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metals Article

Hydrodynamic Modeling and Mathematical Simulation on Flow Field and Inclusion Removal in a Seven-Strand Continuous Casting Tundish with Channel Type Induction Heating Haiyan Tang 1, *, Luzhao Guo 1 and Jiaquan Zhang 1 1

2

*

ID

, Guanghui Wu 1 , Hong Xiao 1,2 , Haiying Yao 2

School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, No. 30 Xueyuan Road, Haidian District, Beijing 100083, China; [email protected] (L.G.); [email protected] (G.W.); [email protected] (H.X.); [email protected] (J.Z.) Electromagnetic Center, Hunan Zhongke Electric Co., Ltd., Yueyang 414000, China; [email protected] Correspondence: [email protected]; Tel.: +86-10-6233-2880; Fax: +86-10-6233-2880

Received: 12 April 2018; Accepted: 19 May 2018; Published: 23 May 2018







Abstract: The tundish with heating instrumentation is attracting more and more attention in continuous casting processes for maintaining a pre-determined constant pouring temperature under a given casting speed, which is beneficial for an improved and consistent steel product quality. However, the fluid flow, temperature distribution and the removal behaviors of non-metallic inclusions in it will be much different from that in a conventional tundish, due to the implementation of the heating practice. In the present work, to reduce the non-metallic inclusion amounts in billets of the second and sixth strands in a seven-strand tundish with channel type induction heating, the flow field profiles and temperature profiles of molten steel in this tundish have been investigated using hydrodynamic modeling coupled with mathematical simulation under isothermal and non-isothermal situations, respectively. The results of the isothermal experiment indicate that the prototype tundish has severe “short-circuiting flow” in the second and sixth strands, which might have caused the increased inclusion amounts in the billets of the two strands. The flow field of the tundish can be greatly improved by changing the channel design and adding two high dams at each side of the tundish. Compared with the prototype structure A0, the average residence time of the optimized case C5 is prolonged by 55.49% (from 501 to 779 s); the dead zone volume fraction is reduced by 66.18% (from 45.57% to 15.41%); and the flow of each strand becomes more consistent with lower standard deviation. The non-isothermal experiments show that the fluid presents an obvious rising tendency when it flows out from the heating induction channel. The larger the temperature difference inside and outside the channel is, the more consistent the fluid flow between different strands and the more homogeneous the flow field in the whole tundish. For the prototype tundish structure, when the temperature difference is 5 ◦ C, the dead zone is basically eliminated, and the minimum residence time is prolonged by 789% (from 38 to 338 s), compared with the 0 ◦ C of temperature difference. A mathematic model has been proposed accordingly, which can explain well the hydraulic phenomena. The inclusion removal rates of different cases were compared by mathematical simulation, and their removal mechanism was studied, as well. Keywords: tundish with channel type induction heating; flow field; temperature field; non-metallic inclusions; physical model; mathematical simulation

Metals 2018, 8, 374; doi:10.3390/met8060374

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1. Introduction Industrial practice and continuous casting theory show that a low superheat degree of constant 1. Introduction temperature casting plays an active role in improving the billet quality and stabilizing the operation Industrial practice continuous casting theory showofthat a low superheat degree of constant of continuous casting,and while controlling the temperature molten steel in the tundish is one of the temperature casting plays an active role in improving the billet quality and stabilizing the operation of most effective means [1]. However, with casting proceeding, the temperature of molten steel in both continuous casting, while controlling the temperature of molten steel in the tundish is one of the most the ladle and tundish will inevitably drop due to heat loss from radiation and convection of refractory effective [1]. during However, with casting proceeding, temperature molten steel in both the ladle lining, means especially ladle exchange and castingthe end. Therefore,ofthe temperature compensation and tundish will inevitably drop due to heat loss from radiation and convection of refractory technology of the tundish has been paid more and more attention in the production processlining, of high especially during ladle and casting Therefore, themain temperature compensation technology quality special steel exchange in the recent years. end. At present, the technologies for the temperature ofcompensation the tundish hasare been paid more and more attention in the production high quality specialis plasma gun and channel type induction heating process (CTIH),ofthe latter of which steel in the recent years. At present, the main technologies for the temperature compensation are studied in the paper. plasmaThere gun and type induction theone latter of which is studied in the the paper. are channel two chambers in this heating kind of(CTIH), tundish, pouring chamber and other the There are two chambers in this kind of tundish, one pouring chamber and the other the discharging chamber, which are separated by a refractory wall. The induction heaterdischarging is installed chamber, which separated bytoa connect refractory The induction installed inside the wall inside the wall are with a channel thewall. two chambers. The heater heatingis operation for temperature with a channel to connect the two chambers. The heating operation for temperature compensation of compensation of liquid steel is illustrated in Figure 1 [1]. According to the electromagnetic induction liquid steel is illustrated in Figure 1 [1]. According to the electromagnetic induction principle, as the principle, as the induction coil is supplied with medium frequency alternating current, the main induction is supplied withcore medium frequency alternating current, the magnetic flux will in thebe magneticcoil flux in the iron will be established. Consequently, themain induced current iron core will be established. Consequently, the induced current will be generated in the electrical generated in the electrical conductive molten steel, which will produce joule heat to heat the molten conductive molten steel,the which will produce joule to heat the molten steelout passing the steel passing through induction channel. Theheat heated molten steel flows to thethrough discharging induction Theand heated molten steelmolten flows out the discharging of tundish and mixes chamberchannel. of tundish mixes with the steeltothere. Therefore, chamber the temperature of molten steel with the molten steel there. Therefore, the temperature of molten steel in the discharging chamber in the discharging chamber can be kept at a pre-determined value. In the actual casting process, when can kept at a pre-determined value. In the casting process, when the temperature of molten thebetemperature of molten steel drops to actual a certain value, the induction heating device will be steel drops to a certain value, the induction heating device will be automatically turned on and adjust automatically turned on and adjust the electric power according to the temperature of molten steel the electric power according to the temperature of molten steel to ensure a constant and uniform to ensure a constant and uniform temperature in the discharging chamber. temperature in the discharging chamber.

Figure1.1.Schematics Schematicsofofthe thechannel channeltype type inductionheating heating (CTIH) principle the tundish. Figure induction (CTIH) principle ofof the tundish.

The CTIH technology of the tundish verified in production to many have many advantages The CTIH technology of the tundish has has beenbeen verified in production to have advantages such such as high heating efficiency, easy control of the temperature, convenient installation and as high heating efficiency, easy control of the temperature, convenient installation and maintenance. maintenance. However, the following issues should be considered for steel plants with its adoption: However, the following issues should be considered for steel plants with its adoption: (a) its unique (a) its unique withchannel the induction channel involved; the heating power is usually variable geometry with geometry the induction involved; (b) the heating (b) power is usually variable in operation in operation as mentioned above or even in power-off state, which is simply based on the pouring as mentioned above or even in power-off state, which is simply based on the pouring temperature of temperature of molten steel from the for ladle or the needetc. forFor steel grades, in etc.the For example, in casting, the early molten steel from the ladle or the need steel grades, example, early stage of stage of casting, it does not work due to the high molten steel temperature; while in the later stage of it does not work due to the high molten steel temperature; while in the later stage of casting, its electric casting, its electric power will be increased step by step with the decrease in the temperature power will be increased step by step with the decrease in the temperature of molten steel, which willof molten steel, whichofwill result in the difference change of inside the temperature difference insidechannel and outside the result in the change the temperature and outside the induction and the induction channel and the change of fluid flow accordingly. In addition, for plain carbon steel, the change of fluid flow accordingly. In addition, for plain carbon steel, the induction device usually induction device usually remains in the power-off state. For cost-efficient control in sequence casting, remains in the power-off state. For cost-efficient control in sequence casting, an overall improved fluid an overall fluid flow pattern in the tundish should be designed based on the geometrical flow pattern improved in the tundish should be designed based on the geometrical and operational characteristics and operational characteristics of this kind of new vessel. of this kind of new vessel. seven-strandtundish tundishwith witha asymmetrical symmetricalinduction inductionheating heatingchannel channelhas hasbeen beencommissioned commissioned AAseven-strand recently in a steel plant of China, which is used to produce high-quality bearing and spring steelsatat recently in a steel plant of China, which is used to produce high-quality bearing and spring steels

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lower, but constant pouring temperature. It has been proven practically in test production that the temperature of liquid steel leaving the ladle furnace can be decreased by 10–15 ◦ C compared with the original process with the conventional tundish, and the casting temperature can be kept at the given temperature within ±2 ◦ C. However, it was also observed in the following industrial tests that the billets from the second and sixth strands contained more non-metallic inclusions than other strands, which is suspected to be related to the improper tundish structure while adopting the heating channel. Therefore, it is of great necessity to optimize its structure and improve the flow field of molten steel in order to decrease the overall amount of non-metallic inclusions in billets. For the conventional tundishes, many investigations [2–11] have been performed in the past three decades by changing their shapes and flow control devices such as a dam, weir, turbulence inhibitor and baffle with inclined holes to improve its flow field. These studies also indicate that hydrodynamic modeling [12–14], combined with mathematical simulation [15–19], is a useful method to study the flow field and temperature profile of molten steel in the tundish. As the effect of the temperature decrease of molten steel with casting on its flowing state is usually ignored, isothermal cold water is frequently adopted to model the molten steel. However, for a tundish with induction heating, different heating conditions will exert various temperature differences, so an isothermal cold water model is not enough to reflect its actual flowing behavior. Therefore, a non-isothermal experiment should be also performed in the present study. There have been fewer studies on the induction heating tundish to the present. The earliest one began from a patent proposed by Ueda et al. [20] in 1984. In the same year, Mabuchi et al. [21] investigated the flow characteristics of molten steel by performing the residence time distribution (RTD) in the tundish with induction heating. They found that the molten steel and inclusions lifted upward under the action of buoyancy due to the induction heating. Later on, Miura et al. [22] performed some industrial tests on the induction heating tundish of the No. 2 continuous caster at Yawata Works and found that the inclusion removal ratio was increased and the surface quality of slab was significantly improved, which was attributed to the contribution of both the electromagnetic force and buoyancy-driven flow. In recent years, Wang et al. [23,24] developed a mathematical model mainly to simulate the joule heating and temperature distribution in an “H-type” channel tundish with 800, 1000 and 1200 kW of induction heating power, respectively. Their results indicated that the heat loss of molten steel could be compensated effectively by joule heating, and the temperature distribution became more homogeneous in the tundish with induction heating. Yue et al. [25] developed a magneto-hydrodynamic model to study the flow and heat transfer in a twin-channel induction heating tundish and showed that electromagnetic force had a significant effect on the flow of molten steel. From the summary above, it can be seen that the previous studies mainly focused on the effect of induction heating and electromagnetic force on the flow of molten steel, while few on the effect of induction channel position and heating time, especially for multi-strand tundishes. In the present work, the structure of a seven-strand induction heating tundish is comprehensively optimized by a physical model combined with a mathematical simulation method under both isothermal and non-isothermal conditions, which is expected to make an effective improvement of the multi-strand induction heating tundish with special intention to decrease the non-metallic inclusion amounts in the second and sixth strand billets; meanwhile, the flow characteristic and behavior of molten steel in the tundish with induction heating will be revealed, which is beneficial to the better application of this innovative vessel in industry. To verify the optimized results, the removal ratios of different particle sizes of inclusions are also numerically simulated and their removal mechanism discussed.

