2024 年 64 巻 6 号 p. 1010-1018
The fluid flow and slag entrainment in a slab continuous casting mold were investigated by establishing a full-scale water model. Meanwhile, the heat transfer and solidification process of liquid steel in the mold were studied through numerical simulation. The effect of two different submerged entry nozzles (SENs) was compared and analyzed, named as original SEN and L1 SEN, respectively. The results indicate that the structure of the SEN has a significant influence on the fluid flow pattern and solidification process in the slab mold. For the original SEN, the liquid level in the mold fluctuated obviously and the slag phase was easily entrained into the mold. The percentage of ±3 mm level fluctuation was 57.2–74.3%. By enlarging the exit size, the L1 SEN considerably reduced the jet velocity at the nozzle exit and subsequently decreased the surface velocity at the top surface. The level fluctuation and slag entrainment in the mold have been effectively controlled. The percentage of ±3 mm level fluctuation was increased to 91.7–98.6%. Furthermore, under the condition of L1 SEN, the thickness of the solidifying shell at the mold outlet was increased from 13.5 mm to 16.4 mm, which was beneficial to decrease the risk of breakouts and quality problems.
The flow pattern of liquid steel in the slab mold significantly affects the quality of the final products. Excessive surface velocities can lead to inclusion defects due to slag entrainment and level fluctuations.1,2,3,4,5,6) The fluid flow in the slab mold greatly depends on the submerged entry nozzle (SEN) design, casting speed, strand cross-sectional dimensions, and SEN immersion depth.7,8,9,10,11,12,13,14) When the strand cross-sectional dimensions and casting speed are fixed, the SEN design is of great importance to obtain an appropriate flow pattern in the slab mold. Relevant investigations have been reported through experimental works and numerical simulations.
Bai et al.7) demonstrated that the nozzle with a square port produced a larger jet speed and allowed a stronger swirl to exit the port, leading to asymmetrical flow in the mold, compared with the nozzle with a rectangular port. Chaudhary et al.8) found that the well-bottom nozzle produced less surface fluctuations in the mold and it was recommended over the mountain-bottom shape for steel quality. Calderón-Ramos et al.9) compared three different SENs with the same bore size in a slab mold and the nozzle with square ports was the best choice to control the turbulence and decrease the quality problems. Gan et al.10) reported that the nozzle with an approximately oval exit performed better than the nozzle with a rectangular exit in stabilizing the top surface and decreasing the incidence of slag entrainment in the mold. Jiang et al.11) have also obtained similar results. Ren et al.12,15) found that the kinetic energy loss of the jet was reduced when the outlet angle of the SEN was 0° and the flow pattern in the mold became more symmetrical. It was beneficial to melt the mold flux. Lee et al.16) pointed out that for SEN port angles in the range of 0–15°, the flow velocity in the upper circulation zone of a conventional slab mold oscillated in an unstable manner. For port angles of 20° or more, the flow velocity decreased sharply and became stabilized. Chen et al.17) obtained that the swirling flow in the SEN could reduce the impinging on the narrow face and inhibit the slag entrapment. Li et al.18) and Yang et al.19) reported the influence of SEN clogging on the fluid flow and steel cleanliness. These studies above indicate that the SEN design greatly affects the flow behaviors of the jet in the SEN and mold.
Recently, the inclusion defects caused by slag entrainment in a chamfered slab mold were found in cold-rolled plates at a steel plant. Sometimes, a W-shaped macrosegregation was also observed in the slab. Based on the preliminary analysis, these defects were probably related to the flow pattern of liquid steel in the mold. In the present study, physical modeling experiments were first conducted to investigate the fluid flow and slag movement in the slab mold. Second, the velocity fields and thickness of the solidifying shell in the mold were simulated by developing a mathematical model, considering the flow, heat transfer, and solidification process. The effect of two different SENs was also studied by comparing the level fluctuation, slag entrainment, velocity distribution, and shell thickness.
