Channel parameter optimization of one-strand slab induction heating tundish with double channels

: A generalized three-dimensional mathematical model is built to study the in ﬂ uences of channel parameters (channel angle, channel section diameter, and channel distance) on the molten steel ﬂ ow, heat transfer, and inclusion removal in the induction heating tundish. The results demonstrate that as the channel angle increases, the ﬂ ow of molten steel in the discharging chamber gradually slows down. When the channel angle is 6°, the temperature of the discharging chamber is slightly lower than when the channel angles are 2° and 4°. When the channel angle is 2°, the inclusion removal rate is lower than when the channel angles are 4° and 6°, while the latter two have little di ﬀ erence. As the channel section diameter increases, the ﬂ ow of molten steel in the discharging chamber gradually slows down. When the channel section diameter is 100 mm, the temperature distribution in the discharging chamber is uneven. While the temperature distributions of the discharging chamber are even and similar,whenthechannelsectiondiametersare150and200mm. As the channel section diameter increases, the removal rate of inclusion gradually decreases. The variation of channel distance haslittlee ﬀ ectonthetemperaturedistributionofthedischarging chamber. When the channel distance is 600 mm, the removal rate of inclusion is lower than when the channel distances are 1,000 and 1,400 mm. Moreover, for the latter two, the removal rates of inclusions have little di ﬀ erence. For this model, the best channel angle is 4°, the best channel section diameter is 150mm, and the best channel distance is 1,000 mm.


Introduction
Tundish, which is the last vessel with basic and monolithic refractory lining, plays a very important role in the continuous casting process.It is used to distribute the liquid steel and as a secondary refining reactor.Consequently, a tundish should be designed with the following considerations: the residence time of molten steel should be sufficiently long, the dead volume should be small, more inclusions should be removed, and liquid steel temperature should be promoted [1][2][3][4][5][6].The distribution of liquid steel temperature is a key factor in the final steel property.Therefore, tundishes with induction heating are developed to improve liquid steel temperature and maintain the temperature steady during the whole pouring course [7].
In the 1980s, Ueda et al. [8] designed an induction heating device composed of transformers, induction heaters, main relays, thyristor conversion controllers, capacitors for power compensation, and cooling water circulation systems to make up for the heat lost from the molten steel in the package.Since then, various countries have invested in research and development and improvement of the process [9][10][11].The induction heating device was perfected and improved, and today's relatively mature electromagnetic induction heating technology was finally developed.This technology can not only heat liquid steel and stabilize the superheat, but also has a strong purification function, can reduce the total oxygen content in liquid steel, and can reduce the inclusion of small inclusions [12][13][14], thus improving the cleanliness of liquid steel.It also provides favorable conditions for the research and development of new steel grades.Many physical and mathematical models are employed in induction heating tundish studies [15][16][17][18].Wang et al. [7,19] performed a mathematical model to investigate the flow of molten steel, heat transfer, and inclusion removal in induction heating tundish with H-type channels, demonstrating that the Joule heat could supply the heat loss effectively.Moreover, the temperature field turned more homogeneous in the discharging chamber.The inclusion removal rate increased as the heating power increased.Yue et al. [20] numerically simulated the electromagnetic induction heating in a tundish with channel-type induction heating in a steel plant.The corresponding work illustrated the relationship between magnetic flux density and electromagnetic force.The results would be favorable in the channel parameter design.
The use of induction heating technology makes the shape design and lining construction of tundish different from the traditional tundish.The shape design of tundish should not only satisfy the performance of the traditional tundish design, but also consider the layout of the receiving chamber, discharging chamber and channel, the position of the sensor, the insulation of the tundish shell, and the cooling of the sensor.Among them, the channel is the key component connecting the receiving chamber and discharging chamber of induction heating tundish, and its layout and parameters are the main factors affecting the heating efficiency of the heater, the flow condition of the molten steel, and the removal of inclusions in the tundish.Therefore, it is very necessary to study the layout and parameters of convection steel channels [21].Chen et al. [22] provided an induction heating tundish with four channels and built mathematical model to study the electromagnetic, fluid flow, and heat transfer characteristics.At the same time, they compared the new-type induction heating tundish with the traditional one of the same parameters.Yang et al. [23] focused on the structural influences of the channel-type induction heating tundish on multiphysical field.They found that the depth of the induction heating chamber and channel diameter are important in the multiphysical field of the induction heating tundish.Traditional induction heating tundish has issues, such as low heating velocity.Therefore, Xing et al. developed a bent-channel induction heating tundish, which could settle the aforementioned problems [24].Also, the movement and removal of inclusions in newly designed and conventional tundishes were contrasted.However, few literature studies were focused on the effect of channel parameters on the fluid field, temperature field, and inclusion removal.This is beneficial to the improved application of tundish induction heating in the industry.
In this work, a 3-D transient mathematical model is provided to investigate the effect of channel parameters on the multiphysical field and inclusion removal in the channel-type induction heating tundish.