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2. Physical Physical Modelling Modelling 2. 2.1. 2.1. Description Description of of the the Tundish Tundish An An industrial industrial sized sized seven-strand seven-strand metallurgical metallurgical tundish tundish with with induction induction heating heating was was used used as as prototype design the theexperimental experimentalwater water model. Its schematic is shown in Figure 2, in which prototype to design model. Its schematic is shown in Figure 2, in which Figure Figure 2a–c represents solid view,and toppartial view view and of partial view of the tundish, 2a–c represents the solid the view, top view the tundish, respectively. Therespectively. geometrical The sizetundish of the prototype tundish is listed in Tableparameters 1 and the in operating parameters size geometrical of the prototype is listed in Table 1 and the operating Table 2. The pouring in Table 2. The pouring chamber and discharging chamber are connected by the coupled heating chamber and discharging chamber are connected by the coupled heating channels. The molten steel channels. steel flows intoonly the discharging flows intoThe the molten discharging chamber through the chamber channel. only through the channel.

Figure 2. Schematics of the tundish: (a) solid view, (b) top view and (c) partial view. Figure 2. Schematics of the tundish: (a) solid view, (b) top view and (c) partial view. Table 1. Geometry of the prototype tundish. Table 1. Geometry of the prototype tundish. Parameters Data

Parameters

Data

Length of bottom surface of discharging chamber (A) 9504 mm Length of bottom surface of discharging chamber (A) 9504 mm Length of top surface of discharging chamber (B) 9882 mm of top surface of discharging chamber 9882 WidthLength of bottom surface of discharging chamber (C)(B) 480mm mm bottom of discharging chamber (C) 480 WidthWidth of top of surface of surface discharging chamber (D) 820mm mm WidthWidth of pouring (E)discharging chamber (D) 1173mm mm of topchamber surface of 820 Distance from shroud to the Outlet 950mm mm Width ofthe pouring chamber (E) 4 (F) 1173 Length of the channel (G) 1600mm mm Distance from the shroud to the Outlet 4 (F) 950 Distance between two outlets (H) 1500 mm Length of the channel (G) 1600 mm Height of the channel’s export to bottom surface (I) 300 mm ◦ Distance between two outlets (H) 15005mm Inclination of the channel (α) Height of the channel’s export to bottom surface (I) 300 mm Volume of the tundish 6.3 m3 Inclination of the channel (α) 5° 3 Volume of the tundish 6.3 Table 2. Operating parameters of the prototype tundish. m

Table 2. Operating parameters of the prototype tundish. Parameters Data Section size of billetParameters caster Casting speed Section size of billet caster Depth of the molten bath Casting speed Volumetric flowrate of every inlet Depth of the molten bath Volumetric flowrate of every inlet

200 mm × 200 mm Data

0.8 m/min 200 mm × 200 mm 870 mm 0.8 m/min 0.034 m3 /min 870 mm 0.034 m3/min

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The experimental scale factor is 1:3. According to a similar principle, the geometrical and dynamic similarities need to be guaranteed between the prototype tundish and the model one [6,7]. For the dynamic similarity, fluid flow characteristics can be decided by the Reynolds number Re and Froude number Fr. The experimental work of Koria and Singh [7] indicated that the magnitude of Re in different scale tundishes was very similar under the turbulent flow conditions. Therefore, the essential conditions for dynamic similarity between the prototype and the model can be expressed as: Frm = Frp where m represents the model of the tundish and p represents the prototype. The Froude number is defined as: u2 Fr = gL

(1)

(2)

where u is the flow velocity, g is the acceleration of gravity and L is the characteristic length. Thus, the main geometrical and operation parameters between the model and prototype can be formulated with scale factor λ as follows: Lm /Lp = λ,Vm /Vp = λ3 , um /up = λ0.5 , Qm /Qp = λ2.5

(3)

where V is the volume of the tundish and Q is the volumetric flow rate of the molten steel. Substituting in the data in Tables 1 and 2, V m and Qm can be obtained as 0.234 m3 and 2.545 × 10−4 m3 /s, respectively. The motion behavior of molten steel in the tundish depends on the natural convection and forced convection, which are controlled by the buoyancy force and inertia force, respectively. Therefore, the dimensionless Archimedes number (Ar) can describe the convection pattern as the ratio of buoyancy force to inertia force [8]. According to the similarity principle: Arm = Arp

(4)

The Ar is expressed as: Ar =

Gr Re2

(5)

where Gr is the Grashof number and Re is Reynolds number:

Gr =

gβL3 ∆T ν2 (6)

Re =

uL ν

where ν is the kinematic viscosity. Substituting Equation (6) into Equation (5), Ar is obtained as: Ar =

βgL∆T u2

(7)

where β is the thermal expansion coefficient and ∆T is the temperature difference of fluid inside and outside the channel. Substituting βp = 3.9 × 10−4 (1/◦ C), βm = 3.48 × 10−4 (1/◦ C) [5] and the relationship of L, u between the model and prototype in Equation (3) into Equations (4) and (7), the following formula can be obtained as: 3.48∆Tm ∼ (8) = 3.9∆Tp

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Equation (8) is used to calculate the temperature difference of the fluid in the model, corresponding to the induction heating effect in the prototype. 2.2. Method and Criteria of Hydrodynamic Modelling 2.2.1. Experimental Setup and Method The traditional stimulation-response method [2,3,5–7] was applied to the 1:3 reduced scale Pexiglass hydrodynamic model with ambient temperature water and heated water. Water was put in a model ladle on the top of the tundish and flowed into the pouring chamber of the tundish through the ladle shroud, then into the discharging chamber only by the induction channel illustrated in Figure 2. When the water levels in both the ladle and tundish in the hydrodynamic system were controlled to be stable for more than 20 min, the saturated KCl solution of 75 mL was injected as a pulse tracer at a side port mounted at the upper position of the ladle shroud; meanwhile, the conductivities of water at the submerged entry nozzle (SEN) of 1st–4th strands (the tundish is symmetrical; only four strands is enough) were online measured by a conductivity meter with a time interval of 1.0 s. All the conductivity data were collected by a recorder (DJ800, IWHR, Beijing, China) and input into a computer to obtain residence time distribution (RTD) curves, and then, these data were further processed to calculate the flow characteristics of fluid. Each experiment was repeated three times, and the characteristic parameters take their average values from the three times. The theoretical mean residence time (921.54 s) is calculated by [3]: ta =

Vm Qm

(9)

The actual average residence time is calculated by: N

∑ Cj (ti )×ti

tf, j =

i =1 N

∑ C j ( ti )

i =1

(10)

ti ∈ [0, 2ta ] For a specific strand j of the multi-strand tundish, Cj (ti ) is the molar concentration of the tracer measured in this strand at given time ti and tf, j is the actual average residence time of strand j (j = 1, 2, 3, 4). As for the whole tundish, the average residence time, tf , is the average value of four strands, in which C(ti ) is calculated by the average molar concentration of the tracers of four strands as: C ( ti ) =

1 4 C j ( ti ) 4 i∑ =1

(11)

According to the modified mixing model of flow [2,9], the volume fraction of plug flow V p , dead zone V d and well-mixed zone V m can be determined by: Vp = (tmin + tpeak )/2t a , Vd = 1 − tf /t a , Vm = 1 − Vp − Vd

(12)

where tmin is the minimum residence or breakthrough time of the tracer and tpeak is the time to attain the peak concentration.

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The flow consistency between strands is expressed by the standard deviation S in Equation (13) in this paper: v u n 2 u u ∑ (x j − x) t j =1 (13) S= n−1 where x j represents the measured value of strand j for a certain parameter, x is the averaged value of four strands and n is the total number of strands, n = 4. Herein, the standard deviations St f , Smin and Speak of the average residence time, minimum residence time and peak time were calculated, respectively, by the above equation. The smaller the value of S, the more consistent the fluid flowing among different strands. To observe the fluid flowing, the ink was added from the position where KCl was injected in the experiment, and its dispersion was recorded by the camera. 2.2.2. Schemes of the Physical Experiments (1)

Non-isothermal experimental work

The molten steel is heated when it flows through the induction channel. Various heating effects can be obtained by different electric powers. To observe the influences of induction heating on the liquid flow and temperature field, non-isothermal experiments with various temperature differences (∆T = 0, 5, 10, 20, 30 ◦ C) of fluid between inside and outside the induction channel were firstly carried out for the structure of the prototype tundish. Applying the ambient temperature water to model the molten steel without being heated in the tundish (outside the induction channel), various temperatures of hot water were injected from the induction channel inlet to simulate the effect of induction heating. The experimental scheme is given in Table 3. Table 3. Scheme of the non-isothermal experiment.

