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Numerical Simulation of the Dynamic Formation of Slag Skin and Heat Flow Distribution during the Electroslag Remelting Process Jia Yu, Fubin Liu, Zhouhua Jiang,* Congpeng Kang, Kui Chen, Huabing Li,* and Xin Geng for obtaining a smooth ingot surface, but a thicker slag skin is the cause of the surface defects that must be removed by mechanical grinding prior to forging.[5–7] The ESR process is always accompanied by the absorption and release of heat related to the dynamic formation of slag skin, which affects the interior and surface quality of the ingot. Hence, investigating dynamic formation of slag skin and heat flow distribution is important for controlling the solidification quality of ingot. However, due to the use of opaque material as well as the complexity and high expense of running an ESR experiment, it is impractical to study the dynamic formation of slag skin and the heat flow distribution by trial and error. Consequently, an alternative method of numerical simulation has been widely developed and used. Currently, the methods used for simulating slag skin in the ESR process can be classified into two categories: The first category is indirect methods, which are accomplished by applying electrical and thermal resistance at the mold wall to consider the effects of slag skin.[5] Kharicha et al.[8,9] established a 1D slag skin thickness model according to the energy balance within the slag skin, and simultaneously considered the effects of melt rate on slag skin thickness. Their model can predict the variations of slag skin thickness along the mold wall and includes the effects of mold current on slag skin thickness. The first method is recommended for industrial applications to estimate the thickness of slag skin, with the advantage of saving computation resources. The second method is to simulate the formation of slag skin directly in the same way as the metal using the liquidus and solidus temperature as input parameters. Weber et al.[10] developed a comprehensive model to investigate the solidification of molten slag and metal with the enthalpy method. Yanke et al.[11,12] explored the effects of current level and mold diameter on slag skin using the volume of fluid (VOF) model and neglected the difference between molten slag and slag skin in electrical conductivity. Hugo et al.[7] and Jardy et al.[13] demonstrated the effects of mold current on slag skin at the same current level and found that the slag skin thickness increased with the existence of mold current.

A 2D axisymmetric model is established to investigate the dynamic formation of slag skin and heat flow distribution during the electroslag remelting process. The growth of ingots is addressed with the dynamic mesh technique, and the volume of fluid model is employed to trace the slag/metal interface. The results indicate that the slag skin thickness at the slag/mold interface increases with the distance from the free slag surface, with a maximum thickness of 4 mm at the slag/pool interface. With the growth of ingot, the slag skin at the slag/pool interface is partially remelted by the hotter metal and finally solidifies around the solidified ingot with a thickness of 1 mm. The calculated percentage of heat flow is in reasonable agreement with the measurement. The loss of heat flow to the mold accounts for 67% of the power input, and approximately 28% of that power is absorbed by droplets in a laboratory scale ESR unit. The heat loss to slag/mold interface first increases with increasing slag temperature and then slowly decreases with decreasing slag bath height. The heat of the ingot primarily escapes from the baseplate at the initial stage. However, as the ingot grows, the heat loss in the radial gradually becomes dominant.

1. Introduction Electroslag remelting (ESR) is a secondary refining process with consumable electrodes for the production of high quality special steels and superalloys with compact structures, homogeneous components, and controlled solidification characteristics.[1–4] A schematic sketch of the ESR process is illustrated in Figure 1. The current passes through the highly resistive molten slag creating a great amount of Joule heat that is enough to melt electrode forming metallic droplets. The metallic droplets sink through the less dense molten slag and then gather in the watercooled copper mold where they solidify directionally. Meanwhile, molten slag that is in contact with mold solidifies, forming a layer slag skin. A layer of thin and uniform slag skin is favorable Dr. Z. H. Jiang, Prof. H. B. Li, J. Yu, Dr. F. Liu, C. P. Kang, K. Chen, Dr. X. Geng School of Metallurgy Northeastern University Shenyang, 110819, China E-mail: [email protected]; [email protected]

