Accepted Manuscript

Title: 3D Numerical Simulation of Electrical Arc Furnaces forthe MgO Production

Author: Zhen Wang You Fu Ninghui Wang Lin Feng

PII: S0924-0136(14)00165-4DOI: http://dx.doi.org/doi:10.1016/j.jmatprotec.2014.04.033Reference: PROTEC 13985

To appear in: Journal of Materials Processing TechnologyReceived date: 10-2-2014Revised date: 26-4-2014Accepted date: 29-4-2014

Please cite this article as: Wang, Z., Fu, Y., Wang, N., Feng, L.,3D Numerical Simulationof Electrical Arc Furnaces for the MgO Production, Journal of Materials ProcessingTechnology (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.04.033This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.

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3D Numerical Simulation of Electrical Arc Furnaces for the MgO Production

Zhen Wanga, You Fub, Ninghui Wangb, *, Lin Fenga

a School of Innovation Experiment, Dalian University of Technology, Dalian 116023, China b College of Electrical Engineering, Dalian University of Technology, Dalian 116023, China

* Corresponding author. Tel.: +86 0411-84708576; fax: +86 0411-84708576.

E-mail address: ninghuiw@263.net

Abstract: targeted at the 3000 kVA and 1500kVA electric arc furnaces for MgO production, 3D models are

developed to characterize the thermal behavior in the furnaces. The electromagnetic stirring effect of the molten

bath is studied respectively with a rated current, and its influence on the temperature field is predicted by the

model in FLUENT. Some calculated results are proved reliable by comparison with the measurements. It can be

seen that a stronger stirring effect leads to a higher average flow velocity in the 3000kVA furnace, and the size of

its molten bath is much larger than that in the 1500kVA furnace. The appropriate location of the three electrodes

can help to maintain a homogenous bath temperature distribution. The comparison between the calculated results

and the measurements proves that the dimensional designs of the two furnaces are acceptable for the prevention of

the local overheating or overcooling. Large-capacity electric arc furnaces are qualified with significant advantages

in energy conserving and increase of productivity.

Key words: Electric Arc Furnace; Mgo; Numerical Simulation; Temperature Field; Flow Field

1. Introduction

The improvements in the production of MgO are currently centered around automatic control algorithms. Wu et al. (2011) identified as main factors affecting the process the dynamic characteristics of the electrodes, the strong coupling and non linearity and the frequently changing boundary conditions. The complexity of the problem makes difficult to achieve satisfactory control.

The use of CFD to model steelmaking processes has been an active area of research for the last three decades, and all these steelmaking processing steps involve highly coupled complex transport phenomena (Chattopadhyay et al., 2010). For example, Arzpeyma et al. (2013) established an AC EAF (Electric Arc Furnace) model through ANSYS FLUENT to study the influence of electromagnetic stirring to the molten bath of waste steel and iron. The applications of the AC EAF encounter similar problems in other industrial areas. Di Barba et al. (2012) developed a 3D Finite Element (FE) model of a submerged arc electric furnace to define an equivalent electric circuit model able to describe the furnace operations for the production of ferroalloys. E. Scheepers et al. (2006) made use of FLUENT to establish CFD model of submerged-arc furnace for the production of phosphorus to investigate the influence of changing operating conditions on energy distribution within the solid-gas region and reaction characteristics such as the position of the solidgas reaction zone. In their subsequent studies (E. Scheepers et al., 2010), the model accounted for fully developed gas flows generated from the packed bed, the energy associated with chemical reactions, heating, and melting, as well as thermal conductivity and the particleparticle radiation within the burden. However, the model did not solve Maxwell equations to calculate Joule heating, and the liquid phase of molten slag and alloy phase were modeled as stagnant liquid phases. Kadkhodabeigi et al. (2011) also established models in FLUENT to study the tapping process in the submerged-arc furnace for silicon and ferrosilicon production. In the

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field of MgO production, Li et al. (2011) developed an adaptive neuro-fuzzy inference system for the EAF to improve the quality and the quantity of the MgO single crystal production. Different to the AC mode, a twin-electrode DC EAF was designed for MgO crystal production and this technique was found to be another effective method to grow high quality MgO single crystals. Wang et al. (2011) made use of a 3D model to determine the electromagnetic field, temperature field, and flow field of this DC EAF and estimate its power consumption.

