3d Fully Nonlinear Sloshing Fluid in Tanks

Three-dimensional tank in smooth tank is of concern in various engineering applications. Sloshing waves in moving tanks have been studied numerically, theoretically and experimentally in past several decades and many significant phenomena have been considered in those studies, especially the linear and nonlinear effects of sloshing wave with inviscid or viscid liquid in a tank. The reported studies were the tanks excited by limited exciting directions and with a fixed excitation frequency throughout the excitation. In reality, for earthquake induced tank sloshing, the excited directions are actually multi-degree of freedoms(coupled surge/sway/heave/pitch/roll/yaw). The sloshing waves may vary with various excited directions and oscillating frequencies.In present study, a 3-D tank with various fluid depths, excited amplitudes, excitation frequencies and multiple degrees of freedoms of eccitation are considered. The developed time-independent finite difference method¹ is extended to incorporate the incompressible and inviscid Navier-Stokes equations, fully nonlinear kinematic and dynamic free surface conditions in the analysis of the seismic response of sloshing fluid in a 3-D rectangular tank with square basin. The boundary of the tank is mapped on to a fixed square domain through proper mapping functions. The benchmark study shows the acceptance and accuracy of the proposed numerical scheme. The sloshing waves of different water depths and various frequencies of excitation are simulated. The coupling effect of surge, sway and heave motions are also included and discussed. The present results show four types of waves, which is 'diagonal wave', 'square-like wave', 'swirling wave' and 'irregular wave', and discover that 'square-like wave' and 'irregular wave' not only occur at the tank under near the resonant frequency but also at the excitation frequencies far away from the first natural frequency of the tank. The swirling wave will occur when the tank is under near resonant excitation frequency, while the phenomenon is insignificant as the excited angle is close to 45 o. The swirling waves will change swirling directions (counterclockwise to clockwise) according to the phase lags between swirling periods and the fundamental period of the tank system. For the effect of coupling Surge, sway and heave motions, the results shows there is an unstable influence when the excited frequency of heave motion is twice as large as the fundamental natural frequency