DOI: 10.1002/srin.201700481

steel research int. 2018, 1700481

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© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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magnetic field intensity could be expressed with pharos: ^ jwt . Because the geometry is 2D axisymmetric, the H ¼ He magnetic only has an azimuthal component. Given the large electrical conductivity gradient existing in the electroslag ^ is remelting system, the electromagnetic stream function r H regarded as the main variable to describe the magnetic field transport equation,[13] which can be simplified as follows: ! ! ^θ ^θ ^θ 1@ 1 @ rH @ 1 @ rH 1 @ rH r þ 2 r @r rσ @r @z rσ @z σr @r ^θ ¼0 jωμ0 H

ð1Þ

^ is a function of the position, Here, the complex amplitude H A/m; ω is the angular frequency, Hz; and σ is the electric conductivity, Ω1 m1. The current density is calculated with the distribution of magnetic field. ~ ~ J ¼rH

Figure 1. Schematic sketch of the ESR process.

The above literature primarily focused on the effects of process parameters on slag skin thickness, such as current, mold diameter, fill ratio, etc. However, few studies have considered the dynamic formation process of slag skin. In addition, no analysis of heat flow distribution has been reported that simultaneously considers the formation of slag skin. Hence, a 2D transient axisymmetric model is developed to investigate the dynamic formation of slag skin based on the VOF model and dynamic mesh technique, which considers the difference between slag skin and molten slag in electrical conductivity. Furthermore, the electromagnetic field, fluid flow, and temperature field are also analyzed. In addition, the heat flow distribution is calculated based on the energy conservation principle, which enables us to gain a profound insight into the heat transport process in the ESR process.

2. Mathematical Modeling In the present paper, the geometry is 2D axisymmetric containing the slag bath and ingot at the initial time. The immersion depth of electrode is ignored, and both the electrode tip and slag/pool interface are assumed to be flat. Apart from the density in the buoyancy term and the electric conductivity of slag, other physical properties of slag, and ingot are assumed to be constant.[14–16] In order to simulate the dynamic formation of slag skin, the Maxwell equations, Navier Stokes equations, and energy conservation equation coupled with the solidification model are solved simultaneously.

2.1. Electromagnetic Field The transport of magnetic field is dominated by the magnetic diffusion in the ESR process because the magnetic Reynolds number remains very low. For the sinusoidal AC field, the


ð2Þ

The Lorenz force and Joule heat are calculated with Equation 3 and 4 and added to the momentum and energy conservation equations as source terms, respectively. ~ ~ F ¼ μ0~ J H

ð3Þ

~ J ~ J σ

ð4Þ

Q¼

2.2. Multiphase Flow It is well known that the electroslag remelting process involves the motion of the slag and liquid metal, and the velocity field can be obtained by solving mass and momentum conservation equations[17]: ~ ¼0 r ρV

ð5Þ

~ @ ρV ~V ~ ¼ r μ rV ~ þ rV ~T þ r ρV rP @t ~ ~ g ðT T 0 Þ þ F þ F p þ ρ0 β~

ð6Þ

~ is the velocity, m s1; m is the Here, ρ is the density, kg m3; V dynamic viscosity, Pa s; β is the thermal expansion, K1; ~ F is the Lorentz force, N m3; and ~ F p is the drag force blocking the flow in mushy zone, N m3. The effect of turbulence is addressed with the RNG κ-e model including an enhanced wall function in the near-wall region. The standard κ-e model is generally used for the flow of high Reynolds number. However, the RNG κ-e model incorporates the flow of a high Reynolds number with a low Reynolds number, resulting in a wider class of flows than the standard κ-e model.[18]

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The motion of slag and liquid metal is a classical multiphase flow problem, which is described with the VOF model.[19,20] The VOF model is a robust and reliable interface tracking technique, and the geometric reconstruction scheme represents the interface using a piecewise-linear approach. The volume fraction of each phase in each cell is calculated with Equation 7. @ α q ρq @t

~q ¼ 0 þ r α q ρq V

ð7Þ

~ q is the Here, αq is the volume fraction of the qth phase and V velocity of phase q that is equal to the velocity of mixture phase. The material properties appearing in the transport equations are calculated using the volume fraction of each phase in each cell. For example, in a two-phase system, the property ϕ is interpolated by the following formula: ϕ ¼ f 1 ϕ1 þ f 2 ϕ2 with f 1 þ f 2 ¼ 1

T T solidus T liquidus T solidus

ð11Þ

The solidification of molten slag and metal is dealt with enthalpy-porosity model, where the mushy zone is treated as a porous medium and the liquid fraction decreases from one to zero as the molten slag and metal solidify. The drag force ~ Fp blocking the flow in the mushy zone is calculated with the Darcy’s law and added to the momentum conservation equation as a source term. 2 1fl ~ ~ and Amush ¼ 180μ Fp ¼ Amush V d22 f 3l

ð12Þ

Here, Amush represents the mushy zone constant; m is the viscosity, Pa s; and d2 is the secondary dendritic arm space, m.