Numerical calculations are used for energy and cooling optimization and also for finding best constructive solutions regarding furnace design. The computational modelling of the EAF is conducive to reduce the blindness of design including distances between two electrodes, electrode diameter and diameter of furnace body to a greater extent. As the molten MgO temperature will reach a minimum of 3100K, numerical simulation can be used to effectively estimate the shape of the molten bath, temperature and flow of melt, and other important information when conventional measuring methods become infeasible to monitor conditions inside the furnace. 2. Simulation objects

This paper takes the newly built 3000kVA large-capacity and fully enclosed EAF as the research object. Such especially designed EAF for MgO production is installed with automatic electrode control, water cooling, feeding control and dust collection systems. When compared with the former 1500kVA furnace, 3000kVA-capacity design is improved in three aspects: 1. increased diameter and height of furnace body; 2. increased electrode space; 3. reduced electrode diameter; with detailed parameters indicated in Table 1. Rated power of this improved EAF is significantly enhanced and the charged materials are increased from 15t to 45t per furnace.

Table 1 Dimensions of the furnaces with different capacities

Capacity 3000 kVA 1500 kVA

Height (mm) 3000 2000 Diameter (mm) 2600 2000

Electrode diameter (mm) 300 350 Distance between electrodes (mm) 700 650

Operation Depth (mm) 1500 1000

Fig. 1 is vertical cross section of 3000kVA or 1500kVA three-phase AC EAF along central line of EAF and one bar of electrode.

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Fig. 1. The vertical cross section through the center line of the furnace and one of the electrodes with a

being the free surface of the melt, b one electrode, c the shell wall, d the center line of the furnace, e the bottom of the furnace, f the exterior boundary of the furnace, and g the interface of the molten bath and the raw materials.

2.1 Hypothesis on the model of EAF

The equipment of three-phase AC EAFs for MgO production is similar to that of submerged-arc furnaces used in other areas of the metallurgy industry. EAFs are mainly composed, for example, of transformers, busbars, water cooling cables, conductive cross arms, graphite electrodes, and furnace walls. In actual operation, the shape of the molten MgO bath is influenced by various factors. According to the methods of Wang Zhen et al. (2011), the boundary of molten bath in an AC furnace can also be determined. The calculated shape agrees well with measurements on site. Subsequently, a 3D furnace model including the molten bath with a known boundary was constructed in CATIA V5. The CFD analysis was conducted for the molten bath in ANSYS FLUENT. Such calculations must meet the following basic hypothetical conditions:

(1) When the line current to 3000kVA-capacity EAF reaches 14,000A, the three-phase current will be balanced and the shape of molten bath is kept basically constant. The unchanging shape of the molten bath means that there is basically the same speed of melting at the top and solidifying at the bottom of the molten bath. In addition, the molten bath is in a dynamic balance in its occupied space. When the line current of 1500kVA EAF reaches 7,000A, the EAF will be in heat balance and the boundary of the molten bath will be fixed.

(2) The electromagnetic field is time harmonic, and the influence of high-order harmonic currents is considered to be neglected.

(3) The Lorentz force is the dominant driving force for the melt flow, and the flow pattern is laminar (Reynold's number Remax = vL/1

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bath. As the molten bath is located inside an EAF, it is far from other short network system with the exception of graphite electrodes. This paper therefore does not consider the influence of this part on stirring of the molten bath. 2.2 Governing equation and boundary conditions

The three-dimensional governing equation of steady state flow issue can be described as: Mass conservation:

( ) 0 =v (1) Momentum conservation:

( ) ( )1 = + + + Tvv P v v f (2) v is the flow velocity, is the density of flux, 1 is the viscosity, P is the pressure and f is the body force. Boundary conditions: Furnace and electrode surface:

v = 0 (3) Top surface of molten bath:

v n = 0, ( ) 0 =v t n (4) n refers to normal vector and t refers to tangential vector. Energy conservation:

( ) ( )pC T K T Q = +v (5) K is heat conductivity, Cp is specific heat, Q is the item of heat source and T is temperature. Boundary conditions: Inner surface of furnace wall:

( ) ( )0K T h T T = n (6) Upper surface of molten bath:

( ) ( )4 40sbK T T T = n (7) Surface of molten bath exposed to heating area of electric arc:

q = Pa / Sa (8) In the above formula, T0 is ambient temperature, h is heat conductivity coefficient, is emissivity, sb is constant of Stefan-Boltzmann, q is equivalent heat flux, Pa is effective arc heating power, and Sa is the bath surface exposed to arcs. The temperature of the boundary surface of molten bath reaches 3100K. Body force f is defined in the following way:

= + f g J B (9) g refers to acceleration of gravity and the production term of Lorentz force is the product of multiplying magnetic induction intensity B with current density J.

