3 DYNAMIC RESPONSE OF ELEVATED LIQUID STORAGE RESPONSE OF … · liquid retaining structures is one of the prime concerns. Liquid storage tanks are very important components of industrial

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print),

ISSN 0976 – 6316(Online) Volume 1, Number 1, May - June (2010), © IAEME

27

DYNAMIC RESPONSE OF ELEVATED LIQUID STORAGE

ELASTIC TANKS WITH BAFFLE

Damodar Maity

Associate Professor

Department of Civil Engineering

IIT Kharagpur, India

E-Mail: [email protected]

C. Naveen Raj


IIT Guwahati, India

Indrani Gogoi

Associate Professor


NITK Surathkal, India

ABSTRACT

The dynamic response of elevated baffled liquid storage tanks, including the

hydrodynamic interaction, is presented in this paper. Both the tank and fluid are

discretized by finite elements. The tank wall and baffle are made of elastic, isotropic

material. The liquid in the tank is considered as water. The equation of the liquid motion

is expressed in terms of pressure by neglecting the viscosity and nonlinear term of the

Navier-Strokes equation. The fluid is modeled with twenty seven node solid (3-D)

elements whereas the elastic tank wall and its baffle are modeled with nine node (2-D)

shell elements using ADINA–FSI, a multi-physics simulation program. The response of

the coupled system is obtained considering fluid structure interaction effects.

Hydrodynamic pressure generated in the fluid-structure interface and the displacement of

the tank wall is evaluated. A parametric study has been carried out to study the

effectiveness of a baffle for damping liquid oscillations in order to evaluate efficient

baffle configuration in an elevated tank.

International Journal of Civil Engineering

and Technology (IJCIET), ISSN 0976 – 6308(Print)

ISSN 0976 – 6316(Online) Volume 1

Number 1, May - June (2010), pp. 27-45

© IAEME, http://www.iaeme.com/ijciet.html

IJCIET

© I A E M E



28

Key words: Elevated tank; baffle; fluid-structure interaction; hydrodynamic pressure;

seismic response

1. INTRODUCTION

In the recent years there has been an upsurge of unrest in the safety of all

structures, components and facilities that can produce both primary and secondary health

hazards in the event of an earthquake. The structural integrity of liquid operational and

liquid retaining structures is one of the prime concerns. Liquid storage tanks are very

important components of industrial and agricultural facilities used for storing toxic or

inflammable liquids and water respectively. Observations from available field reports on

the structural performance of tanks during recent earthquakes indicate that the steel tanks,

rather than concrete tanks, are more susceptible to damage and eventual collapse

(Hamdan 2000). Failure of tanks and their accessories is not only limited to the

immediate danger to nearby human lives, but also to a large extent leads to serious

consequences and long-term environmental damages.

Unlike buildings, predicting seismic behavior of liquid containing tanks are (i)

affected by hydrodynamic force on tank walls and base exerted by liquid during seismic

excitation and (ii) liquid containing tanks are less ductile and have less redundancy. In

big cities, sometimes swimming pools are constructed on the terrace of the buildings,

which may disturb the structural integrity as a whole during the earthquake, if

hydrodynamic pressure is not taken into account properly while designing the structural

system. Heavy damages were caused to liquid storage tanks especially elevated tanks by

strong earthquakes such as Niigata in 1964, Alaska in 1964 and Parkfield in 1966. A

review of seismic codes on liquid containing tanks carried out by Jaiswal et al. (2007)

concludes that all the codes design for higher seismic force for liquid containing tank as

they possess low ductility and redundancy. A lower value of response modification factor

is prescribed as compared to a building system. However, there is a large variation in

assigning of response modification factor for different types of tanks.

When a tank like container, partly filled with liquid is excited by external forces,

sloshing takes place. Sloshing is the term used to describe the motion of a liquid in a

partially filled tank. The hydrodynamic pressure is developed due to the liquid movement



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and the pressure is exerted on the tank wall. The tank wall should therefore be strong

enough to withstand these hydrodynamic forces in addition to hydrostatic pressure. An

additional structural member called baffle can be provided to control sloshing. For ease

of installation, a disk-type baffle with inner hole is being widely used for liquid storage

tanks.

Both experimental and theoretical studies related to the vibration of liquid in a

stored container have been reported in the literature. A numerical investigation was

carried out by Haroun and Tayel (1985) on partly filled axi-symmetric tanks in which the

shell was modeled by finite elements and liquid region treated analytically. Natural

frequencies and mode shapes were evaluated. Hwang (1989) studied the dynamic

response of liquid storage tank during to earthquake by combining boundary element

method and finite element method. The tank wall 3 and the fluid domain were treated as

two substructures of the total system. The boundary element method was used to find the

hydrodynamic forces associated with small amplitude excitations.

