Analysis of Power Supply Parameter Control and Its Influence Factors for Electromagnetic Induction-controlled Automated Steel-teeming System

Abstract

The steel-teeming time, which is directly affected by the output parameters of the power supply, is one of the most important technical indicators of an electromagnetic steel-teeming system. Therefore, this work employs numerical simulation to build a power supply output parameter model for the electromagnetic steel-teeming system of a 110 t ladle of a steel mill. The correctness of the model is verified through a high-temperature offline test. The results of the simulation correspond closely to those of the offline test. Furthermore, the best combination of power supply output parameters was found to be: frequency 35.3 kHz, output current 152.9 A, output power 40.1 kW, and steel-teeming time 113 s. The factors influencing these parameters and the teeming time are summarized as follows: the magnitude of each power supply output parameter (i) increases, (ii) decreases initially then increases, (iii) decreases slightly, (iv) decreases initially then increases, and (v) decreases initially, increases rapidly, and then changes gradually with increasing (i) diameter of the liquid steel channel, (ii) length of the liquid steel channel, (iii) static pressure of the ladle, (iv) steel-teeming temperature, and (v) standing time, respectively; larger power supply output parameters are needed for the horn-shaped (as shown in Fig. 3) liquid steel channel than for the cylindrical channel. This article will serve as a theoretical reference for reducing the steel-teeming time of the electromagnetic steel-teeming system.

1. Introduction

Achieving the shortest production cycle possible and producing spotless and high-value-added products in unit time represent two of the major goals of modern steel enterprises. However, the traditional steel-teeming process is inadequate in some respects.^1,2,3) For example, the steel-teeming rate is <100%,⁴⁾ stuffing sand can reduce the purity of the molten steel,^5,6,7) and the chromium contained in the stuffing sand results in severe environmental pollution.⁸⁾ He et al.^9,10) evaluated an electromagnetic teeming system in an attempt to resolve these problems. An electromagnetic steel-teeming system uses electromagnetic induction heating technology in the following manner: a certain amount of Fe–C alloy is added to the nozzle brick shortly before the ladle is filled with liquid steel; after the tapping of the electrical furnace or converter, the steel is subjected to an external refining and casting process. These links use the heat of the liquid steel to form a Fe–C alloy blocking layer of a certain thickness. When the casting begins, the electromagnetic induction heating technology is used to melt the edge of this layer, thereby completing the steel-teeming process. Therefore, a pouring rate of 100% can be guaranteed, and pollution of the liquid steel by the stuffing sand is prevented. The steel-teeming time is one of the most important technical indicators in the metallurgical industry, but the electromagnetic steel-teeming system employed in industry may suffer from the following two drawbacks: (i) the high heating intensity will shorten the life of induction heating workpieces and (ii) different steel mills use different sizes of ladle, nozzle, and nozzle brick, which leads to different diameters, lengths, and shapes of the liquid steel channel and different static pressure above the blocking layer. In addition, various tapping temperatures and standing times for different types of steels will result in diverse power supply parameters, which will have an impact on the steel-teeming time. This represents a key factor in determining whether the electromagnetic steel-teeming system can be industrialized, applied, and popularized.

To solve these problems, considering the conditions including changeable working condition and environment, various disturbances, high ladle bottom temperature, too many dangerous factors,¹¹⁾ and especially, short steel-teeming time which is insufficient for long-time online experiment. Therefore, in this work, numerical simulation results and high-temperature offline test results were compared in order to obtain the best match of: output current, output power, and frequency of the power supply associated with a 110 t ladle to the relevant steel-teeming time. Large friction between the blocking layer and the wall of the liquid steel channel prevents fall off of the blocking layer when the liquidus temperature of this layer is initially reached. Therefore, the model employed in this work used high-temperature offline tests to measure the diameter of the blocking layer. The results revealed that fall off of occurs when 5 mm of the layer edge has melted. Since different nozzle bricks, nozzles, and steel grades are used by different steel enterprises, widespread applicability of the electromagnetic steel-teeming system must be ensured. The 110 t ladle numerical simulation model was therefore used to investigate the influence of power supply parameters on the steel-teeming time of the electromagnetic teeming system. This influence was revealed by varying the diameter, length, and shape of the liquid steel channel, static pressure above the blocking layer, as well as the tapping temperature and standing time of the steel grades. Theoretical and experimental foundations for shortening the steel-teeming time of the system are obtained based on the behavior of these parameters.