In the paper, molten bath is the primary subject of research. In the EAF, MgO in smelting will become conductive. The electromagnetic field calculation of molten bath and surrounding regions should thus meet the requirements of Maxwells equations. As the engineering issues studied in this

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paper are mainly related with low-frequency electromagnetic fields, the displacement current is ignored. In order to ensure the unique solution to vector potential, governing equations of the electromagnetic field should be simplified into the following equations using coulomb gauge.

Within the conduction area,

1 1 0t

+ = AA A+ (10)

0t

+ = A

(11)

Not in the conduction area,

1 1 A A = J (12) A is vector potential, is scalar potential. , 0 and refer to electric conductivity, magnetic permeability of air and magnetic permeability of iron respectively.

Boundary conditions for calculating electromagnetic field: The bottom of the molten bath:

= 0 (13) Outer surface of model:

B n = 0 (14) Three-phase power frequency AC current is imposed to upper surface of three electrodes respectively.

PJ Joule heating power is calculated with the following formula.

J VP Qdv= (15)

With V as the volume of molten bath, Joule heat power of unit volume is calculated with the following formula.

Q = E J (16) 3. Results and discussion

This paper used the following steps in calculation: 1. The model of EAF (including molten bath with fixed boundary) was built with 3D modeling

software CATIA V5; 2. A three dimensional mesh was generated; 3. The electromagnetic field was calculated by finite element method; 4. Electromagnetic forces and Joule heating powers were imposed to FLUENT mesh cell to

calculate temperature field and flow field of the molten bath; 5. The temperature field of the whole EAF was calculated except for the molten bath. Two simulation models were constructed, including 3000kVA-capacity EAF with rated current

reaching 14,000A and 1500kVA-capacity EAF with rated current reaching 7,000A. Magnesite and light burned MgO were utilized as the raw materials respectively for 3000kVA and 1500kVA EAF with relevant physical property parameters indicated in the following table.

Table 2 Physical properties of the main materials used in the simulation

Properties Values

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Emission 0.5 (wall), 0.3 (melt) Convection/ (Wm-2K-1) 10

Thermal conductivity/ (Wm-1K-1) 2.1 (magnesite), 6~15 (light burned MgO), 8 (melt) Specific heat capacity/ (Jkg-1K-1) 48.99+0.00314t-1172000t-2 (Ma and Fang, 1979)

Density/ (kgm-3) 2900~3000 Resistivity of the melt/ (m) 0.00035~0.00045 (Leu et al, 1975)

Resitivity of the graphite electrode/ (m) 8.510-6 3.1 Electromagnetic field of 3000kVA EAF

HIOKI 3470 magnetic field detector was selected as the measurement instrument. In 10Hz-2kHz mode, 24 measuring points on the platforms of 1st floor and 2nd floor were selected. Tri-axial RMS and composite RMS values of magnetic induction intensity were recorded. If the tri-axial RMS components of one measuring point are Bx, By and Bz, the composite RMS value Bcomp will be written in the following form.

Bcomp = (Bx2 + By2 + Bz2)1/2 (17) With the central point at the bottom of EAF as the origin, cylindrical-coordinate systems are used

with the selection of R, and Z components as the radial direction, angle direction and height direction of EAF. If is equal to 0, the plane formed is simply the plane formed by central axis of EAF and electrode A. When the line current of 3000kVA EAF reaches 14,000A, 9 typical points of the 24 measuring points are listed and compared with the simulation calculation results as indicated in the following table. One group of calculated results is based on the method similar to the former work (Wang et al., 2011). By this method, liquid and solid phases of the raw materials were treated as a uniform region to deal with moving meltsolid interface, and a large viscosity was given to ensure flow velocity in the region was zero when temperature was less than or equal to solid temperature. The electromagnetic field was calculated (unpublished data) with a less accurate meltsolid interface location than a fixed one.