Mathematical model 2.1 Geometric model
Figure 1 presents the geometric model of the channel-type induction heating tundish.The model building is based on a one-strand induction heating tundish with actual sizes.The receiving and discharging chambers are linked by the channels.The heating equipment is installed between the channels [6,7,24].

Control equations 2.2.1 Electromagnetic model
The differential forms of the Maxwell equations are as follows: where ⎯ → B is the magnetic flux density, T; t is the time, s; ⎯ → H is the magnetic field intensity, A•m −1 ; and ⎯ → J is the conduction current density [6,[25][26][27], A•m −2 .

Fluid dynamics model
The continuity equation and the Navier-Stokes equation are as follows: where ρ is the density of the liquid steel, as a function of temperature ( = − ρ T 8,523 0.8358 ), kg•m −3 ; → u is the liquid steel velocity, m•s −1 ; p is the static pressure, Pa; → g is the gravitational acceleration vector [28,29], m•s −2 ; µ eff is the effective viscosity [30], kg•(m•s) −1 ; and ⎯ → F m is the volumetric force [7], N•m −3 .

Heat transfer model
The energy equation is as follows: where λ is the heat transfer coefficient of liquid steel, W•(m•K) −1 ; c p is the specific heat at constant pressure of liquid steel, J•(kg•K) −1 ; S T is the viscosity dissipation factor, W•m −3 ; and Q is the Joule heat generated by the electromagnetic induction [33,34], W•m −3 .

Motion equation of inclusion
The motion equation of inclusion includes gravity, buoyancy, drag, lift, added mass, Brownian, electromagnetic pressure, and thermophoretic forces.The collision and coalescence of inclusions are also considered [7,24,30].
According to the Newton's second law, the motion equation of inclusion is as follows: where ρ p , d p, and ν p are the density, size, and velocity of the inclusions in kg•m −3 , μm, and m•s −1 , respectively; F g is the gravity acting on the inclusions, N; F f is the buoyancy, N; F d is the drag force, N; F l is the Saffman force, N; F p is the electromagnetic pressure, N; F t is the thermophoretic force, N; and F b is the Brownian force, N.

Collision-growth equation of inclusions
In unit time and volume, the collision rate of inclusions r i and r j is defined as: where r and n are the radius (μm) and number density (m −3 ) of the inclusions, respectively; i and j are the series number of the inclusions; and β (r i , r j ) is the collision rate in m 3 /s, which is called the collision volume [35,36].
Channel parameter optimization of induction heating tundish  3

Brown collision
The collision rate of the inclusions is decided by [37]: where k l is the molten steel turbulent kinetic energy, J; T l is the molten steel temperature, K; and µ l is the molten steel dynamic viscosity, Pa•s.

Turbulent collision
The turbulent collision rate is decided by [38]: where ρ l is the molten steel density, kg•m −3 ; and ε l is the molten steel turbulent kinetic energy dissipation rate, %.