A baffle is a supplementary structural member, which supplies a sort of passive

control during earthquake motion. Baffle has been introduced recently with the objective

of improving the seismic safety and reducing the risk of damage or failure of thin walled

cylindrical liquid storage tanks. The effects of a rigid baffle on the seismic response of

liquid in a rigid cylindrical tank was studied by Gedikli and Erguven (1999). The

parametric eigen characteristics of baffled cylindrical liquid storage tank was investigated

by Cho et. al. (2002) with the coupled structural acoustic finite element method. Biswal

et al. (2004) demonstrated coupled formulation for the free vibration analysis of liquid-

filled cylindrical tank - baffle system that can be used to compute the low frequencies

associated with liquid sloshing modes and high frequencies associated with the coupled

vibration modes. Maity et al. (2009) showed the effective location of baffle and its

dimension to obtain minimum response of the tank-water coupled system under seismic

excitations. Eswaran et al. (2009) investigated the effect of ring baffles on liquid sloshing

for partially filled cubic tank. The effect of various factors like depth of liquid, tank

geometry, the amplitude and nature of the tank motions on sloshing severity were

studied. The results obtained were further used to verify the effectiveness of numerical

simulation technique.



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Following the development of FEA tools used for structural analysis, significant

advances in the fluid analysis have empowered the fluid analysts with a number of

commercial CFD codes that are robust and efficient for general fluid flow analysis

(Freitas 1995, Bathe et al. 1995, Zhang et al 2003, Bathe and Zhang 2004). The

Lagrangian-Eulerian formulation in the fluid system can efficiently be solved by using

ADINA–FSI, a multi-physics simulation program (Andersson and Andersson 1997,

Bathe et al 1999, Wang 1999, Panigrahy et al 2009). Moreover, recent efforts have

resulted in a very smart design of the user-interface such as providing effective ways to

generate meshes, set modeling assumptions, and state boundary conditions.

The present study focuses on the study on the response of elevated liquid storage

tank with the presence of baffle. The steel tank and the water domain are discretized by

finite elements. The tank material is considered as isotropic and elastic. The tank wall and

baffle are discretized by nine node shell elements. The liquid in the present analysis is

water and is assumed to be inviscid, linearly compressible and is under small amplitude

of excitation. Pressure degree of freedom is taken for fluid element. The fluid domain is

modeled using twenty seven noded elements. The fluid and the tank domain are treated as

two sub-structures coupled through their interface by an iterative scheme. The dynamic

response of elevated baffled liquid storage tank has been studied extensively to study the

influence of baffle on the response control of the coupled system.

2. MATHEMATICAL MODELING

The results of any dynamic analysis depend on the approximation involved in the

development of the mathematical models for the systems. It is not possible always to obtain a

closed form analytical solution for many engineering problems. With the advent of faster

generation computers, one of the most powerful numerical techniques that have been

developed in the realm of engineering analysis is the finite element method. The method,

being general, can be used for the analysis of liquids and solids of complex shapes and

complicated boundary conditions. In the present study, nine noded shell elements for the tank

wall and twenty seven noded 3D solid elements for the liquid are chosen (Fig. 1 and Fig. 2)

for the analysis. Three noded 3-d frame elements (Fig. 1) have been considered to model the

steel column and bracing of the elevated tank.



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2.1 Mathematical Modeling of Liquid:

Using the principles of classical mechanics, the motion of continuous fluid

medium in a fixed Cartesian coordinate frame of reference can be expressed using the

Eulerian approach in terms of mass, momentum and energy as

The characteristic properties of the medium are considered as functions of time

and space in the frame of reference. In the above equations, t is the time, ρ is the density,

v is the velocity vector, fB is the body force vector of the fluid medium, τ is the stress

tensor and given by

τ = (− p +λ�.v)I + 2µe (4)

Here, p is hydrodynamic pressure distribution in excess of the hydrostatic

pressure; µ and λ are the two coefficients of fluid viscosity. The heat flux q and the

specific rate of heat generation qB are neglected in the present problem. E is the specific

total energy and is defined as

Here b is the specific kinetic energy and e is the velocity strain tensor, which may

be expressed as:

The body forces included in fB (Eq. 2-3) is the gravitational force which may be

written as

where g is the gravitational acceleration vector. Since the flows are basically

incompressible, a constant density (ρ) throughout the governing equations has been



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assumed except in the continuity equation. The non-conservative form of the continuity

equation in slightly compressible flows becomes

where, ρm is the fluid density with the compressibility and ρ is the density at p = 0 and

thus can be relating as:

Here, k is the bulk modulus of elasticity of the fluid. Thus for the small amplitude

of motion and with the absence of body force, the continuity and momentum equations of

the fluid can be simplified to:

2.2 Mathematical Modeling of Solid:

Material for solid parts is assumed to be isotropic elastic with small displacements

and strains. The tank wall and its baffle (Figure 1) are modeled using the standard

Lagrangian formulation for displacement and strain, which is as follows:

where, is the ijth components of the Cauchy stress tensor for (i, j = 1, 2, 3), is

the displacement component in the co-ordinate i direction and is the mass density.

