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Effects of operating parameters on the flow field in slab continuous casting molds with narrow widths

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  • Corresponding author:

    Jian Yang    E-mail: yang_jian@t.shu.edu.cn

  • Received: 11 November 2019Revised: 15 January 2020Accepted: 17 January 2020Available online: 11 February 2020
  • Computational simulations and high-temperature measurements of velocities near the surface of a mold were carried out by using the rod deflection method to study the effects of various operating parameters on the flow field in slab continuous casting (CC) molds with narrow widths for the production of automobile exposed panels. Reasonable agreement between the calculated results and measured subsurface velocities of liquid steel was obtained under different operating parameters of the CC process. The simulation results reveal that the flow field in the horizontal plane located 50 mm from the meniscus can be used as the characteristic flow field to optimize the flow field of molten steel in the mold. Increases in casting speed can increase the subsurface velocity of molten steel and shift the position of the vortex core downward in the downward circulation zone. The flow field of liquid steel in a 1040 mm-wide slab CC mold can be improved by an Ar gas flow rate of 7 L·min−1 and casting speed of 1.7 m·min−1. Under the present experimental conditions, the double-roll flow pattern is generally stable at a submerged entry nozzle immersion depth of 170 mm.
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Effects of operating parameters on the flow field in slab continuous casting molds with narrow widths

  • Corresponding author:

    Jian Yang    E-mail: yang_jian@t.shu.edu.cn

  • 1. State Key Laboratory of Advanced Special Steel, Shanghai University, Shanghai 200444, China
  • 2. Hunan Valin Lianyuan Iron & Steel Co., Ltd., Loudi 417000, China

Abstract: Computational simulations and high-temperature measurements of velocities near the surface of a mold were carried out by using the rod deflection method to study the effects of various operating parameters on the flow field in slab continuous casting (CC) molds with narrow widths for the production of automobile exposed panels. Reasonable agreement between the calculated results and measured subsurface velocities of liquid steel was obtained under different operating parameters of the CC process. The simulation results reveal that the flow field in the horizontal plane located 50 mm from the meniscus can be used as the characteristic flow field to optimize the flow field of molten steel in the mold. Increases in casting speed can increase the subsurface velocity of molten steel and shift the position of the vortex core downward in the downward circulation zone. The flow field of liquid steel in a 1040 mm-wide slab CC mold can be improved by an Ar gas flow rate of 7 L·min−1 and casting speed of 1.7 m·min−1. Under the present experimental conditions, the double-roll flow pattern is generally stable at a submerged entry nozzle immersion depth of 170 mm.

    • The production of automobile exposed panels involves several steelmaking processes, such as converter blowing, secondary refining, and continuous casting (CC), as well as hot rolling, cold rolling, and hot-dip galvanizing. Improvement of surface quality is one of the key issues of automobile exposed panel production. Improper control of the flow field of liquid steel in slab CC molds causes great fluctuations that may result in surface defects of large Al2O3 clusters, Ar bubbles + Al2O3 inclusions, and entrapped mold powder particles [1]. Thus, the flow field of liquid steel in slab CC molds has an important influence on the surface quality of slabs used to produce automobile exposed panels.

      The influences of different operating parameters on the flow field of liquid steel in slab CC molds have been extensively investigated to enable parameter optimization. For example, velocities near the mold surface have been studied by many researchers using physical modeling and numerical simulations [210]. Chen et al. [11] used an large eddy simulation (LES) + volume of fluid (VOF) + discrete phase modle (DPM) to investigate slag entrapment and multiphase flow in a CC mold and found that Ar bubbles influence the flow characteristics in the mold. Cho et al. [12] reported that electromagnetic braking and Ar bubbles directly affect the stability of liquid steel transient flow. Kubota et al. [13] indicated that control of the flow field in slab CC molds is important to prevent slag entrapment; the group subsequently developed control technology to optimize the flow field of liquid steel. Cao and Zhu [14] proposed a critical Ar gas flow rate to maintain a double-roll flow (DRF) pattern in the mold. Deng et al. [15] showed that increased Ar gas flow rates could change the flow pattern from DRF to single-roll flow (SRF), which tends to deteriorate the flow field. Many other researchers [1620] have revealed that Ar gas bubbles could slow down the velocity of liquid steel and uplift the jet zone.

