SIMPLIFIED DYNAMIC ANALYSIS OF SLOSHING PHENOMENON IN .

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Mahmood Hosseini and Pegah FarshadmaneshCOMPDYN 2011III ECCOMAS Thematic Conference onComputational Methods in Structural Dynamics and Earthquake EngineeringM. Papadrakakis, M. Fragiadakis, V. Plevris (eds.)Corfu, Greece, 26–28 May 2011SIMPLIFIED DYNAMIC ANALYSIS OF SLOSHING PHENOMENONIN TANKS WITH MULTIPLE BAFFLES SUBJECTED TOEARTHQUAKEMahmood Hosseini1 and Pegah Farshadmanesh2*12Structural Eng. Research Center, Int’l Institute of Earthquake Engineering and Seismology (IIEES)No. 21 Arghavan, North Dibaji St., Farmanieh, Tehran 19537, Iranhosseini@iiees.ac.irHydraulic Eng. Group, Civil Eng. Dept., Tehran South Branch of the Islamic Azad University (IAU)Ahang Blvd, Tehran, Iran(p.farshadmanesh@gmail.com)Key words: Multiple vertical baffles, Time history analysis, Neural network, Requiredcalculation timeAbstract. Sloshing is a well-known phenomenon in liquid storage tanks subjected to base orbody motions. In recent years the use of baffles for reducing the sloshing effects in tankssubjected to earthquake has been studied by some researchers. However, the use of multiplebaffles has not been taken into consideration so much. On the other hand, although some ofthe existing computer programs are capable to model sloshing phenomenon by acceptableaccuracy, the full dynamic analysis subjected to random excitations such as earthquakeinduced motions is very time consuming, particularly when there are vertical and horizontalbaffles inside the tank, which postpone the convergence of response calculations. Therefore,a simplified method for evaluation of sloshing effects in baffled tanks is desired. In this papera method is presented for this purpose based on conducting several dynamic analysis cases,by using a powerful Finite Element (FE) method for rectangular tanks with variousdimensions, subjected to both harmonic and seismic excitations, and then using neuralnetwork to create simple relationships between the dominant frequency and amplitude of thebase excitations and the maximum level of liquid in the tank during the sloshing and also themaximum dynamic pressure on the tank wall. At first, the FE numerical modeling has beenverified by using some existing experimental data. Then, dynamic analyses have beenconducted to obtain the required numerical results for teaching the neural network. In thenext stage, the neural network model has been developed. Finally, the predicted results of theneural network have been compared with those obtained by some other cases of analyses ascontrol values, to make sure on the accuracy of the neural network model. The proposedsimplified neural network model can be used also for finding the proper number and featuresof baffles for minimizing the sloshing effect on the tank for a group of given earthquakes, orother cases of base excitations.

