# Improved Metallurgical Effect of Tundish through a Novel Induction Heating Channel for Multistrand Casting

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Models

#### 2.1. Geometric Model and Meshing

#### 2.2. Mathematical Modeling Assumptions

#### 2.3. Governing Equations

#### 2.3.1. Control Equations of the Electromagnetic Field

#### 2.3.2. Fluid Dynamics and Heat Transfer Equations

_{i}is coordinate in i direction, m.

_{eff}is effective viscosity, ${\mathrm{kg}\xb7\mathrm{m}}^{-1}{\xb7\mathrm{s}}^{-1}$; g is acceleration of gravity, ${\mathrm{m}\xb7\mathrm{s}}^{-2}$; $\overrightarrow{{F}_{t}}$ is the source term of additional force, including thermal buoyancy and electromagnetic force, ${\mathrm{N}\xb7\mathrm{m}}^{-3}$.

_{k}is source term of turbulence energy; μ and μ

_{t}are dynamic and turbulent viscosity coefficients, respectively, kg·m

^{−1}·s

^{−1}; C

_{1ε}, C

_{2ε}, C

_{μ}, σ

_{k}and σ

_{ε}are constants given by Launder and Spalding [35], and their values are taken 1.44, 1.92, 0.09, 1.0 and 1.3, respectively.

^{−1}; $\overrightarrow{{B}_{s}}$ is external applied magnetic field; $\overrightarrow{F}$ is electromagnetic force, ${\mathrm{N}\xb7\mathrm{m}}^{-3}$.

_{eff}is effective thermal conductivity, ${\mathrm{W}\xb7\mathrm{m}}^{-1}\xb7{\mathrm{K}}^{-1}$; T is temperature, K; S is the joule heat by the eddy loss of molten steel under the action of a magnetic field.

_{eff}is component diffusion coefficient, taking default value 2.88 × 10

^{−5}m

^{2}/s.

#### 2.4. Boundary Condition and Solution Method

^{−6}for energy equation and to be 10

^{−4}for the other equations. When the flow field is converged to steady state, the solver is converted to the transient state to solve the transient tracer dispersion. The injection time of tracers at the inlet is set as 1 s. After that, its concentration variation with time is computed at the outlet plane of the tundish to obtain the residence time distribution (RTD) curve of tracers. The calculation time is set as 3000 s.

## 3. Results and Discussion

#### 3.1. Grid Independence Test

#### 3.2. Model Validation

#### 3.3. Electromagnetic Field and Joule Heat Distribution in Case S0 under Heating Power 1000 kW

#### 3.4. Comparison of Flow Field and Temperature Field in Tundish for Case S0 with and without Induction Heating

_{min}, t

_{peak}and t

_{av}represent the respond time of molten steel, the peak time and the actual average residence time, respectively. They are obtained according to the method in Reference [37].