Stokes collision
The Stokes collision rate is decided by [39]: where g is the gravitational acceleration, m•s −2 ; and Δρ is the density difference between the molten steel and inclusion, kg•m −3 .The plug zone (V p ), mixing zone (V m ), and dead zone (V d ) of induction heating tundish are calculated by the classical combination model [3,7] in this work.

Boundary conditions
In electromagnetic calculation, the current density and current frequency are applied to the cross-section of the coil.It is also necessary to apply magnetic parallel boundary conditions on the surface of the air layer, i.e., the tangential component of the magnetic strength is parallel to the outer surface of the air surrounding the brake, and the normal component is perpendicular to the outer surface of the air [7].
In the calculation of flow and heat transfer, mass flow inlet and mass flow outlet are adopted to ensure the mass conservation of liquid steel.Since the k-ε turbulence model of the standard two-equation is suitable for high Reynolds number flow and low Reynolds number flow near the wall, the standard wall function is also used at the wall.The free liquid surface of the tundish is set as a non-slip wall, and the pressure is one atmosphere [18].The inlet temperature of molten steel is considered constant and is set at 1,823 K.The second type of boundary condition is adopted for heat dissipation of tundish wall.The parameters used in this work [6,7,18] are shown in Table 1.
For simplification, the inclusions are assumed as spherical solids.Two inclusions coalesce together to be a highersized one once a collision happens.An inclusion would be caught by the walls or tundish powder if its velocity was lower than an attachment point, or it would be bounced back into the steel, with about 40% momentum lost.Seven lower-sized inclusions (1, 2, 5, 10, 20, 30, and 50 μm) are uniformly released at the inlet.The relevant speed and direction are in accord with those of the liquid steel [19,24,35].

Solution method
The governing equations used to compute the electromagnetic field, flow field, and temperature field are solved by commercial software ANSYS 14.0 and FLUENT 14.0, respectively [40].The finite element method is used to calculate the electromagnetic field by ANSYS.The finite volume method based on FLUENT is applied to calculate the flow and temperature field.During each iteration, once the residuals are less than 10 −6 , convergence is assumed to be achieved.FLUENT's discrete phase model is used to solve the motion equation of inclusions [19].

Model validation
The mathematical model in this work is validated by temperature data in the industrial test with the same sizes and parameters of the one-strand slab induction heating tundish in the industrial test [3].The blackbody cavity continuous temperature-measuring device (accuracy ± 3 K) developed by Northeastern University was adopted, and the temperature-measuring point was at the position of ≥250 mm molten steel inserted above the outlet of the tundish.During the test, the electromagnetic induction heating was turned on when the tundish was poured for 600 s, and the electromagnetic induction heating was turned on for 1,680 s.The heating power is 600 kW. Figure 2 presents the temperature rise period of the experiment and computation.They have good consistency with each other.In addition, the inclusion removal model is validated by the experimental results in the study by Vives and Ricou [26]. Figure 3 shows the contrast of the removal rates between the experimental and calculated results.In this work, experimental data in the reference are used to validate the inclusion removal model.It could be seen in Figure 3 that the numerical simulation results are in good match with the experimental ones.
To sum up, the mathematic model in this article can be used to study the induction heating tundish.

