Initial stage of formation of vortex flow in an inductor with counter-rotating magnetic fields

In this article, unsteady flows of electrically conductive fluid in a cylindrical cavity under the action of differently directed rotating magnetic fields are investigated. The relevance of the study is due to the presence of such a flow in the flow meter for liquid-metal heat carrier which is currently under development. The subject of study is the process of formation of the spin-up flow stage in a combined inductor of a rotating magnetic field. The acceleration or the spin-up stage is characterized by a significant change in the angular velocity of the liquid and begins with the formation of low pressure areas due to centrifugal forces. The alternation and movement of low and high pressure areas lead to velocity pulsations. For small values of the control parameter, which is the Taylor number, the flow energy gradually increases. In this case, the steady flow consists of two azimuthal and several poloidal vortices with clearly defined structures. When the Taylor number exceeds a critical value, strong pulsations occur in the flow, resulting in the decay of large-scale vortices. The intensity of the current is characterized by the Reynolds number. A power-law relationship with an exponent of 1.57 has been established between the Reynolds and Taylor numbers. It has been found that the time of formation of a steady flow varies from several seconds to tens of seconds, depending on the value of the Taylor number. The estimates of the control parameters have been obtained for a flowmeter operating in a typical mode. It has been shown that for the correct measurement of flow velocity in the flowmeter, it is necessary that that the Taylor numbers be higher than 108. The study is carried out using mathematical modeling and the obtained results are verified by experiment. The average calculated profiles are located within the confidence intervals of the experimental profiles.