Mahmood Hosseini and Pegah Farshadmanesh1INTRODUCTIONOne of the most important phenomena in fluid storage tanks, either buried, semi-buried,aboveground or elevated, is the oscillation of fluid due to the movements of the tank body,because of its base motions during an earthquake. Past earthquakes have shown that thisphenomenon can result in sever damages to water storage tanks. To prevent tanks againstsloshing induced damages, the use of baffles have been suggested and studied by someresearchers since mid 60s [1], however, just few studies have been conducted on using bafflesfor reducing the earthquake induced sloshing effects.As one of the first works in this regard Shaaban and Nash (1977) studied on response ofpartially filled liquid-storage circular cylindrical tank with or without an interior cylindricalbaffle under seismic actions using Finite Element (FE) technique [2]. They worked on anelastic cylindrical liquid storage tank attached to a rigid base slab. Their studied tank waseither empty or filled to an arbitrary depth with an in-viscid, incompressible liquid. Theypresented a FE analysis for both tank and liquid, to investigate the free vibration of thecoupled system permitting determination of natural frequencies and associated mode shapes.They employed Sanders shell theory to express the strain-displacements relationship in thederivation of the shell FE. They determined the response of the tank to artificial earthquakeexcitation, and performed similar investigations with the addition of an elastic cylindricalperforated baffle to control the system natural frequencies.In 1999 Gedikli and Ergüven worked on the seismic analysis of a liquid storage cylindricaltank with a rigid baffle [3]. In that study the fluid was assumed to be incompressible and inviscid, and its motion was assumed to be ir-rotational. They implemented method ofsuperposition of modes to compute the seismic response, and used the boundary elementmethod to evaluate the natural modes of liquid in the tank. In that study the linearized freesurface conditions was taken into consideration.Yasuki and his colleagues (2000) conducted a study on suppression of seismic sloshing incylindrical tanks with baffle plates [4]. The purpose of that study was proposing theevaluation model of damping characteristics of cylindrical tank with ring baffle plates. Theycarried out shaking table tests, in which the location and geometry of the baffle plates werevaried, with sinusoidal excitation. Their experimental results showed that the dampingcharacteristic is dependent on the location and geometry of baffle plates. Their model forsolid baffle plates was extended to be applicable to both solid and perforated baffle plates, andthe validity of their evaluation model was confirmed with the experimental results.Maleki and Ziyaeifar (2007) conducted a study on damping enhancement of seismicisolated cylindrical liquid storage tanks using baffles [5]. Mentioning that in moving liquidcontainers, baffles play an important role in damping the liquid motion, to study the effects ofusing baffles in seismically isolated tanks, in the first instance they have analyzed the velocitycontours in a cylindrical tank to determine the most effective shape of baffle. Then they havedetermined the damping coefficients analytically for horizontal ring shape and vertical bladeshape baffles. To estimate the sloshing height level and the damping ratio, Maleki andZiyaeifar have developed a methodology, based on Tank Body Spectra, in which the highersloshing amplitude and the relative fluid velocity with respect to baffles in base isolated tanksare taken into consideration. They have also developed a computer program to put all thesetogether and investigate the effect of baffles for different tank dimensions under the effect ofearthquakes. Their results show that the average damping ratio of sloshing mode due to ringbaffle increases with a decrease in liquid height and highest damping may be achieved forheight to radius ratios of 1.0 to 1.5. In addition, for reasonable ring baffle dimensions, anaverage reduction of 6% in base displacement of base isolated tanks and an average reduction

Mahmood Hosseini and Pegah Farshadmaneshof more than 30% in the sloshing height of base isolated and fixed base tanks may beachieved. To study the effect of baffles on the distribution of hydrodynamic and tank bodyforces with height, Maleki and Ziyaeifar have proposed a simple dynamic model. The resultsof analyses using this model indicate a constant reduction in sloshing forces and differentreductions in moment and shear forces for different heights. This happens becausecontribution of the sloshing force to the total hydrodynamic force varies with height.Wu (2010) has conducted a thorough study the nonlinear liquid sloshing in a 3D tank withbaffles, in which the mechanism of liquid sloshing and the interaction between the fluid andinternal structures have been investigated [6]. He has applied a developed 3D timeindependent finite difference method to solve liquid sloshing in tanks with or without theinfluence of baffles under the ground motion of six-degrees of freedom. He has solved the 3DNavier-Stokes equations and has transformed to a tank-fixed coordinate system, and hasconsidered the fully nonlinear kinematic and dynamic free surface boundary conditions forfluid sloshing in a rectangular tank with a square base. In that study the fluid was assumedincompressible. The complicated interaction in the vicinity of the fluid-structure interface wassolved by implementing one dimensional ghost cell approach and the stretching gridtechnique near the fluid-structure boundaries were used to catch the detailed evolution of localflow field. A PC-cluster was established by linking several single computers to reduce thecomputational times due to the implementation of the 3D numerical model. The MessagePassing Interface (MPI) parallel language and MPICH2 software were utilized to code thecomputer codes and to carry out the circumstance of parallel computation, respectively.Wu has verified his developed numerical scheme by rigorous benchmark tests, and has alsoperformed some further experimental investigations [6]. In that study for a tank withoutinternal structures, the coupled motions of surge and sway were simulated with variousexcitation angles, excitation frequencies and water depths. The characteristics of sloshingwaves were dissected in terms of the classification of sloshing wave types, sloshingamplitude, beating phenomenon, sloshing-induced forces and energy transfer of sloshingwaves. Six types of sloshing waves, named single-directional, diagonal, square-like, swirlinglike, swirling and irregular waves, were found and classified in Wu’s study and he found thatthe occurrence of these waves are tightly in connection with the excitation frequency of thetank. The effect of excitation angle on the characteristics of sloshing waves was explored anddiscussed, especially for swirling waves. In that study the spectral analyses of sloshingdisplacement of various sloshing waves were examined and a clear evidence of the correlationbetween sloshing wave patterns and resonant modes of sloshing waves were demonstrated.The mechanism of switching direction of swirling waves was also discussed by investigatingthe situation of circulatory flow, the instantaneous free surface, the gravitational effect and theinstantaneous direction of external forcing.Wu also considered a 2D tank with vertically tank bottom-mounted baffles and hasdiscussed the influence of baffle height on the natural mode of the tank, the evolution ofvortices and vortex shedding phenomenon, the relationship between the vortex sheddingfrequency and the excitation frequency of the tank, the vortex size generated in the vicinity ofthe baffle tip, and the interaction of vortices inside the tank [6]. Based on the results thebaffle height shows a significant influence on the shift of the first natural frequency of thebaffled tank and the liquid depth also plays an important part in determining this influence. Inother words, the shift of the first natural mode due to various baffle heights varies with waterdepths. Wu has claimed that the design of two baffles separated by 0.2 times the tank breadthis an efficient tool to not only reduce the sloshing amplitude, but also switch the first naturalfrequency of the tank. The results also show that sloshing displacement is affected distinctlyby different numbers of baffles mounted vertically on the tank bottom. The more baffles