      The flow field developed under high casting speeds in slab CC molds has been investigated by a number of scholars [2123]. Deng et al. [21], for instance, found that DRF is easily formed by high casting speeds in the slab mold and indicated that investigating the effects of mold width and casting speed on the flow field using the mass flow rate of molten steel is reasonable. Yu et al. [22] investigated subsurface inclusions in the slab at high casting speeds and found that increased casting speeds and superheating can effectively reduce the hook depth and number of large-sized inclusions in the subsurface of slabs. Deng et al. [23] found that well-bottom nozzles could effectively reduce level fluctuations and slag entrainment at high casting speeds in molds with narrow widths whereas mountain-bottom nozzles are more suitable for low casting speeds in molds with large widths.

      Several velocity measurement technologies for liquid steel in molds have been described in many publications [2425]. Miki and Takeuchi [24] proposed that the flow velocity of molten steel could be measured by a propeller-type velocity meter in water modeling experiments. Using this method, the fluctuation period was measured to be 15 s and the flow velocity was 0–0.6 m·s−1. Liu et al. [25] indicated that the nail dipping method is useful for measuring the subsurface velocity of molten steel under high-temperature conditions; the group found that the velocity of steel increases with increasing casting speed or decreasing Ar gas flow rate.

      While the influences of operating parameters and high casting speeds on the flow field in slab CC molds have been extensively investigated, molten steel flow in molds with narrow widths, which is particularly important in the production of automobile exposed panel because of its high ratio of surface defects, has received relatively little attention. Direct measurement of velocities near the mold surface at high temperatures with high accuracy is crucial for investigations of the flow field in slab molds and verification of the calculated results.

      In the current work, the subsurface velocities of liquid steel were directly obtained under high-temperature conditions using the rod deflecting method to explore the effects of casting speed, Ar gas flow rate, and submerged entry nozzle (SEN) immersion depth on the flow field in slab CC molds with narrow widths. The calculated results of molten steel velocities were then compared and verified with the measured values. The flow fields of molten steel in the central vertical and horizontal planes located at different distances from the mold surface were calculated by using the verified mathematical model to optimize the operating conditions of the CC process and decrease sliver defects during the production of automobile exposed panels.

    2.   High-temperature measurement of velocities near the mold surface
    • In the present work, all high-temperature measurement results were obtained at the steelmaking plant of Hunan Valin Lianyuan Iron & Steel Co., Ltd. in China.

      The device used for high-temperature velocity measurements in this work is composed of an equilibrator, angle indicator, deflection pointer, deflection bearing, and velocity measurement rod. A schematic of the device is illustrated in our previous paper [26]. The magnitudes and directions of velocities at different positions near the mold surface can be measured by this device, and the flow pattern of molten steel in the mold can be determined according to the directions of the surface velocities.

      The velocity measurement rod is usually inserted 50 mm into the molten steel and deflected under the impact of molten steel flow. Upon insertion, the velocity measurement rod is subjected to three types of forces, namely, the impact force of molten steel flow, the gravity of the rod, and the buoyancy force of the immersion portion of the rod. When the rod becomes stable, the deflection angle is recorded. Three velocity measurement rods are inserted below the surface of liquid steel under the same condition to measure subsurface velocities, and approximately 30 data points are obtained to ensure the reliability of the measurement results. In this paper, the velocity of molten steel 50 mm below the surface is regarded as the subsurface velocity. The subsurface velocity is obtained on the basis of the torque balance of the velocity measurement rod by using Eq. (1):

      where U0 is the liquid steel velocity, L1 is the distance between the rotational pivot and barycenter of the velocity measurement rod, L2 is the distance between the rotational pivot and acting point of the flow impact force, G is the gravity of the velocity measurement rod, Ff is the buoyancy force of the immersed portion of the rod, θ is the detection angle of the rod, A is the projection area of the immersed portion of the rod, CD is the drag force coefficient, and ρ is the density of the liquid steel. A detailed description of the measurement method is provided in our previous paper [26].

    3.   Model formulation
    • The mathematical model used to simulate the process of CC in a mold with a narrow width is based on the Eulerian–Lagrangian approach. Here, the molten steel is considered the continuous phase, and Ar gas bubbles are treated as the discrete phase. Several reasonable assumptions, which are detailed in our previous paper [26], are included in the present model to simplify it.

