Numerical studies of the motion of particles in current-carrying liquid metals flowing in a circular pipe
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I. INTRODUCTION
THE motion of particles in current-carrying liquid metals constitutes the basis for a number of electrometallurgical processing operations. Examples include the deposition of nonconductive oxide particles on the inner walls of induction furnaces,[1] the acceleration, deceleration, and transverse motions of liquid metal droplets passing through liquid slag in electroslag smelting and welding operations,[2] the electromagnetic separation[3,4] and its application to the design of split tundish in continuous casting to move the inclusions to the wall of the heating system[5] and to conventional casting mold to move inclusions to the boundary of the solidifying shell,[6] the filtration of non-metallic inclusions by pumping the melt through a bundle of current-applied thin pipes in aluminum scrap recycling,[7] as well as the on-line liquid metal cleanliness analyzer (LiMCA)[8,9] by measuring the voltage pulse produced when a particle with different electrical conductivity from that of liquid metal passes through an electric sensing zone (ESZ),[10] a small orifice built in an electrically insulating probe, in the presence of an electric current applied between an electrode outside and another inside the sampling tube. Essentially, all these processes involve the motion of particles in currentcarrying liquid metals in a circular pipe. Therefore, a numerical study of the particle trajectory in current-carrying liquid metals in a circular pipe is necessary both to the understanding of these processes and to the corresponding engineering MEI LI, Graduate Student, and RODERICK I.L. GUTHRIE, Macdonald Professor, FRSC, and Director, MMPC, are with the McGill Metals Processing Center, Department of Mining and Metallurgical Engineering, McGill University, Montreal, PQ, Canada H3A 2B2. Manuscript submitted April 12, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS B
design. Especially, a numerical study of the particle trajectory in a current-carrying liquid metal in a finite length circular tube will help LiMCA to realize particle discrimination due to the fact that the height and shape of the small voltage pulse depend on the size[11,12] and also the trajectory of the particles,[13,14] and possibly enable LiMCA to register only the signals from harmful solid particles. Much effort has been devoted to study the motion of particles in current-carrying liquids. Leenov and Kolin[15] derived the electromagnetic force on a spherical particle whose electrical conductivity is different from that of the surrounding liquid. Shilova[1] studied the motion of nonconducting particles suspended in a stagnant conducting liquid contained within a cylindrical tube through which a uniform electric current flows along the axis. He found that the pinch force generated by the electric current and its induced magnetic field was directed along the radius toward the center of the tube and was balanced by a radial pressure gradient, resulting in an outward radial motion of the particle towards the tube wall. The study was later extended to t
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