2. Method of Numerical Simulation

2.1. Modeling

The liquid steel channel in the nozzle brick of a 110 t ladle used in practical production is taken as a sample for building the finite element analytical model. The structure of the brick is shown in Fig. 1. In the previous stage of the project, simulations were based on the assumption that the blocking layer would fall off immediately after the layer-edge temperature reaches the liquidus. This incorrect assumption was corrected by applying a fixed power to the electromagnetic induction affecting zone in the simulation. Furthermore, the post-processing module of PROCAST was used to measure the thickness of the liquid Fe–C alloy that melted from the blocking layer. The inner wall of the liquid steel channel was designated as the 0 point of melted thickness (i.e., the reference for zero melting thickness of the blocking layer). According to previous reports of experiments and high-temperature offline tests,^{12,13,14,15,16)} the blocking layer will fall out with either total or partial melting of the layer edge located 0–5 mm from the inner wall of the liquid steel channel. The time for the falling off of the blocking layer (i.e., the steel-teeming time) was recorded.

Fig. 1.

Structure of nozzle brick.

The numerical model of the liquid steel channel in the nozzle brick is shown in Fig. 2. A number of nodes at the edge of the blocking layer (in the solid-liquid state) are selected as study objects. This layer is jointly affected by various factors including the induction heating intensity, size of the interspace between particles, distance to induction heating workpieces, and heat transfer of the liquid steel above the blocking layer. The melting time for the nodes varies although the distances between the nodes and the liquid steel channel are the same. Fall off of the blocking layer is ensured by assuming that the blocking layer fall offs only when the regions located 0–5 mm from the edge have totally melted into the liquid. Therefore, in the numerical simulation, the nodes with the longest melting time are selected as a reference for the actual working condition. The position selected in the simulation is shown in Fig. 1.

Fig. 2.

Numerical model and mesh generation for the ladle (110 t).

2.2. Basic Assumption

The simulation is enabled by the finite element analytical software PROCAST. In the simulation, the following basic assumptions are made in accordance with the characteristics of the experiment.

1. Heat dissipation of the blocking layer is ignored;

2. The blocking layer can fall out only when the regions located 0–5 mm from the inner wall of the liquid steel channel are totally melted;

3. When the power supply is in the ON state, the current is evenly distributed over the coil section;

4. The erosion and composition of the nozzle brick lining are neglected and considered constant, respectively;

5. The interspace between the particles of the Fe–C alloy is taken as 0 mm, and the Fe–C alloy filler is evenly distributed in the liquid steel channel;

6. When the blocking layer edge has melted into the liquid, the nodes located 5 mm away from the inner wall of the liquid steel channel in the model are selected as study objects. The node with the longest melting time required for transitioning to the solid-liquid state is taken as the referential node for the actual working condition.

2.3. Theoretical Foundation

According to the Maxwell Equation Set and the finite element equation of harmonic electromagnetic field analysis:   

$$\left[\text{K}+\text{j}\omega \hspace{0.17em}\text{C}\right]\left\{\text{u}\right\}=\left\{\text{F}\right\}$$(1)

Where [K], coefficient matrix; j, current density (A/m²); ω, angular frequency (rad/s); [C], damping matrix; {F}, external load vector (current load is adopted in this paper); and vector {u}, the variable to be determined. Each variable of the electromagnetic field can be determined from Eq. (1).

The magnetic-thermal coupling, described in the literature,^21,22) was considered. The induced current Joule heat produced by the magnetic field is the heat source. The induced eddy intensity of the temperature field during electromagnetic induction heating is given as follows:   

$$q_V=\rho {\left|\overrightarrow{{\text{J}}_{\text{e}}}\right|}^2,$$(2)

Where, q_v, internal heat source intensity (W/m³); ρ, resistivity of the supplies (Ω∙m); $\overrightarrow{{\text{J}}_{\text{e}}}$, induced current surface density (A/m²).