2.3 Modeling of FSI Problems:

In case of fluid-structure interaction (FSI) problems, fluid forces are applied on

the structure and the structural deformation changes the fluid domain. Difficulties arise in

the FSI analysis not only because of the non-linear governing equations for fluid; but also

because of description of the governing equations for fluid and structure in different

coordinates. The computational domain is divided into fluid and structural domain, where



33

a fluid model and a structural modelare defined respectively, through their material data,

boundary conditions etc. The interaction occurs along the interface of the two domains.

One can perform simulations and predict many physical phenomena when these two

models are coupled together. The coupling conditions at the fluid-structure interfaces are:

Here, f is the traction vector acting on the structure surface, and n is the unit vector normal to

the

interface. Using an Arbitrary-Lagrangian-Eulerian coordinate system (ALE) i.e., eqs. (10)-

(11)

for fluid; eq. (12) for solid and application of the boundary conditions eq. (13) to the discrete

finite element equations of the fluid and the structure, the finite element equations of the

coupled fluid-structure system can be expressed as

where, are the solution vectors of the coupled system. Xf and Xs are the fluid

and solid vectors defined at the fluid and solid nodes respectively. Ff and Fs are the finite

element equations corresponding to the fluid and structure model. The decoupled fluid

and solid equations can be represented by respectively.

3. RESULTS AND DISCUSSIONS

The types of problems addressed through this formulation are that of a rectangular

thin walled elevated water filled tank and is subjected to external excitations. The tank

wall is considered in this case to be elastic in nature.

3.1 Validation for empty tank without baffle

To validate the correctness of the developed models a benchmark problem has

been considered and results are compared with the results available in the literature. A

cylindrical ground supported circular steel tank of modulus of elasticity,



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Poisson’s ratio, υ = 0.3 and mass density, has

been considered for analysis and compared with the results obtained by Haroun and

Tayel (1985). The thickness of tank wall and its radius is considered as 25.4 mm and

18.29 m respectively.

Figure 1 Finite element discretization of Elevated tank

Figure 2 Finite element discretization of fluid domain

Free vibration analysis of the above tank has been carried out to validate the

developed finite element model. The variations of natural frequencies with various

heights to radius ratio of the tank have been studied and the results are tabulated in Table

1 along with the results obtained from literature by Haroun and Tayel (1985). In Table 1,



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H/R represents the ratio of height to radius of the tank. A convergence study has been

done to find the results with a desired level of accuracy. For example, in case of H/R =

0.67, the discretization has been taken as 5×40 in which the results are converging

sufficiently. The comparison of results at R = 18.29 m, show that the frequencies

obtained by the proposed model agree quite well with those obtained in literature.

Table 1 Variation of fundamental frequency of empty tank

3.2 Response of elevated tank

The dynamic analysis of elevated tank has been carried out to study the stability

of the developed modeling. The geometry and material properties of the tank are

considered as follows: Tank: length = 6 m, width = 6 m, height = 4 m, Thickness = 20

mm, column spacing = 4 m, column height = 15 m. The tank wall is made of steel having

the material properties of modulus of elasticity, Poisson’s ratio, υ

=0.3 and density . The mass density and velocity of sound in water

are assumed as and 1438.7 m/s respectively. The above dimensions and

material properties has been considered throughout the study unless it is mentioned.

The horizontal displacements of the elevated tank under different sinusoidal

excitation frequencies with unit amplitude of acceleration are plotted in Figures 3 to 5.

The frequencies under consideration are the fundamental natural frequency along with

some different frequencies. It is observed that the displacement is increasing continuously

(Figure 4) when the tank is excited at its natural frequency as expected. The first three

mode shapes of the elevated empty tank have been plotted in Figure 6.