Effect of channel angle 3.2.1 Flow field
Figure 4 shows the flow field of tundish with different channel angles at a heating power of 600 kW.As shown in Figure 4, when the channel angle is 2°, the molten steel is heated while passing through the channel, the temperature rises, and the density decreases.Then, the molten steel directly moves upward under the buoyancy after flowing out of the channel [7].On account of the channel angle, the molten steel quickly reaches the top of the discharging chamber and subsequently moves down to the bottom.This will lead to the molten steel flow in the top region of the discharging chamber to become violent, probably breaking the slag layer and causing slag entrapment, which is unbeneficial to steady casting.When the channel angle is 4°, the molten steel flows downward for a certain distance after flowing out of the channel, due to the channel angle, and consequently moves upward.Finally, it spirals down to move to the bottom after reaching the top surface of the discharging chamber.Such flows prolong the flow path of molten steel in tundish, which are beneficial to inclusion removal and reduce slag entrapment.When the channel angle is 6°, due to the further increase of channel angle, the molten steel moves downward for a longer distance after flowing out of the channel and consequently moves upward.This movement further prolongs the flow path of molten steel in tundish, relieving the risk of slag entrapment and impacts on the front wall of the discharging chamber.
Table 2 shows the analysis results of the residence time distribution (RTD) curve with different channel angles at a heating power of 600 kW. Figure 5 shows the RTD curves with different channel angles at a heating power of 600 kW.It could be seen that with the increase of the channel angle, the average residence time of the molten steel in the tundish gradually increases and the dead zone volume gradually decreases, which is consistent with the description of the flow field in Figure 4.However, the ratio of the piston zone to the dead zone is larger than that of the channel angle of 4°compared with the channel angle of 6°, so the flow characteristics of the liquid steel with the channel angle of 4°are better.

Temperature field
Figure 6 indicates the temperature field at the vertical section of tundish with different channel angles at a heating power of 600 kW.It could be observed that the temperature distributions in the discharging chamber are similar, and the difference is that the high-temperature region in the discharging chamber is due to different channel angles.Figure 7 shows the outlet temperature of tundish with different channel angles at a heating power of 600 kW.It could be seen that with increasing channel angle, the outlet temperature decreases by degrees, from 1,836 to 1835.58 K.The reason is that with the increase of average residence  time, the temperature of molten steel decreases gradually, which is consistent with the description of the flow field in Figures 4 and 5.

Turbulence intensity
Figure 8 shows the turbulence intensity at the vertical section of tundish with different channel angles at a heating power of 600 kW.It could be observed that when the channel angle is 2°, the molten steel flows upward directly after flowing out of the channel.Consequently, the turbulence intensity in the upper region of the discharging chamber is high, which has the risk of slag entrapment and secondary oxidation, while it is not conducive to steady casting.When the channel angle is 4°, the turbulence intensity in the upper region of the discharging chamber is slightly lower than when the channel angle is 2°.But the turbulence intensity in the upper region of the discharging chamber is still high.When the channel angle is 6°, the turbulence intensity in the upper region of the discharging chamber is lower than the former two.This occurs mainly because the molten steel moves downward for a longer distance prior to moving upward.This flow can ease the impact of molten steel to the top surface and front wall of the discharging chamber.

Inclusions
Figure 9 presents the inclusion removal rates with different channel angles at a heating power of 600 kW.As it could be observed, with the increase of channel angle, the removal rate of inclusions increases gradually, from 60 to 66%, an increase of 10%.The inclusion removal rate with the channel angle of 4°is 6% higher than that of the channel angle of 2°, while the inclusion removal rate with the channel angle of 6°is 3.1% higher than that of the channel angle of 4°, and the inclusion removal efficiency gradually decreases.The reason is that the short  flow path of molten steel with the channel angle of 2°does not allow enough time for the inclusions to be removed by the slag.
In addition, due to the channel angle, the channel length with the channel angle of 2°is shorter than the latter two.Consequently, the inclusions adsorbed by the channel are also reduced in amount.Another reason is that the molten steel flow in the upper part of the discharging chamber is disordered, which might cause the inclusions adsorbed by the slag to bounce back into the molten steel again (Figures 4a and 8a).
The inclusion removal rate when the channel angle is 6°is slightly higher than that when the channel angle is 4°; this occurs mainly because the longer channel length and flow path of molten steel will lead to additional inclusions becoming adsorbed by the channel and the slag.

