Simulation and experimental studies of effect of current on oxygen transfer in electroslag remelting process

International Journal of Heat and Mass Transfer 113 (2017) 1021–1030

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Simulation and experimental studies of effect of current on oxygen transfer in electroslag remelting process Qiang Wang a,b, Fang Wang c, Guangqiang Li a,b,⇑, Yunming Gao a,b, Baokuan Li c a

The State Key Laboratory of Refractories and Metallurgy, Wuhan University of Science and Technology, Wuhan, Hubei 430081, China Key Laboratory for Ferrous Metallurgy and Resources Utilization of Ministry of Education, Wuhan University of Science and Technology, Wuhan, Hubei 430081, China c School of Metallurgy, Northeastern University, Shenyang, Liaoning 110819, China b

a r t i c l e

i n f o

Article history: Received 1 April 2017 Received in revised form 10 May 2017 Accepted 3 June 2017 Available online 13 June 2017 Keywords: Electroslag remelting Oxygen transfer Thermochemical reaction Electrochemical reaction Numerical simulation

a b s t r a c t A transient three-dimensional (3D) coupled mathematical model has been established to clarify the effect of current on oxygen transfer behavior in electroslag remelting process. Finite volume approach was utilized to simultaneously solve the mass, momentum, energy, and species conservation equations. The oxygen transfer rates induced by the thermochemical and the electrochemical reactions at the slag-metal interfaces were defined by a metallurgical thermodynamic and kinetics module. A series of experiment was conducted, and the contents of oxygen in the metal and the ferrous oxide in the slag were detected. A reasonable agreement between the simulated and measured data is obtained. When the current changes from 80 A to 160 A, the highest temperature and the maximal Reynold number increases from 1931 K to 2334 K and from 247 to 498, respectively. The final oxygen mass percent in the metal increases from 0.0537% to 0.0577% when the current changes from 80 A to 100 A, but decreases to 0.0559% if the current increases to 120 A, and again rises to 0.0616% while the current constantly increases to 160 A. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Electroslag remelting (ESR) technology, widely used in metallurgical industry, could effectively remove nonmetallic inclusions and notably refine grain size in alloys [1]. A schematic of the ESR process was shown in Fig. 1. A direct current travels from a positive consumable electrode, which composition is the same as the designed alloy, to a negative baseplate, and creates lots of Joule heating in a highly resistive calcium fluoride-based molten slag. With enough heating, the electrode begins to melt. As a consequence, a dense metal droplet is formed at the electrode tip, and then sinks through the less dense slag [2]. In this process, the hot electrode is easily oxidized by air, which creates solid ferrous oxide at the side wall of the electrode. Then the solid ferrous oxide would be melted with the electrode, and continuously enter into the slag. Once the oxygen potential of the slag exceeds that of the metal, ferrous oxide in the slag would be decomposed at the slag-metal interfaces, and the oxygen is then transferred to the metal:

⇑ Corresponding author at: The State Key Laboratory of Refractories and Metallurgy, Wuhan University of Science and Technology, Wuhan, Hubei 430081, China. E-mail address: [email protected] (G. Li). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.06.007 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

1 Fe þ O2 ! ðFeOÞ 2

ð1Þ

ðFeOÞ ! ½Fe þ ½O

ð2Þ

where [ ] and () indicate that the matter is in the metal and slag, respectively. As a result, the oxygen in the air would be brought into the metal, which goes against the alloy properties [3]. Shi et al. have experimentally studied the oxygen transfer in the ESR process [4]. The results indicated that using inert gas could effectively prevent the oxidation. The decrease amplitude of the oxygen content in the alloy however was smaller than expected. The electrochemical migration of the oxygen in the slag and metal, induced by the current, was assumed to be the main reason. Kato et al. found that the oxygen content in the ingot first reduced and then rose with an increasing current density [5]. The electrochemical transfer of the oxygen was enhanced by the greater current. Meanwhile, the electrode oxidation and the oxide thermal decomposition in the slag were also promoted. It was recognized that the final oxygen content in the remelted ingot was determined by the competition between the thermochemical and electrochemical reactions. It is of interest then, to examine the nature of electrochemical and thermochemical reactions, with the aim of predicting how the current would influence the oxygen transfer behavior during the ESR process. Experimental results confirmed that the oxygen

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Nomenclature A ! A aðFeOÞ a½Fe a½O ! B c c0 cp;m cp;s D Ds;FeO Dm;FeO Ds;O Dm;O E eOj

specific surface area for reaction (m1) magnetic potential vector (Vs/m) activity of ferrous oxide in the slag activity of iron in the metal activity of oxygen in the metal