In the simulation calculation, the Fourier columnar solid heat conduction differential equation is given as follows:   

$$\frac{{\partial }^2\mathrm{T}}{\partial {\mathrm{x}}^2}+\frac{{\partial }^2\mathrm{T}}{\partial {\mathrm{y}}^2}+\frac{{\partial }^2\mathrm{T}}{\partial {\mathrm{z}}^2}+\frac{q_{\mathrm{V}}}{\mathrm{k}}=\frac{{\rho }^{\prime }\mathrm{c}}{\mathrm{k}}\cdot \frac{\partial \mathrm{T}}{\partial \mathrm{t}}$$(3)

Where, T, thermodynamic temperature (K); k, heat conduction coefficient of the isotropic material (W m⁻¹∙K⁻¹); ρ′, material density (kg m⁻³); c, specific heat of the material (J kg⁻¹∙K⁻¹); t, time (s); q_v, internal heat source intensity (W m⁻³).   

$$\delta =\frac{1}{2\pi }\sqrt{\frac{{\rho }_{\text{Fe}-\text{C}}{10}^9}{{\mu }_{\text{r}}\text{f}}}=5\mathrm{\hspace{0.17em} }030\sqrt{\frac{{\rho }_{\text{Fe}-\text{C}}}{{\mu }_{\text{r}}\text{f}}}$$(4)

Where, δ, μ_r, f, and ρ_Fe–C are the electrical conductivity (S/m) of the melt, magnetic conductivity (H/m) of the melt, f (Hz) frequency of the electromagnetic field, and electrical resistivity (Ω·m) of the Fe–C alloy.

2.4. Boundary Conditions

1. A constant environmental temperature of 1373 K^15,16) was maintained in the liquid steel channel;

2. The compositions of the Fe–C alloy are listed in Table 1. The induced current Joule heat produced by the electromagnetic field represents the heat source. Furthermore, the particles of the Fe–C alloy are ferromagnetic and, hence, the magnetic conductivity of the alloy will decrease to one when the temperature is higher than the Curie temperature of the alloy. The ladle will be warmed up to 1373 K prior to use. The corresponding temperature-dependent magnetic conductivity, electrical conductivity, thermal conductivity, and enthalpy of the Fe–C alloy are μ_r =1,9.3×10⁵(s/m), 24.02 W/(m∙K), and 1350 J/(kg∙K),^17,18,19,20) respectively.

Table 1. Compositions of Fe–C alloy in the experiments.

Name	Chemical composition (%)
10#steel	C	Si	Mn	P	S	Cu	Ni
Element content	0.07–0.13	0.17–0.37	0.35–0.65	≤0.035	≤0.035	≤0.25	≤0.25

2.5. Analysis and Discussion of Simulation Results

As a technical requirement, the steel-teeming process must be finished within 120 s. The influence of frequency variations on the steel-teeming time was investigated for fixed values of output current I and output power P. Frequencies of 10 kHz, 20 kHz, 30 kHz, and 40 kHz were employed in the experiment. The results showed that fall off of the blocking layer began at frequency values ranging from 20 kHz to 35.7 kHz, but the time surpassed 120 s (i.e., the required steel-teeming time was exceeded). However, when the power supply frequency reached values ranging from 35.7 kHz to 40 kHz, the steel-teeming time decreased with increasing frequency and was always within 120 s (i.e., fall off occurred within the required steel-teeming time). Considering that the life of the induction heating workpieces will decrease with increasing frequency, a frequency of 35.7 kHz was selected for further experiments.

This phenomenon is attributed mainly to the skin effect, where the electromagnetic induction intensity in the metal melt decreases with increasing depth into the sample. Compared with that occurring at low frequency, at high frequency, the (i) electromagnetic-field penetration of a given melt will be lower (see Eq. (4)) and (ii) heating is more concentrated and the heating time is shorter. Therefore, the Fe–C alloy contacting the liquid steel channel melted before the center of the blocking layer. The last referential node located 5 mm away from the inner wall of the channel melted when the frequency increased to a certain value (which satisfies the requirement of the steel-teeming time of the 110 t ladle). This value corresponds to the optimal frequency for steel teeming of the 110 t ladle of a steel mill.

