Waves Simulation in an Excited Cylindrical Tank Using σ-Transformation

Free surface motions of the liquid in partially filled tanks under gravity are of practical significance particularly in marine and road transportation applications. For this reason, liquid sloshing has always been a research subject attracting great concern during the last several decades. Numerical experiments of sloshing wave motion are undertaken in a 2-D tank which is moved horizontally. Results of liquid sloshing induced by sinusoidal base excitations are presented for small to steep non-breaking waves. The numerical model is valid for any water depth except for small depth when viscous effects would become important. Solutions are limited to steep non-overturning waves. In this paper, the semi-circular domain with time-varying fluid surface was mapped onto a rectangular domain by the σ-transformation. Based on the inviscid flow equations, a fully non-linear finite difference model has been developed. The simulations are limited to a half-filled container. The liquid free surface elevation and wave phase-plane diagram have been plotted for different tank excitation frequency. It has been observed that while increasing the tank frequency, the liquid wave height in the tank changes according to the system natural frequency. Finally, the proposed computational scheme has been applied to a real engineering problem to capture the irregular behavior of liquid free surface inside the tank. For this, acceleration-time history of EW and NS components of the EL-Centro earthquake, California has been studied and analyzed.