F ! F !e F !s F st ! Ft f ½O

magnetic flux density (T) mass percent of species initial mass percent of species specific heat of metal at constant pressure (J/(kgK)) specific heat of slag at constant pressure (J/(kgK)) diffusion coefficient of species (m2/s) diffusion coefficient of ferrous oxide in slag (m2/s) diffusion coefficient of ferrous oxide in metal (m2/s) diffusion coefficient of oxygen in slag (m2/s) diffusion coefficient of oxygen in metal (m2/s) internal energy of mixture phase (J/m3) interaction coefficient of the element j with respect to the oxygen Faraday law constant (C/mol) Lorentz force (N/m3) solute buoyancy force (N/m3) surface tension (N/ m3) thermal buoyancy force (N/m3) activity coefficient of oxygen in the metal

J K k k0 kT L LFeO M ðY i Þ _ m

current density (A/m2) reaction equilibrium constant generation rate of the ferrous oxide (kg/s) constant for Eq. (27) effective thermal conductivity (W/(mK)) latent heat of fusion (J/kg) ferrous oxide distribution ratio molecular weight of species Yi in slag melt rate (kg/s)

*

Fig. 1. Schematic of electroslag remelting process.

movement immensely depended on the distributions of the current density, velocity and temperature, which could be clearly clarified by numerical simulation. Many numerical models have been proposed to describe the electromagnetic, flow, temperature fields, as well as the solidification during the ESR process. [6–8] The finite volume method was invoked to implement the solutions of the mass, momentum and

n Q QJ p R ST SE T t !

v

w½Fe w½O wðFeOÞ wðFeOÞ

number of the electrons entering in the reaction activation energy of metal (J/mol) Joule heating (W/m3) pressure (Pa) gas constant (J/(molK)) mass transfer rate at the slag-metal interface caused by the thermochemical reaction mass transfer rate at the slag-metal interface caused by the electrochemical reaction temperature (K) time (s) velocity (m/s) mass percent of iron in the metal close to the slag-metal interface (%) mass percent of oxygen in the metal (%) mass percent of iron in the slag (%) mass percent of iron in the slag close to the slag-metal interface (%)

Greek symbols a volume fraction l viscosity of mixture phase (Pas) l0 permeability of vacuum (Tm/A) r electrical conductivity of mixture phase (X-1m-1) u electrical potential (V) uc concentration overpotential (V) / mixture phase property /m metal property /s slag property cFeO activity factor of ferrous oxide qm density of metal (kg/m3) qs density of slag (kg/m3) n power coefficient

energy conservation equations. The Joule heating and Lorentz force, solved by Maxwell’s equations, were coupled. The interface between the slag and metal was tracked using volume of fluid (VOF) method. Besides, the solidification was modeled by using an enthalpy-based technique. K. Fezi et al. have numerically investigated the mass transfer of five elements during the ESR process of Alloy 625. [9] The effect of the applied current on the macrosegregation of the five elements was demonstrated. The segregation increased with the increasing current to a maximum, beyond which the segregation slowly decreased. They indicated that it was due to the competition between the interdendritic flow and the cooling rate. In order to study the electrochemical reaction in a molten multi-ion slag, E. Karimi-Sibaki et al. have developed a coupled numerical model. [10] The ion transport is defined by the Poisson-Nernst-Planck equations, while the kinetics of the reaction at the slag-metal interface was described by the ButlerVolmer formula. As discussed above, up to now, there have been few works concerning the oxygen transfer induced by the thermochemical and electrochemical reactions in the ESR process. This fact has motivated the present work, which purpose was to understand the effect of the current on MHD flow, heat transfer and oxygen migration. A transient 3D comprehensive model of the ESR process was built, in which a metallurgical thermodynamic and kinetics module was used to represent the mechanism of the oxygen thermochemical and electrochemical reactions. Besides, a series of experiments was carried out. The oxygen content in the remelted metal was measured by an oxygen and nitrogen analyzer, and

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the compositions of the slag were detected using a X-ray Fluorescence (XRF). The experimental and the numerical results were compared for model validation.

The magnetic field was thus obtained by combining Eqs. (10) and (11). The Lorentz force and the Joule heating were then expressed as:

! ! Fe ¼ J  B

!

2. Mathematical model

ð9Þ

! !