Table 3 Comparison between measurement and calculation of magnetic field

Measuring

point

number

R (m) (degree) Z (m) Average measured

value (mT)

Calculated results

by former method

(mT)

Calculated results

in this paper (mT)

1 2.75 0 0 0.074 0.056 0.058

2 3.0 120 0 0.052 0.047 0.049

3 3.0 -120 0 0.049 0.047 0.049

4 1.5 0 3.15 1.58 0.42 0.45

5 1.5 120 3.15 0.52 0.42 0.45

6 1.5 -120 3.15 0.45 0.42 0.45

7 2.5 0 3.15 2.43 0.17 0.17

8 2.5 120 3.15 0.21 0.17 0.17

9 2.5 -120 3.15 0.17 0.17 0.17

According to the data in the above table, it can be seen that the order of magnitude of measuring

magnetic field fits the simulation results well. As No. 1, No. 2 and No. 3 measuring points were located at the plane zone of the bottom of EAF far away from the molten bath and electrodes, their magnetic

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induction intensity was reduced. As No. 4 measuring point was located at the top of the EAF outside the furnace wall and because it was relatively closer to the conductive cross arms when compared with No. 5 and No. 6 measuring points, therefore its magnetic induction intensitys signals were significantly increased. For the same reasons, No. 7 measuring point was closer to the conductive cross arms as compared to No. 8 and No. 9 measuring points, although far away from the furnace wall. Positions of measuring points 1 to 9 are shown in the horizontal and vertical views in Fig. 2.

Fig. 2. A schematic drawing of measuring points with respect to the position of EAF elements: A is one of the

electrodes, B is one of the conductive cross arms, and C is the furnace shell.

The calculated results by the two methods are found to agree with the measured values well if the

selected measuring points are far away from the conductive cross arms. There is a long enough distance between the location of molten bath and the conductive cross arms, so the magnetic stirring calculations are conducted without the consideration of the arms in the model. 3.2 Flow velocity and temperature field

Fig. 3 is about vertical and horizontal cross sections of flow velocity field of 3000kVA EAF. The distribution of the flow velocity field shows that the flow pattern of melt is very complicated under the influence of electromagnetic stirring. From vertical cross section in Fig. 3(a), the formation of two vortexes can be seen with the formation of another vortex indicated in horizontal cross section in Fig. 3(b). Max flow velocity reaches 0.03m/s with its main location at the surface of molten bath below the three electrodes. The area of the molten bath below each electrode is featured with the maximum current density and the strongest electromagnetic force, so the flow velocity there is the largest. Fig. 4(a) and (b) relate to the corresponding flow field distributions of horizontal and vertical cross sections in 1500VA EAF. From these figures, it can be seen that though the design and rated power of the two types of furnaces vary, flow patterns of the molten baths do not significantly vary between them, with the difference lying only in that under such conditions, stirring effects of electromagnetic force becomes weakened to a greater extent due to reduced current and maximum flow velocity of melt is less than 0.006m/s.

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Fig. 3. The velocity field of the 3000kVA furnace (m/s): (a) the vertical cross section ( = 0, = 180), and (b)

the horizontal cross section (Z = 1.5).

Fig. 4. The velocity field of the 1500kVA furnace (m/s): (a) the vertical cross section ( = 0, = 180), and (b)

the horizontal cross section (Z = 1.0).

Such flow patterns inside molten baths result in strong effects on the shape of the molten bath.

This influence is shown in Fig. 5. The figure is temperature fields cross section of 3000kVA EAF. The area with the temperature reaching a minimum of 3100K molten bath indicates that the materials are completely melted. The area with temperature lower than 3100K is non-melted area. Through examination of the cross-sectional drawings of vertical Fig. 5(a) and horizontal Fig. 5(b), it can be seen that the radial distance of solid-liquid interface becomes larger in the area adjacent to electrodes, but is reduced in the area between electrodes. Though the calculated highest temperature of molten bath reaches at least 3800K approaching the boiling point of MgO, the overall temperature of the molten bath becomes homogeneous under the strong stirring conditions of electromagnetic force. Three high temperature zones are produced below the three electrodes. The ratio of the max radical distance of the solid-liquid interface (long radial distance of molten bath: Rmax) and the minimum radial distance (short radical distance of molten bath: Rmin) is about 1.18 at the surface, and the bottom of the molten bath is nearly ball-shaped with the ratio approaching 1. The above calculation result reveals that large molten bath is easily formed when the line current of 3000kVA EAF reaches 14,000A so that it is conducive to smelt newly added raw materials completely. If the current is reduced, the dimension of molten bath will noticeably contract. Rmax and Rmin will be reduced with the reduction of the current, but the range of reduction of Rmin is larger. If Rmin is not large enough, it will be difficult for the newly added raw materials to melt completely. If the dimension of molten bath at the early stage of the melting process

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cannot satisfy the requirements, it is easy to stop the furnace due to arc breaking in the subsequent charging stage and result in a large amount of materials failing to be melted completely.

