Magnetohydrodynamic Effects on Insulating Bubbles and Inclusions in the Continuous Casting of Steel
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GNETIC fields are often used in the processing of liquid metals to dampen unwanted fluid motion at free surfaces, control the degree of turbulence, or stir the liquid. Although electrically insulating inclusions or bubbles in a conducting fluid do not experience a direct Lorentz force, a magnetic field can still have a significant influence on their motion. Because the surrounding conducting liquid is affected by Lorentz forces, immersed insulating objects can experience noticeable magnetohydrodynamic effects indirectly. The most well known of these forces is the electromagnetophoretic force, which is also known as the electromagnetic buoyancy force or electromagnetic Archimedes force.[1] This force acts as a reaction to the Lorentz force experienced by the fluid, similar to its gravitational counterpart. Some quantitative results regarding this important force can be found in References 2 and 3. The electromagnetophoretic force is used frequently to separate nonmetallic inclusions from molten metals as a preprocessing step in the manufacturing of metals. This separation technique, which was practiced in the early 1970s in the former Soviet Union,[4] took off in the West after a publication by Marty and Alemany.[5] Occasionally, the electromagnetophoretic force is included explicitly in computational models; see Reference 6 for an example regarding rigid inclusions. As we will argue, the influence of the electromagnetophoretic force on the dynamics of a dispersed gas phase can also be significant. J.W. HAVERKORT is with Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands. Contact e-mail: [email protected] T.W.J. PEETERS is with Tata Steel Research, Development & Technology, 1970 CA IJmuiden, The Netherlands. Manuscript submitted June 17, 2010. Article published online August 12, 2010. 1240—VOLUME 41B, DECEMBER 2010
Another effect that received far less attention in the modelling of insulating immersions in liquid metals is the observation that in the presence of a magnetic field, the drag force on insulating objects increases. For rigid spherical objects, significant theoretical,[7–9] experimental,[10–12] and computational[13–15] work has been reported. Recently, experiments with deformable bubbles have been performed[16,17] showing that in this case, a magnetic field modifies the drag coefficient as well. For an applied magnetic field perpendicular to the bubble motion, a magnetohydrodynamically induced increase in drag coefficient similar to that of a rigid sphere has been reported.[16] For bubble motion parallel to the magnetic field, however, the drag coefficient was found to decrease for bubbles larger than approximately 5 mm. This effect could be attributed to the fact that fluid motion perpendicular to the bubble trajectory is, in this case, damped by the perpendicular magnetic field. This process causes the bubble to move in a straighter path, leading to a lower apparent drag force. Recent numerical simulations[18] show that a perpendicular magnetic field acts to make a bubble more spherical, causing an incr
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