2.1. Assumptions

QJ ¼

In order to keep a reasonable computational time, this model relied on the following assumptions: (1) The domain included the slag and the metal, while atmosphere was disregarded [9]. (2) The two fluids were incompressible Newtonian fluid. The densities of the slag and metal were a function of the temperature, and the slag electrical conductivity depended on the temperature. Other metal and slag properties were assumed to be constant [11]. (3) The coefficient of the interfacial tension between the metal and the slag remained the same. (4) Solidification behavior was not taken into account. (5) The slag and the metal were assumed to be electrically insulated from the mold [2,12]. This assumption was questionable and needed to be confirmed. Indeed, in some cases, the electric current could enter to the mold through the slag-mold interface, although a solid slag layer was formed between the melt and the mold wall. The solidified slag layer however could not ensure perfect insulation under the high temperature. 2.2. VOF method For modeling two-phase flow, the VOF method was adopted to track a scalar field variable a, namely volume fraction, in the whole domain [7]:

@a ! þ r  ð v aÞ ¼ 0 @t

ð3Þ

Here, it stood for the distribution of the metal, and was updated at every time step. Explicit tracking scheme was then employed to discretize the above equation. Meanwhile, the properties of the mixture phase such as electrical conductivity, density and viscosity were related to the volume fraction:

/ ¼ /m a þ /s ð1  aÞ

ð4Þ

Surface tension force between the metal and slag was described by the continuum surface force model. 2.3. Electromagnetism

JJ

ð10Þ

r

2.4. Fluid flow and heat transfer The continuity and time-averaged Navier-Stokes equations were invoked to define the flow of the slag and the metal [11]:

@q ! þ r  ðq v Þ ¼ 0 @t

ð11Þ

! h i ! @ðq v Þ ! ! ! ! þ r  ðq v  v Þ ¼ rp þ r  lðr v þ r v T Þ þ F st @t !

!

!

þ Fe þ Fs þ Ft

ð12Þ

! ! where F s and F t were the solutal and the thermal buoyancy forces determined by the Boussinesq approximation. In the present work, the ESR process was implemented in an iron crucible with a 15 mm inner diameter. The turbulent viscosity should be particularly considered. Generally, the maximal velocity, found in the slag layer, was in 101 order of magnitude [11]. We supposed that the maximum velocity was also in 101 order of magnitude, and the crucible diameter was the characteristic length. The largest Reynolds number therefore was around 224, which indicated that the flow in the crucible was far from the turbulence. As a result, the laminar flow was chosen here rather than the turbulence model. The energy conservation equation, shared between the slag and metal phases, was [7]:

@ðqEÞ ! þ r  ð v qEÞ ¼ r  ðkT rTÞ þ Q J @t

ð13Þ

where E was the internal energy of the mixture phase, which was solved based on the specific heat of the two phases and the temperature:

E¼

aqm cp;m T þ ð1  aÞqs cp;s T aqm þ ð1  aÞqs

ð14Þ

2.5. Mass transfer of oxygen The convection and diffusion of oxygen in the melt was described by species conservation equation:

The electric current was obtained by solving the electrical potential u from the current continuity equation and the Ohm’s law [13]:

@ðqcÞ ! þ r  ðq v cÞ ¼ r  ðaDrcÞ þ ST þ SE @t

r  ðrruÞ ¼ 0

ð5Þ

! J ¼ rru

ð6Þ

The equation was then established in the slag and in the metal, respectively. The source term ST and SE indicated mass transfer rate at the slag-metal interface caused by the thermochemical and electrochemical reactions. In order to satisfy the mass conservation, the source terms in both equations were numerically equal but opposite in sign. An auxiliary metallurgical thermodynamic and kinetics module was used to estimate the thermochemical reaction rate mentioned above, which could be written in terms of the film theory [14]:

At the same time, the magnetic potential vector was introduced to solve the magnetic field:

! ! B ¼r A

ð7Þ

! The Ampere’s law r  B ¼ l0 J therefore could be rewritten as a Poisson equation: !

! ! r2 A ¼ l0 J

ð8Þ

ST ¼

Ds;FeO Dm;FeO qs LFeO AðwðFeOÞ  wðFeOÞ Þ Dm;FeO qm þ Ds;FeO qs LFeO

ð15Þ

ð16Þ

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where wðFeOÞ  wðFeOÞ indicated the mass percent difference of ferrous oxide close to the slag-metal interface, which pushed the species transfer between the two phases. To assess the ferrous oxide mass percent at the slag-metal interface, the ferrous oxide distribution ratio LFeO was proposed, which expressed the measure of the ratio of the ferrous oxide mass percent in the slag to the iron mass percent in the metal close to the slag-metal interface [15]:

LFeO ¼

wðFeOÞ ¼ w½Fe

X aðFeOÞ M FeO wðY i Þ=M ðY i Þ i

ð17Þ

cFeO

Here, we assumed the iron mass percent in the metal was equal to one hundred percent, because the iron was the main component of the metal (Table 1). The above equation therefore could be simplified:

X aðFeOÞ M FeO wðY i Þ=M ðY i Þ

LFeO ¼ wðFeoÞ ¼

i

ð18Þ

cFeO

where aðFeOÞ was the activity of ferrous oxide in the slag, which could be estimated through the thermodynamic equilibrium constant of reaction (3):

log K ¼ log

a½Fe  a½O 6150 þ 2:604 ¼ T aðFeOÞ

ð19Þ

where a½Fe was the iron activity in the metal, and was supposed to be equal to one referred to 1 mass% standard solution. The ferrous oxide activity thus could be written:

aðFeOÞ ¼

a½O a½O ¼ ð6150þ2:604Þ K 10 T

ð20Þ

where a½O was the activity of oxygen in the metal referred to the infinitely diluted solution, and was calculated:

a½O ¼ f ½O  w½O log f ½O ¼

ð21Þ

X j ðeO  w½jÞ

ð22Þ

j

where j represented the dissolved elements in the metal. All the elements should be considered except the solvent, i.e., iron. w½j meant eOj

was the interaction the mass percent of element j in the metal. coefficient of the element j with respect to the oxygen, and the interaction coefficients were taken from relevant Ref. [16]. On the other hand, the oxygen migration rate induced by the electrochemical reaction occurred at the two slag-metal interfaces was related to the intensity of the electron flow [17]:

nDs;O F ! j J jc RT

ð23Þ

Slag-metal pool interface:

SE ¼ 

2.6. Boundary conditions Due to a presence of ion concentration gradient in the metal, a concentration overpotential was created at the inlet and was calculated by Nernst equation:

uc ¼

  RT c ln nF c0

ð25Þ

According to the derivation of Nernst equation, it is valid at equilibrium state without net current. But if the electrochemical reaction is very fast, the Nernst equation is also appropriate when there is a net current. In the ESR process, the electrochemical reaction kinetics is not the rate-limiting step because of the strong current and the high temperature. We therefore adopted the Nernst equation to evaluate the concentration overpotential caused by the oxygen ion. Besides, a varied mass flow rate was adopted at the inlet, which was determined by the Joule heating:

_ ¼ m

nQ J L

ð26Þ

where n represented power efficiency. Since the power efficiency changed with operation conditions, it was difficult to estimate its exact value. A reasonable power efficiency was obtained from the reviewed literature [18–20], but was then adjusted according to the conditions of our experiment. As for the oxygen transfer process, a constant oxygen mass percent, equal to the oxygen mass percent in the electrode, was supplied at the inlet. According to the oxidation kinetics proposed by Schwerdtfeger, the generation rate of the ferrous oxide could be described by Arrhenius law [21]:

  Q k ¼ k0  exp  RT

ð27Þ

This equation was applied to the top surface that close to the inlet for representing the entry of the ferrous oxide to the slag pool. We did not allow the oxygen to flow out through the wall or the bottom by using a zero flux condition. Other boundary conditions used for the computation of electromagnetism, two-phase flow and heat transfer could be found in Ref. [22]. 3. Numerical treatment

Slag-metal droplet interface:

SE ¼ þ

We assumed that the source was positive when the oxygen moved from the slag to the metal. According to the direction of the current, the electron and the oxygen migrate upward in the domain, and thus, the source was positive at the slag-metal droplet interface and negative at the slag-metal pool interface.

nDm;O F ! j J jc RT

ð24Þ

where n referred to the number of the electrons entering in the reaction (in this case n = 2). Depending on the oxygen transfer direction, the source term had either a positive or negative sign.

Commercial software ANSYS-FLUENT 12.1 was employed to complete the numerical simulation. Using an iterative procedure, the governing equations for electromagnetism, two-phase flow, heat transfer and solute transport were integrated over each control volume and solved simultaneously. Through user-defined functions, we implemented the introduction of the magnetic potential vector, and the developments of the metallurgical thermodynamic and kinetics module. The widely used SIMPLE algorithm was adopted for the solution of Navier-Stokes equation. In