Case A0 A1 A2 A3 A4

(2)

Temperature Difference, ∆T/◦ C Prototype

Model

0 5 10 20 30

0 5.6 11.2 22.4 33.6

Isothermal experimental work

When the induction heating of the tundish runs for a period of time, the temperature difference of molten steel inside and outside the induction channel will reduce until it disappears. At that time, the molten steel in the tundish will tend to isothermal flow. In addition, the induction heating operation is usually used for some special steel grades such as bearing and spring steels for economical consideration. For normal steel grades, the heating function of channels will be kept in a power-off state. Under this case, the flow of molten steel through the channel is also isothermal. Therefore, for the structural optimization of a tundish with induction heating, the isothermal experiment of the hydrodynamic model is also of great necessity. In the present work, it is described by Part B and Part C, respectively. Figure 3 illustrates the top view of the tundish structure in Part B, in which the channel inclination and the height of the added dam h are chosen as variables. The degree of dam inclination is designed as 45◦ , and the distance from the right dam to the third outlet J is fixed as 750 mm. The experimental scheme is listed in Table 4.

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Figure 3. Top view of the optimization structure of the isothermal experiment Part B. Figure 3. 3. Top TopTable view of of the the optimization structureof ofexperiment theisothermal isothermal experiment PartB. B. Figure view optimization structure the experiment Part 4. Scheme of the isothermal Part B.

Case of (°) I (mm) h (mm) Table isothermal experiment Part Table4.4.Scheme Scheme of the the α isothermal experiment Part B. B. A0 (prototype) 5 300 0 Case α (°) I (mm) h (mm) 300 80h (mm) Case B1 α (◦5) I (mm) A0 (prototype) 5 300 0 B2 5 300300 160 0 A0 (prototype) 5 B1 5 300 80 160300 0 80 B1 B3 5−5 B2 5 300 160 B2 B4 5−5 160300 80 160 B3 −5 160 0 B3 B5 −5−5 160 160 160 0 B4 B4 −5−5 160 160 80 80 B6 10 440 0 B5 B5 −5−5 160 160 160 160 440440 80 0 B6 B7 1010 B6 10 440 0 B7 B8 1010 440440 160 80 B7 10 440 80 B8 B9 10 −10 160440 0 160 440 160 0 B9 B8 −1010 160 B10 −10 160 80 B10 B9 −10 160 −10 160 0 80 B11 −10 160 160 B11 B10 −10 160 −10 160 80 160 160160 0 B12 B12 00 0 B11 160 160 B13 B13 0−10 0 160160 80 80 B12 160 0 B14 B14 0 00 160160 160 160 B13 0 160 80 B14 0 160 160 In Part C, the height of the channel channel exit (I) was risen to 590 mm with 0° 0◦ of of inclination. inclination. Dams Dams were were symmetrically installed installed between between Outlets Outlets 22 and 3 and between Outlets 5 and 6 as in Figure 4. Choosing Choosing In Part C, the height of the channel exit (I) was risen to 590 mm with 0° of inclination. Dams were the distances (a) from Dam 1 to Outlet 3 and (b) from Dam 2 to Outlet 2 and the heights of the dams symmetrically installed between Outlets 2 and 3 and between Outlets 5 and 6 as in Figure 4. Choosing (c and d), as variables, the experimental scheme is in Table Table 5. 5. the distances (a) from Dam 1 to Outlet 3 and (b) from Dam 2 to Outlet 2 and the heights of the dams (c and d), as variables, the experimental scheme is in Table 5.

Figure Figure 4. 4. Front Front view view of of the the optimized optimized tundish tundish structure structure in in the the isothermal isothermal experiment experiment Part Part C. C. Figure 4. Front view of the tundish structure in the isothermal Table 5. optimized Scheme Part C. C. experiment Part C. Table 5. Scheme of of the the isothermal isothermal experiment experiment Part

Case I (mm) a (mm) b (mm) experiment c (mm) Part d (mm) Table 5. Scheme of the isothermal C. Case I (mm) a (mm) b (mm) c (mm) d (mm) C1 590 0 0 Case I (mm) a (mm) b (mm) c (mm) d (mm) C1 590 C2 590 -4500 0 245 0 C2C1 590 590 --450 00 0245 C3 590 225 0 245 C3C2 590 225 245 590 -450 00 245 C4 590 240 375 245245 510510 C4 590 240 375 C3 590 225 0 245 C5 590 240 375 510510 510510 C5 590 240 375 C4 590 240 375 245 510 C5 590 240 375 510 510

3. Mathematical Model

A mathematical model containing four main equations, as the continuity equation, momentum 3. Mathematical Model conservation equation, i.e., Navier-Stokes equation, the standard k-ε transport equations for the A mathematical model containing four main equations, as the continuity equation, momentum turbulent model and the energy conservation equation [15,16,18,19], has been developed to calculate conservation equation, i.e., Navier-Stokes equation, the standard k-ε transport equations for the turbulent model and the energy conservation equation [15,16,18,19], has been developed to calculate

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3. Mathematical Model A mathematical model containing four main equations, as the continuity equation, momentum conservation equation, i.e., Navier-Stokes equation, the standard k-ε transport equations for the turbulent model and the energy conservation equation [15,16,18,19], has been developed to calculate the flow field profiles and temperature profiles of molten steel in the prototype and optimized tundish under the non-isothermal and isothermal conditions at casting speed as 0.8 m/min for a billet section of 200 mm × 200 mm. 3.1. Control Equations The major governing equations are as follows: (1)

(2)

Continuity equation: ∂(ρui ) =0 ∂xi

(14)

∂u j ∂(ρui u j ) ∂p ∂ ∂u =− + [µe f f ( i + )] + ρgi ∂x j ∂xi ∂xi ∂x j ∂xi

(15)

Momentum conservation equation:

where ρ is the density, ui is the fluid velocity, µe f f is the effective viscosity, p is the pressure, gi is the gravitational accelerate and x represents the spatial coordinates for i and j directions. (3)

Turbulent equations:   ∂ µt ∂k ∂(ρkui ) = (µe f f + ) + G − ρε ∂xi ∂xi σk ∂xi

(16a)

  ∂(ρεui ) ∂ µt ∂ε ε2 ε = (µe f f + ) + C1 G − C2 ρ ∂xi ∂xi σε ∂xi k k

(16b)

where k is the turbulence kinetic energy and ε is the turbulent kinetic energy dissipation rate. σk and σε represent the Schmidt number for k and ε. The generation rate of turbulence energy G and effective viscosity µe f f is calculated as follows: G = µt

∂u j ∂ui ∂u j ( + ) ∂xi ∂x j ∂xi

µe f f = µ + µt = µ + ρCµ

k2 ε

(17)

(18)

The constants of the k-ε two-equation turbulence model are taken as: C1 = 1.44, C2 = 1.92, Cµ = 0.09, σk = 1.0, σε = 1.3. (4)

Energy equation:   ∂ ∂ ∂T (ρTui ) = Ke f f ∂xi ∂xi ∂xi

where T is the temperature and Ke f f is the effective thermal conductivity.

(19)

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Species transport equation: ∂ ∂C ∂ ∂C + (u C ) = ( De ) ∂t ∂xi i ∂xi ∂xi

(20)

where C is the concentration of the tracer and t is time. Under the flow field of fluid, the effective mass-diffusion coefficient De can be calculated as follows: µe f f ≈1 ρDe

(21)

3.2. Assumptions and Boundary Conditions 3.2.1. Main Assumptions (i)

Molten steel is treated as a three-dimensional steady incompressible viscous fluid. The physical properties of the molten steel such as density, viscosity, specific heat and thermal conductivity are shown in Table 6. (ii) The influences of slag layer and re-oxidation are ignored, and the slag-steel surface is treated as a free surface. The stopper rod is assumed to have no effect on the fluid flowing. (iii) The induction heating effect is simulated by changing the temperature of molten steel at the induction channel exit. Table 6. Physical properties of molten steel [23]. Parameters Density Viscosity Specific heat Thermal conductivity Mass diffusion coefficients of tracer

Data 8523–0.8358 T kg/m3 0.006 kg/(m·s) 750 J/(kg·K) 41 W/(m·K) 1.1 × 10−8 m2 /s

3.2.2. Boundary Condition and Solution Method The simulation domain includes the pouring chamber, channels and discharging chamber of the tundish. The velocity inlet boundary condition has been applied at the inlet of the tundish, and its value is determined to be 0.62 m/s by the operating parameters of the tundish. The outflow boundary condition is taken at the outlet, and the flow rate weighting of each outlet is set as one. The solid walls in the tundish are taken to be no-slip boundaries and near wall using a standard wall function. The heat loss of the tundish is caused by heat radiation and conduction. The values of heat flux through the slag layer, side walls, bottom wall and channel wall of the tundish are shown in Table 7. Table 7. Values of heat flux [23]. Parameters Slag layer Side wall Channel wall Bottom wall

