Procedia Engineering 111 ( 2015 ) 115 – 120

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1877-7058 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP)doi: 10.1016/j.proeng.2015.07.064

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XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP) (TFoCE 2015)

Numerical simulation of oil tank behavior under seismic excitation. fluid – structure interaction problem solution

Alexandr M.Belostotskiya, Pavel A.Akimovb, Irina N.Afanasyevac, Anton R.Usmanovd,Sergey V.Scherbinae, Vladislav V.Vershinin f*

aHead of Research and Educational Center of Computational Simulation of Unique Structures, Professor, Moscow State University of Civil Engineering,26, Yaroslavskoye Shosse, Moscow 129337, Russia

b Senior Researcher of Research and Educational Center of Computational Simulation of Unique Structures, Moscow State University of Civil Engineering,26, Yaroslavskoye Shosse, Moscow 129337, Russia

c,d,e,f Assistant of Research and Educational Center of Computational Simulation of Unique Structures, Moscow State University of Civil Engineering,26, Yaroslavskoye Shosse, Moscow 129337, Russia

Abstract

The present paper is devoted to numerical simulation of sloshing inside a partially filled cylindrical thin-wall tank induced by seismic loads. During the calculations fluid structure interaction (FSI) problems are taken into account. The numerical simulations are performed for both linear (Lagrangian formulation – ANSYS Mechanical) and nonlinear (arbitrary Lagrangian-Eulerian formulation – ABAQUS/Explicit) conditions. Problem formulation, finite element discretization, simultaneous and partitioned solution procedures are discussed. As an example designed and/or already erected oil tank are considered. The results obtained are compared with an analytical solution and domestic code technique.© 2015 The Authors. Published by Elsevier B.V.Peer-review under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP)

Keywords: Wave sloshing; Free surface flow; Liquid storage tank; Finite element (FE) methods; Arbitrary Lagrangian-Eulerian formulation; Lagrangian formulation; ANSYS Mechanical; ABAQUS/Explicit.

* Corresponding author. Tel.: +7-926-177-60-43; fax: +7-499-183-59-94.E-mail address: niccm@mgsu.ru

© 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP)

116 Alexandr M. Belostotskiy et al. / Procedia Engineering 111 ( 2015 ) 115 – 120

1. Introduction

Fluid structure interaction problems represent a large and continuing interest in science, industry and other applications. A prerequisite for a detailed study of the aerohydroelasticity nature and searching of the appropriate solution methods related to civil engineering problems has served a number of tragic cases of collapse (such as Tacoma Narrows Bridge collapse in 1940; cooling towers collapse at the Ferrybridge Power Stationin in 1965; destruction of the tanks as a result of interaction with the fluid after seismic impact in Japan 1955 (Kobe), 2003 (Tomakomai)).

Coupled three-dimensional dynamical problems of aerohydroelasticity is very far from being complete solved and require scientific-methodical, software and algorithmic development and research. Analysis of existing engineering methodic and domestic design codes and procedures showed that they require significant improvements and development.

In order to solve the practical knowledge-intensive problems the numerical simulation is basic and, in fact, no alternative approach. Existing mathematical models and numerical methods allow to study dynamic behavior of complex three-dimensional aerohydroelasticity coupled systems directly [1, 2, 3]. For the purposes of this research the universal software application packages for numerical simulation of continuum mechanics (ANSYS Mechanical,ANSYS CFD, Abaqus\Explicit) were used [4, 5].

2. Mathematical formulation [2, 3]

Lagrangian formulation of basic momentum equations (1) is normally employed to model the behavior of solid structure:

Bftu2

2(1)

where: – density; u – vector of displacements; t – time; – stress tensor; Bf – vector of externally applied forces.

The dynamic behavior of a liquid/gas is described by the classical Navier-Stokes equations. It is assumed that both laminar and turbulent flows obey these equations. The momentum equations of an incompressible Newtonian fluid (Navier-Stokes equations) in the ALE (arbitrary Lagrangian-Eulerian) formulation have the form:

ˆ[( ) ] BU U U U ft

(2)

ˆ( ) 0U U Ut

(3)

ˆ( ) Be U U e D q qt (4)

– U – fluid velocity; U – coordinate system velocity; – stress tensor in fluid; Bf – the vector of externally applied forces in fluid; e – specific internal energy; D – strain rate tensor.

To model multiphase flow the Euler formulation with free surface technique is used. Interaction between different phases (liquid and gas) is taken into account by inserting additional variable – volume fraction [4, 5].

When the interaction of the viscous liquid flow with a solid medium occurs, equilibrium and compatibility equations must be performed on the contact surface:

117 Alexandr M. Belostotskiy et al. / Procedia Engineering 111 ( 2015 ) 115 – 120

nn FS (5)

)(ˆ)( tutu II (6)

ˆ( ) ( ) ( )I

I Iu t U t U t (8)

ˆ( ) ( ) ( )II Iu t U t U t (9)

where: n – normal vector to the contact surface; u – vector of structure displacements; u – vector of fluid displacements at the contact surface; U – fluid velocity; U – coordinate system velocity; superscripts I, S, F denote contact surface, solid and liquid respectively.

Numerical approximation of the basic equations typically is performed by finite element method (for structuresand fluid) and finite volumes method (for liquid). To solve the above problem depending on its nature direct or iterative algorithms are used. Calculation of the coupled systems "structure – liquid" reduces to direct integrationover time of momentum equations. Implicit or explicit schemes with options of different termination condition areused.