Effect of channel section diameter 3.3.1 Flow field
Figure 10 shows the flow field of tundish with different channel section diameters at a heating power of 600 kW.It could be observed that when the channel section  diameter is 100 mm, due to the small channel section diameter, the impact force of molten steel increases while flowing through the channel, which might cause the erosion of the refractory lining.Moreover, after flowing out of the channel, the molten steel strongly impacts the front wall of the discharging chamber.In this case, the impact force of molten steel is dominant and its influence is higher than the convection caused by density difference.Then, the molten steel is divided into two parts.The molten steel flowing upward has a high speed, which might break the slag and cause slag entrapment.However, the molten steel flowing downward might lead to it directly flowing out of the outlet and form a short-circuit flow, which will lead to the inclusions flow into the mold and finally affect the product quality.When the channel section diameter is 150 mm, the flow of molten steel is shown in Figure 4c and d.
The impact force of molten steel is lower.When the diameter is 200 mm, the impact force of molten steel during the flow through the channel becomes significantly lower, due to the further increase of the channel section diameter.Therefore, the impact force of the molten steel flowing out of the channel is also reduced.As a result, the convection caused by density difference is dominant and the molten steel starts to rise after flowing out of the channel.Such flow leads to the impact avoidance on the front wall of the discharging chamber to a high extent.Simultaneously, the risk of slag entrapment is also highly reduced.However, it should be noted that as the impact force decreases, the influence of the proximity effect increases.Therefore, the electromagnetic force of molten steel in the channel near the induction coil is higher than afar from the induction coil [7].Therefore, the molten steel will produce a large bias flow after flowing out of the channel, resulting in uneven flow field in the discharging chamber, which is not conducive to steady casting.Table 3 shows the analysis results of the RTD curve with different channel section diameters at a heating power of 600 kW. Figure 11 shows the RTD curves with different channel section diameters at a heating power of  600 kW.It could be concluded that when the channel diameter is 150 mm, the average residence time of the molten steel in the tundish is the longest, the volume of the dead zone is the smallest, and the volume of the total mixing zone is the largest.Although the volume ratio of the piston zone to the dead zone when the channel diameter is 200 mm is larger than that of 150 mm, it can be concluded from Figure 10 that the discharging chamber will generate bias flow when the channel diameter is 200 mm.It is not conducive to steady casting.In summary, the flow characteristics of molten steel are better when the channel diameter is 150 mm.

Temperature field
Figure 12 gives the temperature field at the vertical section of tundish with different channel section diameters at a heating power of 600 kW. Figure 13 shows the outlet temperature of tundish with different channel section diameters at a heating power of 600 kW.As it could be observed, when the channel section diameter is 100 mm, the flow of molten steel in the discharging chamber is quite intense due to the high impact after the steel flows out of the channel, which results in uneven temperature distribution and short average residence time in the discharging chamber, and the outlet temperature is 1834.28K.The temperature distribution is uniform when  the channel section diameter is 150 mm and the outlet temperature is 1835.85K.When the channel section diameter is 200 mm, the temperature distribution of the discharging chamber is similar to the case, in which the channel section diameter is 150 mm, while the low-temperature region at the bottom of the discharging chamber is slightly larger due to the bias flow and the outlet temperature is 1835.57K.

Turbulence intensity
Figure 14 illustrates the turbulence intensity at the vertical section of tundish with different channel section diameters at a heating power of 600 kW.It could be observed that when the channel section diameter is 100 mm, the turbulence intensity of molten steel in the channel is quite strong, while the turbulence intensity after the molten steel flows out of the channel is also quite strong.Then, the molten steel violently impacts the front wall of the discharging chamber, causing the refractory lining erosion.When the channel section diameter is 150 mm, the turbulence intensity in the channel is lower.Consequently, the turbulence intensity is also lower after the molten steel flows out of the channel.However, the molten steel might still impact the front wall of the discharging chamber inevitably and cause slag entrapment.When the channel section diameter is 200 mm, the turbulence intensity in the channel is reduced further, due to the increase of the channel diameter, along with the turbulence intensity after the molten steel flows out of the channel.This flow almost avoids the impact on the front wall of the discharging chamber and the risk of slag entrapment.