Table 1 Compositions of the electrode, %. C

Al

Mn

Cr

Ni

P

S

O

Fe

0.08

0.01

0.34

0.017

0.022

0.007

0.011

0.0136

Balance

Q. Wang et al. / International Journal of Heat and Mass Transfer 113 (2017) 1021–1030

order to ensure the accuracy, all the equations were discretized through the application of the second order upwind scheme. Before moving on to the next step, the iterative procedure continued until all normalized unscaled residuals were less than 106. The metal pool was prone to become higher with time because of the metal droplet falling. A dynamic mesh was therefore invoked for considering the growing of the computational domain. Once the control volumes of the top layer became 1.25 times the height of its original value, it spawned a new layer on the top. We thoroughly tested the mesh independence. Three families of structured meshes were generated, with the respective sizes of 0.02 mm, 0.05 mm, and 0.1 mm. After a typical simulation, the velocity and temperature of some points in the domain were carefully compared. The deviation of simulated results between the first and second mesh was about 3 percent, while it was approximately 8 percent between the second and third mesh. Considering the high expense of computation, we retained the second mesh to use throughout the rest of this work. Fig. 2 shows the mesh at its initial state. Here, the grid pattern is coarsely displayed for the convenience of the reader visualize. Due to the complexity of the coupling simulation, we kept a small time step, 0.001 s, to ensure that the above converge criteria were fulfilled. Using 8 cores of 4.00 GHz, a typical simulation case took approximately 260 CPU hours.

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4. Experiment We conducted a series of experiment using an iron crucible with an open air atmosphere as displayed in Fig. 3. A direct current power was adopted to provide the current, which ranged from 80 A to 160 A in experiments. The consumable electrode was served as the positive pole, while the graphite baseplate connected to the negative pole. An annular groove with 10 mm width and 5 mm depth was prepared on the top surface of the graphite baseplate, and was filled with insulated solid slag. The iron crucible was then placed on the solid slag for preventing the current flowed through the iron crucible. The crucible inner diameter, height and lateral wall thickness were 15 mm, 35 mm and 6 mm, respectively. The consumable electrode had a 3.2 mm diameter, and the slag cap thickness remained constant at approximately 8 mm. The compositions of the electrode and the slag were displayed in Tables 1 and 2. Before the experiment, the slag was premelted by using a resistance furnace, and then added to the crucible. The circuit could be connected once the electrode touched the graphite baseplate. The Joule heating subsequently melted the premelted slag. The electrode would continuously move downward during the experiment, so as to maintain the circuit. In order to improve the measurement accuracy of the voltage, we punched a 1 mm hole along the axis of the graphite baseplate, and inserted a molybdenum wire, which could directly contact with the liquid metal. After the experiment, we took samples from the solidified metal with the help of wire-electrode cutting, and measured the oxygen mass percent using an oxygen and nitrogen analyzer. Besides, a XRF was employed to detect the ferrous oxide mass percent in the slag.

5. Results and discussions 5.1. Electric, MHD two-phase flow and temperature fields Fig. 4 illustrates electric current streamlines and electric potential distribution with a current of 120 A at 18.12 s. As soon as the current comes into the slag, it spreads around and subsequently moves downward, travelling through the molten slag and molten metal. It is obvious that most potential drop occurs within the slag layer because of its poor electric conductivity. As a consequence, the slag generates lots of Joule heating, which drives the remelting process. Besides, the current streamlines, located at the center of the domain, are warped under the effect of the metal droplet.

Fig. 2. (a) Mesh and (b) boundaries.

Fig. 3. Experimental device.

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Q. Wang et al. / International Journal of Heat and Mass Transfer 113 (2017) 1021–1030 Table 2 Compositions of the slag,%. CaF2

Al2O3

70

30

Fig. 5. Distribution of temperature with a current of 120 A at 18.12 s.

Fig. 4. Distribution of electric current streamlines and electric potential with a current of 120 A at 18.12 s.

Fig. 5 displays the temperature distribution. The highest temperature, approximately 2050 K, is observed in the slag that close to the inlet. With more Joule heating, the slag is much hotter than the metal, and would heat the metal droplet during its falling process. A lower temperature region therefore is noted at the middle. Moreover, the temperature gradually decreases along the crucible radial direction. The heat in the area that in the vicinity of the wall is taken away by the cooling water, causing the sinking of the slag and the metal. Two clockwise circulations are created in the slag layer and the metal pool, respectively, as showed in Fig. 6. Meanwhile, the inward Lorentz force along with the falling metal droplet generate a counterclockwise cell at the center of the slag. Additionally, the center region of the slag-metal pool interface bulges upward under the combined effect of the inward Lorentz pinch force and the interfacial tension.

5.2. Oxygen transfer behavior Figs. 7 and 8 indicate the distribution of the oxygen mass percent in the metal and the slag at different time instants with the 120 A current. We can see that the oxygen concentration in the metal droplet gradually increases with its growing. Subjected to the Lorentz force, interfacial tension and gravity, the droplet then detaches itself from the inlet. As displayed in Fig. 7(b), the oxygen content in the upper part of the droplet is about 2.1 times higher than its original content. When the droplet impacts the slagmetal pool interface, the oxygen immediately spreads out, and its distribution is dominated by the flow pattern.

Fig. 6. Distributions of flow streamlines and phase distribution with a current of 120 A at 18.12 s.