A frequency of 35.7 kHz was selected for the study aimed at determining the influence of the output current I and output power P of the induction heating power supply on the heating time. The values of I and P were varied during the study. When P was (i) 31.3 kW and 34.1 kW and (ii) 40.2 kW, the Fe–C alloy in the nozzle brick (i) resisted melting in the aforementioned schedule time and (ii) melted to the set node within 120 s, respectively. The time for melting of the blocking layer edge and, hence, the time required for fall off of the blocking layer decreased with increasing heating power. Consider the match of induction workpieces. (owing to the skin effect, the effective sectional area for the current in the conductor decreased and, hence, the resistance and power loss increased. In addition, the strength of the eddy, and eddy-current loss increased with increasing frequency, whereas the life of the coil decreased). When the power increased to 40.2 kW, the corresponding heating time corresponded to the theoretical optimal value. The frequency, output current, and steel-teeming time corresponding to this value were 35.7 kHz, 152.9 A, and 117.6 s, respectively. The variation in the calculated (via numerical simulation) value with heating frequency is shown in Table 2 (the calculation of other schemes is similar to that of this scheme and, hence, a detailed explanation of this calculation was deemed unnecessary).

Table 2. The result of the numerical simulation.

I/A	139.6	146.9	152.9	161.2	171.6	179.3	183.3	192.5
f/kHz	35.7	35.7	35.7	35.7	35.7	35.7	35.7	35.7
P/kW	31.3	34.1	40.2	42.7	48.4	50.6	52.5	57.9
t/s	unmelted	unmelted	117.6	113.4	108.6	106.7	101.8	97.8

This results mainly from the fact that when the blocking layer edge has melted to the set node, a certain temperature field distribution occurs (see Fig. 3). Therefore, the blocking layer forms at temperatures below the solidus and liquidus temperatures. During the heating process, the temperature of the pointed node increases gradually. The blocking layer edge then melts to the pointed node, and begins to fall off due to the static pressure of the liquid steel and the effect of gravity. The electromagnetic steel-teeming process is completed with this fall off.

Fig. 3.

The temperature nephogram of the blocking layer at the time of falling off (f=35.7 kHz, I=192.5 A, P=40.2 kW).

3. High-temperature Offline Test

3.1. Experimental Method

Actual production conditions were simulated in the high-temperature offline test, as Fig. 4 shows. In the experiment, the nozzle brick was enclosed in the heating chamber, consisting of two side walls that were each equipped with a length of resistance wire. For even heating of the chamber, the resistance wires on both sides were heated simultaneously. Temperature controller was connected to the end of wire, and thermocouples were embedded in the controller to monitor the temperature in the chamber. A constant temperature of 1373±5 K was maintained by using the feedback of the temperature signals to control the heating intensity of the wires. This temperature was maintained for 90 min (i.e., the time for the entire process from tapping to casting of a 110 t ladle of a steel mill). The sliding plate was then opened, and the loose Fe–C alloy below the blocking layer fell freely with gravity. The power supply was then started and the parameters were adjusted in accordance with the established scheme. The following was noted: whether the metal liquid flows out beneath the upper nozzle and if the Fe–C alloy falls simultaneously. Moreover, the timer installed in the power supply was used to record the heating time.

Fig. 4.

Schematic illustration of high-temperature offline test.

3.2. Analysis and Discussion of Experimental Results

Frequencies of 10 kHz, 20 kHz, 30 kHz, and 40 kHz were selected for the experiment, which lasted for 120 s (see Table 3 for the experimental results). When the power is increased, the over current will shorten the life of the coil. The optimal frequency was obtained at a power supply frequency of 35.3 kHz. For frequency f=35.3 kHz, output current I <152 A, and output power P <40 kW, the Fe–C alloy failed to fall off within 120 s; when I was >152 A and P >34 kW, the alloy started to fall off, and the melting time decreased with increasing I and P. To ensure long lifetime and stability of the coil under current working conditions, I and P values of 152.9 A and 40.1 kW respectively, were considered the most suitable for the electromagnetic teeming experiment of the 110 t ladle. The corresponding steel-teeming time was 113 s.

Table 3. The result of high-temperature offline test.

I/A	139.6	146.9	152.9	161.2	171.6	179.3	183.3	192.5
f/kHz	35.3	35.3	35.3	35.3	35.3	35.3	35.3	35.3
P/kW	31.2	33.6	40.1	42.4	48.5	50.1	52.3	57.6
t/s	unmelted	unmelted	113 s	109 s	103 s	100 s	95 s	89 s

4. Analysis and Discussion

4.1. Compare Numerical Simulation Results with High-temperature Offline Test Results

The numerical simulation results and high-temperature offline test results are compared in Fig. 5. For f=35.3 kHz, the simulation results differ slightly from the test results. This is attributed mainly to the fact that, to achieve good simulation results, the last melted node was selected for recording the time at which the blocking layer falls off. So the steel-teeming time will be longer compared to experiment result. However, the simulation and test results exhibit the same trends, and the values are almost identical, confirming that the best match of power supply parameters for the 110 t ladle is: frequency f=35.3 kHz, output current I=152.9 A, and output power P=40.1 kW, for a corresponding steel-teeming time of t=113 s.

