Hydrodynamic Modeling and Mathematical Simulation on Flow Field and Inclusion Removal in a Seven-Strand Continuous Casting Tundish with Channel Type Induction Heating
Abstract
:1. Introduction
2. Physical Modelling
2.1. Description of the Tundish
2.2. Method and Criteria of Hydrodynamic Modelling
2.2.1. Experimental Setup and Method
2.2.2. Schemes of the Physical Experiments
3. Mathematical Model
3.1. Control Equations
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.
3.2.2. Boundary Condition and Solution Method
3.3. Condition for Inclusions Behavior Simulation
4. Results and Discussions
4.1. Results of the Non-Isothermal Experiment
4.2. Results of the Isothermal Experiment
4.3. Results of Mathematical Simulation
4.4. Inclusion Removal Behavior
5. Conclusions
- (1)
- The non-isothermal experiment and mathematical simulation 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 will be the fluid flows among different strands, and the more homogeneous the flow field in the tundish. For the prototype tundish, when the temperature difference is 5 °C, the dead zone is basically eliminated, and the residence time of fluid is prolonged by 300 s. The rising trend of fluid will decay with the further elongation of the heating time to 5000 s. Under this case, the non-isothermal flow will be developed into 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 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%.
- (3)
- 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
Acknowledgments
Conflicts of Interest
References
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Parameters | Data |
---|---|
Length of bottom surface of discharging chamber (A) | 9504 mm |
Length of top surface of discharging chamber (B) | 9882 mm |
Width of bottom surface of discharging chamber (C) | 480 mm |
Width of top surface of discharging chamber (D) | 820 mm |
Width of pouring chamber (E) | 1173 mm |
Distance from the shroud to the Outlet 4 (F) | 950 mm |
Length of the channel (G) | 1600 mm |
Distance between two outlets (H) | 1500 mm |
Height of the channel’s export to bottom surface (I) | 300 mm |
Inclination of the channel (α) | 5° |
Volume of the tundish | 6.3 m3 |
Parameters | Data |
---|---|
Section size of billet caster | 200 mm × 200 mm |
Casting speed | 0.8 m/min |
Depth of the molten bath | 870 mm |
Volumetric flowrate of every inlet | 0.034 m3/min |
Case | Temperature Difference, /°C | |
---|---|---|
Prototype | Model | |
A0 | 0 | 0 |
A1 | 5 | 5.6 |
A2 | 10 | 11.2 |
A3 | 20 | 22.4 |
A4 | 30 | 33.6 |
Case | α (°) | I (mm) | h (mm) |
---|---|---|---|
A0 (prototype) | 5 | 300 | 0 |
B1 | 5 | 300 | 80 |
B2 | 5 | 300 | 160 |
B3 | −5 | 160 | 0 |
B4 | −5 | 160 | 80 |
B5 | −5 | 160 | 160 |
B6 | 10 | 440 | 0 |
B7 | 10 | 440 | 80 |
B8 | 10 | 440 | 160 |
B9 | −10 | 160 | 0 |
B10 | −10 | 160 | 80 |
B11 | −10 | 160 | 160 |
B12 | 0 | 160 | 0 |
B13 | 0 | 160 | 80 |
B14 | 0 | 160 | 160 |
Case | I (mm) | a (mm) | b (mm) | c (mm) | d (mm) |
---|---|---|---|---|---|
C1 | 590 | - | - | 0 | 0 |
C2 | 590 | - | 450 | 0 | 245 |
C3 | 590 | - | 225 | 0 | 245 |
C4 | 590 | 240 | 375 | 245 | 510 |
C5 | 590 | 240 | 375 | 510 | 510 |
Parameters | Data |
---|---|
Density | 8523–0.8358 T kg/m3 |
Viscosity | 0.006 kg/(m·s) |
Specific heat | 750 J/(kg·K) |
Thermal conductivity | 41 W/(m·K) |
Mass diffusion coefficients of tracer | 1.1 × 10−8 m2/s |
Parameters | Data, W/m2 |
---|---|