A full-scale water model of the slab mold was built with transparent plexiglass. The height of the mold was 950 mm. To avoid the influence of the reversed flow on the flow field in the mold, the model was extended to 2200 mm, as shown in Fig. 1. The level fluctuations at three different positions were measured through a wave-height sensor (DJ 800, produced by China Institute of Water Resources and Hydropower Research). The three positions are located at 30 mm from the SEN exit, at 1/4 mold width, and at 20 mm from the narrow face, respectively. The dimensions and parameters of the prototype and water model are listed in Table 1. Two types of SENs were considered in the present study, as shown in Fig. 2. They were named as original SEN and L1 SEN, respectively. Both of them have racetrack ports. The original SEN is widely used for continuous casting of slab and it has a round bore. The L1 SEN is a newly one (designed by National Engineering and Research Center for Continuous Casting Technology, Central Iron and Steel Research Institute). Compared with the original SEN, the bore and port sizes of the L1 SEN are enlarged to reduce the kinetic energy of the jet in the SEN and at the nozzle exit and stabilize the fluid flow in the mold.
| Parameters | Prototype | Model |
|---|---|---|
| Cross section of mold (mm2) | 230×1820 | 230×1820 |
| Size of nozzle exit (mm2) | 52×80 | 52×80 |
| Diameter of submerged entry nozzle (mm) | 55 | 55 |
| Immersion depth (mm) | 130, 140 | 130, 140 |
| Exit angle (°) | 15 | 15 |
| Casting speed (m/min) | 1.25 | |
| Flow rate in the water model (m3/h) | 34.9 |
The flow rate in the water model is calculated based on the Froude similarity criterion.
| (1) |
where the subscripts m and p represent the model and the prototype, respectively.
Based on Eq. (1), the flow rate in the water model was 34.9 m3/h. The physical properties of each phase in the prototype and water model are shown in Table 2. During experiments, the flow rates at the tundish inlet and the mold bottom were controlled through the turbine flow meter. The adjustment of a stopper rod was used to stabilize the liquid level. The liquid level remained almost unchanged for 5 minutes. After that, the level fluctuations in the water model were measured using the DJ 800 equipment. The measured data were collected for 50 seconds. Each experiment was repeated three times. To display the fluid flow in the mold, ink tracer experiments were conducted. Furthermore, a commercial silicon oil was added to the water model to study the movement of the slag phase. The oil phase was determined based on the viscosity ratio,20,21,22,23) as shown in Eq. (2). The thickness of the oil phase was 15 mm and its movement was recorded using a CCD camera during experiments.
| (2) |
where μ is the viscosity (Pa·s).
| Density (kg/m3) | Viscosity (Pa·s) | |
|---|---|---|
| Water | 998 | 0.001 |
| Silicon oil | 955 | 0.033 |
| Liquid steel | 7020 | 0.0067 |
| Slag | 2600 | 0.20 |
| Interfacial tension between liquid steel and slag (N/m) | 1.15 | |
The three-dimensional (3-D) single-phase transient fluid flow, heat transfer, and solidification in the mold were modeled by calculating the continuity equation, Navier-Stokes equations, realizable k-ε turbulence model, energy equation, and solidification equations.24,25,26) The energy conservation equation is expressed by
| (3) |
where ρ is the fluid density (kg/m3), H is the enthalpy (J/kg), ui is the fluid velocity at direction i (m/s), t is time (s), xi is the coordinate at direction i (m), keff is the effective thermal conductivity (W/m/K), and T is the temperature (K).
The enthalpy-porosity technique was used to track the liquid-solid front.27,28) The liquid-solid mushy zone is treated as a porous zone. It uses the liquid fraction to describe the mushy zone. The liquid fraction β is defined as
| (4) |
where Ts is the solidus temperature of the steel (K), and Tl is the liquidus temperature of the steel (K).
The solidification of liquid steel would lead to the losses of momentum and turbulence, which were considered by adding a source term to the momentum equation and turbulence equation. The momentum source term Sm is represented as
| (5) |
where Amush is the mushy zone constant, and uC is the casting speed (m/s).
The turbulence source term St is described as
| (6) |
where ϕ is the turbulence quantity.
3.2. Boundary Conditions and Computational ProcedureIn this work, the system of equations was solved by a commercial CFD software (Fluent version 14.0). Considering the symmetry of the liquid steel flow, only half of the geometric model was built as a computational domain, as shown in Fig. 3. The total height of the computational domain was 3000 mm. The number of cell grids was approximately 900, 000.