Fig. 5.

Numerical simulation data compared with experimental data (f=35.3 kHz).

4.2. Influence of Liquid Steel Channel Diameter, Length, Shape, and Static Pressure on Steel-teeming Time

The applicability of the electromagnetic steel-teeming system to different nozzle bricks and nozzle sizes was determined by using the aforementioned numerical model to assess the influence of the (i) liquid steel channel diameter, length, and shape and (ii) static pressure above the blocking layer on the power supply parameters. Various diameters (70 mm, 90 mm, and 110 mm) and lengths (320 mm, 420 mm, and 620 mm) were selected as the study objects. A horn-shaped and a cylindrical channel were used. In addition, the influence of the static pressure was determined for 110 t, 260 t, and 300 t ladles. The dependence of the power supply parameters on each of the aforementioned factors is shown in Figs. 6, 7, 8, 9.

Fig. 6.

Influence of diameter of liquid steel channel on parameters of power supply.

Fig. 7.

Influence of length of liquid steel channel on power supply parameters.

Fig. 8.

Influence of shape of liquid steel channel on power supply parameters.

Fig. 9.

Influence of static pressure on steel liquid channel on power supply parameters.

The influence of the liquid steel channel diameter on the power supply parameters is shown in Fig. 6. The current, power, and frequency all increase with increasing diameter of the channel. This results mainly from the fact that, when the diameter of the channel increases, the: (i) diameter of the blocking layer that must be melted by coil heating, resulting magnetic flux leakage, and watt-less power as well as the current, frequency, and power also increase, and (ii) heating area for downward heat transfer (via the ladle) increases. Therefore, the rate of heat transfer and the amount of heat absorbed in unit time increase. These factors all contribute to an increase in the steel-teeming time.

The dependence of the power supply parameters on the length of the liquid steel channel is shown in Fig. 7. With extension of the channel, the current, power, and frequency decrease initially, and then increase continuously thereafter. This results mainly from the fact that, compared with that required for a shorter liquid steel channel, for a longer channel (i) a larger amount of the Fe–C alloy filler is needed, and (ii) more heat must be absorbed by the Fe–C alloy below the blocking layer. This increased heat absorption leads to a decrease in the bulk temperature of the Fe–C alloy in the channel, thereby resulting in slight upward movement of the blocking layer. At a certain length of the channel, the blocking layer becomes the most intensely induction-heated region, and the minimum current, power, and frequency for steel teeming occur at this length. Therefore, when the length of the liquid steel channel increases, the current, frequency, power, and the corresponding steel-teeming time decrease initially and then increase.

The shape of the liquid steel channel influences the power supply parameters as shown in Fig. 8. During the electromagnetic steel-teeming process, the current, frequency, and power required for the horn-shaped channel are higher than those required for the cylindrical channel. This results mainly from the fact that, as Fig. 8(a) shows, the heat absorbed from the liquid steel will increase, owing to a large lower-end face of the blocking layer. Consequently, the blocking layer moves slightly upward (compare Figs. 8(a) and 8(b)). The current, frequency, power, and corresponding steel-teeming time increase slowly with increasing shape change of the channel.

The influence of the static pressure on the liquid steel channel is shown in Fig. 9. As the figure shows, the parameters all decrease with increasing static pressure of the ladle. The main reason is that with other conditions unchanged, a constant amount of heat is absorbed by the blocking layer. Increasing the static pressure yields a slight increase in the heat-transfer rate and, hence, accelerates the melting of the blocking layer edge slightly, but the position and thickness of the layer remains almost unchanged. Therefore, the current, frequency, power, and the relevant steel-teeming time decrease only slightly with increasing static pressure.

4.3. Influence of Tapping Temperature on Steel-teeming Time

In an electromagnetic steel-teeming system, different parameters of power supply are required for different tapping temperatures. Temperatures of 1823 k, 1873 K, and 1893 K were selected as study objects in an effort to broaden the range of steel grades for which the electromagnetic steel-teeming technology is applicable. The aforementioned numerical simulation model of the 110 t ladle was employed to determine the best combinations of power supply parameters for different types of steel (see corresponding results in Fig. 10).

