Numerical Analysis of Transient Vortex Formation at the Outlet of a Tank Containing Gas-Liquid Phases

One of the basic phenomena when a liquid leaves a tank is the formation of vortices. This phenomenon can have a significant impact on the liquid mass remaining in the tank and the ingress of air and bubbles into the system. As a result, the performance of the system can be disturbed. The purpose of this study is to numerically investigate the effect of gas pressure on vortex formation and critical height. It also verifies the relationships presented for turbulent viscosity. In addition, the near-wall behavior of the analytical relationships proposed for the tangential velocity is revised based on the boundary layer theory. Some common effective factors such as angular velocity, discharge time, and liquid height are also investigated. The volume of fluid (VOF) model and the Transitional SST k-ω turbulence model were used to solve the two-phase turbulent flow. The results show that increasing the gas pressure from 1 to 5 bar and its direct impact on the liquid surface significantly accelerates the formation of the vortex and the critical height. This phenomenon causes the air core to reach the inlet of the outlet pipe approximately 7 seconds earlier after the start of the liquid discharge. As a result, much more liquid mass remains in the tank. The increase in the angular velocity of the reference frame from 0.1 to 1 rad/s also causes the critical height to be reached much earlier and the remaining liquid mass to increase by 32 kg. In addition, the amount and variations of turbulent viscosity differ significantly from the semi-empirical constants, limiting their use to certain flows.