Download Analysis Methods for Tanks

Application of Fluid-Structure
Interaction Algorithms to Seismic
Analysis
Zuhal OZDEMIR, Mhamed SOULI
Université des Sciences et Technologies de Lille
Laboratoire de Mécanique de Lille
University of Bosphor, Istanbul
GDR IFS
3 - 4 Juin 2010
UTC Compiegne
Outline of the Presentation
General Objective of the Studies Carried out on Tanks
Difficulties in the Analysis of Tanks
Analysis Methods for Tanks
Fluid-Structure Interaction for Tank Problems
2D Rigid Tank
3D Flexible Tank
General Objective of the Studies
Carried out on Tanks
- Limit the tank damages observed during earthquakes
- Determine the response parameters in order to take
precautions
- sloshing wave height (freeboard)
- uplift displacement (flexible attachments for pipes)
Difficulties in the Analysis of Tanks
- Three different domains
* Structure
* Fluid
* Soil
- Material and geometric nonlinearities
- Complex support condition
* Anchored
* Unanchored
General Performance of Tanks
during Earthquakes
- Violent sloshing which causes damage at the tank
wall and shell
- Large amplitude wall deformations (Buckling)
- High plastic deformation at the tank base
Sloshing damage
Tank Shell Buckling
Elephant-Foot Buckling (Elasto-Plastic Buckling)
Diamond Shape Buckling (Elastic Buckling)
Analysis Methods for Tanks
- Simplified Analytical Methods
Fluid :
Laplace equation
 2  0
Irrotational flow, incompressible and inviscid fluid (potantiaql flow theory)
Structure :
rigid tank
Spring-Mass Equivalent Analogue
k5 / 2
M5
k3 / 2
M3
k1 / 2
M1
k5 / 2
k3 / 2
k1 / 2
M0
h3
h1
h0
h5
Base Shear
and
Overturning
Moment
Ordinary
Beam
Theory
Shell Stresses
(Axial
Compressive
and Hoop)
Most of the provisions recommended in the current tank design codes employ a modified
version of Housner’s method
Fluid-Structure Interaction for Tank
Problems
Structure
Lagrangian Formulation
Fluid
Dynamic Structure equation


dv

 div ( )  f
dt
Navier Stokes equations in
ALE Formulation
2D Tank Problem
width = 57 cm
height = 30 cm
Hwater= 15 cm
Sinusoidal harmonic motion
non-resonance case
resonance case
The sketch of the 2D sloshing experiment (Liu and Lin, 2008)
2n  g
 (2 n  1) 
(2 n  1) 
tanh 
2a
2a

o = 6.0578 rad/s

h 

2D Tank Problem
Lagrangian
2D Tank Problem
non-resonance case
amplitude = 0.005 m
 = 0.583 o
resonance case
amplitude = 0.005 m
 = 1 o
3D Tank Problem
Cylindrical tank size:
- radius of 1.83 m
- a total height of 1.83 m
- filled up to height of 1.524 m
3
Maximum ground acceleration = 0.5 g in horizontal direction
(El Centro Earthquake record scaled with 3 )
Large mesh Deformation
Large mesh Deformation
Lagrangian Method
Coupling Method
Fluid Structure Coupling
2) Euler Lagrange Coupling
Structure
Fluid
Up Lift for sloshing Tank
3D Tank Problem
Comparisons of the time histories of pressure for the numerical method and
experimental data
3D Tank Problem
Comparisons of the time histories of pressure for the numerical method and
experimental data
3D Tank Problem
Comparisons of the time histories of surface elevation for the numerical method and
experimental data
3D Tank Problem
Comparisons of the time histories of tank base uplift for the numerical method and
experimental data
Conclusions
(1) ALE algorithm lead highly consisted results with the experimental
data in terms of peak level timing, shape and amplitude of pressure
and sloshing.
(2) Method gives reliable results for every frequency range of external
excitation.
(3) ALE method combined with/without the contact algorithms can be
utilized as a design tool for the seismic analysis of rigid and flexible
liquid containment tanks.
(4) As a further study, a real size tank will be analysed
Merci
Analysis Methods for Tanks
(cond)
- Numerical Methods
* 2D finite difference method
* FEM
* BEM
* Volume of fluid technique (VOF)
FEM is the best choice, because
-structure, fluid and soil can be modelled in the same system
-proper modelling of contact boundary conditions
-nonlinear formulation for fluid and structure
-nonlinear formulation for fluid and structure interaction effects
3D Tank Problem
Pressure distribution inside the tank
Analysis Methods for Tanks
(cond)
- Experimental Methods
* Static tilt tests
* Shaking table tests
Schematic view of static tilt test
A cylindrical tank mounted on the shaking table
3D Tank Problem
Change of free surface in time
3D Tank Problem
Von Mises stresses on the anchored tank shell
3D Tank Problem
Von Mises stresses on the unanchored tank shell
(displacements magnified 10 times)
2D Tank Problem
ALE
2D Tank Problem
width = 57 cm
height = 30 cm
Hwater= 15 cm
Sinusoidal harmonic motion
non-resonance case
resonance case
The sketch of the 2D sloshing experiment (Liu and Lin, 2008)
2n  g
 (2 n  1) 
(2 n  1) 
tanh 
2a
2a

o = 6.0578 rad/s

h 
