Numerical calculation of the electromagnetic expulsive force upon nonmetallic inclusions in an aluminum melt: Part II. C
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I. INTRODUCTION
IN the first part of the present study, the electromagnetic expulsive force upon an insulating spherical particle was numerically calculated, in combination with evaluating the effect of the electromagnetic-engendered fluid streaming around the particle, using the finite-element method. Agreement between numerical results and analytical predictions in the range of small particle sizes or a low-intensity force field has shown the validity of the method employed. As we know, inclusion particles presented in aluminum melt are generally irregular and may appear as rod-like or disklike in shape. In this part of the article, we will further consider the cases of such insulating particles with cylindrical shapes. [1]
II. OVERVIEW OF THE PREVIOUS THEORETICAL AND EXPERIMENTAL INVESTIGATIONS RELATIVE TO CYLINDRICAL OBSTACLES Three configurations for a cylindrical particle have been theoretically investigated in References 2 through 4: case 1, in which the cylinder axis is parallel to the imposed electric current, case 2, in which the cylinder axis is parallel to the imposed magnetic field, and case 3, in which the cylinder axis is parallel to the electromagnetic force field (Figure 1). The following assumptions were made, and the obtained results for insulating cylinders are summarized in Table I. (1) The cylinder is considered to be infinitely long. (2) The fluid is unbounded. (3) The Reynolds number, Re 5 rvd/m, is low enough to
DA SHU and TIAN-XIAO LI, Doctoral Candidates, BAO-DE SUN and YAO-HE ZHOU, Professors, and JUN WANG and ZHEN-MING XU, Associate Professors, are with the School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, People’s Republic of China. Manuscript submitted February 3, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS B
neglect the inertial terms in the Navier–Stokes equations. (4) The magnetic field and the velocity field are unrelated. Experimental investigations[4,5,6] have also been conducted to directly measure the expulsive force acting on the insulating cylinder obstacles. While the experimental values of the force agree with the theoretical predictions in general, a great discrepancy exists for certain orientations of the cylinder, as indicated most strikingly by the data on the first line in Table II. In addition, Marty and Alemany[4] measured the velocity profile around the insulating cylinder for case 3. The measured velocity as a function of the azimuth (u) angle shows the induced flow arranged in four quadrants around the cylinder, as predicted by the theory. However, the variation of the measured velocity with distance to the cylinder axis r (Figure 2) differs significantly from that of theoretical predictions. It was found that the measured velocity has an extreme value near the cylinder along the radial direction, which should not appear, according to the theory. III. NUMERICAL RESULTS AND DISCUSSION As shown previously, the analytic solutions for an infinitely long cylinder may not account for real cases of cylindrical particles.
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