In the slag layer, the oxygen content at the lower part is much higher than that at the upper part. Because with the action of electrochemical reaction as discussed aftermentioned, the oxygen in the metal pool would continuously pass through the slag-metal

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Fig. 7. Evolution of oxygen mass percent in the metal with time when the current is 120 A: (a) t = 14.49 s, (b) t = 18.12 s, (c) t = 18.24 s.

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Fig. 8. Evolution of oxygen mass percent in the slag with time when the current is 120 A: (a) t = 14.49 s, (b) t = 18.12 s, (c) t = 18.24 s.

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In the present work, the applied current changed from 80 A to 160 A, which considerably influenced the potential map. The potential drop along the vertical centerline of the domain increases from 17.61 V to 36.33 V as illustrated in Fig. 9. The curve could be divided into three sections, namely: within the metal droplet (Z > 0.01 m), within the slag layer, and within the metal pool (Z < 0.0042 m). It is clear that the voltage drop within the slag layer accounts for the major proportion of the entire voltage drop. Although the electrical conductivity is the same, the descent rate of the voltage within the metal droplet is larger than that within the metal pool. The concentration overpotential caused by the oxygen concentration gradient in the metal droplet is supposed to be responsible for it. During the process, the thermochemical and electrochemical reactions all push the oxygen ions to migrate from

the slag to the metal droplet, and the proportion of the concentration overpotential increases from 5.74% to 8.75% when the current ranges from 80 A to 160 A as displayed in Fig. 10. Fig. 11 demonstrates the comparison of the simulated and measured potential drops. It is seen that the measured values are larger in general than the computed values. Because the concentration gradient of other ions such as iron, aluminum and sulfur ions would also create the overpotential, while in the simulation, only the overpotential caused by the oxygen ion was taken into account. However, the relative error is within the acceptance range, which is about 7.93% even when the current increases to 160 A. Larger current would generate more heat as well as stronger Lorentz force in the slag, and therefore improve the melt temperature and flow in the domain. The highest temperature and the maximal Reynold number increases from 1931 K to 2334 K and from 247 to 498, respectively when the current changes from 80 A to 160 A as shown in Fig. 12. Furthermore, the simulated time average melt rate also increases from 1.41  104 kg/s to 5.61  104 kg/s as indicated in Fig. 13. And the whole remelting time reduces from around 90 s to 20 s. Since the concentration overpotential is underestimated, the measured melt rate are larger than the calculated melt rate, and the difference gradually becomes bigger with the current. As mentioned above, the thermochemical reaction of the ferrous oxide could increase the total oxygen content in the metal. The increased current, which would produce more heat and generate a hotter slag, dramatically promotes the formation of the ferrous oxide. Fig. 14 shows the distribution of the ferrous oxide content along the centerline of the top surface. A higher ferrous oxide content is found in the slag that is close to the electrode, and the content then decreases along the radius as the ferrous oxide spreads around. With the increase of the current, the ferrous oxide concentration becomes larger as expected, especially in the case of the heavy current. We also measured the ferrous oxide mass percent at a certain point in the slag and compared with the simulated value as demonstrated in Fig. 15, and a reasonable agreement is obtained. We can see that the mass percent increases by approximately 8.7% when the current changes from 80 A to 100 A, while increases by 25% when the current ranges from 140 A to 160 A. More ferrous oxide is supposed to promote the oxygen transfer from the slag to the metal. However, the variation trend of the oxygen concentration in the metal tells a different story. Fig. 16 indicates the evolution of the oxygen mass percent at a certain point in the metal over time in case of the five currents. The final oxygen mass percent increases from 0.0537% to 0.0577% when the current

Fig. 9. Effect of the current on the potential variation along the vertical centerline of the domain.

Fig. 10. Evolution of the concentration overpotential and its proportion with the current.

pool interface and migrate to the slag resulting in the rising of the oxygen content at the base of the slag layer. Meanwhile, the oxygen in the upper slag that is close to the metal droplet surface would go into the droplet, which leads to the oxygen concentration decline. As stated above, the ferrous oxide is produced as the air oxidation, and then enters the slag with the electrode melting. If the oxygen potential of the slag is higher than that of the metal, the ferrous oxide would be decomposed into the iron and oxygen ions. The iron and oxygen ions then shift from the slag to the metal through the two slag-metal interfaces with chemical reaction, which contributes to the oxygen concentration increase in the metal. On the other hand, the electric field could induce the directional migration of the oxygen in the slag and the metal. The electrons move from bottom to top since the current flows downward. The oxygen atom in the metal pool therefore captures two electrons and comes into the slag in ion status through the slagmetal pool interface. The oxygen in the metal thus becomes less. While the oxygen ion in the slag typically lose two electrons and goes into the metal droplet as oxygen atom when the electrons pass through the slag-metal droplet interface. As a result, the oxygen content in the droplet increases, and moreover, these oxygen would be brought back to the metal pool with the droplet falling. According to the above findings, we may conclude that the thermochemical reaction of the ferrous oxide certainly increases the oxygen concentration in the metal. The electrochemical reaction induced by the current however redistributes the oxygen between the slag and the metal, and could not change the total oxygen content. 5.3. Influence of current

