Abstract
By means of external coupling between electromagnetic (EM) problem in ANSYS and hydrodynamic problem in FLUENT, a numerical model for the liquid metal free surface flow in an alternate EM field has been developed and verified in the first part of the article. Volume of Fluid (VOF) algorithm has been used for tracking of free surface. In this work, improved performance of the model is presented. General validation of the VOF algorithm is performed by comparison of the calculated free oscillations of the liquid column to its analytical solution. The 3D/VOF calculation of coupled EM field and free surface flow with Large Eddy Simulation turbulence description for the first time is applied for modeling of conventional EM levitation. Calculation results are compared with 2D/VOF and 3D/VOF models that use less precise k–ε and k–ω SST turbulence formulations. Obtained time-averaged droplet shapes are used for single-phase flow calculations with different turbulence models and free-slip/no-slip velocity conditions at the fixed free surface for validation of the flow. Meanwhile, series of levitation melting experiments are performed for verification of the simulated droplet shapes. In conclusion, parameter impact on the fully developed flow and the levitated droplet shape is discussed.
Similar content being viewed by others
References
Siemens & Halske A.G.: German patent 518499, 1931.
O. Muck: German patent 422004, 1923.
E. Okress, D. Wroughton, G. Comenetz, P. Brace, J. Kelly: J. Appl. Phys., 1952, vol. 23, pp. 545-552.
J. W. S. Rayleigh: Proc. Royal Soc. London, 1879, vol. 29, pp. 71-79.
I. Egry, G. Lohoefer, G. Jacobs: Phys. Rev. Lett., 1995, vol. 75(22), pp. 4043-4046.
A. Bratz, I. Egry: J. Fluid Mech., 1995, vol. 298, pp. 341-359.
D. L. Cummings, D. A. Blackburn: J. Fluid Mech., 1991, vol. 224, pp. 395-416.
R. F. Brooks, A. P. Day: Int. J. Thermophys., 1999, vol. 20(4), pp. 1041-1050.
H. Lamb: Hydrodynamics. Dover: New York, 1945.
L. M. Racz, I. Egry: Rev. Sci. Instrum., 1995, vol. 66(8), pp. 4254-4258.
T. Richardsen, G. Lohoefer: Int. J. Thermophys., 1999, vol. 20(4), pp. 1029-1039.
R. W. Hyers: Meas. Sci. Technol., 2005, vol. 16, pp. 394-401.
Y. Takeda: Nuclear Technology, 1987, vol. 79, pp. 120-124.
R. Ricou, C. Vives: International Journal of Heat and Mass Transfer, 1982, vol. 25, pp. 1579-1588.
M. Scepanskis, M. Sarma, R. Nikoluskins, K. Thomsen, A. Jakovics, P. Vontobel, T. Beinerts, A. Bojarevics, E. Platacis: Magnetohydrodynamics, 2015, vol. 51(2), pp. 257-266.
E.M. Schwartz: Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1995.
J-H. Zong, J. Szekely, E. Schwartz: IEEE Transactions on Magnetics, 1992, vol. 28(3), pp. 1833-1842.
V. Bojarevics, K. Pericleous: ISIJ Int., 2003, vol. 43(6), pp. 890-898.
K. Pericleous, V. Bojarevics, and A. Roy: Int. J. Microgravity. Sci. Appl., 2013, vol. 30(1), pp. 56–63.
C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang: Spectral Methods in Fluid Dynamics, Springer, Berlin, 1988, p. 567.
D.C. Wilcox: Turbulence Modelling for CFD, DCW Industries, La Canada, CA, 1998, p. 540.
V. Bojarevics, K. Pericleous, M. Cross: Metall. Mater. Trans. B, 2000, vol. 31B, pp. 179-189.
S. Easter: Ph.D. Thesis, University of Greenwich, London, 2012.
B. Q. Li: Ann. N. Y. Acad. Sci., 2006, vol. 1077, pp. 1-32.
X. Ai: Ph.D. Thesis, Washington State University, Pullman, WA, 2004.
B. Q. Li: Int. J. Eng. Sci., 1993, vol. 31(2), pp. 201-220.
S. K. Lele: J. Comp. Phys., 1992, vol 103(1), pp. 16-42.
H. Le, P. Moin: Int. J. Numer. Meth. Fl., 1991, vol. 92(2), 369-379.
R. W. Hyers, G. Trapaga, B. Abedian: Metall. Mater. Trans. B, 2003, vol. 34B, pp. 29-36.
S. R. Berry, R. W. Hyers, L. M. Racz, B. Abedian: Int. J. Thermophys., 2005, vol. 26(5), pp. 1565-1581.
Team TEMPUS: Proc. IX Eur. Symp. On Gravity-Dependent Phenomena in Phys. Sci. Lecture Notes in Physics 464, 1996, Springer, New York, pp. 233–52.
C. W. Hirt, B. D. Nichols: J. Comp. Phys., 1981, vol. 39, pp. 201-225.
P. Chapelle, A. Jardy, D. Ablitzer, Yu. M. Pomarin, G. M. Grigorenko: J. Mater. Sci., 2008, vol. 43, pp. 3001-3008.
V. Bojarevics, K. Pericleous: Magnetohydrodynamics, 2001, vol. 37(1/2), pp. 93-102.
S. Spitans, A. Jakovics, E. Baake, B. Nacke: Metall. Mater. Trans. B, 2013, vol. 44B(3), pp. 593-605.
E. Baake: Dr.-Ing. Thesis., Leibniz University, Dusseldorf, 1994.
M. Kirpo. Ph.D. Thesis, University of Latvia, Riga, 2008.
V. Bojarevics, A. Roy, K. Pericleous: Magnetohydrodynamics, 2010, vol. 46(4), pp. 317-329.
O. Pesteanu, E. Baake: ISIJ International, 2011, Vol. 51(5), pp. 707-721.
S. Spitans, E. Baake, B. Nacke, A. Jakovics: Magnetohydrodynamics, 2015, vol. 51(1), pp. 121-132.
C. Bullard, R. W. Hyers, B. Abedian: IEEE T. Magn., 2005, vol. 41(7), pp. 2230-2235.
J. Priede and G. Gerberth: J. Appl. Phys., 2006, vol. 100, p. 911.
V. Shatrov, J. Priede, G. Gerberth: Phys. Fluids, 2007, vol. 19, 078106.
S. Spitans, E. Baake, B. Nacke, A. Jakovics: Magnetohydrodynamics, 2015, vol. 51(3), pp. 567-578.
Acknowledgments
This work has been supported by the European Social Fund within the project “Support for Doctoral Studies at University of Latvia” No. 2009/0162/1DP/1.1.2.1.1/09/IPIA/VIAA/004. The authors wish to acknowledge the German Research Association for supporting this study under the Grant No. BA 3565/3-2. The authors would like to thank Dr. Valdis Bojarevics for kindly sharing his simulation data of Okress et al. experiment within personal communication.
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript submitted April 5, 2015.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Supplementary material 1 (MP4 4239 kb)
Supplementary material 2 (MP4 30282 kb)
Rights and permissions
About this article
Cite this article
Spitans, S., Baake, E., Nacke, B. et al. Numerical Modeling of Free Surface Dynamics of Melt in an Alternate Electromagnetic Field. Part II: Conventional Electromagnetic Levitation. Metall Mater Trans B 47, 522–536 (2016). https://doi.org/10.1007/s11663-015-0515-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11663-015-0515-7