2.4. Melt Rate Calculation

The distribution of temperature field in the slag bath and ingot is governed by the enthalpy conservation equation[21]: @ ðρHÞ ~ H ¼ r kef f rT þ Q þ r ρV @t

ð9Þ

where keff is the effective thermal conductivity, W/(m K), and Q is the Joule heating, W m3. H is the enthalpy consisting of the sensible enthalpy and the latent heat: Z

fL ¼

ð8Þ

2.3. Heat Transfer and Solidification

H ¼ h þ f l L and h ¼ href þ

fl is the liquid fraction derived from the lever rule:

T

ð10Þ

Cp dT T ref

The electrode melt rate depends on the heat flux provided to the electrode and can be calculated according to the heat balance across the electrode tip. The heat transferred to the electrode can be divided into two parts[11,12]: the heat flux diffused into the electrode (qSensible) and the latent heat (qLatent). qslag ¼ qLatent þ qSensible

ð13Þ

The latent heat (qLatent) is proportional to the electrode melt rate and determined as follows: qLatent ¼

mL Selectrode

ð14Þ

L is the latent heat of fusion, J kg1; m is the electrode melt rate, kg s1; and Selectrode is the cross-sectional area of the electrode tip, m2.

Table 2. The operating conditions and geometry.

Table 1. Physical properties of the slag and metal.

Parameter

Value

Value

Geometry

Parameter

Slag

Metal

Ref

Density, kg m3

2800

7200

21

Electrode radius, mm

40

0.02

0.006

21

Mold radius, mm

63

10

Slag thickness, mm

70

Dynamic viscosity, Pa s 1

470

Latent heat, kJ kg

1

271

Operation parameter

1255

752

15

Thermal conductivity, W m1 K1

6

30.52

11

Electrical conductivity, Ω1 m1

216 (Liquid), 4 (Solid)

714000

11,16

1.26 106

1.26 106

21

Emissivity of free slag surface

9 105

1 104

21

hmax, W m2 K1

Liquidus temperature, K

1620

1740

10,26

hmin, W m2 K1

92

Solidus temperature, K

1570

1700

10,26

Slag/metal interfacial tension, N m1

0.9

Specific heat, J kg

K

1

Magnetic permeability, H m1 Thermal coefficient of cubical expansion, K1


Power, kW

110

Current Frequency, Hz

50

Heat transfer at the slag-air wall, W m2 K1

188

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0.6 1900




Figure 2. The distribution of electromagnetic quantities a) magnetic field intensity b) current density vectors c) Joule heat d) Lorentz force at 300 s.

In order to obtain the heat flux qsensible transferred into the electrode, the heat flux is assumed to travel across a layer liquid metal film with a thickness of δ, which is similar to the parameter reported in the literature.[22] In this paper, δ takes the value of 3 mm for the electrode material AISI 304 stainless steel, which was determined from the actual melt rate in an ESR experiment. qSensible ¼ km

T1 Ts δ

ð15Þ

where Tl and Ts represent the liquidus and solidus temperature of the metal and km denotes the thermal conductivity of the metal, W/(m K).

Figure 3. Calculated velocity field and streamlines at 300 s.


2.5. Treatment of Metal Droplets In fact, as metal droplets sink through a slag bath, mass, momentum and energy transfer processes occur. In this paper, droplets are not directly simulated and are instead assumed to immediately cross the slag/pool interface. The mass, momentum and energy transport arising from metal droplets are considered with the appropriate source added to the corresponding conservation equations. However, due to the uncertainty of the velocity of metal droplets through the slag/pool interface, the momentum source is neglected.[23,24] The dynamic mesh technique is employed to consider the growth of ingot, and a mass source is added to the mass conservation equation to ensure the mass balance.