Fig. 6 relates to the cross section drawing on the temperature field of 1500kVA EAF. From the figure, it can be seen that the shape of the molten bath is similar, but the ratio of Rmax and Rmin is about 1.28, which is higher than the value in the 3000kVA EAF. Though stirring effects of electromagnetic force are weak, the temperature distribution becomes uniform with the highest temperature reaching a minimum of 3400K. The dimension of molten batch formed with the use of the two types of furnaces is indicated in Fig. 7. In the figure, the calculated values of 3000kVA and 1500kVA furnaces were determined according to the methods proposed by Wang Zhen et al. (2011). By comparing calculation and measuring results of dimensions of molten baths, it can be determined that the model is reliable for prediction of the dimensions of molten baths. Max depth Hmax of molten baths will fluctuate in real time during the smelting process. After smelting is completed, the height of the final is higher than Hmax with the rising of electrodes and addition of new materials. The accurate height of molten bath, therefore, cannot be reflected in the solidified product. Thus in Fig. 7, no comparison is made on max depth of molten bath.

Fig. 5. The temperature field of the 3000kVA furnace (K): (a) the vertical cross section ( = 0, = 180), and

(b) the horizontal cross section (Z = 1.5).

Fig. 6. The temperature field of the 1500kVA furnace (K): (a) the vertical cross section ( = 0, = 180), and

(b) the horizontal cross section (Z = 1.0).

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

HmaxRminRmax

Dim

ensi

ons /

m

3000 kVA calculated values 1500 kVA calculated values 3000 kVA measured values 1500 kVA measured values

Fig. 7 Comparison of the bath dimensions of the two furnaces

The shape of molten bath calculated fits with the shape of solidified product in production testing.

Due to extremely low heat conductivity of the material and favorable effects of heat preservation, the temperature gradient outside the solid-melt interface will reach at least 6000K/m. 50-100mm incompletely melted raw materials will be formed outside molten bath and the materials outside incompletely melted raw material layer are not fused. The vertical cross section of the solidified product in a 3000kVA furnace is shown in Fig. 8. If lightly burned MgO is charged as raw material, high purity MgO crystals will form inside this incompletely melted raw material layer. The vertical cross section of the solidified product in a 1500kVA furnace is shown in Fig. 9. If magnesite is adopted as raw material, a small amount of 98-99% MgO may be acquired inside incompletely melted raw material layer. During the molten bath solidification process, some impurities will be transferred out through capillary action, thus causing distribution to the incompletely melted raw material layer. The residual impurities will be transferred inside and eventually gather at the central area. Some impurities such as SiO2 and Al2O3 with low melting point will reach or approach their boiling points respectively in fusion of MgO. As a result, most of them are transferred to air and exhausted outside.

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Fig. 8. The vertical cross section of the solidified product in a 3000kVA furnace: Region 1 is the solidified

bath; Region 2 is the incompletely melted raw materials; Region 3 was charged with raw materials before the

removal of the shell.

Fig. 9. The vertical cross section of the solidified product in a 1500kVA furnace: Region 1 is the solidified

bath; Region 2 is the incompletely melted raw materials; Region 3 was charged with raw materials before the

removal of the shell.

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During the smelting process, electric arc plasma jets and molten baths inside the EAF are located at high temperature zones as well as the center of the raw materials. In addition, the high concentration dust at the opening of furnace reaches high temperatures, thus leading to low visibility inside the furnace. Therefore, at present it is impossible to directly collect temperature data inside the electric arc and at nearby areas of the molten bath. The traditional method for data measurements is to monitor the temperature of the furnace wall on site, for example, with the use of infrared thermometers or thermal imaging infrared cameras. As the highest temperature areas on furnace wall, they are correspondent with locations of the three electrodes which produce three local high temperature zones. The calculated temperature for both types of furnaces reaches about 750K. As the model is symmetric, 1/6 furnace wall area (select the area with between 0 and 60) is adopted to compare the two types of furnaces just as indicated in Fig. 10. From the figure, it can be seen that both simulated and measured temperatures of furnace wall of 3000kVA furnace are higher. At the position with = 0, it is the nearest position to the boundary of the molten bath with the highest temperature. With the increase of angle, the temperature decreases gradually to a minimum value near the central part of the two electrodes. In the figure, the measured temperature is kept basically constant within certain stage after reaching an objective value of electric current during the process of smelting. Repeated measurements were conducted at corresponding positions to determine average values. Simulation results of temperatures correspond well to the measured values.