Inclusions
Figure 15 shows the inclusion removal rates with different channel section diameters at a heating power of 600 kW.It could be observed that the inclusion removal rate gradually decreases as the channel section diameter increases, from 68.5 to 61.7%, a decrease of 9.9%.This occurs mainly because the turbulence intensity in the channel gradually decreases, while the probability of collisions and growth of the inclusions decreases.Also, the inclusions removed by  the channel are reduced in amount.Moreover, the impact force of molten steel flowing out of the channel is also gradually reduced.Therefore, the turbulence intensity in the discharging chamber is gradually reduced (Figure 14), along with the probability of collisions, growth, and removal of inclusions.

Effect of channel distance 3.4.1 Flow field
Figure 16 gives the flow field of tundish with different channel distances at a heating power of 600 kW.As shown in Figure 16, when the channel distance is 600 mm, the molten steel impacts the front wall of the discharging chamber after flowing out of the channel, consequently producing an outward bias flow, while flowing upward due to the small channel distance.Furthermore, when the channel distance is 1,400 mm, due to the excessive channel distance, the molten steel flows upward and inward after flowing out of the channel, creating two high-sized eddies in the discharging chamber, which is not conducive to steady casting and inclusion removal.Moreover, the molten steel might erode the side walls of the discharging chamber after flowing out of the channel, causing the refractory lining erosion.Therefore, when the channel distance is 1,000 mm (Figure 4c and d), the flow field is the best for steady casting and inclusion removal.Table 4 shows the analysis results of the RTD curve with different channel distances at a heating power of 600 kW. Figure 17 shows the RTD curves with different Figure 16: Flow field of tundish at a heating power of 600 kW: (a) with a channel distance of 600 mm, (b) at the vertical section with a channel distance of 600 mm, (c) with a channel distance of 1,000 mm, (d) at the vertical section with a channel distance of 1,000 mm, (e) with a channel distance of 1,400 mm, and (f) at the vertical section with a channel distance of 1,400 mm.channel distances at a heating power of 600 kW.It could be seen that with the increase of channel distance, the average residence time of molten steel in tundish and the volume ratio of piston zone to dead zone decrease first and then increase, and the dead zone volume increases first and then decreases.However, as shown in Figure 12, the flow mode of molten steel in tundish is not conducive to steady casting whether the channel distance is too small or too large, and may cause erosion on the side wall of refractory materials.heating power of 600 kW. Figure 19 shows the outlet temperature of tundish with different channel distances at a heating power of 600 kW.The variation of channel distance has little effect on temperature distribution of the discharging chamber, while the temperature distribution is similar.And with the increase of channel distance, the outlet temperature increases first and then decreases; the reason is that the average residence time of molten steel in tundish is shorter than that of the other two when the channel distance is 1,000 mm.

Turbulence intensity
Figure 20 illustrates the turbulence intensity of tundish with different channel distances at a heating power of 600 kW.It could be observed from Figure 20a, c, and e that the turbulence intensity distributions at the vertical section of tundish with different channel distances are similar.Since the channel distance changes in the crossdirection, the turbulence intensity at the cross-section of tundish is recorded to observe the variation effect of channel distance.It could be observed from Figure 20b, d, and f that different channel distances lead to the position change of the molten steel flowing out of the channel.When the distance is 1,400 mm, the turbulence intensity near the side walls of the discharging chamber is strong, impacting the side walls and causing the refractory lining erosion.