The inlet velocity of the SEN was calculated according to the casting speed and cross-sectional area of the slab. The casting temperature was set as 1816 K (1543°C). The outflow boundary condition was set at the domain bottom. The top surface of the mold was treated as a free surface with a zero-shear stress. Non-slip conditions were chosen at the walls. The heat fluxes at the narrow and wide faces of the mold were obtained according to the flow rate and temperature difference of cooling water in the mold walls. The convection and mixed heat transfer conditions were set at wide and narrow faces of the extended region, respectively. The standard wall functions were used to model the turbulence characteristics in the near-wall region. The PISO scheme was used for the pressure-velocity coupling. The convergence criterion for the energy equation was set to 10−6 and 10−4 for other variables. The time step was 0.001 seconds. All computations were performed on a Windows 10 PC with Intel 3.5 GHz CPU and 512 GB RAM. The parameters of liquid steel and heat transfer conditions in numerical simulations are listed in Table 3.
| Parameters | Value |
|---|---|
| Density (kg/m3) | 7020 |
| Viscosity (Pa·s) | 0.0062 |
| Specific heat (J/kg/K) | 760 |
| Thermal conductivity (W/m/K) | 31 |
| Latent heat (J/kg) | 272000 |
| Solidus temperature (K) | 1748 |
| Liquidus temperature (K) | 1791 |
| Heat flux at the narrow face of the mold (kW/m2) | −1500 |
| Heat flux at the wide face of the mold (kW/m2) | −1600 |
Figure 4 shows the fluid flow in the mold at different moments using the original SEN. The immersion depth of the SEN was 130 mm. It can be seen that the jets from the nozzle exit firstly impinged upon the narrow faces, and then flowed upwards and towards the SEN, forming a typical double roll flow in the mold. The level fluctuations at different immersion depths were measured, as shown in Fig. 5. The liquid level in the water model fluctuated obviously. Increasing the immersion depth of the SEN could not decrease the level fluctuation. Furthermore, the level fluctuation at 1/4 mold width was relatively higher and the percentage of ±3 mm level fluctuation was only 57.2–57.3%, as shown in Fig. 6. For the immersion depth of 130 mm, the percentage of ±3 mm level fluctuation was 57.3–74.3%, while it was 57.2–68% for the immersion depth of 140 mm.
Figure 7 shows the level fluctuations in the mold at different immersion depths using L1 SEN. Compared with the original SEN, the level fluctuations in the mold using L1 SEN were significantly decreased. Increasing the immersion depth of the SEN from 130 mm to 140 mm slightly decreased the level fluctuation in the mold. For the immersion depth of 130 mm, the percentage of ±3 mm level fluctuation was 91.7–96%, as shown in Fig. 8. It was 94.7–98.6% for the immersion depth of 140 mm. Moreover, the use of L1 SEN could effectively control the level fluctuation at 1/4 mold width and the percentage was considerably increased to 96–98.6%.
Figure 9 shows the distribution of the oil phase in the mold at different moments using the original SEN. During experiments, the immersion depth of the SEN was 130 mm. It can be observed that the water-oil interface using the original SEN became active and the oil phase near the left narrow face was pushed towards the 1/4 mold width, as shown in part (a). A certain amount of small oil droplets was dragged into the water model in part (b). Due to the shear effect of the surface flow, the thickness of the oil phase near the left narrow face had become thinner and it was occasionally opened, as shown in part (c). It indicated that the original SEN could easily cause the entrainment of the mold flux in the prototype and the entrained flux might become a source of exogenous inclusions in the slab.
The application of L1 SEN significantly decreased the oil entrainment, as shown in Fig. 10. These results in Fig. 10 correspond to the same moments in Fig. 9. The water-oil interface using L1 SEN remained relatively stable. Only a small amount of oil phase was entrained into the water model, and then this part of the oil phase could rapidly float up leaving a cleaner bath. Although the oil phase near the left narrow face had become thinner, it was never opened during experiments.
To validate the present mathematical model, a simulation work for a one-quarter scale water model of a 200 mm× 2040 mm slab mold was conducted. The velocity fields in the water model have been measured using a particle image velocimetry (PIV) equipment in previous investigations.12) The predicted velocities below work level at 3 mm along the mold width at the center plane with those measured by PIV are compared in Fig. 11. It can be observed that the velocities from the SEN to 1/4 mold width gradually increase and there is good agreement between predicted and measured values. The discrepancies between them are from 1/4 mold width to the narrow face, where the measured values drop at a faster rate. Taking into account the overall distribution, the present mathematical model provides reasonable predictions of velocity fields in the slab mold.