      The continuity and momentum equations of molten steel are given by Eqs. (2) and (3):

      where ρ is the fluid density, ui and uj are the fluid velocity components (i, j = 1, 2, 3), xi and xj are the direction of components, t is the time, p is the pressure, μ is the effective fluid viscosity, gi is the compnents of gravity acceleration, F is the momentum source, respectively.

      μt refers to the turbulent viscosity of fluid, which is computed from

      where Cμ = 0.09, k is the instantaneous turbulent kinetic energy, and ε is the turbulent dissipation rate.

      The standard kε model is used to calculate the turbulence process; k and ε are solved by using the following equations.

      where Gk is the generation of turbulent kinetic energy due to the mean velocity gradient, C1 and C2 are constants, σk and σε are the turbulent Prandtl numbers for k and ε, respectively. In the model, σk = 1.0, σε = 1.3, C1 = 1.44, and C2 = 1.92.

      In the present paper, the transient transport of Ar gas bubbles is calculated by using Eq. (8), which is Newton’s second law:

      where mb is the mass of bubble, and ub is the velocity of bubble. The right-hand side of Eq. (8) includes forces acting on the Ar bubbles. The terms on the right-hand side of Eq. (8) are drag force (Fd), gravitational force (Fg), buoyancy force (Ff), and other forces (Fx). Fx is an additional source term, mainly including virtual mass force, the pressure gradient force, and the lift force. Relevant details of these forces are provided in our previous work [27].

      The mathematical model was solved by using the commercial CFD software ANSYS 16.1, and simulations were conducted on a Windows 10 server equipped with two Intel cores of E5-2630.

    • Fig. 1 shows the geometry and grids of the computational domain and SEN. The region of the nozzle is partially meshed with refinement to improve the accuracy and stability of the calculations. The number of grids is approximately 570000 cells, and the time step is set to 0.001 s. The calculation domain and parameters are given in Table 1.

      Figure 1.  Geometry and grids of the computational domain and SEN.

      Parameters Values Parameters Values
      Slab length / mm 3000 Fluid density / (kg·m−3) 7020
      Slab thickness / mm 230 Fluid dynamic viscosity / (N·s·m−2) 0.0056
      Slab width / mm 1040, 1080 Gas density / (kg·m−3) 0.27
      Casting speed / (m·min−1) 1.3, 1.5, 1.7 Gas bubble radius / (mm) 0.5
      Gas flow rate / (L·min−1) 1, 4, 7 Gravity acceleration / (m·s−2) 9.81
      Immersion depth of SEN / mm 140, 170, 190 SEN port angle / (°) 20

      Table 1.  Geometric and process parameters of simulation and experiment

      An initial velocity of the molten steel is set at the top of the SEN on the basis of the casting speed. The boundary condition at the bottom of the mold is outflow. The surface of molten steel is considered to have free-slip conditions. Based on our previous work [26], the radius of bubbles is 0.5 mm. The walls of the SEN can reflect Ar gas bubbles. Ar gas bubbles can escape from the top surface and outlet of the mold, whereas the walls of the mold can capture these bubbles.

    4.   Results and discussion
    • Fig. 2 compares between the measured and calculated subsurface velocities of molten steel at points corresponding to 100 mm from the narrow wall and 1/4 the width of the mold. The black dash-dotted line in the figures shows the calculated subsurface velocity profile of molten steel along the mold width in the central vertical plane corresponding to the point 50 mm below the meniscus. The measurement conditions in Fig. 2 are consistent with the calculation conditions, which include a casting speed of 1.5 m∙min−1, Ar gas flow rate of 4 L∙min−1, and SEN immersion depth of 170 mm in a 1040 mm-wide mold. The simulated and measured results clearly show good agreement. At the point corresponding to 1/4 the width of the mold, the subsurface velocity of liquid steel is approximately 0.2 m∙s−1. The subsurface velocities of liquid steel have positive values at points corresponding to 100 mm from the narrow wall and 1/4 the width of the mold, thus indicating that the molten steel flows from the narrow wall to the SEN. Therefore, the flow pattern in the mold is DRF.

      Figure 2.  Comparison of the measured and calculated velocities of molten steel with 1040 mm mold width, 1.5 m·min−1 casting speed, 4 L·min−1 gas flow rate, and 170 mm immersion depth.