Fig. 10.

Power supply parameters under different tapping temperature.

Figure 10 reveals tapping temperatures of 1873 K, 1893 K, and 1823 K for current and power values ranked in ascending order. A previous study (via experiments)²³⁾ explained the occurrences associated with these temperatures as follows. Consider a tapping temperature of 1873 K and the following physical parameters: type of steel: 10# steel, particle size: 2.0, and cylindrical size of the Fe–C alloy. In this case, the blocking layer lies in the most intensely heated region, which exhibits the highest heating efficiency. The blocking layer therefore falls off faster (than at other temperatures) and the minimum current and power occur at this temperature. At temperatures of 1823 K and 1893 K, the blocking layer moves slightly up and down, respectively, owing to the temperature difference compared with 1873 K. The temperature gradient and, hence, the displacement of the layer are smaller at 1893 K than at 1823 K. In an electromagnetic steel-teeming system, the current and power for steel teeming depend mainly on the heating efficiency of the coil and the heat transfer of the liquid steel. The liquid steel has a significant influence on the displacement of the blocking layer from the most intensely heated region. The coil heating efficiency decreases with increasing displacement. Therefore, at 1893 K, the blocking layer falls off faster, and the current and power are smaller than those at 1823 K. In addition, due to the skin effect, the depth of penetration decreases with increasing frequency, whereas the heating effect improves. The frequency must, however, satisfy only the process requirements regarding (for example) the coil life and costs and, hence, changes only slightly, but exhibits the same tendency as the current and power.

4.4. Influence of Ladle Standing Time on Steel-teeming Time

In the metallurgical industrial process, the standing time varies with the type of steel. Understanding the correlation between the standing time of the liquid steel and the parameters of the power supply is therefore essential for broadening the range of steels to which electromagnetic steel-teeming technology is applicable. According to the requirements of a steel mill, the longest standing time for liquid steel is 30 min. The aforementioned numerical simulation model of the 110 t ladle was repeated and inspection points separated by 5 min intervals were selected as study objects. A steel-teeming time of 120 s was guaranteed. The dependence of each parameter on the time is shown in Fig. 11.

Fig. 11.

Power supply parameters with different standing time.

As Fig. 11 shows, the current, frequency, and power decrease with increasing standing time (0–10 min) of the liquid steel, increase for times ranging from 10 to 15 min, and plateau thereafter. This is attributed mainly to the fact that at a standing time of 10 min, the blocking layer occurred in the most intensely heated region. The current and power needed for induction heating in the electromagnetic steel-teeming system are the smallest at this standing time. Therefore, the current and power decrease in this time interval (0–10 min). For times ranging from 10 to 15 min, the heat dissipation from the ladle is rapid, owing to the large gradient between the liquid steel temperature and the environmental temperature. This gradient results in upward movement of the blocking layer, corresponding to deflection from the most intensely heated region. As a result, the current and power required for completing the electromagnetic steel-teeming process increase. At a standing time of 15–30 min, the (i) gradient between the ladle temperature and the environmental temperature is lower, (ii) heat dissipation is less rapid, (iii) movement of the blocking layer is slower, and (iv) current and power are slightly higher than those occurring at a standing time of 10–15 min. In addition, the frequency required for enhancing the heating effect when the blocking layer is deflected from the most intensely heated region increases, owing to the skin effect. The current, frequency, and power therefore exhibit similar trends for different standing times. The same tendency is observed for the relevant steel-teeming time.

5. Conclusions

(1) For the 110 t ladle, the steel-teeming time can be adjusted by changing the output parameters of the power supply, and decreases with increasing magnitude of these parameters.

(2) For the 110 t ladle, an output frequency, output current, output power, and a steel-teeming time of 35.3 kHz, 152.9 A, 40.1 kW, and 113 s, respectively, were found to be the best combination of output parameters for the power supply.

(3) The current, frequency, power, and steel-teeming time increase with increasing diameter of the liquid steel channel.

(4) When the length of the liquid steel channel increases, the current, frequency, power, and steel-teeming time decrease initially and then increase continuously.

(5) During the electromagnetic steel-teeming process, the horn-shaped liquid steel channel requires greater current, frequency, power, and steel-teeming time than the cylindrical channel.