Figure 4. The temperature field at 300 s.

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Smass ¼ m=V

ð16Þ

m represents the melt rate, kg/s, V is the volume of control cell, m3. The heat brought into the metal pool via metal droplets could be divided into two parts that contains the sensible and latent heat. Hence, the energy source takes the following form. Z Senergy ¼ mh=V and h ¼

T

Cp dT þ L

ð17Þ

T0

T denotes the final temperature of the metal droplet, K. Further, the superheat absorbed by the metal droplets through the slag bath is treated as a distributed volumetric heat sink in the slag phase to ensure energy conservation. Ssink ¼ m Cp ΔT=V slag

ð18Þ

Vslag is the volume of slag bath, m3, and ΔT represents the superheat of droplet.

2.6. Boundary Conditions

1) Electromagnetic Field The flux of magnetic field intensity is assumed to be zero at the electrode tip and ingot bottom. The value of magnetic field intensity is imposed at the free slag surface and mold wall, which is calculated with Ampere’s rule.[25] 2) Fluid Flow A no-slip condition is applied at all liquid/solid interfaces, such as the electrode/slag interface, liquid slag/mold interface, liquid metal/mold interface. In addition, the free slip condition is imposed on the free slag surface. 3) Temperature Field The temperature filed boundary condition in the computation domain is somewhat complex, particularly in the mold wall. The temperature of electrode tip contacted with molten slag is fixed at the alloy liquidus temperature. The heat loss from free slag surface consists of convection and radiation. Due to the complexity, the boundary condition on the mold wall is expressed with the overall heat transfer coefficient calculated with equation (19).[26]

Figure 5. The profile of the metal pool at different times.


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h¼

1 δs =ks þ 1=ðhr þ hc Þ þ δm =km þ 1=hw þ Rcontact


ð19Þ

where δs is the slag skin thickness, m; ks is the thermal conductivity, W/(m K); hr and hc are the radiation and convection heat transfer coefficient for air gap separately, W/ (m2 K); δm is the copper mold thickness, m; km is the thermal conductivity of copper mold, W/(m K); hw is the overall heat

transfer coefficient between the mold surface and the cooling water, W/(m2 K); and Rcontact is the contact thermal resistance, (m2 K)/W. As the slag skin is simulated directly, its thermal resistivity is not included. hmax represents the maximum overall heat transfer coefficient applied on the mold wall, where the air gap does not occur. The maximum air gap width is assumed to be 1 mm, when the ingot has fully solidified across the radius,[24] and the

Figure 6. The variations of the liquid fraction with time.


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corresponding overall heat transfer coefficient is hmin. Other regions are between hmax and hmin, and the overall heat transfer coefficient is a linear interpolation weighted by the wall temperature. Besides, hmax is imposed on the ingot bottom. The parameters for calculating the heat transfer coefficient are listed in literatures.[24,26] hmax ¼

1 δm =km þ 1=hw þ Rcontact

ð20Þ

hmin ¼

1 1=ðhr þ hc Þδm =km þ 1=hw

ð21Þ

2.7. Model Solution In this paper, the dynamic formation of slag skin and the heat flow distribution are investigated using the model based on the VOF model and dynamic mesh technique. The initial computation domain consists of a 0.07 m thick slag and metal with a uniform temperature of 1900 K. In addition, a 2 mm thick initial slag skin at 500 K is included at the mold wall. The

governing equations of electromagnetic field, fluid flow, and temperature field are discretized with the finite volume method and solved simultaneously using the commercial software FLUENT14.5. The Lorentz force and Joule heat are obtained by solving the Maxwell equations incorporated into the FLUENT via User Define Scalar (UDS), which is added to the momentum and energy conservation equation with User Define Function (UDF) separately. The dynamic mesh technique with the layering scheme is employed to consider the growth of ingot. As the motion of metal droplets is not simulated directly, the corresponding sources are applied to represent the mass and energy transport. The metal AISI304 stainless steel and the slag consisting of 70%CaF2–15%CaO– 15%Al2O3 are used in this work, and the material properties are shown in Table 1. The operation parameters and geometry are listed in Table 2.

