This paper describes a coupled boundary and finite element analysis of electromagnetic, free surface deformation and thermal problems in magnetic levitation systems under both normal and microgravity conditions. A computer code is developed, which involves the use of finite elements in the regions of interest and boundary elements in other regions for electromagnetic field calculations, along with an iterative and remeshing scheme for free surface deformation calculations. The code is tested against available analytical solutions and experimental measurements, and then applied to study the free surface deformation and temperature distribution in magnetically levitated droplets on earth and in microgravity. It is found that an accurate assessment of the thermal behavior of a droplet must be made along with its deformation, including the bulk movement, for magnetic levitation systems. In normal gravity, a magnetically levitated droplet assumes a conical shape with its apex pointing downward, and higher temperature occurs in the lower portion of the droplet. In microgravity, on the other hand, surface deformation is primarily attributed to the heating coils and the deformation is symmetric, with the droplet squeezed at the equator plane and bulged out along the axis of symmetry. Positioning coils give rise to a smaller deformation force and a lower Joule heating rate under normal operation conditions. The temperature profiles and free surface shapes induced by the positioning coils, though symmetric, are different from those induced by heating coils.
Issue Section:
Heat Transfer in Manufacturing
Topics:
Finite element analysis,
Magnetic levitation,
Surface deformation,
Drops,
Deformation,
Heating,
Shapes,
Boundary element methods,
Computers,
Electromagnetic fields,
Gravity (Force),
Heat transfer,
Joules,
Liquid metals,
Manufacturing,
Materials processing,
Temperature,
Temperature distribution,
Temperature profiles
1.
Bayazitoglu
Y.
Sathuvalli
U. B.
1994
, “Eddy current heating in an electrically conducting sphere
,” J. Materials Processing and Manuf. Sci.
, Vol. 3
, pp. 117
–141
.2.
Bayazitoglu
Y.
Sathuvalli
U. B.
1996
, “The Lorentz forces on an electrically conducting sphere in an alternating magnetic field
,” IEEE Trans. on Magn.
, Vol. 32
(2
), pp. 386
–400
.3.
Bayazitoglu
Y.
Sathuvalli
U. B.
Suryanarayana
P. V. R.
Mitchell
G. F.
1996
, “The Lorentz forces on an electrically conducting sphere in an alternating magnetic field
,” Physics of Fluids
, Vol. 8
(2
), pp. 370
–383
.4.
Brebbia, C. A., Telles, J. C. F., and Wrobel, L.C., 1984, Boundary Element Techniques: Theory and Applications in Engineering, Springer-Verlag, New York.
5.
Egry
I.
Lohofer
G.
Neuhaus
P.
Sauerland
S.
1992
, “Surface tension measurements of liquid metals using levitation, microgravity and image processing
,” Int. J. Thermophysics
, Vol. 13
, pp. 65
–74
.6.
Getzlev, Z. N., 1971, “Casting in an electromagnetic field,” J. Metals, No. 10, pp. 38–39.
7.
Herlach
D. M.
1991
, “Containerless Undercooling and Solidification of Pure Metals
,” Annu. Rev. Mater. Sci.
, Vol. 21
, pp. 23
–44
.8.
Herlach
D. M.
Feuerbacher
B.
1991
, “Non-equilibrium Solidification of Undercooled Metallic Melts
,” Advances in Space Research
, Vol. 11
, No. 7
, pp. 255
255
.9.
Ida, N., 1986, “A mesh generator with automatic bandwidth reduction for 2-D and 3-D geometries,” in: Computational Electromagnetics, Z. J. Cendes, ed., Elsevier Science, London, pp. 13–22.
10.
HoLe
K.
1988
, “Finite element mesh generation methods: a review and classification
,” J. Computer-Aided Design
, Vol. 20
, pp. 27
–38
.11.
Jackson, J. D., 1975, Classical Electrodynamics, Chaps. 2-6, Wiley, New York.
12.
Keller, W., and Muhlbauer, A., 1981, Floating-Zone Silicon, Marcel Dekker, Inc., New York.
13.
Li
B. Q.
1993
, “The Magnetothermal Phenomena in Electromagnetic Levitation Processes
,” Int. J. Engng Sci.
, Vol. 31
, No. 2
, pp. 201
–220
.14.
Li
B. Q.
1994
a, “The Fluid Flow Aspects of Electromagnetic Levitation Processes
,” Int. J. Engng Sci.
, Vol. 32
, No. 1
, pp. 45
–67
.15.
Li
B. Q.
1994
b, “The Transient Magnetohydrodynamic Phenomena in Electromagnetic Levitation Processes
,” Int. J. Engng Sci.
, Vol. 32
, No. 8
, pp. 1315
–1336
.16.
Lohofer
G.
1989
, “Theory of an Electromagnetically Levitated Metal Sphere I: Absorbed Power
,” SIAM J. Appl. Math.
, Vol. 49
, No. 2
, pp. 567
–581
.17.
