Linear and Nonlinear Sloshing Analysis in Liquid Storage Tanks Under Dynamic Excitation

George Katsikoyiannis

Diploma Thesis, February 2013

ABSTRACT

Liquid sloshing in partially filled liquid containers has great importance in numerous engineering applications. It is generally caused by external tank excitation (e.g. earthquake), and may have a significant influence on the response of the container, if the excitation frequency is close to the natural frequency of the container.Assuming ideal fluid, the fluid flow is described through a velocity potential function, satisfying the Laplace equation within the fluid, and the kinematic and dynamic free-surface conditions. The total liquid motion can be decomposed in two parts, an “impulsive” motion which represents liquid motion that follows the external excitation and the “convective” motion associated with sloshing.

The purpose of the thesis is the linear and non-linear analysis of the sloshing phenomenon in partially filled cylindrical and rectangular liquid storagecontainers during external excitation through the use of second order asymptotic method. During the analysis, the solution of the eigen-value problem (absence of external excitation) provides the natural frequencies of fluid oscillation (sloshing frequencies) for rectangular and cylindrical tanks. In addition, the convective and impulsive sizes (masses, forces, torques) are estimated in both shape of tanks. Finally, the response of storage tanks of various sizes to real earthquakes is investigated, to compute the elevation of free surface resulting from the solution of linear and non-linear problem. The simulation is performed through the use of the earthquake engineering software SeismoSignal and a finite-difference algorithm which was programmed in Microsoft Excel.