3. Results and Discussion 3.1. The Coupled Multi-physical Field Results Figure 2 shows the computed electromagnetic quantities in the ESR process at 300 s. As seen from Figure 2a, the maximum

Figure 7. The thickness of the slag skin at different times.


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magnetic field intensity is approximately 8.5 103 A m1 at the corner of electrode. The distribution of magnetic intensity in the ingot is nearly linear and decays radially from the ingot surface to the center. However, the change in axial is negligible, which denotes that the current is dominant in the axial direction. The current density is illustrated in Figure 2b. It flows into a slag bath through electrode and finally out from the ingot bottom with a maximum value of 1.3 106 A m2 at the corner of the electrode. Due to the poor electrical conductivity of the slag skin, it is widely assumed to insulates the mold from slag and metal.[4,6,10,15] However, Figure 2b shows that the slag skin still conducts current, and this assumption should be considered carefully. Figure 2c displays the distribution of Joule heat. That is mainly released in the slag bath under the electrode tip, with a maximum value of 5.2 109 W m3 at the corner of the electrode. In addition, the distribution of Joule heat when considering the formation of slag skin is different from that without the slag skin. The maximum Joule heat generated within the slag skin reaches up to 1.9 108 W m3, which affects the formation of slag skin and the heat flow distribution. The Lorentz force is shown in Figure 2d. The Lorentz force in the ingot and bulk of the slag bath are directed inwards toward the symmetry axis and decrease from the surface to the center. Under the electrode tip and free slag surface, the Lorenz force has an axial component that results from the interactions between the radial current and magnetic field. The maximum Lorentz force is approximately 7.6 103 N m3 at the corner of the electrode. Figure 3 displays the velocity field and streamlines at 300 s. Two reverse loops dominate the flow in the slag, the counterclockwise loop under the electrode tip driven by the Lorentz force, and the clockwise loop near the mold induced from the buoyancy. The maximum velocity in the slag bath is approximately 0.08 m s1, which occurs near the symmetry axial. The liquid metal driven by the buoyancy flows along the slag/pool interface toward the mold wall and then turns down the

solidification front before floating up to the center to form a clockwise loop. The maximum velocity at the metal pool is approximately 0.01 m s1 at the slag/pool interface near the mold wall. Without considering the movement of droplets, the calculated maximum turbulent intensity at the slag bath is no more than 3.0% and it is weaker at the metal pool, which is in agreement with Weber’s results.[10] The temperature field is illustrated in Figure 4. The highest temperature zone is located at the center of the counterclockwise loop, with a maximum temperature of 2100 K. As the electrode absorbs heat from the slag bath for melting, the temperature under the electrode tip is evidently smaller than that at the highest temperature zone. The bottom of the slag bath has a uniform temperature profile with the help of two loops. The maximum temperature at the metal pool is approximately 1877 K above the alloy liquidus temperature of 137 K. Figure 5 shows the variations of metal pool profile with time. The bottom of the pool is initially flat due to the intense water cooling from the baseplate, as shown in Figure 5a and b. With the growth of ingot, the depth of metal pool increases with the cooling from baseplate gradually decreasing, as shown in Figure 5c–e. When the pool profile reaches a steady state, the pool develops a parabolic shape, as shown in Figure 5f. The pool depth is between 78 and 87 mm for the liquidus and solidus temperature separately, with a maximum mushy width of approximately 9 mm at the center. In addition, the liquid head near the mold wall is approximately 12 mm, which contributes to obtaining a smooth ingot surface.

Figure 8. The variations of the slag skin thickness with time at the point 0.125 m above the bottom of the mold.

Figure 9. Schematic sketch of the heat flow distribution in the ESR process.


3.2. The Dynamic Formation of Slag Skin Figure 6 shows the variations of liquid fraction with time, and the slag skin thickness at the corresponding time is displayed in

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Figure 11. Comparison of the simulated and measured heat flow. Figure 10. The computed melt rate.

