Radu-Mihail BileganStefan NicoliciAlexandru Gheorghita________________________________________________________Center of Technology and Engineering for Nuclear Projects (CITON)409, Atomistilor Street, Magurele, Ilfov County, RomaniaEmail:bileganr@router.citon.ro

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Recent seismic analysis involving sloshing phenomena

SLOSHING is the periodic motion of the free surface of a liquid in a partially filled tank or container

Smooth sloshingViolent sloshingSloshing effect

instabilityrollover failure or damage

of tank wall or bolting

Diamond Shape Buckling Elephant-Foot BucklingGeneral Objective of the Studies Carried out on Tanks Sloshing Effectssloshing wave height (freeboard)uplift displacement (flexible

attachments for pipes)limit resonance effects bolting base restraints

Sloshing induced damage

Difficulties in the Analysis of Tanks

Three different domains

* Structure* Fluid * Foundation

Material and geometric nonlinearities

Complex support condition

* Anchored* Unanchored

Analysis by Numerical Methods

Spring mass system (lumped masses)Distributed fluid mass modelLagrangian modelsModel Smoothed Particle Hydrodynamics (SPH)Arbitrary Lagrangian-Eulerian (ALE) Coupled CFD + FEA

Previous WorkView of the tank FE model Comparison of results in terms of maximum shear force (normalized by Model I maximum and minimum values)1 Two-way model2 One-way model3 Lumped mass model4 Distributed mass model

Model Method of analysis Comments

Model IFSI two-way coupling FEACFD 2-way coupling Model II FSI one-way coupling CFDFEA 1-way coupling Model III Springlumped masses FEA dynamic analysis Model IV Distributed fluid mass FEA dynamic analysis

CFD/FEA ModelTank dimensions:4000 mm inside diameter 6000 mm high 20 mm thicknessLiquid height 2000 mm2D model approachTwo time history analyses have been performed using CFD+FEM method: Bidirectional (fully coupled)One-way (only the solution data from CFX is exported to the mechanical application)Base excitation was represented by El Centro earthquake record (May 18, 1940)

View of the tank geometry

Excitation velocity profile variation in time

CFD/FEA Model

Assumptions: the two-phase fluid motion is considered homogeneous;the gaseous phase is taken compressible (this maintain stability because incompressible fluids in a closed domain can react with large pressure spikes to boundary motion);no heat transfer is considered in the CFX model;

Ansys MFX iterative procedureCoupling:The two solvers (CFX and Mechanical) are linked through Ansys Multi-Field (MFX) capability00Coupling detailsAnsys CFD Solution methods

Advection SchemeHigh ResolutionTurbulence NumericsFirst OrderVolume Fraction Coupling CoupledTransient FormulationSecond Order Backward EulerSolver PrecisionDouble

Stagger Loop Max/Min Iterations10/5CFX Loop Max/Min Iterations15/30Under relaxation Factor0.75Coupling Time Step [s]0.025

Time Loop

End Time Loop

Coupling/Stagger Loop

End Coupling/Stagger Loop

Field Loop

End Field Loop

SPH modeling description

Liquid particle distribution for SPH model Defining of the particle neighbors in two dimensional case The particle methods is a relatively new technique for solving computational continuum dynamics problems. The main characteristic of the approach is that the material continuum is represented by arbitrary lattice of interacting particles (interpolation points or computational nodes). Each particle represent a discrete part of the material and is not a simply interacting mass, but represents an interpolation point where the values of the function and its derivatives are evaluated.

SPH analysis has been performed using the AutoDyn code implemented in the Ansys Workbench interface

SPH modeling description

Defining of the particle neighbors in two dimensional case

Weighting function (Kernel) for 3D case

SPH Particle Size Sensitivity

c) Horizontal liquid mean velocitya) Horizontal component velocity at free surface levelb) Vertical component velocity at free surface leveld) Vertical liquid mean velocity

General Fluid Movement

Area averaged velocities (right-horizontal component; left-vertical component) of the liquid for an amplification factor of the velocity of 2.5

General Fluid Movement

Area averaged velocities (right-horizontal component; left-vertical component) of the liquid for an amplification factor of the velocity of 4

Pressure Distribution

SPH pressure variation (right-tank bottom; left-free surface) No Filter Applied

Pressure Distribution

SPH pressure variation (right-tank bottom; left-free surface) Filter Low-Pass=100 HzSPH pressure variation (right-tank bottom; left-free surface) Filter Low-Pass=50 Hz

Local Pressure DistributionCFD vs.CFD/FEA vs. SPH

The sloshing phenomena simulation using CFD, coupled FEA/CFD and SPH presented in this paper have shown that the results are dependent on the numerical methodology. The results are reliable as long as all the tank geometry and flexibility affecting the liquid dynamics are considered.

Container flexibility modifies the maximum amplitudes of the impulsive pressure and liquid wave height; the coupling phenomena was found to have great significance in the case of fluidstructure interaction analysis.

The SPH model has given, for the situations analyzed in this paper, the highest values for the area averaged velocities leading to conservatively resultant reactions on the tank walls and supporting structure.

The use of a one-way (CFD with rigid walls) model to analyze the sloshing phenomena in partially filled containers could under predict the maximum/minimum values of the base shear force, leading in some situations to anchorage failure.

Radu-Mihail BileganStefan NicoliciAlexandru Gheorghita________________________________________________________Center of Technology and Engineering for Nuclear Projects (CITON)409, Atomistilor Street, Magurele, Ilfov County, RomaniaEmail:bileganr@router.citon.ro