Data, W/m2 15,000 4000 1200 1800

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The commercial CFD software FLUENT 14.5 (ANSYS, Pittsburgh, PA, USA, 2012) has been employed to perform the calculation, in which the velocity fields of the isothermal condition are calculated with the steady state solution, while those with induction heating are calculated with transient state solution. The SIMPLE algorithm is used for pressure velocity coupling in the momentum equation. The convergence criteria for scaled residuals are set to be less than 10−5 . Once the flow field is converged to steady state, the solver is converted to the transient state to solve the transient tracer dispersion. The injection time of tracers at the inlet is set as 1 s. After that, its concentration variation with time is computed at the outlet plane of the tundish to obtain the RTD curve. 3.3. Condition for Inclusions Behavior Simulation The movement of non-metallic inclusions in the molten steel has been simulated with the Euler-Lagrange approach. According to the law of action and reaction, the non-metallic inclusion suspended in the molten steel suffers various forces, such as gravity Fg , buoyancy Fb , drag Fd , lift Fl , added mass Fa and Brownian forces Fbrow [24]. The force balance of an inclusion in molten steel is expressed as: π dv p ρ p d3p = Fg + Fb + Fd + Fl + Fa + Fbrow (22) 6 dt where ρ p is the density of the inclusion, d p is its diameter and v p is movement velocity. To simplify the calculation, the inclusion is assumed to be an inert spherical solid with a constant density of 3900 kg/m3 , and its size will not change even if a collision happens; the motion of inclusions does not influence the macroscopic flow pattern. Considering the chaotic effect of the turbulent motion, the random walk model is applied to the calculation of the inclusion track. The inclusion is assumed to be removed only through the absorption of the slag layer. When it reaches the solid wall, a non-perfect elastic collision will occur [26–28]. Four particular sizes of inclusions of 5, 10, 30 and 50 µm in diameter and 70 in original number for every particle size are counted to compare their removal ratios. The removal ratio was calculated as the percentage trapped by the slag layer in the total number of inclusion particles for each particular size, which is described as: Inclusion removal ratio =

The number of inclusions trapped by slag Total number of inclusions

(23)

4. Results and Discussions 4.1. Results of the Non-Isothermal Experiment As the structure of the tundish is symmetric, half of its geometry, i.e., Strands 1–4 (corresponding to tundish Outlets 1–4 in Figures 2, 4 and 5), is investigated. In the non-isothermal experiment, the flow characteristics of fluid under the conditions of ∆T = 0, 5, 10, 20, 30 ◦ C were studied to reveal the influence of induction heating on fluid flow for the structure of the prototype tundish. Their characteristic parameters are presented in Table 8, in which tmin and tpeak represent the minimum breakthrough time and the peak concentration time of the whole tundish, while tmin,2 and tpeak,2 represent those of Strand 2, respectively; they are selected to compare with the whole tundish because the position of Strand 2 is close to the induction channel, and its flow has a large influence on the whole tundish. The tf ,Vp , Vm and Vd in Table 8 are parameters for the whole tundish. The typical RTD curves of these experimental cases are illustrated in Figure 5.

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Table 8. Characteristic parameters of non-isothermal experiment cases. Case

Case

A0 A0 A1 A1 A2 A3 A2 A4 A3 A4

tmin,2

Table 8. Characteristic parameters of non-isothermal experiment cases.

tpeak,2

tmin

tmin,2 (s)(s)

tpeak,2 (s) (s)

tmin (s)(s)

38 38 215 215 378 439 378 422

48 48 600 600 528 594 528 581

38 38 338 338 357 430 357 372

439 422

594 581

430 372

tpeak

tpeak (s) (s)

8080 555 555 528 661 528 624 661 624

tf

(s) tf (s)

501.27 501.27 914.28 914.28 893.32 986.71 893.32 1001.31 986.71 1001.31

Vp

Vm

V(%) p (%)

V(%) m (%)

Vd (%) (%)

6.41 6.41 48.48 48.48 48.05 59.23 48.05 52.61

48.02 48.02 50.79 50.79 48.95 40.77 48.95 47.39 40.77 47.39

45.57 45.57 0.73 0.73 3.01 0 3.01 0 0 0

59.23 52.61

Vd

Stf

Stf

91.01 91.01 63.94 63.94 21.12 7.40 21.12 7.58 7.40 7.58

Smin

Smin

61.39 61.39 71.33 71.33 21.00 55.45 21.00 30.47 55.45 30.47

S

peak Speak

88.15 88.15 32.33 32.33 15.53 31.64 15.53 30.79

31.64 30.79

Figure 5. 5. RTD RTDcurves curvesofofnon-isothermal non-isothermalexperiment experimentatatdifferent different ∆T: case 0 ◦(b) C; A1, (b) A1, Figure ΔT: (a)(a) case A0,A0, ΔT∆T = 0=°C; ◦ ◦ ◦ ◦ C; (c) (c) A2, A2, 10 10 °C; C;(d) (d)A3, A3, 20 20 °C; C;(e) (e)A4, A4,30 30°C. C. 55 °C;

t

t

From Table 8, the value of min,2 of Strand 2 is close to min of the whole tundish in most cases, verifying that the flow of Strand 2 has a large influence on the characteristics of the whole tundish.

t

For the condition of ΔT = 0 °C (case A0), min,2 is only 38 s. The reason can be explained by the RTD curves of Figure 5a. The peak concentration C/C0 of Strand 2 exceeds 4.5, much higher than other

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From Table 8, the value of tmin,2 of Strand 2 is close to tmin of the whole tundish in most cases, verifying that thePEER flowREVIEW of Strand 2 has a large influence on the characteristics of the whole tundish. Metals 13 Metals 2018, 2018, 8, 8, xx FOR FOR PEER REVIEW 13 of of 25 25 For the condition of ∆T = 0 ◦ C (case A0), tmin,2 is only 38 s. The reason can be explained by the RTD strands, shows sharp shape, which most directly from Outlet 2. curves Figure 5a. aaThe peak concentration C/C0 that of Strand 2 exceeds 4.5, flows much higher than other strands,ofand and shows sharp shape, which suggests suggests that most tracer tracer directly flows out out from Outlet 2. strands, and shows a sharp shape, which suggests that most tracer directly flows out from Outlet ttmin,2 ttpeak,2 V Vd is From Table 88 and Figure 5, and peak,2 of the other cases are greatly delayed, and the From Table and Figure 5, 5,min,2 2. From Table 8 and Figure tmin,2and and tpeak,2of ofthe theother othercases casesare are greatly greatly delayed, delayed,and and the the Vdd is obviously reduced when ΔT increases. The zones of cases A3 and A4 were wholly eliminated ΔT increases. The dead and A4 A4 were were wholly wholly eliminated eliminated obviously reduced when ∆T dead zones of cases A3 and

=0 Vd = =00. with their VV with their dd .. Comparing cases A1–A4, A1–A4, with the the increase of of ∆T, concentration C/C  T their dimensionless Comparing Comparing cases cases A1–A4, with with the increase increase of  T ,, their their dimensionless dimensionless concentration concentration C/C C/C000 decreases, and the RTD curves of four strands become more coincident. The standard deviations (S) in decreases, decreases, and and the the RTD RTD curves curves of of four four strands strands become become more more coincident. coincident. The The standard standard deviations deviations (S) (S) Table 8 are also relatively small for these cases. Tocases. explain the above phenomena, the ink dispersions in in Table Table 88 are are also also relatively relatively small small for for these these cases. To To explain explain the the above above phenomena, phenomena, the the ink ink of cases A0 and A4 were tracked as in Figures 6 and 7, respectively. dispersions of cases A0 and A4 were tracked as in Figures 6 and 7, respectively. dispersions of cases A0 and A4 were tracked as in Figures 6 and 7, respectively.

Figure 6. dispersion behavior in the prototype case A0: (a) 23 s, (b) 38 s, (c) 101 s, (d) 205 s. 6. Ink prototype case case A0: A0: (a) (c) 101 101 s, s, (d) (d) 205 205 s. s. Figure 6. Ink dispersion behavior in the prototype 23 s, (b) 38 s, (c)

Figure Figure 7. 7. Ink Ink dispersion dispersion behavior behavior in in the the case case A4: A4: (a) (a) 56 56 s, s, (b) (b) 76 76 s, s, (c) (c) 311 311 s, s, (d) (d) 585 585 s. s. Figure 7. Ink dispersion behavior in the case A4: (a) 56 s, (b) 76 s, (c) 311 s, (d) 585 s.