1 mm. Finally, the solidified ingot is wrapped by a 1 mm thick uniform slag skin. Figure 7. At t ¼ 0 s, a 2 mm thick slag skin is assumed to solidify on the mold wall. At t ¼ 10 s, the thickness of the slag skin at the slag/mold interface slightly increases under intense water cooling, with a maximum thickness of approximately 4 mm at the slag/pool interface. In addition, the slag skin that is in contacted with the hotter metal pool is partially remelted, which results in the thickness decreasing. At t ¼ 20 s, the thickness of the slag skin at the slag/mold interface continues to decrease as the slag temperature increases; the thickness of the slag skin that is in contacted with the metal pool reduces to 1 mm. At t ¼ 30 s, the thickness of the slag skin below the free slag surface further decreases, and the corrugate slag skin at the lower ingot surface disappears. With the growth of ingot, a 1 mm thick slag skin is continuously created around the solidified ingot, and the slag skin at the slag/mold interface achieves dynamic balance during the remelting process. A uniform and thin slag skin obtained by controlling the process parameters is favorable for building an ingot free of surface defects. Figure 8 shows the variations of the slag skin thickness with time at the point 0.125 m above the mold bottom. At t ¼ 0 s, the initial slag skin thickness is 2 mm. At t ¼ 10 s, due to the low slag temperature, the thickness of the slag skin increases to 3.2 mm. As the slag temperature increases, the thickness gradually decreases to 1.7 mm. After that, the thickness gradually reaches a maximum of approximately 4 mm until the point enters the metal pool. Subsequently, the slag skin at the point is partially remelted, and its thickness decreases to

3.3. The Heat Flow Distribution The ESR process is always accompanied by the release and absorption of heat, and a schematic sketch of the heat flow distribution is shown in Figure 9. The Joule heat Qj generated in the slag bath is the heat source for the entire ESR system. Nevertheless, the consumption of heat primarily includes the following: 1) the heat used to form the metal droplets Qse; 2) the heat absorbed by metal droplets passing through the slag bath Qd; 3) the heat loss to the air from the electrode Qea; 4) the heat loss to the air from the free slag surface Qa; 5) the heat loss to the mold from the slag bath Qsm; 6) the heat loss to the mold from the ingot Qim; 7) the heat loss to the baseplate Qbm; 8) the sensible heat stored in ingot Qs. These parameters satisfy the following relations: Q j ¼ Q se þ Q d þ Q ea þ Q a þ Q sm þ Q si

ð22Þ

Q si þ Q se þ Q d ¼ Q im þ Q bm þ Q s

ð23Þ

Qsi denotes the heat transferred to the metal pool from the slag bath. According to Mitchell’s research,[27] the superheat of metal droplets entering the pool is assumed to be 100 K. Hence, Qse and Qd can be calculated with the melt rate. As seen from Figure 10,

Table 3. The heat flow distribution in the ESR process at 300 s.

Items

Heat Flow/kW

Percentage of the power input/%

Items

Heat Flow/kW


Items

Heat Flow/kW


Qse

29.5

26.8

Qsm

30.8

28.0

Qsi

29.7

27.0

Qd

1.6

1.4

Qim

43.3

39.5

Qinput

110.0

100

Qea

10.6

9.6

Qbm

6.0

5.4

—

—

—

Qa

7.8

7.1

Qs

11.5

10.4

—

—

—


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Figure 12. The heat flux along the mold wall at 300 s.

the calculated melt rate agrees well with the measurement. Qsi and Qs are obtained by solving Equations 22 and 23, and other heat flows are acquired from the model. The calculation results of heat flow distribution at 300 s are listed in Table 3. The heat used for producing metal droplets is 29.5 kW, which accounts for 26.8% of the total power input. Besides, the mold takes 67.5% of the total power input to the cooling water, resulting in a low thermal efficiency. The heat transferred to metal pool contains two parts: the convection transfer from slag bath and the sensible and latent heat of droplets. The first accounts for 27.0% of the power input and the latter accounts for 28.2% of the power input. Both of these results coincide with Jiang’s results.[28] These results indicate that the heat from metal droplets and slag bath is of equally important to the metal pool in a laboratory-scale ESR unit. The sensible heat stored in the ingot accounts for approximately 10.4% of the power input, some of which could still be exploited once the ingot is sent to a heating furnace at a hot state. Figure 11 shows a comparison of the key heat flow between the simulated and measured results.[27,28] The calculated percentages of Qsi, Qse þ Qd, and Qim that accounts for the