#### 3.5. Flow Field and Temperature Field of Tundish When Using Split Channel

#### 3.5.1. Comparison of Flow Field between Three Split Channel Schemes upon Heating for 200 s at 1000 kW

#### 3.5.2. Comparison of Temperature Field in Split Channel Schemes upon Heating for 200 s

#### 3.6. Comparison of Heating Process between Cases FK-A0 and S0 at 1000 kW

#### 3.7. Effect of Heating Power on Flow and Temperature Distribution for Case FK-A0

## 4. Industrial Experiments

## 5. Conclusions

- (1)
- Induction heating can increase the temperature of molten steel and flow velocity in the tundish. However, the maximum temperature difference between the outlets is as large as 10 K when with a conventional simply straight channel structure.
- (2)
- With a novel bifurcated split channel, the induction heating tundish can effectively improve the overall flow and temperature distribution for multi-strand casting. During heating operation, the temperature difference between each outlet of the tundish is obviously dropped as compared with the situation while using conventional straight channel. The maximum temperature difference between each strand outlet in its FK-A0, FK-A5 and FK-A15 cases is 2 K, 4 K and 3 K, respectively. The case FK-A0 with its diameters of “Channel out2” at 130 mm without inclination angle upwards is advantageous over the other two cases in the flow and temperature distribution of molten steel.
- (3)
- The comparisons of temperature and fluid flow at different heating powers for the case FK-A0 suggest that the temperature increases with the increasing heating power under little changed flow field. However, an excessive heating power will lead to a relatively poor temperature uniformity in the tundish and probably a dropping flow rate in the channel due to the appearance of a large electromagnetic pinch effect. In actual production, the heating power can be chosen according to the temperature of molten steel and superheat requirement.
- (4)
- The industrial tests show that using the split case FK-A0 can decrease the average and maximum temperature differences of molten steel between strands in tundish by 4.25 and 8 °C, respectively, as compared with the conventional straight channel. The study provides a novel design idea and application case for the upgrading metallurgical effect with channel-type induction heating tundish.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Multi-physics coupling calculation process for the induction heating tundish. MHD: magnetic induction equation.

**Figure 5.**Location of the reference point: (

**a**) channel exit section for S0 case; (

**b**) “Channel out1” section for FK-A0 case.

**Figure 6.**Comparison of RTD (residence time distribution) curves for case FK-A0: (

**a**) hydrodynamic modeling experiment; (

**b**) mathematical simulation.

**Figure 7.**Numerical simulation and reference measurement results of magnetic field distribution on Z = −20 cm channel section: (

**a**) left channel; (

**b**) middle channel. Reprinted with permission from ref. [36]. Copyright 1991 Springer Nature.

**Figure 8.**Comparison of magnetic induction intensity in Y direction between calculated and measured values: (

**a**) left channel; (

**b**) middle channel.

**Figure 12.**Three-dimensional (3D) streamline comparison of case S0: (

**a**) without induction heating; (

**b**) with induction heating.

**Figure 13.**Comparison of RTD (residence time distribution) curves of case S0: (

**a**) without induction heating; (

**b**) with induction heating.

**Figure 14.**Velocity vector in channel longitudinal section for case S0: (

**a**) without induction heating; (

**b**) with heating for 200 s at 1000 kW.

**Figure 15.**Velocity vector at vertical plane passing through all outlet centers of case S0: (

**a**) without induction heating; (

**b**) with heating for 200 s at 1000 kW.

**Figure 16.**Temperature field at the plane passing through all outlet centers for case S0: (

**a**) without induction heating; (

**b**) with heating for 200 s at 1000 kW.

**Figure 17.**Three-dimensional (3D) streamline contour of three split channel schemes: (

**a**) FK-A0; (

**b**) FK-A5; (

**c**) FK-A15.

**Figure 18.**Velocity vectors of split channel schemes in the planes passing through the center of all outlets (left), “Channel out1” (middle) and split port (right): (

**a1**–

**a3**) FK-A0; (

**b1**–

**b3**) FK-A5; (

**c1**–

**c3**) FK-A15.

**Figure 19.**Temperature field in the plane passing through outlet center for different cases: (

**a**) FK-A0; (

**b**) FK-A5; (

**c**) FK-A15.

**Figure 20.**Temperature field in the longitudinal planes of main channel (

**left**) and port (

**right**) for split schemes: (

**a**) FK-A0; (

**b**) FK-A5; (

**c**) FK-A15.

**Figure 22.**Velocity vector in the vertical planes passing through the center of all outlets (

**left**), main channel (

**middle**) and port (

**right**) for case FK-A0 under different heating power: (

**a**) 800 kW; (

**b**) 1000 kW; (

**c**) 1200 kW.

**Figure 23.**Temperature field of the plane passing through all outlet center for case FK-A0 under different heating power: (