Mahmood Hosseini and Pegah Farshadmaneshmounted onto the tank bottom, the smaller the sloshing displacement is presented in both thetransient and steady-state periods. Wu has categorized the processes of the evolution ofvortices near the baffle tip into four phases: the formation of separated shear layer andgeneration of vortices, the formation of a vertical jet and shedding of vortices, the interactionbetween shedding vortices and sloshing flow (the generation of snaky flow) and theinteraction between snaky flow and sloshing waves. Results show that vortex sheddingphenomenon due to stronger vertical jets occurs when the excitation frequency is close to thefirst natural mode of the baffled tank, and that is discussed and the size of vortex, generatednear the baffle tip, is closely correlated with the baffle height. In that study two types of 3Dtuned liquid dampers, a vertically tank bottom-mounted baffle and a vertical plate, werediscussed for a tank under coupled surge-sway motions. Results show that the wave types ofdiagonal and single-directional waves switch to the swirling type due to the influence of thebaffle. The phenomenon of square-like waves or irregular waves coexisting with swirlingwaves is found in the baffled tank under diagonal excitation. The shift of the first naturalmode of the baffled tank due to various baffle heights is remarkable. The length of the platecan cause a significant influence on not only the variation of the natural frequencies but thetype of the sloshing waves. The influence of the vertical plate on the irregular waves isinsignificant and several peaks appear in the spectral analysis of the sloshing displacement forthe irregular waves and the numbers of peaks are more than that of the baffled tank.It is seen in the review of the literature that the analysis of baffled tanks in general is verycomplicated and time consuming, even with just one or two baffle(s). It is then clear thatmultiple baffles make the behavior of the liquid inside the tank more complicated, andaccordingly makes the analysis much more difficult and time consuming. In this study asimplified method for evaluation of sloshing effects in rectangular tanks with multiple bafflesis presented. The method is based on conducting several dynamic analysis cases, by using apowerful FE method for tanks with various dimensions, subjected to both harmonic andseismic excitations, and the use of neural network to create simple relationships between thedominant frequency and amplitude of the base excitations and the maximum level of liquid inthe tank during the sloshing and also the maximum dynamic pressure on the tank wall. Thedetails of the study are discussed in the following section of the paper.2FINITE ELEMENT MODELING AND ITS VERIFICATIONIn order to verify the numerical modeling of the tanks by FE analysis at first the numericalFE model of a tank, previously tested at the Hydraulic Institute of Stuttgart University onshake table (Figure 1) by some other colleagues (Goudarzi et al. 2010) [7], were developed bythe employed computer program.Figure 1: The scaled-down tank model on the shake-table [7]

Maahmood Hosseeini and Pegahh FarshadmanneshThe length, heigght, and widdth of the liquidlvolumme inside thhe tank havve been resppectively1.00, 0.64, and 0.440 meters. Figures 2 and 4 showw experimenntal, analyttical, and nuumericalresults ofo sloshing in the conssidered scalled tank moodel all togeether, studieed by Gouddarzi andhis colleeagues subjected to sinnusoidal basse excitationns ,5in twocases off, respectiveely, resonannt ( N) and with a lower frequuency ( N), and FiguresF3and 5 shhow the resuults obtaineed by the FEE model devveloped in thhis study.Figurre 2: Experimeental, analyticcal and numerical results off sloshing in thhe tank scaledd model subjeccted tosinusoidal basee excitations ata resonance [77]Figure 3: Numerical reesults obtainedd by FE analyssis of sloshingg in the tank scaled model wwhose experimmental andanalyticcal results for sinusoidal basse excitations at resonance are shown in Figure 2Figure 4: Experimeental, analytical, and numerrical results off sloshing in thhe tank scaledd model subjeccted tosinusoidal baase motion witth N, [7]]g in the tank scaled model wwhose experimmental andFigure 5: Numerical reesults obtainedd by FE analyssis of sloshinganalyticcal results for sinusoidal basse excitations with N are shown in Figure 4