0 20 40 60500

550

600

650

700

750

800

850

Tem

pera

ture

/K

Y /degree

3000kVA calculated values 1500kVA calculated values 3000kVA measured values 1500kVA measured values

Fig. 10. Comparison of the wall temperatures of the two furnaces

3.3 Effects comparison between two EAFs

If the resistivity of the MgO molten bath is within the range indicated in Table 2, the calculated power according to formula (16) due to Joule heat effects accounts for about 2.5%-6.8% of total 3000kVA capacity of the EAF transformer. The computed power is 102kW to 203kW with the current range from 10000A to 14000A. If the transformer capacity of the EAF is 1500kVA, the computed power is 47kW to 185kW with the current range from 7000A to 14000A, and the Joule heat power accounts for about 3.1%-12.4% of the total capacity. The dimension of molten bath is larger in a

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3000kVA EAF, but the current is merely increased to 14,000A. As a result, the rate of total power inside the molten bath due to consumption of impedance is reduced. The heating effect by increasing current was proved by experiments to be very limited, for the Joule heating power only accounts for about 10% or less of the total capacity of the transformer according to the calculations. So it is concluded that the majority of the effective power is released by the electric arcs.

If the conductive parts of graphite electrodes to 3000kVA and 1500kVA furnaces reach 2.6m and 2.0m respectively, the power consumption calculated according to formula (15) will reach 100kW and 40kW. Due to heat dissipation effects of the convection current and heat radiation along the furnace wall and bottom, the dissipated power reaches 240kW and 150kW respectively.

45t raw materials are required in a 3000kVA furnace. Magnesite ore contains approximately 45-47% MgO and it will be decomposed into MgO and CO2 by heating. The distribution of different grade products: 3t MgO above 98%, 3.8t will be 97%, 4-5t will be above 96%, 3-5t will be above 95% and 1t will be composed of incompletely melted raw materials. Total product accounts for between 12t and 14t. When using the 1500kVA EAF, 15t raw materials of light burned MgO are needed. 1t MgO product needs 2.6t raw materials with the distribution of different grades as follows: 0.8t MgO above 98%, 1.2t above 97%, 1.2-1.5t above 96% and 1.4t below 95%. As a result, total product accounts for between 4t and 5t. For production of 1t fused MgO with the use of 1500kVA EAF, power consumption reaches about 2600-3000 kWh, but the power consumption for production of 1t fused MgO with the use of a 3000kVA EAF reaches approximately 2300-2900 kWh. As a result, the smelting capacity for the 3000kVA EAF is improved three-fold, thus offering a tripling of productive output. Heat dissipation, however, for electrodes, furnace walls, and bottom is increased by less than two-fold. Therefore, large-capacity EAFs are possessed of superior advantages in energy conservation and increasing output.

4. Conclusions

In order to characterize the thermal behavior inside the EAF for MgO production, 3D numerical modeling was used to study magnetic stirring effect on the molten bath. The main conclusions can be summarized as follows: 1. It is found that electromagnetic stirring effects in a 3000kVA EAF are significantly strengthened with a larger size molten bath compared with a 1500kVA EAF. 2. As the thermal conductivity of MgO powder is quite low, the temperature gradient between molten bath and furnace wall is more than 6000K/m. 3. By measuring magnetic fields and temperature fields around the furnace, as well as dimensions of the solidified product, the calculated results have been proved reliable. 4. The model predicts the design schemes of the two types of furnaces to be both reasonable for high productivity. 5. Large-capacity EAFs are in possession of significant advantages in terms of energy conserving and increasing output. 6. The Joule heating power is very limited comparing the total capacity of the transformer, so the majority of the effective power should be released by the electric arcs.

Acknowledgments The authors gratefully acknowledge the supports of the National High Technology Research and

Development Program (863 Program) of China (No. 2011AA060102) and the Fundamental Research

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Funds for the Central Universities (DUT12RC(3)82).