(6) The current, frequency, power, and steel-teeming time decrease slightly with increasing static pressure of the ladle.

(7) The current, frequency, power, and steel-teeming time of the 110 t ladle decrease with tapping temperatures ranging from 1823 K to 1873 K, and increase at temperatures ranging from 1873 K to 1893 K.

(8) For the 110 t ladle, in the initial 10 min of the ladle standing time, the required current, frequency, power, and corresponding steel-teeming time decrease initially, increase rapidly in 10–15 min, and increase slowly thereafter.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (U1560207).

References

• 1)   E. Q.  Li,  J. X.  Yin and  W. C.  Zhang: Electric Induction Furnace for Casting, Machine Press, Beijing, (1997), 7.
• 2)   K.  Wünnenberg: Rev. Métall., 102 (2005), 687.
• 3)   H.  Suito and  R.  Inoue: ISIJ Int., 36 (1996), 528.
• 4)   J. C.  He,  K.  Marukawa and  Q.  Wang: A Ladle with Heating Tapping Equipment and Its tapping Method, China Patent ZL1810417, (2006).
• 5)   H.  Tanaka,  R.  Nishihara,  I.  Kitagawa and  R.  Tsujino: ISIJ Int., 33 (1993), 1238.
• 6)   H.  Tanaka,  R.  Nishihara,  R.  Miura,  R.  Tsujino,  T.  Kimura,  T.  Nishi and  T.  Imoto: ISIJ Int., 34 (1994), 868.
• 7)   X. H.  Wang: Clean Steel, Metallurgical Industry Press, Beijing, (2006), 4.
• 8)   K. D.  Xu,  L. J.  Xiao,  Y.  Gan,  L.  Liu and  X. H.  Wang: Acta Metall. Sin., 48 (2012), 1.
• 9)   J.  Gu,  K. W.  Song and  J. S.  Qian: Fly Ash, 2 (2007), 32.
• 10)   J. F.  Yan,  J. X.  Chen and  L.  Hu: Chromium Metallurgy, Metallurgic Industry Press, Beijing, (2007), 121.
• 11)   A.  Gao,  D. J.  Li,  Q.  Wang,  K.  Wang,  B. J.  Jin,  K.  Marukawa and  J. C.  He: ISIJ Int., 50 (2010), 1770.
• 12)   D. J.  Li,  Q.  Wang,  X. A.  Liu,  A.  Gao,  X. B.  Wang,  J.  Dong,  K.  Marukawa and  J. C.  He: J. Iron Steel Res. Int., 19 (2012), 766.
• 13)   A.  Gao,  Q.  Wang,  D. J.  Li,  H. S.  Chai,  L. J.  Zhao and  J. C.  He: Acta Metall. Sin., 47 (2011), 219.
• 14)   D. J.  Li,  X. A.  Liu,  Q.  Wang, R. H. Ou yang, H. S. Chai and J. C. He: J. Iron Steel Res. Int., 24 (2012), 16.
• 15)   A.  Gao,  Q.  Wang,  B. G.  Jin and  J. C.  He: J. Northeast. Univ.(Nat. Sci.), 31 (2010), 515.
• 16)   A.  Gao,  Q.  Wang,  D. J.  Li,  B. G.  Jin,  K.  Wang and  J. C.  He: Acta Metall. Sin., 46 (2010), 634.
• 17)   D. J.  Li,  X. A.  Liu,  Q. Wang and  J. C.  He: J. Northeast. Univ. (Nat. Sci.), 33 (2012), 661.
• 18)   X. A.  Liu,  Q.  Wang,  C. Y.  Shi,  H. X.  Li, T, Liu and J. C. He: J. Cent. South Univ. (Nat. Sci.), 46 (2015), 3188.
• 19)   X. A.  Liu: Ph.D. thesis, Northeast University China, (2015).
• 20)   K.  Sadeghipour,  J. A.  Dopkin and  K.  Li: Comput. Ind., 28 (1996), 195.
• 21)   J. Y.  Jang and  Y. W.  Chiu: Appl. Therm. Eng., 27 (2007), 1883.
• 22)   T. P.  Fredman,  J.  Torrkulla and  H.  Saxen: Metall. Mater. Trans. B, 30 (1999), 323.
• 23)   H.  Stöcker: Physical Manual, Peking University Press, Beijing, (2004), 182.