Slag layer | 15,000 |
Side wall | 4000 |
Channel wall | 1200 |
Bottom wall | 1800 |
Case | (s) | (s) | (s) | (s) | (s) | (%) | (%) | (%) | |||
---|---|---|---|---|---|---|---|---|---|---|---|
A0 | 38 | 48 | 38 | 80 | 501.27 | 6.41 | 48.02 | 45.57 | 91.01 | 61.39 | 88.15 |
A1 | 215 | 600 | 338 | 555 | 914.28 | 48.48 | 50.79 | 0.73 | 63.94 | 71.33 | 32.33 |
A2 | 378 | 528 | 357 | 528 | 893.32 | 48.05 | 48.95 | 3.01 | 21.12 | 21.00 | 15.53 |
A3 | 439 | 594 | 430 | 661 | 986.71 | 59.23 | 40.77 | 0 | 7.40 | 55.45 | 31.64 |
A4 | 422 | 581 | 372 | 624 | 1001.31 | 52.61 | 47.39 | 0 | 7.58 | 30.47 | 30.79 |
Case | (s) | (s) | (s) | (s) | (s) | (%) | (%) | (%) | |||
---|---|---|---|---|---|---|---|---|---|---|---|
A0 | 38 | 48 | 38 | 80 | 501.27 | 6.41 | 48.02 | 45.57 | 91.01 | 61.39 | 88.15 |
B1 | 39 | 57 | 40 | 102 | 475.82 | 7.71 | 43.77 | 48.52 | 21.18 | 25.41 | 35.72 |
B2 | 49 | 84 | 51 | 127 | 545.97 | 9.69 | 49.59 | 40.72 | 69.56 | 29.84 | 28.52 |
B3 | 40 | 54 | 43 | 102 | 568.15 | 7.90 | 53.79 | 38.31 | 147.22 | 80.03 | 161.50 |
B4 | 40 | 67 | 41 | 110 | 572.61 | 9.45 | 52.73 | 37.82 | 312.93 | 44.92 | 39.72 |
B5 | 48 | 82 | 52 | 156 | 569.15 | 11.29 | 50.51 | 38.20 | 61.22 | 38.66 | 26.89 |
B6 | 38 | 47 | 39 | 93 | 529.57 | 7.17 | 50.33 | 42.50 | 44.05 | 31.58 | 67.17 |
B7 | 40 | 57 | 41 | 119 | 521.41 | 8.71 | 47.90 | 43.39 | 50.19 | 30.70 | 71.87 |
B8 | 36 | 53 | 36 | 191 | 525.22 | 9.69 | 49.59 | 40.72 | 66.15 | 36.01 | 72.77 |
B9 | 33 | 53 | 34 | 72 | 578.56 | 5.75 | 57.06 | 37.19 | 155.29 | 44.51 | 85.68 |
B10 | 45 | 71 | 46 | 116 | 544.40 | 8.79 | 50.31 | 40.90 | 213.2 | 49.07 | 55.05 |
B11 | 63 | 98 | 61 | 161 | 573.35 | 12.08 | 50.17 | 37.57 | 17.49 | 36.95 | 37.10 |
B12 | 36 | 55 | 37 | 103 | 500.36 | 8.31 | 45.18 | 46.51 | 220.07 | 82.61 | 130.19 |
B13 | 40 | 66 | 41 | 126 | 445.86 | 9.07 | 39.24 | 51.59 | 175.16 | 32.98 | 29.97 |
B14 | 49 | 75 | 49 | 140 | 431.24 | 10.26 | 36.56 | 53.18 | 41.10 | 32.59 | 30.66 |
Case | (s) | (s) | (s) | (s) | (s) | (%) | (%) | (%) | |||
---|---|---|---|---|---|---|---|---|---|---|---|
C1 | 46 | 65 | 46 | 218 | 636.42 | 14.33 | 54.77 | 30.90 | 82.58 | 57.47 | 109.22 |
C2 | 36 | 62 | 37 | 94 | 652.80 | 7.11 | 63.77 | 29.12 | 70.03 | 51.68 | 106.87 |
C3 | 42 | 127 | 62 | 176 | 617.82 | 12.92 | 54.16 | 32.92 | 22.5 | 46.39 | 35.81 |
C4 | 82 | 167 | 83 | 171 | 656.23 | 13.79 | 57.46 | 28.74 | 76.01 | 30.27 | 33.22 |
C5 | 77 | 252 | 92 | 212 | 779.03 | 16.50 | 68.09 | 15.41 | 42.67 | 42.70 | 38.40 |
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Tang, H.; Guo, L.; Wu, G.; Xiao, H.; Yao, H.; Zhang, J. Hydrodynamic Modeling and Mathematical Simulation on Flow Field and Inclusion Removal in a Seven-Strand Continuous Casting Tundish with Channel Type Induction Heating. Metals 2018, 8, 374. https://doi.org/10.3390/met8060374
Tang H, Guo L, Wu G, Xiao H, Yao H, Zhang J. Hydrodynamic Modeling and Mathematical Simulation on Flow Field and Inclusion Removal in a Seven-Strand Continuous Casting Tundish with Channel Type Induction Heating. Metals. 2018; 8(6):374. https://doi.org/10.3390/met8060374
Chicago/Turabian StyleTang, Haiyan, Luzhao Guo, Guanghui Wu, Hong Xiao, Haiying Yao, and Jiaquan Zhang. 2018. "Hydrodynamic Modeling and Mathematical Simulation on Flow Field and Inclusion Removal in a Seven-Strand Continuous Casting Tundish with Channel Type Induction Heating" Metals 8, no. 6: 374. https://doi.org/10.3390/met8060374