    • Fig. 3 compares the measured and calculated subsurface velocities obtained at different casting speeds at the point corresponding to 1/4 the width of the mold. The other experimental operating parameters include an Ar gas flow rate of 4 L∙min−1 and SEN immersion depth of 170 mm in a 1080 mm-wide mold. The subsurface velocities of molten steel increase with increasing casting speed, and the calculated results are in good agreement with the measured values. The subsurface velocity of liquid steel increases from approximately 0.1 to 0.3 m∙s−1 as the casting speed increases from 1.3 to 1.7 m∙min−1 because increased casting speeds lead to more kinetic energy when the molten steel flows out of the ports of the SEN. The molten steel stream then comes into contact with the narrow wall to form upward and downward circulation zones. Thus, increased casting speeds can increase the subsurface velocity of molten steel.

      Figure 3.  Comparison of the measured and calculated subsurface velocities at different casting speeds with 1080 mm mold width, 4 L·min−1 gas flow rate, and 170 mm immersion depth: (a) calculated results; (b) comparison of experimental and calculated results.

      Fig. 4 shows the distributions of the velocity vectors of molten steel in the central vertical plane of the mold at different casting speeds. All of the flow patterns of molten steel are DRF when the casting speeds are 1.3, 1.5, and 1.7 m∙min−1. However, the positions of the upward and downward circulation zones change with increasing casting speed. When the casting speed is increased from 1.3 to 1.7 m∙min−1, the subsurface velocities of molten steel slightly increase in the upward circulation zone, but the position of the vortex core drastically shifts downward in the downward circulation zone. Because most Ar bubbles, especially small ones, flow with the stream of molten steel, more bubbles, and inclusions flow into the depth of the mold, which may cause sliver defects [27].

      Figure 4.  Distributions of the velocity vectors of molten steel in the central vertical plane of the mold at casting speeds of (a) 1.3 m∙min−1, (b) 1.5 m∙min−1, and (c) 1.7 m∙min−1 with 1080 mm mold width, 4 L∙min-1 gas flow rate, and 170 mm immersion depth.

      Fig. 5 illustrates the distributions of the velocity contours and vectors of molten steel in the horizontal plane located 50 mm below the surface of the mold under different casting speeds. The peak region of the molten steel flow velocity is located at the point corresponding to 250 mm from the SEN. As the casting speed is increased from 1.3 to 1.5 m∙min−1, the subsurface velocities of molten steel slightly increase. When the casting speed is increased to 1.7 m∙min−1, the velocities of liquid steel obviously increase, and the maximum value is approximately 0.46 m∙s−1. High surface velocities may produce strong shear forces and eddies that can lead to slag entrapment in the mold.

      Figure 5.  Distributions of the subsurface velocity contours (left in figure) and vectors (right in figure) of molten steel in the horizontal plane at casting speeds of (a) 1.3 m∙min−1, (b) 1.5 m∙min−1, and (c) 1.7 m∙min−1 with 1080 mm mold width, 4 L∙min−1 gas flow rate, and 170 mm immersion depth.

      Fig. 6 presents the distributions of the velocity vectors of molten steel in horizontal planes located at different distances from the mold surface at a casting speed of 1.7 m∙min−1. Figs. 6(a)6(c) reveal that two eddies form near the nozzle in horizontal planes located 0–100 mm from the meniscus. When the velocities on both sides of the nozzle are not equal, two vortices tend to form in the low-speed zone on one side. The formation of these vortices may cause slag entrainment in the mold. Fig. 6(b) shows that the flow field in the horizontal plane located 50 mm from the meniscus has larger, more orderly, and better-distributed velocities than those in other horizontal planes. Thus, the flow field in this plane can be used as the characteristic flow field to optimize the flow field in the mold. This is the reason why the point of 50 mm from surface was chosen to measure the subsurface velocities of molten steel in the present work. Moreover, the red velocity vectors in Fig. 6(d) show that the molten steel flows out of the ports and into the jet zone in the horizontal plane located 200 mm from the meniscus.

      Figure 6.  Distributions of the velocity vectors of molten steel in horizontal planes located at different distances from the mold surface with 1.7 m∙min−1 casting speed, 1080 mm mold width, 4 L·min−1 gas flow rate, and 170 mm immersion depth: (a) 0 mm; (b) 50 mm; (c) 100 mm; (d) 200 mm.