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Figure 3 Displacement at top of tank due to sinusoidal ground acceleration for f = 0.8 cps

Figure 4 Displacement at top of tank due to sinusoidal ground acceleration for f=2.134cps

Figure 5 Displacement at top of tank due to sinusoidal ground acceleration for f = 4 cps



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(a) 1

st Mode (b) 2

nd Mode (c) 3

rd Mode

Figure 6 Mode shapes of elevated tank

3.3 Effect of baffle on elevated tank under sinusoidal acceleration

To study the effect of baffle on elevated tank, the baffle is located at mid height of

water level. The baffle location is arrived on the basis of previous work carried by Maity

et al (2009) at which substantial amount of response reduction is expected. The material

properties of the baffle are same as in case of tank wall. A sinusoidal ground acceleration

of frequency 6cps, is applied at the ground. The dynamic responses due to both horizontal

and vertical sinusoidal loadings are shown in Figures 7 to 10. It is observed that the

developed hydrodynamic pressures as well as the tank displacements are reducing due to

the presence of an elastic baffle.

The deformation pattern of the water filled baffled tank under horizontal

sinusoidal ground excitation at different time instant has been plotted in Figure 11. The

time period (T) of the excitation is taken as 0.1676 cps in this analysis. The deformation

patterns are plotted at time, t = 0, T/16, 2T/16, 3T/16 and 4T/16 secs respectively shows

the behaviour of the elevated tank. Figure 12 shows deformation of the same tank at

different time instant due to sinusoidal excitation in vertical direction.



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Figure 7 Top displacement of the tank wall due to horizontal sinusoidal acceleration

Figure 8 Hydrodynamic pressure at the bottom of tank due to horizontal sinusoidal

acceleration

Figure 9 Top displacement of the tank wall due to vertical sinusoidal acceleration



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Figure 10 Hydrodynamic pressures at the bottom of tank due to vertical sinusoidal

acceleration

(a) t = 0 sec. (b) t = T/16 sec. (c) t = 2T/16 sec. (d) t = 3T/16 sec. (e) t = 4T/16 sec

Figure 11 Deformation pattern at different time instant due to horizontal sinusoidal

excitation

(a) t = 0 sec. (b) t = T/16 sec. (c) t = 2T/16 sec. (d) t = 3T/16 sec. (e) t = 4T/16 sec.

Figure 12 Deformation pattern at different time instant due to vertical sinusoidal

excitation



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3.3 Effect of baffle on elevated tank under seismic excitation

The seismic response of the same tank has been plotted in Figures 13 to Figure 16

to study the effectiveness of the baffle. Results presented are used to depict the

distinction between the response obtained with and without the presence of baffle under

horizontal and vertical El Centro (N-E) horizontal earthquake excitation. It is observed

that both the displacement and hydrodynamic pressure are well controlled if the baffle is

present in the water filled tank. Figures 17and 18 show the hydrodynamic pressure

distribution of fluid domain at a particular time instant (in this case 10 sec.) due to El

Centro horizontal earthquake excitation without and with the presence of baffle

respectively. It is observed by comparing above two figures that the magnitude of the

hydrodynamic pressure becomes considerably less if the baffle is present inside the water

tank. Same observations have been noticed in Figures 19 and 20 while the tank is

subjected to El Centro earthquake excitation in the vertical direction.

Figure 13 Top displacement of the tank wall due to horizontal earthquake acceleration

Figure 14 Hydrodynamic pressures at the bottom of tank due to horizontal earthquake

acceleration



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Figure 15 Top displacement of the tank wall due to vertical earthquake acceleration

Figure 16 Hydrodynamic pressures at the bottom of tank due to vertical earthquake

acceleration

Figure 17 Hydrodynamic pressure distribution of water domain due to El Centro

horizontal earthquake (without baffle)



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Figure 18 Hydrodynamic pressure distribution of water domain due to El Centro

horizontal earthquake (with baffle)

Figure 19 Hydrodynamic pressure distribution of water domain due to El Centro vertical

earthquake (without baffle)



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Figure 20 Hydrodynamic pressure distribution of water domain due to El Centro vertical

earthquake (with baffle)

4. CONCLUSIONS

The objective of the present investigation is to gain an understanding of the

behavior of the coupled elevated baffled tank-water system. The FE model using ADINA

program is developed, in which a general time domain analysis of the coupled system is

carried out considering fluid-structure interaction effects. The displacements in the tank

and the pressure developed in the water domain are computed using the developed model

under external excitations. Study has been carried out under horizontal as well as vertical

seismic excitation to have a comparative response of the baffled tank-water system. The

fluid-structure interaction effects are achieved by indirect coupling of the two systems

viz., the elevated baffled tank and water domain. The elevated water tanks are, in general,

very susceptible to earthquakes. The parametric study reveals that the presence of baffle

in the elevated water tank reduces the dynamic response of the coupled system to a large

extent. The response results depict that baffles may be used effectively as controlling

devices for the control of tank displacements and hydrodynamic forces during earthquake

excitations.



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Documents

3 DYNAMIC RESPONSE OF ELEVATED LIQUID STORAGE RESPONSE OF … · liquid retaining structures is one of the prime concerns. Liquid storage tanks are very important components of industrial