power input are in reasonable agreement with the measurements, except for the Qsm. The measured percentage of Qsm is approximately 42%, but the calculated result is approximately 28%. This discrepancy can be attributed to the uncertainties in the physical properties of slags. Due to the high temperature environment, it is difficult to measure the physical properties of slags[1,5]; thus, they were extracted from literatures. The heat flux along the mold wall is shown in Figure 12. There are two peaks on the mold wall, one below the free slag surface and the other at the metal pool. The slag skin below the free slag surface has a minimal thickness and is in good contact with the mold wall such that the heat flux attains the first peak. As the distance from the free slag surface increases, the thickness of slag skin also increases until it reaches a maximum at the slag/ pool interface, which causes the decrease of heat flux. At the metal pool zone, the slag skin, that is, in contacted with the hotter liquid metal is partially remelted, and the heat flux gradually reaches the second peak with the decrease of thickness. In the solidified ingot zone, the ingot surface temperature decreases as the axial distance from the free slag surface increases, resulting in the decrease of heat flux. Figure 13a shows the variations of heat loss with time at the slag/mold interface. At the initial stage, due to the thicker slag skin and the low slag temperature, the heat loss to the slag/ mold interface is small. Then, the heat loss increases with increasing slag temperature until it reaches a maximum of approximately 34 kW. Subsequently, the heat loss slowly decreases with time because the slag bath height is diminished considering the formation of new slag skin around the solidified ingot. The variations in heat loss with time at the ingot/mold interface and baseplate are presented in Figure 13b. At the initial stage, the heat loss to the ingot/mold interface decreases as the pool temperature decreases, which indicates the heat of ingot primarily escapes from the baseplate. With the increase of ingot height, the heat loss to the ingot/mould interface increases, and the heat loss to the baseplate decreases, which indicates the heat loss of ingot is dominant in the radial direction.

Figure 13. The variations of heat loss with time at different interfaces: a) slag/mold interface and b) ingot/mold interface and baseplate.


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4. Conclusions In this paper, a 2D axisymmetric model is established based on the VOF model and the dynamic mesh technique, which considers the difference between the slag skin and molten slag in the electrical conductivity. The dynamic formation of the slag skin and heat flow distribution in the ESR process are investigated by simultaneously solving the governing equations of the electromagnetic field, fluid flow and heat transport, and the main conclusions are summarized as follows: 1) In the ESR process, the slag skin thickness at the slag/mold interface increases with increasing axial distance from the free slag surface and reaches a maximum of approximately 4 mm at the slag/pool interface; with the growth of ingot, the slag skin at the slag/pool interface is partially remelted by the hotter liquid metal, and the thickness decreases to 1 mm; Finally, the solidified ingot is wrapped with a layer uniform and thin slag skin. In addition, the slag skin at the slag/mold interface achieves dynamic balance during the remelting process. 2) The 67.5% power input is removed by the cooling water, and the heat used to create metal droplets accounts for 26.5% of the power input. Besides, the sensible and latent heat of metal droplets and the convection transport from the slag bath make up the heat source of metal pool, both of which account for the comparable proportion in a laboratory scale ESR unit. 3) There are two peaks in the heat flux on the mold wall, the first below the free slag surface and the other at the metal pool. The heat loss to the slag/mold interface first increases with increasing slag temperature and then slowly decreases with decreasing slag bath height. In addition, at the initial stage, the heat of ingot primarily escapes from the baseplate. As the slag/pool interface moves up, the heat loss of ingot gradually becomes dominant in the radial direction.

Acknowledgements This project was supported by the National Nature Science Foundations of China (grant No. 51434004, U1435205, 51674070, and U1560203) and the Transformation Project of Major Scientific and Technological Achievements in Shenyang(grant No. Z17-5-003).

Conflict of Interest The authors declare no conflict of interest.

Keywords Dynamic formation, Electroslag remelting, Heat flow distribution, Slag skin


Received: November 9, 2017 Revised: January 28, 2018 Published online:

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