Inclusions
Figure 21 presents the inclusion removal rates with different channel distances at a heating power of 600 kW.It could be observed that the inclusion removal rate when the channel distance is 1,000 mm is far higher than when the channel distance is 600 mm, from 57 to 64%, an increase of 12.3%.The reason is that the smaller channel distance produces an outward bias flow in the discharging chamber Figure 20: Turbulence intensity of tundish at a heating power of 600 kW: (a) at the vertical section with a channel distance of 600 mm, (b) at crosssection with a channel distance of 600 mm, (c) at the vertical section with a channel distance of 1,000 mm, (d) at cross-section with a channel distance of 1,000 mm, (e) at the vertical section with a channel distance of 1,400 mm, and (f) at cross-section with a channel distance of 1,400 mm.
(Figure 16a and b), in which the inclusions circulate in the bias vortex.In this case, the inclusions do not have sufficient chances to be absorbed by the slag.When the channel distance increases from 1,000 to 1,400 mm, the inclusion removal rate decreases from 64 to 62%, with a slight decrease of 3.1%.This occurs mainly because the two vortices in the discharging chamber are not beneficial to inclusion removal (Figure 16e and f).Furthermore, the molten steel will impact the side walls of the discharging chamber after flowing out of the channel, due to the high channel distance of 1,400 mm, which might lead to the inclusions to be absorbed by the side walls to bounce back into the molten steel again.

Summary and conclusions
Channel is the key component of induction heating tundish, and its structure and parameter design have great influence on the uniformity of flow field, superheat stability, and inclusion removal efficiency in induction heating tundish.However, the basic theory of the influence of channel design on the flow field and temperature distribution of induction heating tundish is weak and needs to be supplemented.Therefore, the study on the influence of channel parameters on flow, heat transfer, and inclusion removal of induction heating tundish in this article has a good reference significance for the application of induction heating continuous casting technology.In conclusion, for this model, the best channel angle is 4°, the best channel section diameter is 150 mm, and the best channel distance is 1,000 mm.When the aforementioned parameters are applied, the flow field and temperature field distribution of induction heating tundish are more reasonable and the removal rate of inclusions is higher.The application of channel-type induction heating technology puts forward new requirements for tundish design.Therefore, in the process of implementation, the space of channel-type induction heating technology should be fully considered when designing the tundish for new plants.For the retrofitting of the old plant to add channel-type induction heating device, the tundish should be modified according to the actual situation and the appropriate channel mode should be adopted.At the same time, in view of the higher temperature and faster flow rate of the molten steel in the induction heating channel, the life of channel is a problem that needs attention in the subsequent application process.
The following results are obtained: (1) When the channel angle is 2°, the top flow of the discharging chamber is strong, which might cause slag entrapment and secondary oxidation.When the channel angle is 4°, the flow path of molten steel is prolonged, which is conducive to inclusion removal and remission of slag entrapment.When the channel angle is 6°, the flow path of molten steel is further prolonged, which highly reduces the risk of slag entrapment.With increasing channel angle, the outlet temperature decreases by degrees.(2) When the channel angle is 2°, the inclusion removal rate is lower than when the channel angles are 4°and 6°.The inclusion removal rates have little difference when the channel angles are 4°and 6°, while the latter is slightly higher.(3) When the channel section diameter is 100 mm, one portion of the molten steel flows upward with a high speed after flowing out of the channel, which might cause slag entrapment; another portion might directly flow out of the outlet and form a short-circuit flow.
When the channel section diameter is 150 mm, the impact of molten steel is reduced, which is beneficial to inclusion removal and remission of slag entrapment.When the channel section diameter is 200 mm, the impact of molten steel after flowing out of the channel is further reduced.However, a large bias flow is generated in the discharging chamber.When the channel section diameter is 100 mm, the temperature distribution in the discharging chamber is uneven.When the channel section diameters are 150 and 200 mm, the temperature distributions are similar and relatively even.(4) As the channel section diameter increases, the inclusion removal rate gradually decreases.(5) When the channel distance is 600 mm, the molten steel will produce an outward bias flow in the discharging chamber while flowing upward.When the channel distance is 1,000 mm, the flow field in the discharging chamber is uniform, which is conducive to inclusion removal and remission of slag entrapment.When the channel distance is 1,400 mm, two large vortices will be produced in the discharging chamber, which is not conducive to steady casting.The variation of channel distance has little effect on temperature distribution of the discharging chamber.(6) The inclusion removal rate when the channel distance is 600 mm is far lower than when the channel distances are 1,000 and 1,400 mm.For the latter two, the inclusion removal rates have little difference.

