ALE and Fluid Structure Interaction for Sloshing Analysis

Abstract

Liquid containment tanks are, generally, subjected to large deformations under severe earthquake conditions due to coupling forces between tank and the contained liquid. The accurate description of these forces is vital in order to diminish or eliminate the potential risk of tank failure during an earthquake. Yet, analytical formulations derived for the seismic analysis of liquid storage tanks are not capable to capture the complex fluid-structure effects since they include many assumptions and simplifications not only for the behavior of fluid and structure but also for the external excitation. On the other hand, an appropriate numerical method allows us to cope with large displacements of free surface of the fluid, high deformations of the structure and correctly predicts the hydrodynamic forces due to the high-speed impacts of sloshing liquid on a tank wall and roof. For this purpose, a new coupling algorithm based on the penalty formulation of finite element method which computes the coupling forces at the fluidstructure interface is developed in this paper. This algorithm is constructed on a two superimposed mesh systems which are a fixed or moving ALE mesh for fluid and a deformable Lagrangian mesh for structure. The fluid is represented by Navier-Stokes equations and coupled system is solved using an explicit time integration scheme. In order to verify the analysis capability of coupling algorithm for tank problems, numerical method is applied for the analyses of a rigid rectangular tank under harmonic excitation and a flexible cylindrical tank subjected to earthquake motion and numerical results are compared with existing analytical and experimental results. Strong correlation between reference solution and numerical results is obtained in terms of sloshing wave height.

Numerical modeling of liquid sloshing in flexible tank with FSI approach

“…The behavior of the fluid inside the tank is described by the Navier-Stokes equations in Arbitrary Lagrangian-Eulerian formulation (Ozdemir et al, 2009;Souli et al, 2016). These equations are derived by combining the continuity and momentum equations, respectively, equations (2) and (3):…”

“…The behavior of the fluid inside the tank is described by the Navier–Stokes equations in Arbitrary Lagrangian–Eulerian formulation (Ozdemir et al , 2009; Souli et al , 2016). These equations are derived by combining the continuity and momentum equations, respectively, equations (2) and (3): where ρ f is the fluid mass density, t is the time, u is the flow velocity, w is the domain displacements velocity, g is the gravity vector f σ , is the surface tension force [equation (12)] and A e is the acceleration due to external excitation.…”

Conjugate Heat Transfer Model Based on SIMPLE and Coupled Energy and Heat Equations

“…In the following study, we consider the two-dimensional incompressible Navier Stokes equations under constant density assumption (minor variation of density) given by continuity, momentum, and energy equation, as shown in Eqs. (1)(2)(3)(4) respectively [11,[14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Three-dimensional Numerical Analysis of Blast-induced Damage Characteristics of the Intact and Jointed Rockmass

“…Additional details on fluid-structure interaction of finite method between sub-grids, such as Lagrangian-Lagrangian and Lagrangian-Eulerian coupling can be found in Refs. Anghileri et al [Anghileri, Castelletti and Tirelli (2005); Alia and Souli (2006); Ozdemir, Moatamedi, Fahjan et al (2009) ;Rabczuk, Gracie, Song et al (2010)]. To make use of the advantages of both the algorithms, the multimaterial fluid-structure interaction method is adopted in this study.…”