For For case case A0, A0, as as marked marked by by the the dashed dashed line, line, the the black black ink ink first first spreads spreads upwards upwards due due to to the the effect effect For case A0, as marked by the dashed line, the black ink first spreads upwards due to the effect of of the tilted channel (Figure 6a). At 38 s, part of the tracer disperses to the liquid surface, while of the tilted channel (Figure 6a). At 38 s, part of the tracer disperses to the liquid surface, while some some the tilted channel (Figure 6a). At 38 s, part of the tracer disperses to the liquid surface, while some reaches Outlet 2, generating “short-circuiting flow”. Under this circumstance, the molten steel can reaches Outlet 2, generating “short-circuiting flow”. Under this circumstance, the molten steel can stay aa short time tundish; inclusions in are sufficiently. The reaches Outlet 2, generating flow”. Under this thefloat molten steel can stay stay only only short time in in the the“short-circuiting tundish; thus, thus, the the inclusions in it itcircumstance, are not not able able to to float sufficiently. The only a short time inV the tundish; thus, the inclusions in it are not able to float sufficiently. The dead Vdd ) in case A0 reaches 45.57% (Table 8), suggesting that approximately half of the dead zone deadvolume zone volume volume ) inA0 case A0 reaches (Table 8), suggesting that approximately half of the zone (Vd ) in(( case reaches 45.57%45.57% (Table 8), suggesting that approximately half of the fluid in fluid in the tundish flows slowly. From Figure 6c,d, a little ink could be observed in the “middle fluid in theflows tundish flows slowly. From a little could in bethe observed the “middle the tundish slowly. From Figure 6c,d,Figure a little6c,d, ink could be ink observed “middleinzone” marked zone” marked the dash square, while concentrated on the right of the tundish. zone” marked as the red red dash square, while most most ink ink concentrated onthe thetundish. right side side offact the indicates tundish. as the red dash as square, while most ink concentrated on the right side of This St f Smin that the “middle zone”the is the main source of themain dead zone. Besides, the St f , SBesides, S min and SpeakSpresent This This fact fact indicates indicates that that the “middle “middle zone” zone” is is the the main source source of of the the dead dead zone. zone. Besides, the the t f ,, min 91.01,S61.39 and 88.15, respectively, showing that the flow characteristics among different strands have Speak peak present 91.01, 61.39 and 88.15, respectively, showing that the flow characteristics among and presentTherefore, 91.01, 61.39 and respectively, showingthe thatinner the flow characteristics among aand big difference. it is of 88.15, great necessity to optimize structure of the prototype different strands have a big difference. Therefore, it is of great necessity to optimize the inner different strands have a big difference. Therefore, it is of great necessity to optimize the inner tundish under the condition of ∆T = 0. structure of the prototype tundish under the condition of ΔT = 0. structure of thefrom prototype tundish theA4 condition of ΔT = 0. Different case A0, the inkunder in case firstly floats towards the liquid surface following the Different A0, ink towards the surface following the Different from case A0, the the (Figure ink in in case case A4 firstly floats towards the liquid liquid surface following the hot water flowfrom fromcase the channel 7a) A4 duefirstly to thefloats driving of buoyancy, which is called “upward hot water flow from the channel (Figure 7a) due to the driving of buoyancy, which is called “upward hot water theand channel (Figure 7a) due to liquid the driving of (Figure buoyancy, is called “upward flow”, andflow thenfrom gathers spreads out the whole surface 7b);which no short-circuiting flow flow”, then gathers and the liquid surface 7b); no flow”, and and then gathersOwing and spreads spreads out the whole whole liquidthe surface (Figure 7b);stay no short-circuiting short-circuiting flow occurs in this process. to theout density difference, cold(Figure flow will at the bottom offlow the occurs occurs in in this this process. process. Owing Owing to to the the density density difference, difference, the the cold cold flow flow will will stay stay at at the the bottom bottom of of the the tundish. When the hot flow gathers to a certain degree, it gradually sinks (Figure 7c) due to the heat tundish. When the hot flow gathers to a certain degree, it gradually sinks (Figure 7c) due to the heat exchange exchange with with the the cold cold flow flow at at the the interface, interface, until until the the whole whole tundish tundish is is filled filled up up with with ink ink (Figure (Figure 7d). 7d).

t

tmin,2 During During this this period, period, the the ink ink takes takes aa longer longer time time before before reaching reaching Outlet Outlet 2; 2; thus, thus, the the min,2 is is significantly significantly prolonged, prolonged, compared compared with with case case A0. A0. Moreover, Moreover, the the hot hot flow flow can can fill fill up up the the whole whole tundish tundish

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tundish. When the hot flow gathers to a certain degree, it gradually sinks (Figure 7c) due to the heat exchange with the cold flow at the interface, until the whole tundish is filled up with ink (Figure 7d). During this period, the ink takes a longer time before reaching Outlet 2; thus, the tmin,2 is significantly prolonged, compared with case A0. Moreover, the hot flow can fill up the whole tundish (Figure 7d); thus the Vd of case A4 is equal to 0.0. With the decrease of ∆T, the effect of buoyancy on hot flow reduces; thus the thermal exchange between hot flow and cold flow becomes fast, which makes tmin of cases A1 and A2 shorter than case A4. 4.2. Results of the Isothermal Experiment (1) Part B The flow characteristic parameters of isothermal experiment Part B are presented in Table 9, and their RTD curves are shown in Figure 8. Comparing prototype case A0 (channel inclination 5◦ ) with B3 (−5◦ ), B6 (10◦ ), B9 (−10◦ ) and B12 ◦ (0 ), their tmin,2 remains at appropriately 40 s, indicating that the channel inclination angle has less effect on the flow of strand 2. This is because the distance from the channel exit to Outlet 2 is short; only varying of the channel angle is not enough to change the flow trajectory of fluid. Comparing the tmin and V d of these cases with different dam heights at a constant channel inclination, such as cases A0–B2, B3–B5, B6–B8, B9–B11 and B12–B14, as in Figure 9, it is seen that 160 mm of dam has a better effect on prolonging tmin than 80 mm of dam except for case B8 (α = 10◦ , I = 440 mm, h = 160 mm). Figure 10 shows the ink dispersion behavior of case B8. As the dam is lower, the ink from the channel can pass across the dam and reaches the second outlet as in Figure 10b,c. This result indicates that the flow characteristics of the fluid can be optimized by elevating the heights of dam and induction channel. In addition, the V d of cases B1–B14 remains at 37.19–53.18% (Figure 9b); no obvious improvement in V d has been shown, compared with the prototype structural case A0 (V d = 45.57%). For this reason, the other schemes for the optimization of the tundish have been presented with an elevated channel and dam, which is given in the following experiment Part C. (2) Part C The flow characteristic parameters in isothermal experiment part C are shown in Table 10, and their RTD curves are in Figure 11. Table 9. Flow characteristic parameters in isothermal experiment Part B. Case

tmin,2 (s)

tpeak,2 (s)

tmin (s)

tpeak (s)

tf (s)

Vp (%)

Vm (%)

Vd (%)

Stf

Smin

Speak

A0 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14

38 39 49 40 40 48 38 40 36 33 45 63 36 40 49

48 57 84 54 67 82 47 57 53 53 71 98 55 66 75

38 40 51 43 41 52 39 41 36 34 46 61 37 41 49

80 102 127 102 110 156 93 119 191 72 116 161 103 126 140

501.27 475.82 545.97 568.15 572.61 569.15 529.57 521.41 525.22 578.56 544.40 573.35 500.36 445.86 431.24

6.41 7.71 9.69 7.90 9.45 11.29 7.17 8.71 9.69 5.75 8.79 12.08 8.31 9.07 10.26

48.02 43.77 49.59 53.79 52.73 50.51 50.33 47.90 49.59 57.06 50.31 50.17 45.18 39.24 36.56

45.57 48.52 40.72 38.31 37.82 38.20 42.50 43.39 40.72 37.19 40.90 37.57 46.51 51.59 53.18

91.01 21.18 69.56 147.22 312.93 61.22 44.05 50.19 66.15 155.29 213.2 17.49 220.07 175.16 41.10

61.39 25.41 29.84 80.03 44.92 38.66 31.58 30.70 36.01 44.51 49.07 36.95 82.61 32.98 32.59

88.15 35.72 28.52 161.50 39.72 26.89 67.17 71.87 72.77 85.68 55.05 37.10 130.19 29.97 30.66

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Figure 8. Cont.

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Figure 8. RTD curves of isothermal experiment Part B: (a–n) correspond to cases B1–B14. Figure 8. RTD curves of isothermal experiment Part B: (a–n) correspond to cases B1–B14. Figure 8. RTD curves of isothermal experiment Part B: (a–n) correspond to cases B1–B14.

Figure 9. Comparison of the minimum break through time (a) and the volume of dead zone (b) in isothermal experiments. Figure 9. Comparison of the minimum break through time (a) and the volume of dead zone (b) in Figure 9. Comparison of the minimum break through time (a) and the volume of dead zone (b) in isothermal experiments. isothermal experiments.

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Figure 10. Ink dispersion behavior in case B8: (a) 30 s, (b) 68 s, (c) 95 s, (d) 309 s.

Figure dispersionbehavior behavior in in case (b)(b) 6868 s, (c) 95 s, Figure 10. 10. InkInk dispersion case B8: B8:(a) (a)3030s, s, s, (c) 95(d) s, 309 (d) s. 309 s.

Table 10. Flow characteristic parameters of tundish in isothermal experiment Part C. Table 10. Flow characteristic parameters of tundish in isothermal experiment Part C. Case Case

tmin,210. Flow tpeak,2characteristic tpeak Vp in isothermal tmin parameters Vm Vexperiment t fof tundish Table d S Part C. tmin,2

tpeak,2

tmin

tpeak

46 37 37 62 62 83 83 92 92

218 218 94 9494 176 176 176 171171 171 212212

(s) (s) (s) (s) (s) tpeak(s) (s) Case tmin,2 (s) (s)tpeak,2 (s)(s) tmin (s) C1 46 65 46 218 C1 C2 C3 C4 C5

C1 46 C2 C2 36 C3 C3 42 C4 C4 82 C5 77 C5

46 36 36 42 42 82 82 77 77

65 65 62 62 62 127 127 127 167 167 167 252 252

252

46 37 62 83 92

212

tf

Vp

(s) (s) tf (s)

636.42

(%) Vp(%) (%)

636.42 636.42 652.80 652.80 652.80 617.82 617.82 617.82 656.23 656.23 656.23 779.03 779.03 779.03

14.33 14.33 7.11 7.11 7.11 12.92 12.92 12.92 13.79 13.79 13.79 16.50 16.50 16.50

14.33

Vm

(%) (%) V m (%)

54.77 54.77 54.77 63.77 63.77 63.77 54.16 54.16 54.16 57.46 57.46 57.46 68.09 68.09 68.09

Vd

tf

Smin

Speak

St f Smin Speak (%) (%) S S Vd (%) 30.90 82.58 tf57.47 Smin 109.22 peak

30.90 57.47 57.47 109.22 30.90 82.58 29.12 70.0382.58 51.68 106.87109.22 29.12 70.03 51.68 106.87106.87 29.12 70.03 51.68 32.92 22.5 46.39 35.81 32.92 22.5 22.5 32.92 46.39 46.39 35.81 35.81 28.74 30.27 33.22 33.22 28.74 76.0176.01 28.74 76.01 30.27 30.27 33.22 15.41 42.70 42.70 38.40 38.40 15.41 42.6742.67 15.41 42.67 42.70 38.40

Figure 11. RTD curves of isothermal experiment Part C: (a–e) represent cases C1–C5.

Figure 11. RTD curves of isothermal experiment Part C: (a–e) represent cases C1–C5. Figure 11. RTD curves of isothermal experiment Part C: (a–e) represent cases C1–C5.