**a**) 800 kW; (

**b**) 1000 kW; (

**c**) 1200 kW.

Parameter | Value |
---|---|

Tundish capacity (t) | 40 |

Molten steel depth (mm) | 900 |

Inner diameter, submerged depth of long nozzle (mm) | 95,300 |

Inner diameter of submerged entry nozzle (mm) | 80 |

Induction channel diameter of S0 case (mm) | 130 |

Induction channel length of S0 case (mm) | 1400 |

Main channel length of FK cases (mm) | 1700 |

Channel out1, out2 diameters (mm) | 80,130 |

Height from channel center to tundish bottom (mm) | 472 |

Case | Inclination Angle Upwards of Channel out2 | Flow Field and Temperature Field without Induction Heating | Flow Field and Temperature Field with Induction Heating at 1000 kW for 200 s | Flow Field and Temperature Field with Different Heating Power |
---|---|---|---|---|

S0 | \ | √ | √ | × |

FK-A0 | 0° | × | √ | √ |

FK-A5 | 5° | × | √ | × |

FK-A15 | 15° | × | √ | × |

Parameter | Value |
---|---|

Current frequency (Hz) | 50 |

Relative permeability of iron core | 1000 |

Induction coil conductivity (S·m^{−1}) | 3.18 × 10^{7} |

Relative permeability of induction coil | 1 |

Relative permeability of air domain | 1 |

Conductivity of molten steel (S·m^{−1}) | 7.14 × 10^{5} |

Relative permeability of molten steel | 1 |

Inlet molten steel temperature (K) | 1800 |

Density of molten steel (kg·m^{−3}) | 8523−0.8358 T |

Dynamic viscosity of molten steel (Pa·s) | 0.0061 |

Thermal conductivity of molten steel (W·m^{−1}·K^{−1}) | 41 |

Specific heat capacity of molten steel (J·kg^{−1}·K^{−1}) | 750 |

Surface heat flux (W·m^{−2}) | 15,000 |

Bottom heat flux (W·m^{−2}) | 1800 |

Long wall heat flux (W·m^{−2}) | 4600 |

Short wall heat flux (W·m^{−2}) | 4000 |

Channel heat flux (W·m^{−2}) | 1200 |

Case | Grids Number | T1/K | T2/K | T3/K |
---|---|---|---|---|

S0 | 606,244 | 1800.47 | 1799.51 | 1797.18 |

779,156 | 1801.12 | 1799.15 | 1796.81 | |

3,718,389 | 1801.25 | 1797.78 | 1796.01 | |

FK-A0 | 487,767 | 1800.84 | 1800.62 | 1799.55 |

808,426 | 1801.02 | 1800.73 | 1799.91 | |

3,096,045 | 1801.17 | 1800.75 | 1799.49 |

Measuring Times (n) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | $\mathrm{Average}\Delta T$ (°C) | |
---|---|---|---|---|---|---|---|---|---|---|

$\Delta T$ (°C) | ||||||||||

Straight channel | 6 | 1 | 6 | 3 | 8 | 9 | 14 | 9 | 7.0 | |

Split channel | 2 | 3 | 3 | 0 | 6 | 2 | 0 | 6 | 2.75 |

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**MDPI and ACS Style**

Tang, H.; Wang, K.; Li, X.; Liu, J.; Zhang, J. Improved Metallurgical Effect of Tundish through a Novel Induction Heating Channel for Multistrand Casting. *Metals* **2021**, *11*, 1075.
https://doi.org/10.3390/met11071075

**AMA Style**

Tang H, Wang K, Li X, Liu J, Zhang J. Improved Metallurgical Effect of Tundish through a Novel Induction Heating Channel for Multistrand Casting. *Metals*. 2021; 11(7):1075.
https://doi.org/10.3390/met11071075

**Chicago/Turabian Style**

Tang, Haiyan, Kaimin Wang, Xiaosong Li, Jinwen Liu, and Jiaquan Zhang. 2021. "Improved Metallurgical Effect of Tundish through a Novel Induction Heating Channel for Multistrand Casting" *Metals* 11, no. 7: 1075.
https://doi.org/10.3390/met11071075