Spin-up of electro-vortex flows under external magnetic field

Electro-vortex flows (EVFs) occur in many industrial devices, in which strong electric current passes through liquid metal. It is known that the structure of such flows can be significantly changed by applying the external magnetic field. Moreover, even a relatively weak magnetic field (say, the magnetic field of Earth) can be sufficient to influence the flow structure. In this paper, we study the influence on the EVF of the "spin-up" of either electric current or the external magnetic field on the EVF, and analyze the inhomogeneous magnetic field of the electric current conductors (power supply unit). Here, the term "spin-up" means a gradual increase in the flow driving force. These factors are inevitable in laboratory experiments, but usually neglected in numerical studies. It is shown that the spin-up of either poloidal or azimuthal driving force reduces the flow energy in the transient regime. At the same time, the spin-up factor does not influence the resulting flow structure. The inhomogeneous magnetic field of the power supply is shown to have a significant impact on the EVF. It can be a major factor to consider when simulating devices, in which the suppression of the poloidal EVF is the essential pre-requisite for their operation.