Q. Wang et al. / International Journal of Heat and Mass Transfer 113 (2017) 1021–1030

Fig. 11. Comparison of the potential drop between the simulation and measurement.

Fig. 12. Evolution of the highest temperature and the maximal Reynold number with the current.

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Fig. 14. Distribution of the ferrous oxide concentration along the centerline of the top surface.

Fig. 15. Comparison of the ferrous oxide mass percent between the simulation and measurement.

Fig. 13. Comparison of the time average melt rate between the simulation and measurement.

Fig. 16. Evolution of the oxygen mass percent in the metal over time in case of five currents.

changes from 80 A to 100 A, but decreases to 0.0559% if the current increases to 120 A, and again rises to 0.0616% while the current constantly increases to 160 A.

This can be attributed to the combined effect of the thermochemical and electrochemical reactions. The thermochemical reaction always causes an enrichment of the oxygen both in the metal

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sured results is within an acceptable range, which suggests the model is reasonable. When the current changes from 80 A to 160 A, the highest temperature and the maximal Reynold number increases from 1931 K to 2334 K and from 247 to 498, respectively. The final oxygen mass percent in the metal increases from 0.0537% to 0.0577% when the current changes from 80 A to 100 A, but decreases to 0.0559% if the current increases to 120 A, and again rises to 0.0616% while the current constantly increases to 160 A. Acknowledgements The authors’ gratitude goes to National Natural Science Foundation of China (Grant No. 51210007) and the Key Program of Joint Funds of the National Natural Science Foundation of China and the Government of Liaoning Province (Grant No. U1508214), and China Postdoctoral Science Foundation Funded Project (Grant No. 2016M600620). Fig. 17. Comparison of the final oxygen mass percent in the metal between the experiment and the simulation.

droplet and the metal pool. While the electrochemical reaction takes the oxygen away from the metal pool at the slag-metal pool interface, and simultaneously brings the oxygen back to the metal droplet at the slag-metal droplet interface. The final oxygen content map thus is determined by the competition between the thermochemical and electrochemical transfer rates. When the current ranges from 80 A to 100 A, the ferrous oxide content in the slag increases, which definitely contributes to the rising of the oxygen content in the metal droplet and the metal pool. Meanwhile, the electrochemical deoxidation at the slagmetal pool interface lags behind the thermochemical reoxidation. The overall oxygen content in the metal pool therefore shows an increasing trend. When the current increases to 120 A, the effect of the electrochemical deoxidation outweighs that of the thermochemical reoxidation, and thus the oxygen content in the metal pool decreases. With the continuous increasing of the current, the flow of the slag becomes more active. Thus, the oxygen at the base of the slag layer could effectively migrate to the upper part, and reenter the metal droplet through the slag-metal droplet interface. The oxygen is then brought back to the metal pool with the falling droplet, resulting in the rebound of the final oxygen content. Fig. 17 shows the comparison of the final oxygen content in the metal between the experiment and the simulation. The agreement between the predicted results and the experimental data gives confidence in the fundamental validity of the developed model. The reoxidation happened at the slag-metal droplet interface is supposed to be enhanced because of the concentration overpotential. The calculated oxygen content thus is lower than the measured one, especially for the strong current.

References [1]

[2]

[3] [4]

[5] [6] [7]

[8] [9] [10]

[11]

[12]

[13] [14]

[15]

[16]

6. Conclusions [17]

The present work has established a transient 3D comprehensive mathematical model to understand the effect of the current on the oxygen transfer in the ESR process. The finite volume approach was employed to simultaneously solve the mass, momentum, energy, and species conservation equations. A metallurgical thermodynamic and kinetics module was used to represent the mechanism of the oxygen thermochemical and electrochemical reactions. In order to validate the model, a series of experiment was conducted. The oxygen mass percent in the metal was measured using an oxygen and nitrogen analyzer, and the ferrous oxide content in the slag was detected by a XRF. The correlation of the simulated and mea-

[18]

[19] [20]

[21] [22]