Mestel
A. J.
1982
, “Magnetic Levitation of Liquid Metals
,” J. Fluid. Mech.
, Vol. 117
, pp. 17
–43
.18.
Muck, O., 1923, German Patent No. 422004.
19.
Natarajan, T. T., and El-Kaddah, N., 1995, “Calculation of the Electromagnetic Field and Melt Shape in Electromagnetic Confinement Systems: A Comparison Between Numerical Methods,” in: Materials Processing in the Computer Age II, V. R. Voller, S. P. March, and N. El-Kaddah, eds., TMS/AIME, Warrendale, PA, pp. 255–265.
20.
Okress
E. C.
Wroughton
D. M.
Comenetz
G.
Brace
P. H.
Kelly
J. C. R.
1952
, “Electromagnetic Levitation of Solid and Molten Metals
,” J. Appl. Phy.
, Vol. 23
, No. 5
, pp. 545
–552
.21.
Rony, P. B., 1969, “The electromagnetic levitation melting of metals,” Trans. Vac. Met. Conf., American Vacuum Society, Boston, pp. 55–135.
22.
Sathuvalli
U. B.
Bayazitoglu
Y.
1993
, “Electromagnetic force calculations for a conical coil
,” Met. Trans.
, Vol. 24B
, pp. 737
–748
.23.
Sathuvalli, U. B., and Bayazitoglu, Y., 1994, “The Lorentz force on a sphere due to an axisymmetric non-homogeneous alternating magnetic field,” ASME AMD-Vol. 194, pp. 293–305.
24.
Schwartz, E., Szekely, J., Ilegbusi, O. J., Zong, J.-H., and Egry, I., 1992, “The Computation of the Electromagnetic Force Fields and Transport Phenomena in Levitated Metallic Droplets in the Microgravity Environment,” in: Magnetohydrodynamics in Process Metallurgy, J. Szekely, J. W. Evans, K. Balzek, and N. El-Kaddah, eds., TMS/AIME, pp. 81–90.
25.
Schwartz, E., and Szekely, J., 1995, “Mathematical Modelling: An Essential Component of the Design of Space Experiments,” in: Materials Processing in the Computer Age II, V. R. Voller, S. P. March, and N. El-Kaddah, eds., TMS/AIME, Warrendale, PA, pp. 147–161.
26.
Song, S. P., and Li, B. Q., 1995, “Coupled Boundary/Finite Element Solution of Thermal and Electrodynamic Problems in Materials Processing,” in: Materials Processing in the Computer Age II, V. R. Voller, S. P. March, and N. El-Kaddah, eds., TMS/AIME, Warrendale, PA, pp. 243–254.
27.
Song, S. P., 1996, “Coupled Finite Element and Boundary Element Method for the Solution of Scalar and Vector Potential Problems Involving Free Surface Deformation,” M. S. Thesis, Louisiana State University, Baton Rouge, LA.
28.
Song, S. P., and Li, B. Q., 1996, “Computation of Magnetically-Supported Free Surface by a Coupled Finite/Boundary Element Method,” EPD Congress-96, G. W. Warren, ed., TMS/AIME, Warrendale, PA, pp. 725–736.
29.
Song
S. P.
Li
B. Q.
Khadadadi
J. A.
1998
, “Coupled boundary and finite element solution of magnetothermal problems
,” Int. J. Num. Meth. Heat and Fluid Flow
, Vol. 8
, pp. 321
–349
.30.
Suryanarayana
P. V. R.
Bayazitoglu
Y.
1991
, “Effect of Static Deformation and External Forces on the Oscillations of Levitated Droplets
,” Phys. Fluids A
, Vol. 3
, pp. 967
–977
.31.
Szekely
J.
Schwartz
E.
Hyers
R.
1995
, “Electromagnetic levitation—a useful tool in microgravity research
,” J. of Metals
, Vol. 5
, pp. 50
–53
.32.
Weatherburn, C. E., 1972, Differential Geometry of Three Dimensions, Cambridge University Press, London.
33.
Zhang
X.
Li
B. Q.
Pang
S. S.
1997
, “A Perturbational Approach to Magnetothermal Problems of a Deformed Sphere in a Magnetic Field
,” J. Eng. Math.
, Vol. 31
, pp. 337
–355
.34.
Zienkiewicz, O. C., and Taylor, R. L., 1989, The Finite Element Method, 4th ed., McGraw-Hill, New York.
35.
Zong
J. H.
Li
B. Q.
Szekely
J.
1992
, “The Electromagnetic and Hydrodynamic Phenomena in Magnetically-Levitated Molten Droplets—I. Steady State Behavior
,” Acta Astronautica
, Vol. 26
, No. 6
, pp. 435
–449
.36.
Zong
J. H.
Li
B. Q.
Szekely
J.
1993
, “The Electromagnetic and Hydrodynamic Phenomena in Magnetically-Levitated Molten Droplets—II. Transient Behavior and Heat Transfer Considerations
,” Acta Astronautica
, Vol. 29
, No. 4
, pp. 305
–311
.
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