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tmin,2 , tpeak,2 and tf of case C1 (α = 0°, I = 590 mm,

without dam) are delayed by 8 s, 17 s and 135.15 s, respectively; the

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Vd

is decreased to 30.90% and

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of 25 the prototype case the A0, peak the tconcentration tf ofstrand case C1 = 0°, I =curves 59018mm, Vp isCompared min,2 , tpeak,2 and increased with to 14.33%. Meanwhile, of every in(α the RTD is

Vd isbefore reduced, which tracer spread for a periodthe of time it flows out of and the without dam) areindicates delayed that by 8the s, 17 s andhas 135.15 s, respectively; decreased to 30.90% ◦ , I = 590 mm, Compared with the prototype case A0, the t , t and t of case C1 (α = 0 min,2 peak,2 f tundish. The dispersion behavior of ink in this case is shown in Figure 12. Due to the elevation of the Vp is increased to delayed 14.33%. by Meanwhile, the 135.15 peak concentration of every in the to RTD curves is without dam) are s, 17far s and s, respectively; Vd strand isliquid decreased induction channel, the tracer 8goes from Outlet 2 and closer the to the surface, 30.90% which and will reduced, which the tracer has spread for period ofdistance time before flows of the Vp is increased toindicates 14.33%. Meanwhile, the peak concentration of every strand RTDout curves is prolong its residence time that in the tundish and shorten the afloatation of in itthe tundish. The dispersion behavior of ink in this case is shown in Figure 12. Due to the elevation of reduced, which indicates that the tracer has spread for a period of time before it flows out of the non-metallic inclusions. inductionThe channel, the tracer goes far from and closer to the whichofwill tundish. dispersion behavior of ink in thisOutlet case is2shown in Figure 12. liquid Due tosurface, the elevation the prolong itschannel, residence ingoes the tundish shorten floatation distance of which will prolong induction thetime tracer far fromand Outlet 2 andthe closer to the liquid surface, non-metallic inclusions. its residence time in the tundish and shorten the floatation distance of non-metallic inclusions.

Figure 12. Ink dispersion behavior in case C1: (a) 25 s, (b) 49 s, (c) 106 s, (d) 321 s.

From the RTD curves, the peak concentration of Strand 2 is further reduced by cases C2 (one Figure 12. Ink dispersion behavior case C1: Outlet (a) 49 s, (d) 321 s. C3 (α = 0°, I = dam) and C3 (one dam), due to the dam’s setin between and cases. Figure 12. Ink dispersion behavior in case C1: (a) 25 25 s, s,2(b) (b) 49 Outlet s, (c) (c) 106 1063.s, s,The (d) 321 590 mm, b = 225 mm, d = 245 mm) has a little advantage over case C2 in improving fluid flow of the From the RTD curves, the peak concentration of Strand 2 is further reduced by cases C2 (one tundish because of curves, the closer from this dam to Outlet 2. Compared with case A0, the tdam) From the RTD thedistance peak concentration of Strand 2 is further reduced by cases C2 (one min,2 dam) and C3 (one dam), due to the dam’s set between Outlet 2 and Outlet 3. The case C3 (α = 0°, I= ◦ and C3 (one dam), due to the dam’s set between Outlet 2 and Outlet 3. The case C3 (α = 0 , I = 590 mm, t and of case C3 are delayed by 4 s and 79 s, respectively; the flow of each strand becomes more 590 mm, b = 225 mm, d = 245 mm) has a little advantage over case C2 in improving fluid flow of the peak,2 b = 225 mm, d = 245 mm) has a little advantage over case C2 in improving fluid flow of the tundish tundish because ofS the distance from this dam to Outlet 2. Compared with case A0, the t min,2 Scloser Speak consistent reduced. because of as thethe closer from thisare dam to Outlet 2. Compared with case A0, the tmin,2 and tpeak,2 t , distance min and t of case C3 are delayed by 4 s and 79 s, respectively; the(α flow strand more and From of case delayed 4 s and 79 s, respectively; each more peak,2 Table tmin,2 tpeak,2 9, C3 theare and by of cases C4 = 0°,ofI each =the 590flow mm,ofabecomes = 240strand mm, bbecomes =consistent 375 mm, cas= the St , Smin and Speak are reduced. S , Smin consistent as the mm) and(α S=peak reduced. 245 mm, = 510 C5 Iare = 590 mm, aC4 = 240 375 mm, mm, ac = = 510 Fromd Table 9,t theand tmin,2 and 0°, tpeak,2 of cases (α =mm, 0◦ , Ib== 590 240 mm, mm, db ==510 375 mm) mm, are delayed to a larger extent than cases C1–C3 when double dams are set between Outlet 2 and ◦ c = 245 mm, d =9,510 (α =of0 cases , I =C4 590(αmm, 240mm, mm,a =b 240 = 375 mm, = 510 tmin,2and tpeak,2 From Table themm) andC5 = 0°, aI ==590 mm, b = c375 mm,mm, c= tmin,2dams tpeak,2 Outlet andare the delayed Vd is further decreased. casewhen A0, the and are case C5 d = 5103,mm) to a larger extentCompared than caseswith C1–C3 double setofbetween 245 mm, d = 510 mm) and C5 (α = 0°, I = 590 mm, a = 240 mm, b = 375 mm, c = 510 mm, d = 510 mm) Outlet 2 and to Outlet 3, and the further decreased. Compared withare case the tmin,2 and t2peak,2 d is Vp is reduced are delayed delayed bya 39 s and 204Vthan s, respectively, and the by 30.16%. Moreover, the larger extent cases C1–C3 when double dams setA0, between Outlet and of case C5 are delayed by 39 s and 204 s, respectively, and the Vp is reduced by 30.16%. Moreover, Outlet 3, andofthe Vd is further decreased. Compared with case theS t min,2 and tpeak,2 of case C5 consistency every flow with theA0, to the consistency of every flowisisalso alsoobviously obviously improved improved with the St S ,S andand SpeakSreducing to 42.67, t ,min min peak reducing

VpStrand 42.70 and respectively. the C/C of Strand andand Strand No.No. 2Moreover, is2reduced to are delayed by 38.40, 39 s and 204Ins,addition, respectively, and the is No.1 reduced by Strand 30.16%. the 42.67, 42.7038.40, and respectively. In addition, the 0C/C 0 of No.1 is reduced below 1.5,1.5, farfar lower than thethe 4.74.7 inin case to below lower than caseA0. A0.The Theink inkdispersion dispersionbehavior behavior in in case case C5 C5 is is shown in consistency of every flow is also obviously improved with the St , Smin and Speak reducing to Figure 13. When When itit flows flowsout outfrom fromthe thechannel, channel,Dam Dam22stops stopsthe theink inkfrom fromdirectly directlyflowing flowingtotoOutlet Outlet2 42.67, 42.70 and 38.40, respectively. In addition, the C/C 0 of Strand No.1 and Strand No. 2 is reduced 2 (Figure13b), 13b),while whileDam Dam1 1guides guidesitittotothe the“middle “middlezone” zone”ofofthe thetundish tundishnear nearOutlet Outlet 44 (Figure (Figure 13c). 13c). (Figure to below far lower than the to 4.7inclusion in case A0. The ink dispersion case C5 shown in This flow 1.5, pattern will contribute removal in steel; thus, it isinchosen as is contribute removal in molten molten steel;behavior the optimal Figure 13. it flows out from the channel, Dam 2 stops the ink from directly flowing to Outlet 2 solution forWhen the improvement of the industrial tundish. industrial tundish. (Figure 13b), while Dam 1 guides it to the “middle zone” of the tundish near Outlet 4 (Figure 13c). This flow pattern will contribute to inclusion removal in molten steel; thus, it is chosen as the optimal solution for the improvement of the industrial tundish.

Figure 13. Ink C5: (a) 226 s. s. Figure 13. Ink dispersion dispersion behavior behavior in in case case C5: (a) 33 33 s, s, (b) (b) 79 79 s, s, (c) (c) 135 135 s, s, (d) (d) 226

Figure 13. Ink dispersion behavior in case C5: (a) 33 s, (b) 79 s, (c) 135 s, (d) 226 s.

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4.3. Results of Mathematical Simulation 4.3. 4.3. Results Results of of Mathematical Mathematical Simulation Simulation (1) Mathematical Model Verification (1) Mathematical Mathematical Model Model Verification Verification (1) Figure 14 shows the comparison of RTD curves of case A0 in the numerical calculation and Figure 14 14 shows shows the the comparison comparison of of RTD RTD curves curves of of case A0 A0 in in the the numerical numerical calculation calculation and and Figure physical experiment. Obviously, their profiles and thecase peak concentrations generally remain physicalexperiment. experiment.Obviously, Obviously, profiles and theconcentrations peak concentrations generally remain physical theirtheir profiles andbehavior the peak remain consistent. consistent. The comparison of tracer dispersion is presented ingenerally Figure 15. The flow wave consistent. The comparison of tracer dispersion behavior is presented in Figure 15. The flow wave The comparison of tracer dispersion behavior is presented in Figure 15. The flow wave profiles are profiles are pretty similar at both 38 s and 101 s, which also suggests the effectiveness of the profiles are pretty similar at both 38 s and 101 s, which also suggests the effectiveness of the pretty similar at both 38 s and 101 s, which also suggests the effectiveness of the mathematical model. mathematical model. mathematical model.

Figure 14. Comparison of RTD curves of case A0 between simulation (a) and experiment (b). Figure Figure 14. 14. Comparison Comparison of of RTD RTD curves curves of of case case A0 A0 between between simulation simulation (a) (a) and and experiment experiment(b). (b).

Figure 15. Tracer dispersion comparison between experiment (upper) and simulation (below) for Figure Figure 15. 15. Tracer Tracerdispersion dispersioncomparison comparisonbetween betweenexperiment experiment(upper) (upper)and andsimulation simulation(below) (below)for forcase case A0: (a) 38 s, (b) 101 s. A0: 38(a) s, (b) case(a) A0: 38 s,101 (b)s.101 s.

