Numerical analysis of vortex core phenomenon during draining from cylinder tank for various initial swirling speeds and various tank and drain port sizes

A dimple appears on a free surface while rotating a cylinder tank filled with liquid. The dimple starts to concentrically deeper to a drain port at the bottom center of the tank. Over time, the dimple penetrates the drain port, a free surface forms a long and slender string shape in the tank, and a so-called vortexing (air core) phenomenon occurs. The generation of a vortex core depends on the size of the tank and drain port, and on the properties of the liquid in the tank. In this study, the liquid level and the time at which the vortex core is initially generated are numerically investigated using different values of tank diameter, drain port diameter, and initial tank rotational speeds. Instead of a full three-dimensional analysis, a two-dimensional axisymmetric simulation is conducted. The momentum conservation equation in the circumferential direction is additionally solved in the two-dimensional mesh system. Several non-dimensional variables are created: the ratio of the air core generation distance and tank diameter, the diameter ratio of the tank and drain port, the rotational Reynolds number, the rotational Froude number, and the rotational Weber number. Finally, the nondimensional air core generation distance is correlated with the other non-dimensional parameters.