Figure 2 :Figure 3 :
Figure 2: Comparison of temperature increase between experimental and calculation results.

Figure 4 :
Figure 4: Flow field of tundish at a heating power of 600 kW: (a) with a channel angle of 2°, (b) at vertical section with a channel angle of 2°, (c) with a channel angle of 4°, (d) at vertical section with a channel angle of 4°, (e) with a channel angle of 6°, and (f) at vertical section with a channel angle of 6°.

Figure 6 :
Figure 6: Temperature field at the vertical section of tundish with different channel angles at a heating power of 600 kW: (a) with a channel angle of 2°, (b) with a channel angle of 4°, and (c) with a channel angle of 6°.

Figure 7 :
Figure 7: Outlet temperature of tundish with different channel angles at a heating power of 600 kW.

Figure 8 :
Figure 8: Turbulence intensity at the vertical section of tundish with different channel angles at a heating power of 600 kW: (a) with a channel angle of 2°, (b) with a channel angle of 4°, and (c) with a channel angle of 6°.

Figure 9 :
Figure 9: Inclusion removal rates with different channel angles at a heating power of 600 kW.

Figure 10 :
Figure10: Flow field of tundish at a heating power of 600 kW: (a) with a channel section diameter of 100 mm, (b) at the vertical section with a channel section diameter of 100 mm, (c) with a channel section diameter of 150 mm, (d) at the vertical section with a channel section diameter of 150 mm, (e) with a channel section diameter of 200 mm, and (f) at the vertical section with a channel section diameter of 200 mm.

Figure 11 :
Figure 11: RTD curves with different channel section diameters at a heating power of 600 kW.

Figure 12 :
Figure12: Temperature field at the vertical section of tundish with different channel section diameters at a heating power of 600 kW: (a) with a channel section diameter of 100 mm, (b) with a channel section diameter of 150 mm, and (c) with a channel section diameter of 200 mm.

Figure 13 :
Figure 13: Outlet temperature of tundish with different channel section diameters at a heating power of 600 kW.

Figure 14 :
Figure14: Turbulence intensity at the vertical section of tundish with different channel section diameters at a heating power of 600 kW: (a) with a channel section diameter of 100 mm, (b) with a channel section diameter of 150 mm, and (c) with a channel section diameter of 200 mm.

Figure 15 :
Figure 15: Inclusion removal rates of tundish with different channel section diameters at a heating power of 600 kW.

3. 4 . 2
Figure 18 presents the temperature field at the vertical section of tundish with different channel distances at a

Figure 17 :
Figure 17: RTD curves with different channel distances at a heating power of 600 kW.

Figure 18 :
Figure18: Temperature field at the vertical section of tundish with different channel distances at a heating power of 600 kW: (a) with a channel distance of 600 mm, (b) with a channel distance of 1,000 mm, and (c) with a channel distance of 1,400 mm.

Figure 19 :
Figure 19: Outlet temperature of tundish with different channel distances at a heating power of 600 kW.

Figure 21 :
Figure 21: Inclusion removal rates at different channel distances at a heating power of 600 kW.

Table 2 :
Analysis results of the RTD curve with different channel angles at a heating power of 600 kW Figure 5: RTD curves with different channel angles at a heating power of 600 kW.

Table 3 :
Analysis results of the RTD curve with different channel section diameters at a heating power of 600 kW

Table 4 :
Analysis results of the RTD curve with different channel distances at a heating power of 600 kW