Numerical study of sloshing liquid in tanks with baffles by time-independent finite difference and fictitious cell method

The numerical analysis of liquid sloshing in tanks is a big challenge when the fully nonlinear and viscous effects are all included in the analysis. The analysis will become more complicate as the tank is attached with internal structures, such as baffles. The width of the baffle is very thin compared with the breadth length and the numerical technique used to capture the detailed flow phenomenon (vortex generation and shedding) around the baffle is very rare in the literatures. In this paper, a time-independent finite difference scheme with fictitious cell technique is used to study viscous fluid sloshing in 2D tanks with baffles. The Navier–Stokes equations in a moving coordinate system are derived and they are mapped onto a time-independent and stretched domain. The developed numerical model is rigorously validated by extensive comparisons with reported results. An experiment setup was also made to validate the present numerical sloshing results in a tank with baffles. The method is applied to a number of problems including impulsive flow past a flat plate, sloshing fluid in a 2D tank with a surface-piercing baffle, sloshing fluid in 2D tanks with bottom-mounted baffles. The effects of baffles on the resonant frequency are discussed. The present developed numerical model can successfully analyze the sloshing phenomenon in 2D tanks with internal structures and can be easily extended to 3D model.