Ph.D Thesis

Ph.D StudentBreitman Nina Liora
SubjectNonlinear Finite Element Analysis of Liquid Sloshing in
Upright Circular and Square-Base Cylindrical
DepartmentDepartment of Mechanical Engineering
Supervisor PROFESSOR EMERITUS Pinhas Bar-Yoseph
Full Thesis textFull thesis text - English Version


The study of liquid sloshing in partially filled liquid storage containers has gained significant attention as the seismic vulnerability of these containers represents a potential source of severe environmental accidents: large amplitude sloshing exerts excessive hydrodynamic loads on the container walls and can create a high risk of both catastrophic mechanical failure and overspill of hazardous liquids. Particular concern is the pressure distribution on the container walls and its local spatio-temporal peaks that can reach during sloshing flow patterns.

The aim of this study is to develop a robust finite element procedure for solving 2D and 3D nonlinear liquid sloshing dynamics modelled by standard potential theory. A computational problem encountered in almost all of the nonlinear simulations of inviscid free-surface flows is the appearance of small-scale spurious oscillations on the free surface as the waves become steep. The proposed post-processing procedure, based on the moving least-squares smoothing algorithm, allows robust recovering more accurate nodal values of potential velocity gradients from conventional finite element solutions. Sloshing motions induced by harmonic and El-Centro seismic excitations are presented for small to steep non-overlapping waves in upright circular and square-base cylindrical containers.

Thesis compares between various techniques to enhance stability and mitigate numerical oscillations, both common and innovative for sloshing problems. The influence of these techniques on the free surface and velocity and pressure profiles has been examined, and the most robust stabilized finite element formulation for potential flow sloshing models has been presented. Present study provides smoothed free surface   elevation, velocity and pressure profiles on the wetted walls of a rigid container. The present FE solution is in perfect match with the reference solution that has been frequently used as a reliable reference solution in comparative computational studies. All computational results are in a good agreement with OpenFOAM simulations using the Navier-Stokes model and unstructured finite volume method. The present post-processing procedure can thus be used to simulate nonlinear liquid sloshing motions in 3D clean rigid containers with reasonable accuracy.