References Wu Z.W., Wu Y.J., Chai T.Y., 2011. Intelligent Control of Fused Magnesium Furnaces Based on SPSA. J Journal Of Shanghai Jiaotong University. 08, 4-9. Chattopadhyay, K., Isac, M., Guthrie, R.I.L., 2010. Applications of Computational Fluid Dynamics (CFD) in iron- and steelmaking: Part 2. Ironmaking and Steelmaking. 37(8), 562-569. Arzpeyma, N., Widlund, O., Ersson, M., Jnsson, P., 2013. Mathematical modeling of scrap melting in an EAF using electromagnetic stirring. ISIJ International. 53(1), 48-55. Di Barba, P., Dughiero, F., Dusic, M., Forzana, M., Mognaschib, E.M., Paiolic, M., Sienia, E., 2012. 3D FE analysis and control of a submerged arc electric furnace. International Journal of Applied Electromagnetics and Mechanics. 39(1-4), 555-61. Scheepers, E., Adema, A.T., Yang, Y., Reuter, M.A., 2006. The development of a CFD model of a submerged arc furnace for phosphorus production. Minerals Engineering. 19(10), 1115-1125. Scheepers, E., Yang, Y.X., Adema, A.T., Boom, R., Reuter, M.A., 2010. Process Modeling and Optimization of a Submerged Arc Furnace for Phosphorus Production. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science. 41(5), 990-1005. Kadkhodabeigi, M., Tveit, H., Johansen, S.T., 2011. Modelling the Tapping Process in Submerged Arc Furnaces Used in High Silicon Alloys Production. ISIJ International. 51(2), 193-202. Li, T., Wang, Z., Wang, N.H., 2011. Temperature Field Analysis and Process Control Strategies for MgO Single Crystal Production Using Adaptive Neuro-Fuzzy Inference System. Open Materials Science Journal. 5(1), 162-169. Wang, Z., Wang, N.H., Li, T., 2011 Computational analysis of a twin-electrode DC submerged arc furnace for MgO crystal production. Journal of Materials Processing Technology. 211(5), 388-395. Ma, Q.F., Fang, R.S., 1979. Practical Thermophysical Property Handbook. Beijing Press, Beijing, pp. 158-159. Leu A., Ma, S. Eyring H., 1975. Properties of Molten MgO. Proceedings of the National Academy of Sciences, USA, 72(3), pp. 1026-1030.

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Figure captions: Fig. 1. The vertical cross section through the center line of the furnace and one of the electrodes with a being the free surface of the melt, b one electrode, c the shell wall, d the center line of the furnace, e the bottom of the furnace, f the exterior boundary of the furnace, and g the interface of the molten bath and the raw materials.

Fig. 2. A schematic drawing of measuring points with respect to the position of EAF elements: A is one of the electrodes, B is one of the conductive cross arms, and C is the furnace shell. Fig. 3. The velocity field of the 3000kVA furnace (m/s): (a) the vertical cross section ( = 0, = 180), and (b) the horizontal cross section (Z = 1.5). Fig. 4. The velocity field of the 1500kVA furnace (m/s): (a) the vertical cross section ( = 0, = 180), and (b) the horizontal cross section (Z = 1.0). Fig. 5. The temperature field of the 3000kVA furnace (K): (a) the vertical cross section ( = 0, = 180), and (b) the horizontal cross section (Z = 1.5). Fig. 6. The temperature field of the 1500kVA furnace (K): (a) the vertical cross section ( = 0, = 180), and (b) the horizontal cross section (Z = 1.0). Fig. 7. Comparison of the bath dimensions of the two furnaces Fig. 8. The vertical cross section of the solidified product in a 3000kVA furnace: Region 1 is the solidified bath; Region 2 is the incompletely melted raw materials; Region 3 was charged with raw materials before the removal of the shell. Fig. 9. The vertical cross section of the solidified product in a 1500kVA furnace: Region 1 is the solidified bath; Region 2 is the incompletely melted raw materials; Region 3 was charged with raw materials before the removal of the shell. Fig. 10. Comparison of the wall temperatures of the two furnaces

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Table captions: Table 1 Dimensions of the furnaces with different capacities Table 2 Physical properties of the main materials used in the simulation Table 3 Comparison between measurement and calculation of magnetic field