(2) (2) (2)

Velocity Field and Temperature Field with Induction Heating Velocity Field and Temperature Field with Induction Heating Velocity Field and Temperature Field by with Although the “upward flow” caused theInduction inductionHeating heating is beneficial for the improvement Although the “upward flow” caused by the induction heating is beneficial for the improvement of flow field as indicated in the physical experiments, however, weisdo not know long it will last Although the “upward flow” caused by the induction heating beneficial forhow the improvement of of flow field as indicated in the physical experiments, however, we do not know how long it will last with the heating. The temperature difference of fluid inside and outside the channel will decrease as flow field as indicated in the physical experiments, however, we do not know how long it will last with with the heating. The temperature difference of fluid inside and outside the channel will decrease as the at the same electricofpower, whichand mayoutside lead tothe a decayed flow”. To the heating heating.proceeds The temperature difference fluid inside channel “upward will decrease as the the heating proceeds at the same electric power, which may lead to a decayed “upward flow”. To clarify the change, the velocity field and temperature field of fluid in case A1 (ΔT = 5 °C) after heating heating proceeds thevelocity same electric power, which may lead to a decayed “upward Toheating clarify clarify the change,atthe field and temperature field of fluid in case A1 (ΔT = 5 flow”. °C) after ◦ C) after 100 s, 500 s the andvelocity 5000 s at theand same electric power were simulated in(∆T the=present study. Figure the change, field temperature field of fluid in case A1 5 heating 10016 s, 100 s, 500 s and 5000 s at the same electric power were simulated in the present study. Figure 16 shows the5000 comparison of velocity field of the molten steel ininthe vertical planes passing through the 500 s and s at the same electric power were simulated the present study. Figure 16 shows the shows the comparison of velocity field of the molten steel in the vertical planes passing through the center of theof channel (Figure all the Figure 17 through is the comparison comparison velocity field of16a) the and molten steeloutlets in the (Figure vertical 16b). planes passing the center of of the the center of the channel (Figure 16a) and all the outlets (Figure 16b). Figure 17 is the comparison of the temperature field16a) of the all the at different moments. channel (Figure andvertical all the plane outletspassing (Figurethrough 16b). Figure 17outlets is the comparison of the temperature temperature field of the vertical plane passing through all the outlets at different moments. outflow angle of molten steelallbythe theoutlets induction channelmoments. exit, it is obvious that the rising field From of thethe vertical plane passing through at different From the outflow angle of molten steel by the induction channel exit, it is obvious that the rising trendFrom of “upward flow” is weakened with time (Figure 16a). Due to the impact strong “upward the outflow of molten the induction exit, of it the is that the trend of “upward flow”angle is weakened withsteel timeby (Figure 16a). Due channel to the impact of theobvious strong “upward flow”, several inisthe tundish at 100time s (Figure 16b), and thetotemperature of rising trend ofvortexes “upwardform flow” weakened with (Figure 16a). Due the impact difference of the strong flow”, several vortexes form in the tundish at 100 s (Figure 16b), and the temperature difference of molten steel from the tundish bottom to the top is larger (Figure 17); the lower temperature zones “upward flow”, several vortexes form to inthe thetop tundish at 100 s (Figure 16b), andtemperature the temperature molten steel from the tundish bottom is larger (Figure 17); the lower zones (1786–1788 K) occupy a larger area. However, with thetop extension of heating time, the area shrinks. difference of molten steel from the tundish bottom to the is larger (Figure 17); the lower temperature (1786–1788 K) occupy a larger area. However, with the extension of heating time, the area shrinks. When the heating K) time reaches 5000 area. s, the zone below 1791 disappears, and thetime, temperature zones occupy a larger with theKK extension of heating the area When (1786–1788 the heating time reaches 5000 s, theHowever, zone below 1791 disappears, and the temperature difference of the whole tundish decreases. Under this circumstance, the rising trend of “upward shrinks. When the whole heatingtundish time reaches 5000 s,Under the zone 1791 K disappears, the temperature difference of the decreases. thisbelow circumstance, the risingand trend of “upward flow” will of weaken, andtundish the fluid in the tundish will gradually transform intotrend an isothermal flowing difference the whole decreases. Under this circumstance, the rising of “upward flow” flow” will weaken, and the fluid in the tundish will gradually transform into an isothermal flowing mode. This also suggests that the electric power of induction heating in industrial practice needs to will weaken, andsuggests the fluidthat in the gradually transform intoinanindustrial isothermal flowing mode. mode. This also thetundish electricwill power of induction heating practice needs to be modified after running a period of time in order to obtain the “upward flow”. be modified after running a period of time in order to obtain the “upward flow”.

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This also suggests that the electric power of induction heating in industrial practice needs to be Metals 2018, 8, x FOR PEER REVIEW 20 of 25 modified after running a period of time in order to obtain the “upward flow”.

Figure16. 16.Velocity Velocity fields vertical planes case A1:(a)(a)vertical verticalplane planepassing passingthrough throughthe thecenter centerofof Figure fields ofof vertical planes ofof case A1: channel; (b) vertical plane passing through all the outlets. channel; (b) vertical plane passing through all the outlets.

(3) Flow Field without Induction Heating The hydrodynamic results of experiment have indicated that the cases C1–C5 have a beneficial effect on the optimization of the flow field of the tundish, and thus, part of them is taken hereby for discussion. The velocity fields of the front side plane (the plane passing through the inner boundary

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Flow Field without Induction Heating

The hydrodynamic results of experiment have indicated that the cases C1–C5 have a beneficial effect on the optimization of the flow field of the tundish, and thus, part of them is taken hereby for Metals 21 Metals2018, 2018,8, 8,xxFOR FORPEER PEERREVIEW REVIEW 21of of25 25 discussion. The velocity fields of the front side plane (the plane passing through the inner boundary “A” of the in Figure 2b2b and perpendicular to thebottom bottomsurface) surface) of cases C1 C5 and C5 are “A” of the in and perpendicular of A0, C1 “A” oftundish the tundish tundish in Figure Figure 2b and perpendicular to to the the bottom surface) ofcases cases A0,A0, C1 and and C5 are are compared in Figure 18 and those of the bottom surface of these cases in Figure 19. compared in Figure 18 and those of the bottom surface of these cases in Figure 19. compared in Figure 18 and those of the bottom surface of these cases in Figure 19.

Figure Temperature fields of vertical through all the outlets. Figure 17. Temperaturefields fieldsof ofvertical verticalplane plane passing passing through allall thethe outlets. Figure 17.17. Temperature plane passing through outlets.

Figure 18. Velocity fields of the front side plane: (a) case A0, (b) C1, (c) C5.

Figure 18. Velocity fields of the front side plane: (a) case A0, (b) C1, (c) C5. Figure 18. Velocity fields of the front side plane: (a) case A0, (b) C1, (c) C5.

Figure Velocity fields the bottom A0, (b) C1, (c) Figure 19.19. Velocity fields surface:(a) (a)case case A0, (c) C5. Figure 19. Velocity fieldsofof ofthe thebottom bottomsurface: surface: (a) case A0, (b)(b) C1,C1, (c) C5. C5.

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As shown in Figures 18 and 19, different cases present various velocity fields in both the front As shown in Figures 18 and 19, different cases present various velocity fields in both the front side surface and bottom surface. In the prototype case A0, the fluid from the channel exit partly flows side surface and bottom surface. In the prototype case A0, the fluid from the channel exit partly flows upwards to the top surface of the tundish and diffuses to the space between Outlet 1 and Outlet 2, upwards to the top surface of the tundish and diffuses to the space between Outlet 1 and Outlet 2, while the other arrives at the front side surface between Outlet 2 and Outlet 3, then directly flows to while the other arrives at the front side surface between Outlet 2 and Outlet 3, then directly flows to Outlet 2 at a speed of appropriately 0.03 m/s, which will generate the “short-circulating flow” at Outlet 2 at a speed of appropriately 0.03 m/s, which will generate the “short-circulating flow” at Outlet Outlet 2. The velocity of fluid between Outlet 3 and Outlet 4 is very small, being below 0.01 m/s. 2. The velocity of fluid between Outlet 3 and Outlet 4 is very small, being below 0.01 m/s. In case C1, the velocity of fluid is around 0.02 m/s when it flows to Outlet 2 (Figure 18b), In case C1, the velocity of fluid is around 0.02 m/s when it flows to Outlet 2 (Figure 18b), generally generally slower than case A0 due to the elevation of the induction channel exit. Additionally, the slower than case A0 due to the elevation of the induction channel exit. Additionally, the fluid has fluid has a greater tendency to flow upward and forms the clockwise circulation in the upper region a greater tendency to flow upward and forms the clockwise circulation in the upper region of Outlet 1 of Outlet 1 and Outlet 2 (Figure 18b). For case C5, because of the obstacle of Dam 2, most fluid does and Outlet 2 (Figure 18b). For case C5, because of the obstacle of Dam 2, most fluid does not directly not directly flow to Outlet 2, while it flows upwards firstly through Dam 2, then downwards to the flow to Outlet 2, while it flows upwards firstly through Dam 2, then downwards to the tundish tundish interior as shown in Figure 18c. The result is in agreement with the ink modelling in interior as shown in Figure 18c. The result is in agreement with the ink modelling in Figure 13. Figure 13. This flow pattern will prolong the residence time of the molten steel and shorten the This flow pattern will prolong the residence time of the molten steel and shorten the floating distance floating distance of non-metallic inclusions, as well as further improve the cleanliness of molten steel. of non-metallic inclusions, as well as further improve the cleanliness of molten steel. 4.4. Inclusion Removal Behavior 4.4. Inclusion Removal Behavior Toassess assessthe theoptimized optimizedtundish tundishstructure structureand andthe theeffect effectofofinduction inductionheating heatingon onthe thenon-metallic non-metallic To inclusions, the removal ratios of different sizes of inclusions in cases A0, C1, C3, C4, C5 and A4 (with inclusions, the removal ratios of different sizes of inclusions in cases A0, C1, C3, C4, C5 and A4 induction heating) were simulated, and the results are presented in Figure 20. (with induction heating) were simulated, and the results are presented in Figure 20.

