergonomic criteria, it is enough to use three partial oscillators for each form of oscillations: longitudinal, transverse and torsional. The principles adopted were used to study the longitudinal and lateral vibrations of a tractor that transports a tank with a liquid on a trailer. A computational study of the change in the parameters of the vehicle movement in the vicinity of the parametric resonance is carried out. During the simulation it is shown that the parametric resonance is significantly influenced by the properties of the transported fluid and the characteristics of the external kinematic excitation.

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.

Resonant three-dimensional nonlinear sloshing in a square base basin. Part 5. Three-dimensional non-parametric tank forcing

Assuming an inviscid incompressible liquid (with irrotational flows) partly filling a square base tank, which performs a small-amplitude sway/surge/pitch/roll periodic motion whose frequency is close to the lowest natural sloshing frequency, a nine-dimensional Narimanov–Moiseev-type (modal) system of ordinary differential equations with respect to the hydrodynamic generalised coordinates was derived in the Part 1 (Faltinsen et al., J. Fluid Mech., vol. 487, 2003, pp. 1–42). Constructing and analysing asymptotic periodic solutions of the system made it possible to classify steady-state resonant sloshing and its stability for the harmonic reciprocating (longitudinal, diagonal and oblique) forcing. The results were supported by experimental observations and measurements. The present paper finalises the case studies by considering the three-dimensional non-parametric (combined sway, pitch, surge, roll and yaw, but no heave) cyclic tank motions. It becomes possible after establishing an asymptotic equivalence of the associated periodic solutions of the modal system to those for a suitable horizontal translatory elliptic forcing so that, as a consequence, resonant steady-state waves and their stability can be considered versus angular position, semi-axis ratio and direction (counter- or clockwise) of the equivalent orbits. The circular orbit causes stable swirling waves (co-directed with the orbit) but may also excite stable nearly standing waves. The orbit direction does not affect the response curves for wall-symmetric (canonic) and diagonal orbit positions. This is not true for the oblique-type elliptic forcing. When the semi-axis ratio changes from 0 to 1, the response curves exhibit astonishing metamorphoses significantly influencing the frequency ranges of stable nearly standing/swirling waves and ‘irregular’ sloshing. For the experimental input data by Ikeda et al. (J. Fluid Mech., vol. 700, 2012, pp. 304–328), the counter-directed swirling disappears as but the frequency range of irregular waves vanishes for .