MAGNETOHYDRODYNAMICS Vol. 55 (2019), No. 1-2, pp. 251–260 DOI: 10.22364/mhd.55.1-2.30 SIMULATION OF FLUID FLOW IN LEVITATED Fe-Co DROPLETS ELECTROMAGNETICALLY PROCESSED ONBOARD THE ISS S. Lomaev 1,2 , M. Krivilyov 2,1 , J. Fransaer 3 , J. Lee 4 , T. Volkmann 5 , D.M. Matson 6 1 Udmurt Federal Research Center, Ural Branch, Russian Academy of Science, 34 Baramzinoy str., 426067 Izhevsk, Russia 2 Udmurt State University, Department of Mathematics, Computer Engineering and Physics, 1 Universitetskaya str., 426034 Izhevsk, Russia 3 KU Leuven, Department of Materials Engineering, Kasteelpark Arenberg 44, 3001 Heverlee, Belgium 4 Iowa State University, Department of Mechanical Engineering, 2010 Black Engr., Ames, IA 50011, USA 5 Institut f¨ ur Materialphysik im Weltraum, Deutsches Zentrum f¨ ur Luft- und Raumfahrt (DLR), D-51170 K¨ oln, Germany 6 Tufts University, Mechanical Engineering Department, 200 College Avenue, Medford, MA 02155, USA In the previous paper [Lomaev, Krivilyov, Fransaer, Magnetohydrodynamics, 2016], exact ana- lytical expressions for the Lorentz force density and Joule heat power induced by an external alternating magnetic field inside an electromagnetically levitated drop have been derived. This yields a close-form analytical solution of the conjugated hydrodynamic-thermal problem for a spherical liquid drop in a gas atmosphere. In this paper, the developed method has been used to analyze structural transitions in fluid flow patterns inside a levitated Fe-Co droplet tested recently in the framework of the PARSEC space experiment onboard the International Space Station (ISS). The convection level is calculated based on the positioning and heating currents in the coil and an optimum flow regime is predicted. Introduction. Containerless processing of metals [1, 2] is used for the production of metastable materials with unique properties [3]. A significant level of undercooling below the melting point is accessible due to the absence of contact with the casting mold which serves as a substrate, where solidification starts. Nowadays, electrostatic (ESL) and electromagnetic (EML) levitation of liquid ceramic or metallic droplets are the widely used techniques for measuring thermophysical properties [4, 5] and for studying solidification kinetics [2, 3]. A typical setup for electromagnetic levitation consists of a metallic sample and a coil system, inside which an alternating electric current passes. The alternating current generates an alternating magnetic field. Faraday’s law of induction dictates that eddy currents are induced in any conductor placed in the alternating magnetic field. Lorentz forces are generated as a result of the interaction between these eddy currents inside the sample and the external magnetic field induced by the current in the coil [6]. Thus the drop levitates, being supported by the net Lorentz force. The eddy currents inside the drop also generate heat which is sufficient to melt the initially solid sample. Subsequent rapid cooling of the liquid sample below the liquidus temperature is implemented by cooling the sample by an inert gas flow or by decreasing the current inside the coil. In microgravity experiments onboard the ISS and in parabolic flights onboard the Airbus Material Science Laboratory a special design of the coil system was used (Fig. 1. The rings of the coil are located in two planes below and above the sample because the required stabilization force is small in microgravity. Two voltage frequencies are superimposed in the coil system: one for heating (350 kHz dipole field) and one for positioning (150 kHz quadrapole field). 251