Figure 20. Comparison of removal ratios of different sizes of inclusions under various cases. Figure 20. Comparison of removal ratios of different sizes of inclusions under various cases.

It is seen that the removal ratio of inclusions generally increases with its increasing size. For the It is seen that the removal ratio inclusions generally increases with its increasing size.60%. For the cases without induction heating, theofremoval ratios of 5 and 10 μm of inclusions are below The cases without induction heating, the removal ratios of 5 and 10 µm of inclusions are below 60%. reason can be explained by the Stokes law [29]. The smaller the inclusion size is, the slower the speed The reason can explained to remove frombethe tundish.by the Stokes law [29]. The smaller the inclusion size is, the slower the speedComparing to remove from tundish. thesethe cases, the removal effect of cases C3 and C5 is generally superior to C1 and C4, Comparing these cases, the removal effect of cases C3dam and prolongs C5 is generally superiortime to C1ofand C4, and obviously superior to case A0, as the setting of the the residence molten and superior case A0, the setting of the dam prolongs the residence time of molten steelobviously in the tundish andto shortens itsasfloating distance. steel in the tundish and shortens its floating distance. To further explain the removal mechanism of different particle sizes of inclusions, their motion Tolines further explain the removal particle sizes of their track in case A0 were simulatedmechanism and shownof indifferent Figure 21. The number ofinclusions, track lines in themotion channel track lines in case A0 were simulated and shown in Figure 21. The number of track lines in the channel is fixed as 25 for every particle size. is fixed 25 for every size. vary after outflowing from the channel. The inclusions of 50 μm It as is obvious that particle their motions It ismove obvious that their vary after and outflowing the channel. Thelayer; inclusions µm in in size upwards to motions the liquid surface will befrom trapped by the slag thus, of its50removal size move upwards to the liquid surface and will be trapped by the slag layer; thus, its removal ratio ratio is higher than the other sizes. However, for the inclusions in 5 and 10 μm, although some isof higher thanarrive the other However, for thesteel, inclusions in 5again and 10 µm, to although some of them them can at thesizes. top surface of molten they will return the molten steel if thecan slag arrive at the top surface of molten steel, they will again return to the molten steel if the slag cannot cannot absorb them quickly and effectively, from Figure 21c,d. Moreover, some of them cannot float absorb quicklywhich and effectively, from Figure Moreover, some of directly them cannot float 2to(without the top to the them top surface, may be driven by the 21c,d. “short-circulating flow” to Outlet surface, may be driven by the “short-circulating flow” directly Outlet 2 (without dam in case dam in which case A0). This is also the reason why the removal ratios of 5- to and 10-μm inclusions in case A0 are lower than those in cases C3–C5 with dams.

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A0). This is also the reason why the removal ratios of 5- and 10-µm inclusions in case A0 are lower Metalsthose 2018, 8,inx cases FOR PEER REVIEW 23 of 25 than C3–C5 with dams.

Figure 21. Path of different sizes of inclusions in case A0: (a) 50 µm, (b) 30 µm, (c) 10 µm, (d) 5 µm. Figure 21. Path of different sizes of inclusions in case A0: (a) 50 μm, (b) 30 μm, (c) 10 μm, (d) 5 μm.

From thethe removal ratioratio of every particle size of inclusions can be significantly improved FromFigure Figure21,21, removal of every particle size of inclusions can be significantly by induction (case A4), (case especially for small-sized inclusions. The removal ratios ofratios 5- and improved by heating induction heating A4), especially for small-sized inclusions. The removal of 10-µm inclusions exceed 80%, while 50-µm inclusions are removed almost completely. This is due 5- and 10-μm inclusions exceed 80%, while 50-μm inclusions are removed almost completely. This is to theto“upward flow” fromfrom induction heating directly carrying these inclusions to the toptop surface of due the “upward flow” induction heating directly carrying these inclusions to the surface the tundish and making them entrapped by the slag. The above studies also indicate that the inner of the tundish and making them entrapped by the slag. The above studies also indicate that the inner structure structureof ofthe thetundish tundishnot not only onlyaffects affects the the flowing flowing of of molten molten steel, steel, but but also also the removal removal of inclusions; thus, thus,ititisisof ofgreat greatnecessity necessityto tooptimize optimizeit. it. ItIt should be pointed out that the calculated should be pointed out that the calculated values valuesof of the the removal removalratios ratiosof of inclusions inclusionsin in number number may may be be larger larger than than the the actual actual due duetotothe thesimplified simplifiedmodel modelassumption. assumption. The The removal removal process process of of inclusions consists of ofthree threelinked linkedsteps, steps, which growing, floating up and separating. inclusions mainly consists which areare growing, floating up and separating. The The separating process, as the step inclusion removal,isiseven eventhe therestrictive restrictivelink link in in many many cases. separating process, as the lastlast step of of inclusion removal, This This process process isis closely closely related related to to the thespeed speed of ofinclusions inclusions floating floating to to the the slag, slag, the the interfacial interfacial tension tension between inclusions and the slag layer and the physical and chemical performances of the slag [30–33]. between inclusions and the slag layer and the physical and chemical performances of the slag [30– In our study,study, these factors have not been taken into consideration. We assume the inclusion 33]. Inpresent our present these factors have not been taken into consideration. Wethat assume that the will be removed long as as it reaches the free surface; the removal might be might larger be than the inclusion will beas removed long as it reaches the freethus, surface; thus, theratio removal ratio larger actual. However, this simulation can be used to explain the removal mechanism and compare the than the actual. However, this simulation can be used to explain the removal mechanism and differences among various among cases. By the above physical modelling and numerical simulation, case C5 compare the differences various cases. By the above physical modelling and numerical has been chosen structure industrial improvement, and itsimprovement, profitable effect simulation, case as C5the hasoptimized been chosen as the for optimized structure for industrial andhas its been confirmed, which will be reported in further work. profitable effect has been confirmed, which will be reported in further work. 5. 5. Conclusions Conclusions Hydrodynamic Hydrodynamicmodeling modelingand andmathematical mathematicalsimulation simulationhave havebeen beencarried carriedout outto toreveal revealthe thefluid fluid flow and inclusion removal behavior for an innovative casting tundish with channel type induction flow and inclusion removal behavior for an innovative casting tundish with channel type induction heating. heating. The The reasonable reasonable structural structural parameters parameters in in the the seven-strand seven-strand tundish tundish with with consideration consideration of of the the channel heating effect have been given based on both isothermal and non-isothermal service situations. channel heating effect have been given based on both isothermal and non-isothermal service The main conclusions can be summarized as follows: as follows: situations. The main conclusions can be summarized (1) non-isothermal experiment experiment and andmathematical mathematicalsimulation simulationshow showthat that fluid presents (1) The non-isothermal thethe fluid presents an an obvious rising tendency when it flows out from the heating induction channel. The larger the obvious rising tendency when it flows out from the heating induction larger the temperature difference inside and outside the channel is, is, the the more more consistent consistent will will be be the the fluid fluid flows among among different different strands, strands, and and the the more more homogeneous homogeneousthe theflow flowfield fieldin inthe thetundish. tundish.For Forthe the ◦ C, the dead zone is basically eliminated, prototype tundish, when the temperature difference is 5 prototype tundish, when the temperature difference is 5 °C, the dead zone is basically eliminated, and the byby 300300 s. The rising trend of fluid willwill decay withwith the the residence residencetime timeofoffluid fluidisisprolonged prolonged s. The rising trend of fluid decay further elongation of the heating time to 5000 s. Under this case, the non-isothermal flow will be the further elongation of the heating time to 5000 s. Under this case, the non-isothermal flow will developed intointo an isothermal flow. be developed an isothermal flow. (2) The isothermal experiments suggest that the prototype tundish has severe “short-circuiting flow” in the second and sixth strands, which has led to the increased number of inclusions in the local billets. Changing the channel inclination and setting dams exerts little effect on the flow characteristics of fluid when the height of the channel exit is lower than 440 mm and the dead

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The isothermal experiments suggest that the prototype tundish has severe “short-circuiting flow” in the second and sixth strands, which has led to the increased number of inclusions in the local billets. Changing the channel inclination and setting dams exerts little effect on the flow characteristics of fluid when the height of the channel exit is lower than 440 mm and the dead zone volume of the tundish remains as 37.19–53.18%. When the channel exit is elevated to 590 mm and the inclination remains at zero degrees, the flow field of the tundish can be greatly improved by adding two high dams at each side of the tundish. Compared with the prototype structure, the average residence time of the optimized case C5 is prolonged by 278 s, and the dead zone volume fraction is reduced by 30.16%. The removal ratio of inclusions can be improved by the optimization of flow fields with consideration of the heating channel effect. The motion tracks of various sizes of inclusions differ at the exit of the channel. The larger size inclusions move upwards to the liquid surface and are directly trapped by the slag layer, while the small sizes cannot be absorbed by the top slag completely due to the back flow observed, which partly explains the reason for the small size inclusions being difficult to remove. It is shown that induction heating can significantly improve the removal ratio of different sizes of inclusions due to the thermal buoyancy force, especially for small-sized inclusions.

Author Contributions: H.T. wrote this manuscript and designed and performed some of the experiments. L.G. performed some experiments and analyzed the data. G.W., H.X. and H.Y. performed some experiments and simulations. J.Z. guided the whole study and revised the manuscript. Acknowledgments: This research was financially supported by Beijing Natural Science Foundation (No. 2182038) and the National Key Research and Development Program of China (No. 2017YFB0304000). Conflicts of Interest: The authors declare no conflict of interest.

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