Mathematical Analysis and Numerical Simulation of High Frequency Electromagnetic Field in Soft Contact Continuous Casting Mold.

Abstract

The electromagnetic parameters in soft contact continuous casting billet mold were analyzed in this paper by mathematical analytic method and numerical simulation; the optimized frequency range was fixed on 20 000-40 000 Hz. The distribution of magnetic flux density and electromagnetic body force in split mold was obtained; the research results achieved respectively by mathematical analytic method and numerical simulation agree with each other. With increase of frequency of electromagnetic field, the electromagnetic body forces acted on the surface of strand increase, and attenuate rapidly towards the center of strand. When the meniscus was located at the middle of coil height, the electromagnetic body force acted on it is biggest, and then decreased along the casting direction to almost zero at the location of charge bottom. On the transverse direction perpendicular to the casting direction, the asymmetrical distribution of magnetic field at the surface of strand permeated through the slit of mold was enhanced slightly with the increase of frequency. The magnetic flux density at the slit area is about 10% higher than that at other area at 40 000 Hz, and the distribution of magnetic body force is almost even on this direction.KEY WORDS: soft contact solidification; electromagnetic continuous casting; mold; mathematical analytic method; finite element method; numerical simulation.fixed on 20 kHz. The authors of literature 4) investigated the shape of meniscus under 5-100 kHz, considered the frequency should be set above 20 kHz. Frequency was aimed at 20 kHz in literature, 5) and it was aimed at 25 kHz in literature, 6) but the reason of selection of frequency was not given out.In this paper, the distribution of electromagnetic field, action of electromagnetic body force permeating slit mold on strand, the decisive effect of frequency on soft contact solidification and optimal frequency range in billet slit mold are discussed here deeply. Theoretical FoundationThe most radical governing equation for electromagnetic field is Maxwell equations. Electromagnetic harmonic wave of definite frequency is emitted by high frequency power source in soft contact technology. Within conductor, rϭ0, J ជ ϭsE ជ where, r, density of free charge (C/m 3 ); J ជ , electric current density (A/m 2 ); s, electrical conductivity (S/m); E ជ , electric field intensity (V/m).The Maxwell equations of alternating electromagnetic field are obtained as: (7) where, B ជ , magnetic flux density (T); D ជ , electric displacement vector (C/m 2 ); H ជ , magnetic field intensity (A/m); m, magnetic permeability (H/m); e, dielectric constant (F/m).The electromagnetic body force imposed on conductor is described as: (13) where h f , residual percentage of electromagnetic field passing through mold wall, related to frequency; t, time (s).The attenuation curves without dimension of electromagnetic wave of different frequencies within 6 mm copper wall, 40 mm radius steel strand and round copper mold filled by liquid steel are shown respectively in Figs. 1, ...

Electromagnetic Field Distribution in Two-section Slitless Mold for Soft-contact Electromagnetic Continuous Casting

“…In view of the rationality of the divisional elements, the width of the gap between the strand and the mold wall was set as 1 mm. Basic assumptions 11) : 1) The liquid metal level was supposed to be plane, and the effect of the meniscus shape on magnetic field was neglected. 2) The liquid metal level was located at the middle of the coil.…”

“…Many researchers carried out long-term studies on the distribution of the electromagnetic field in the soft-contact solidification process and obtained many important results. [11][12][13] But up to now, the researches on the distribution of electromagnetic field have mostly concentrated on the case of the slit mold for SC-EMCC. Investigations on slitless mold for SC-EMCC are very lacking, except for the literatures 8,9) that have introduced the structure of the two-section slitless mold, further research has not been reported.…”

An Experimental Investigation to Facilitate an Improvement in the Design of an Electromagnetic Continuous Casting Mould

“…This results in increasing the Joule heat, exhibited by the increase of mould wall temperature. The enhancement of the mould temperature due to Joule heat can also be found in the numerical simulation work of Na et al [24,25].…”

Numerical Analysis of Thermal-driven Buoyancy Flow in the Steady Macro-solidification Process of a Continuous Slab Caster

“…[1][2][3][4][5][6][7][8][9][10] For example, the thermal-driven buoyancy flow (also called natural convection, thermal convection or non-isothermal flow in some papers) in tundish and ladle with large volume capacity of liquid steel has been widely studied. [11][12][13][14] It is thought that non-isothermal flow has an obvious influence on the temperature distribution and inclusion removal in tundish and ladle.…”