Figure 12 shows the velocity distribution at the symmetry plane in the mold using different SENs. Similarly, a typical double roll flow was also observed in the mold. For L1 SEN, enlarging the bore size significantly decreased the velocity of liquid steel in the SEN, as shown in Fig. 13. The maximum velocity was lowered from 3.6 m/s to 1.6 m/s and it would reduce the erosion on the inner wall of the SEN. The exit size of L1 SEN has also been enlarged and its exit area is 1.825 times that of the original SEN. The velocity of the jet from the nozzle exit was further lowered. For the original SEN, the maximum velocity at the nozzle exit exceeded 3.0 m/s, while the maximum value was reduced to 1.2 m/s for L1 SEN, as shown in Fig. 14. After impinging on the narrow faces, the intensities of both the upper and lower backflows have been decreased.
For the steel-slag systems, the critical velocity of slag entrainment could be determined by the Capillary number Ca and critical Capillary number Ca*.20) They are defined as
| (7) |
| (8) |
where Vsteel is the tangential velocity of liquid steel at the steel-slag interface (m/s), μsteel is the viscosity of liquid steel (Pa·s), σsteel-slag is the interfacial tension between liquid steel and slag (N/m), νslag is the kinematic viscosity of slag phase (m2/s), and νsteel is the kinematic viscosity of liquid steel (m2/s).
Based on the parameters in Table 2, the critical tangential velocity for slag entrainment was 0.52 m/s. Figure 15 shows the velocity distribution at the top surface of the mold using different SENs and the comparison of the velocity magnitude along the dotted line is plotted in Fig. 16. It can be observed that the surface velocity using the original SEN was significantly larger than that using the L1 SEN. The surface velocity at 1/4 mold width was larger than 0.62 m/s and its maximum value was 0.68 m/s, indicating that the slag phase at the top surface was easily entrained into the liquid steel. It also revealed the experimental results in Fig. 9. When the L1 SEN was adopted, the maximum surface velocity was decreased to 0.44 m/s, smaller than the critical tangential velocity for slag entrainment. Therefore, the slag entrainment could be controlled, which has been proved by these results in Fig. 10.
Figure 17 shows the distribution of liquid fraction at the mold outlet using different SENs. It can be seen that the thickness of the solidifying shell was thinner for the original SEN and the shell thickness at the center of the narrow face was 13.5 mm. For L1 SEN, the shell thickness at the mold outlet was increased to 16.4 mm. The predicted shell thickness was also compared with that estimated by the empirical formula,29,30) as shown in Fig. 18. Obviously, the predicted shell thickness using the L1 SEN was consistent with the estimated values. For the original SEN, the jet from the nozzle exit had a large kinetic energy and more heat could be transferred to the narrow face. The solidification process was slowed down and the shell thickness at the mold outlet was reduced. Increasing the shell thickness at the mold outlet was beneficial to decrease the risk of breakouts and quality problems. Consequently, the L1 SEN was recommended to replace the original SEN during the current continuous casting process.
The fluid flow, slag entrainment, heat transfer, and solidification process in a slab continuous casting mold were investigated using physical modeling and numerical simulation. The effect of the submerged entry nozzle (SEN) structure was considered. The conclusions were summarized as follows.
(1) The liquid level in the mold using the original SEN fluctuated obviously and the slag phase was easily entrained into the mold. Increasing the immersion depth of the SEN had little influence on decreasing the level fluctuation and slag entrainment. The percentage of ±3 mm level fluctuation was 57.2–74.3%.
(2) The use of the L1 SEN considerably reduced the jet velocity at the nozzle exit by enlarging the exit size. The level fluctuation and slag entrainment in the mold could be effectively controlled. The percentage of ±3 mm level fluctuation was increased to 91.7–98.6%.
(3) The surface velocity in the mold using the original SEN was significantly larger than that using the L1 SEN. For the original SEN, the maximum surface velocity was 0.68 m/s, while it was decreased to 0.44 m/s for L1 SEN.
(4) When the L1 SEN was adopted, the thickness of the solidifying shell at the mold outlet was 16.4 mm, higher than the value of 13.5 mm for the original SEN. It was beneficial to decrease the risk of breakouts and quality problems.
The authors are grateful for support from the National Natural Science Foundation of China (Grant No. 52274312), Anhui Provincial Natural Science Foundation (Grant No. 2308085Y36), and the University Natural Science Research Project of Education Department of Anhui Province (Grant No. KJ2021A0396).