    • Ar gas injection plays an important role in the removal of inclusions, slag entrapment, and nozzle clogging; thus, it has a great impact on slab surface quality. Fig. 7 compares the measured and calculated subsurface velocities obtained at different Ar gas flow rates, a casting speed of 1.7 m∙min−1, and SEN immersion depth of 170 mm in a 1040 mm-wide mold. The velocities of the molten steel obviously decrease with increasing Ar gas flow rate. The calculated subsurface velocities of molten steel are consistent with the measured results in terms of both trends and values, as shown in Fig. 7. The subsurface velocity of molten steel decreases from 0.30 to 0.12 m∙s−1 as the Ar gas flow rate increases from 1 to 7 L∙min−1.

      Figure 7.  Comparison of the measured and calculated subsurface velocities of molten steel at different Ar gas flow rates with 1040 mm mold width, 1.7 m·min−1 casting speed, and 170 mm immersion depth: (a) calculated results; (b) comparison of experimental and calculated results.

      Fig. 8 illustrates the distributions of the velocity contours and vectors of molten steel in the central vertical plane at different Ar gas flow rates of 1, 4, and 7 L·min−1. The other experimental conditions include a casting speed of 1.7 m·min−1 and SEN immersion depth of 170 mm in a 1040 mm-wide mold. When the Ar gas flow rate is increased from 1 to 4 L·min−1, the flow patterns of molten steel are typically DRF. However, the flow pattern changes from DRF to unstable flow (UF) [28] when the Ar gas flow rate is further increased from 4 to 7 L·min−1.

      Figure 8.  Distributions of the velocity contours and vectors of molten steel in the central vertical plane at Ar gas flow rates of (a) 1 L·min−1, (b) 4 L·min−1, and (c) 7 L·min−1 with 1040 mm mold width, 1.7 m·min−1 casting speed, and 170 mm immersion depth.

      Fig. 9 illustrates the distributions of the velocity contours and vectors of molten steel in the horizontal plane located 50 mm below the mold surface at different gas flow rates. As the Ar gas flow rate increases, the number of Ar bubbles increases and more bubbles show a greater buoyancy force and faster rising velocity. Thus, the subsurface velocities decrease and flow directions become more dispersed as the Ar gas flow rate increases [2829].

      Figure 9.  Distributions of the subsurface velocity contours (left in figure) and vectors (right in figure) of molten steel in the horizontal plane at gas flow rates of (a) 1 L·min−1, (b) 4 L·min−1, and (c) 7 L·min−1 with 1040 mm mold width, 1.7 m·min−1 casting speed, and 170 mm immersion depth.

      Fig. 10 shows the distributions of velocity vectors in horizontal planes located at different distances from the mold surface at an Ar gas flow rate of 7 L·min−1. The distributions of the velocities of liquid steel are similar and well-distributed in horizontal planes located 0 mm (Fig. 10(a)), 50 mm (Fig. 10(b)), and 100 mm (Fig. 10(c)) below the meniscus, which can improve the flow field in the slab CC mold with a narrow width of 1040 mm.

      Figure 10.  Distributions of the velocity vectors of molten steel in horizontal planes located at different distances from the mold surface with 1040 mm mold width, 1.7 m·min−1 casting speed, 7 L·min−1 gas flow rate, and 170 mm immersion depth: (a) 0 mm; (b) 50 mm; (c) 100 mm; (d) 200 mm.

      The casting speed of slab CC molds with a narrow width is usually high, and the corresponding flow pattern is DRF. However, if DRF is too strong, the high surface velocity of molten steel may result in slag entrapment. According to the above results, Ar gas bubbles can decrease the subsurface velocities of molten steel and change the flow pattern in the mold. Therefore, maintaining a relatively large Ar gas flow rate in slab CC molds with a narrow width of 1040 mm could help improve the surface quality of automobile exposed panels.

    • The SEN immersion depth is generally defined as the distance from the mold surface to the upper edges of the SEN ports. The immersion depth of the nozzle determines the initial position of the molten steel stream entering the mold; thus, this parameter affects the flow characteristics of liquid steel in the slab CC mold.