Mahmood Hosseini and Pegah FarshadmaneshComparing Figure 3 with Figure 2 and also Figure 5 with Figure 4, the very goodagreement between the numerical result obtained by the FE model, developed in this study,and the experimental and analytical results can be seen. Based on this verification, theemployed FE modeling process could be used for more detailed analysis of sloshing in tanksas explained in next sections.3CONSIDERED TANKS FOR THE FINITE ELEMENT ANLYSESIn this study the typical double-compartment aboveground water tanks, used in watersupply system in Iran, were used. The general geometric features of the tanks, considered forthe study, are shown in Figure 6.Figure 6: General geometric plan features of the double-containment tanks considered for the studyTo have the minimum length of the tank’s wall (to minimize the amount of requiredconstruction materials) for a given tank’s area, in the case of double-compartment tanksshown in Figure 6, it can be shown easily that b should be around 1.5a. Also usually thewater depth in the tank, h, is considered not to be less than 0.1 of the width, a, and not morethan 6 meters. The common specifications of tanks with different water volumes orcapacities, based on the above conditions, are as shown in Table 1.Table 1: Common specifications of tanks with different water volumes, and their fundamental sloshing periodThe tank watercapacity (m3)125Tank water height,h, in the tank (m)3.0a (m)b 1.5ah/ah/bT 13.434

Maahmood Hosseeini and Pegahh FarshadmanneshThe values of thet first orr fundamenntal sloshingg modes off tanks in Table 1 haave beencalculatted based ono the folloowing formmula which gives the naturalnanggular frequeencies ofsloshingg modes in tankst[8]:2121(1)nandd g in the accceleration ofo gravity. Based on thhe abovewhere n is the sloshhing mode numberexplanaations, and consideringg the exponnentially groowth of thee required computational timewith nummber of eleements in the FE analyssis, on the oneo hand, annd the time step size in the timehistory analysis, on the otherr, explainedd in the nexxt section ofo the papeer, in this study thefollowinng values werew consideered as the basicbcase ofo the tank forfo analyses:a 1.00 mb 1.501 mh 0.150 mBy usingusome appropriatee scaling factors these dimensionss can be used for tankks of realsize, succh as those given in Taable 1. Thee scaling requirements are explainned in the foollowingsection, along withh the presenttation of nuumerical resuults.4SCAALING EFFFECTS ANDASLOOSHING RESPONSERE TO HOORMONICC BASEEXCCITATIONNSRegaarding that in this stuudy the effefects of usinng multiplee vertical bbaffles is the mainconcernn; the base excitationeannd accordinngly the induuced sloshinng have beeen assumed to occurin just oneo main diirection of the tank lenngth. On thhis basis, itt was imporrtant to knoow if thetank’s width,wwhicch is the diimension inn direction perpendicular to the eexcitation direction,ddoes havve any effect on the annalyses resuults. For thiis purpose variousvvaluues were coonsideredfor the parameterpb and by usiing a speciffic excitatioon the analyysis was reppeated, of whichwtheresults area shown inn Figure 7.Figure 7: The effect ofo the tank’s widthwon the waterwlevel varriation when excitationeis aalong the tank’’s lengthFigurre 7 indicatte that, as longlas the excitation is just in oneo main diirection of the tankplan, thhe tank dimmension perppendicular to the excittation direcction does nnot have anny majoreffect on the respoonse values. On this basis,bin all analyses caases, a consstant value ofo 0.1 m(insteadd of 1.5 m) wasw used foor the tank’ss width to reeduce the reequired timee for the anaalysis.

Maahmood Hosseeini and Pegahh FarshadmanneshAnotther importaant factor, whichwaffeccts the required time foor the respoonse analysis, is the

partially filled liquid-storage circular cylindrical tank with or without an interior cylindrical baffle under seismic actions using Finite Element (FE) technique [2]. They worked on an elastic cylindrical liquid storage tank attached to a rigid base slab. Their studied tank was

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