Ludwig, A. Kharicha, M. Wu, Modeling of multiscale and multiphase phenomena in materials processing, Metall. Mater. Trans. B 45B (1) (2014) 36–43. V. Weber, A. Jardy, B. Dussoubs, D. Ablitzer, S. Rybéron, V. Schmitt, S. Hans, H. Poisson, A comprehensive model of the electroslag remelting process: description and validation, Metall. Mater. Trans. B 40B (3) (2009) 271–280. J.H. Wei, A. Mitchell, Changes in composition during AC ESR—II. laboratory results and analysis, Acta Metall. Sin. 20 (5) (1984) 280–287. C.B. Shi, X.C. Chen, H.J. Guo, Z.J. Zhu, H. Ren, Assessment of oxygen control and its effect on inclusion characteristics during electroslag remelting of die steel, Steel Res. Int. 83 (5) (2012) 472–486. M. Kato, K. Hasegawa, S. Nomura, M. Inouye, Transfer of oxygen and sulfur during direct current electroslag remelting, Trans. ISIJ 23 (7) (1983) 618–627. Y.M. Ferng, C.C. Chieng, C. Pan, Numerical simulation of electro-slag remelting process, Numer. Heat Trans. A-Appl. 16 (1989) 429–449. J. Yanke, K. Fezi, R.W. Trice, M.J.M. Krane, Simulation of slag-skin formation in electroslag remelting using a volume-of-fluid method, Numer. Heat Trans. AAppl. 67 (2015) 268–292. X.H. Wang, Y. Li, A comprehensive 3D mathematical model of the electroslag remelting process, Metall. Mater. Trans. B 46B (4) (2015) 1837–1849. K. Fezi, J. Yanke, M.J.M. Krane, Macrosegregation during electroslag remelting of alloy 625, Metall. Mater. Trans. B 46B (2) (2015) 766–779. E. Karimi-Sibaki, A. Kharicha, J. Bohacek, M. Wu, A. Ludwig, Toward modeling of electrochemical reactions during electroslag remelting (ESR) process, Steel Res. Int. 88 (5) (2017) 1700011. B. Hernandez-Morales, A. Mitchell, Review of mathematical models of fluid flow, heat transfer, and mass transfer in electroslag remelting process, Ironmak. Steelmak. 26 (6) (1999) 423–438. M. Hugo, B. Dussoubs, A. Jardy, J. Escaffre, H. Poisson, Impact of the solidified slag skin on the current distribution during electroslag remelting, in: Proceeding of the 2013 International Symposium on Liquid Metal Processing & Casting, 2013, pp. 80–85. A. Kharicha, A. Ludwig, M. Wu, Shape and stability of the slag/melt interface in a small dc ESR process, Mater. Sci. Eng., A 413–414 (2005) 129–134. L. Jonsson, D. Sichen, P. Jönsson, A new approach to model sulfur refining in a gas-stirred ladle-a coupled CFD and thermodynamic model, ISIJ Int. 38 (3) (1998) 260–267. W.T. Lou, M.Y. Zhu, Numerical simulation of desulfurization behavior in gasstirred systems based on computation fluid dynamics-simultaneous reaction model coupled model, Metall. Mater. Trans. B 45B (5) (2014) 1706–1722. Z.H. Jiang, D. Hou, Y.W. Dong, Y.L. Cao, H.B. Cao, W. Gong, Effect of slag on titanium, silicon, and aluminum contents in superalloy during electroslag remelting, Metall. Mater. Trans. B 47B (2) (2014) 1465–1474. G.H. Zhang, K.C. Chou, F.S. Li, Deoxidation of liquid steel with molten slag by using electrochemical method, ISIJ Int. 54 (12) (2014) 2767–2771. E. Karimi-Sibaki, A. Kharicha, J. Bohacek, M. Wu, A. Ludwig, A dynamic meshbased approach to model melting and shape of an ESR electrode, Metall. Mater. Trans. B 46B (5) (2015) 2049–2061. A. Mitchell, S. Joshi, The thermal characteristics of the electroslag, Metall. Trans. 4 (1973) 631–642. Y.W. Dong, Z.H. Jiang, J.X. Fan, Y.L. Cao, D. Hou, H.B. Cao, Comprehensive mathematical model for simulating electroslag remelting, Metall. Mater. Trans. B 47B (2) (2016) 1475–1488. K. Schwerdtfeger, S.X. Zhou, A contribution to scale growth during hot rolling of steel, Steel Res. Int. 74 (9) (2003) 538–548. Q. Wang, Z. He, G.Q. Li, B.K. Li, C.Y. Zhu, P.J. Chen, Numerical investigation of desulfurization behavior in electroslag remelting process, Int. J. Heat Mass Transfer 104 (2017) 943–951.