      Fig. 11 compares the measured and calculated subsurface velocities at the point corresponding to 1/4 the width of the mold at different SEN immersion depths. Here, the casting speed is 1.7 m·min−1 and the Ar gas flow rate is 4 L·min−1 in a 1040 mm-wide mold. The subsurface velocities of the molten steel first decrease and then increase with increasing SEN immersion depth. The calculated results are consistent with the measured values in Fig. 11. The subsurface velocity of liquid steel decreases from 0.2 to 0.15 m∙s−1 as the SEN immersion depth increases from 140 to 170 mm. However, when the SEN immersion depth is further increased from 170 to 190 mm, the velocity increases from 0.15 to 0.33 m∙s–1 because the molten steel flow in the upward circulation zone is incompletely developed when the immersion depth of SEN is 140 or 170 mm. At a SEN immersion depth of 190 mm, however, the position of the jet zone moves downward and the stream of molten steel has sufficient space to develop and increase the velocity near the mold surface in the upward circulation zone, which can be seen in Fig. 12.

      Figure 11.  Comparison of the measured and calculated subsurface velocities at different SEN immersion depths with 1040 mm mold width, 1.7 m·min−1 casting speed and 4 L·min−1 gas flow rate: (a) Calculated results; (b) Comparison of experimental and calculated results.

      Figure 12.  Distributions of the velocity contours and vectors of molten steel in the central vertical plane at SEN depths of (a) 140 mm, (b) 170 mm, and (c) 190 mm with 1040 mm mold width, 1.7 m·min−1 casting speed and 4 L·min−1 gas flow rate.

      Fig. 12 shows the distributions of the velocity contours and vectors of molten steel in the central vertical plane at different SEN immersion depths of 140, 170, and 190 mm. Here, the casting speed is 1.7 m·min−1 and the Ar gas flow rate is 4 L/min in a 1040 mm-wide mold. The regional scale of the upward circulation zone increases with increasing SEN immersion depth. The complete development of liquid steel flow in the upward circulation zone occurs at the SEN immersion depth of 190 mm.

      Fig. 13 shows the distributions of the velocity contours and vectors of molten steel in the horizontal plane located 50 mm below the surface at different SEN immersion depths. The velocity of molten steel at the SEN immersion depth of 170 mm is smaller than the velocity of molten steel at immersion depths of 140 mm or 190 mm. Too-shallow SEN immersion depths may cause SRF or UF, while too-steep immersion depths cause inclusions to flow into the downward circulation zone and become captured by the solidified shell front. Thus, under the present experimental conditions, the DRF pattern is generally stable when the SEN immersion depth is 170 mm, which helps improve the surface quality of automobile exposed panels.

      Figure 13.  Distributions of the subsurface velocity contours (left in figure) and vectors (right in figure) of molten steel in the horizontal plane at SEN depths of (a) 140 mm, (b) 170 mm, and (c) 190 mm with 1040 mm mold width, 1.7 m·min−1 casting speed, and 4 L·min−1 gas flow rate.

    5.   Conclusions
    • In the present work, computational simulations and high-temperature measurements of subsurface velocities were conducted by using the rod deflection method to investigate the effects of various operating parameters on the fluid field of molten steel in slab CC molds with a narrow width. Based on the calculated and measured results, the conclusions can be summarized as follows.

      (1) The rod deflection method may be successfully used to directly measure the subsurface velocities of molten steel. The calculated results are consistent with the measured values of molten steel at points corresponding to a distance of 100 mm from the narrow wall and 1/4 the width of the mold near the mold surface under different casting speeds, Ar gas flow rates, and SEN immersion depths.

      (2) The flow field in the horizontal plane located 50 mm from the meniscus has larger, more orderly, and better-distributed velocities than those in other horizontal planes. Therefore, the flow field in this plane can be used as the characteristic flow field for optimizing the flow field in the mold.

      (3) Increased casting speeds can increase the subsurface velocity of molten steel and shift the position of the vortex core downward in the downward circulation zone. Eddies may be easily produced by high casting speeds, resulting in slag entrainment in the mold.

      (4) The subsurface velocity of liquid steel slows down and the flow pattern of molten steel changes with increasing Ar gas flow rate. The flow field in a 1040 mm-wide slab CC mold can be improved by implementing an Ar gas flow rate of 7 L/min and casting speed of 1.7 m/min.

      (5) The velocity of liquid steel near the mold surface first decreases and then increases with increasing SEN immersion depth. Under the present experimental conditions, the DRF pattern is generally stable at a SEN immersion depth of 170 mm.

    Acknowledgements
    • This work was financially supported by the Hunan Valin Lianyuan Iron & Steel Co., Ltd., China (No. 18H00582). The authors are grateful to Hunan Valin Lianyuan Iron & Steel Co., Ltd., China for their assistance with the industrial measurement of velocities near the mold surface.

Reference (29)

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