3. Verification of the developed technique of numerical simulation [1, 6]

Numerical modeling technique of fluid tank behavior under seismic excitation was developed, verificated and approbated. Multivariate verification computational studies of static and dynamic behavior of liquid in the tank(different levels of water were tested) taking into account the interaction with the thin-walled experimental model of tank on a movable frame were carried out. Static loads (own weight and hydrostatics) and the different pulse duration impact were applied.

a) b) c)

d)

Fig. 1. a) Experimental model of the cylindrical water tank (scale 1:17.5); b), c) «ideal» FE-model of the experimental model and d) FE-model of the experimental model with initial imperfections of the shell (Lagrangian formulation, FLUID 80, ANSYS Mechanical).

118 Alexandr M. Belostotskiy et al. / Procedia Engineering 111 ( 2015 ) 115 – 120

At the validation stage of the developed detailed finite element models of the hydroelastic system (check the adequacy of the selected FE (FLUID80 and SHELL181), specified boundary conditions at the contact areas of the liquid with the reservoir structure and the contact zones of the bottom of the tank to the frame) modal and static analysis was conducted. Ideal numerical model and model with initial imperfections of the shell (experimental model) were tested (Fig. 1).

Comparative model analysis showed that the eigenfrequencies of the empty elastic tank (~152 Hz) lie in the range two orders of magnitude higher than the eigenfrequencies of the coupled hydroelastic system (~1 Hz). This fact should be expected that the dynamic behavior of the system in the low frequency range will be reduced to the sloshing of the liquid in the tank with rigid walls. Comparative model analysis for model with and without initial imperfections of the shell showed that the eigenfrequencies are very sensitive to such geometrical imperfections. This fact should be expected that the dynamic behavior of the shell will depend on it too. It leads to mismatching between numerical and experimental results (stress - strain state parameters of the shell).

The main results showed that the dynamic response of the hydroelastic system occurs at a system-wide low frequency determined by the spring constant and the mass installation. Complex dynamic forms of wave into the tank were identified for different levels of water. At the same time good quality (wave form of liquid) and quantitative (wave height) matching of numerical results with experimental data (error is less than 5%) were achieved (Fig. 2).

a) b)

Fig. 2. The shape and the height of the wave at time t = 3.4 (s) after impact. The maximum wave height 7.5 cm. a) Experimental results; b) results of numerical simulationl (Lagrangian formulation, FLUID 80, ANSYS Mechanical).

4. Approbation of the developed technique of numerical simulation [1, 6]

Practically important and complex real hydroelastic system "thin-walled tank with floating roof - oil" capacity of 50 000 m3 (Fig. 4) located in seismic zone was chosen for approbation of the developed numerical technique. Dynamic stress-strain state of the tank structures and wave formation on the surface of the liquid were simulated under an 8-point seismic impact given the earthquake accelerograms (Fig. 3). For solving this coupled problem alternative numerical approaches (Lagrangian formulation – ANSYS Mechanical and ALE – ABAQUS/Explicit)were used.

At the validation stage of the developed detailed finite element models of the hydroelastic system modal and static analysis were conducted.

Fig. 3. Applied seismic excitation (8-point of magnitude accelerogram)

119 Alexandr M. Belostotskiy et al. / Procedia Engineering 111 ( 2015 ) 115 – 120

a) b)

Fig. 4. a) Real object of research – the oil tank RVSPA-50000, b) FE-model of the oil tank RVSPA-50000 (Lagrangian formulation, FLUID 80, ANSYS Mechanical).

Practically close values of the main criterion parameters of dynamic stress-strain state (eigenfrequencies and mode shapes, height and shape of the waves of oil, displacements, the maximum component of principal and equivalent strains and stresses) were obtained by two alternative numerical approaches: Lagrange formulation implemented in ANSYS Mechanical, and ALE formulation implemented in ABAQUS/Explicit. The calculations were carried out with and without taking into account the floating roof. Shown that the values of stress-strain state in reservoir structures, where the interaction between free surface or floating roof with thin wall occurs, are close. Butmaximum wave height (for the case with floating roof) increased by flattening of water surface (Fig. 5).

a)

b)

Fig. 5. Results of numerical simulation of oil tank behavior under seismic excitation:a) oil tank RVSPA-50000 without floating roof, b) oil tank RVSPA-50000 with floating roof.

120 Alexandr M. Belostotskiy et al. / Procedia Engineering 111 ( 2015 ) 115 – 120

5. Conclusions

Analysis of existing engineering methodic and domestic design codes and procedures showed that they require significant improvements and development. In order to solve the practical knowledge-intensive FSI problems the technique of numerical simulation, based on existing mathematical models and numerical methods allowed to study dynamic behavior of complex three-dimensional aerohydroelasticity coupled systems directly, was developed. For the purposes of this research the universal software application packages for numerical simulation of continuum mechanics (ANSYS Mechanical, ANSYS CFD, Abaqus\Explicit) were used.

Based on the results obtained the verification and approbation computational research showed practical importance and efficiency of the developed technique of numerical simulation of oil tank behavior under seismic excitation. But further investigations are desired.

References

[1] A. M. Belostosky, P. A. Akimov, T. B. Kaytukov, I. N. Afanasyeva, A. R. Usmanov, S. V. Scherbina, V. V. Vershinin, About Finite Element Analysis of Fluid – Structure Interaction Problems.// Procedia Engineering, Volume 91, 2014, pp 37–42.

[2] K. J. Bathe, Finite Element Procedures.//Prentice-Hall, New York, 1996.[3] K. J. Bathe, H. Zhang, X. Zhang, Some advances in the analysis of fluid flows. //Computers& Structures, 1997, Vol. 64, pp. 909-930.[4] ANSYS, Inc., ANSYS 14.5 Help, 2013.[5] Dassault Systèmes (2010), ABAQUS Documentation.[6] I. N. Afanasyeva, Adaptive technique of numerical simulation of three-dimensional dynamic problems of civil aerohydroelasticity.//

PhD thesis, Moscow State University of Civil Engineering, 2014.