# Optimization of the Liquid Steel Flow Behavior in the Tundish through Water Model Experiment, Numerical Simulation and Industrial Trial

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Geometry Model

## 3. Water Model Experiment

#### 3.1. Experimental Equipment

_{m}and u

_{r}are the velocity in the experimental and industrial tundish, respectively. $\lambda $ is the similar factor, which is 1/3 in this study. The system of the water model is described in Figure 2. It includes a water supply system, a tracer injector, a tundish model built by polymethyl methacrylate (PMMA), and a data collection system.

#### 3.2. Experimental Procedure

^{3}(1174 kg/m

^{3}for saturated KCl solution) was prepared by mixing 800 mL water, 225 mL ethanol, and 47.34 g crystal KCl.

## 4. Mathematical Model

#### 4.1. Model Assumptions

#### 4.2. Governing Equation and Boundary Condition

**U**is the velocity vector, m/s; p is pressure, Pa; μ is the molecular viscosity; μ

_{t}is the turbulence viscosity, which is solved by the SST k-ω model [19]:

^{2}/s.

#### 4.3. Validation of Numerical Simulation Model to Experiment Data

^{3}; Q

_{V}is the total flow rate, m

^{3}/s; ${Y}_{i}\left(\theta \right)$ is the KCl mass concentration at the dimensionless time θ at the ith outlet. ${Q}_{{V}_{i}}$ is the flow rate at the ith outlet, m

^{3}/s, which is controlled by the valve with the help of the flow meter in the experiment. The upper limit of the integration in Equation (9) is 3. The total RTD curves obtained through the water model experiment and simulation are compared in Figure 3.

## 5. Simulation Result and Discussion

_{II}, and the existence of the dam, as shown in Figure 1 and given in Table 3.

#### 5.1. Flow Field

_{II}increases, the velocity of the jet from Orifice II slows down, letting the vertex near the orifice in the discharging zone move upward.

_{II}decreases, as shown in Figure 4f–h. The reason is that the decrease of d

_{II}accelerates the liquid steel flow in Orifice II and reduces the momentum of the jet so that it becomes easier to change jet flow behavior.

#### 5.2. Tracer Behavior at Outlets

#### 5.3. Dead Zone Ratio and Uniformity

## 6. Industrial Trials

#### 6.1. Experiment Process

#### 6.2. Trial Results

^{2}to 14.10/mm

^{2}.

## 7. Conclusions

- A recipe for a new tracer with a density close to that of water was proposed to reduce the buoyant effects of the tracer on the water flow behaviors. Based on the experimental data, a numerical simulation model was established and verified.
- The enlargement of Orifice II makes the vertex in the discharging chamber move upwards and the mean residence time at outlet S3 prolongs, which then promotes the floating of the inclusion in the tundish. Among all investigated cases, the C1 and C4 schemes provide a small dead volume ratio and great uniformity and were chosen for industrial trials.
- The crack of the baffle in the C1-based tundish industrial trial indicates that the structural strength of the baffle should be considered when the tundish structure changes.
- By enlarging the diameter of Orifice II to 200 mm and moving it down by 30 mm, the C4-based tundish industrial trial proved that it can reduce the mass fraction of inclusion by 43.81% and the number density of inclusion by 20.93%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison of the total residence time distribution curve obtained from the water model experiment and numerical simulation.

**Figure 4.**Flow field of the liquid steel at the plane crosses the centerline of the orifice. (

**a**) Scheme of location of the plane; (

**b**) Flow field of Case C0; (

**c**) Flow field of Case C1; (

**d**) Flow field of Case C2; (

**e**) Flow field of Case C3; (

**f**) Flow field of Case C4; (

**g**) Flow field of Case C5; (

**h**) Flow field of Case C6.

**Figure 5.**The tracer behavior at each outlet of different cases. (

**a**) Dimensionless minimal residence time of different cases; (

**b**) Dimensionless mean residence time of different cases.

**Figure 8.**Industrial trial result of C1-based tundish. (

**a**) Crack in the trial of C1-based tundish and scheme of the crack; (

**b**) Baffle structure in the original and C1-based tundish.

Liquid Steel Level/mm | Billet Section/mm × mm | Casting Speed/M·s^{−1} | |
---|---|---|---|

Value | 850 | 180 × 180 | 1.3 |

Numerical Simulation | Water Model Experiment | Error | |
---|---|---|---|

Dead zone ratio/% | 12.77 | 11.46 | 1.31 |

Case No. | d_{LD}/mm | d_{I}/mm | d_{II}/mm | d_{III}/mm | h_{II}/mm | α_{II}/° | Dam |
---|---|---|---|---|---|---|---|

C0(prototype) | 30 | 150 | 150 | 150 | 220 | 10 | No |

C1 | 30 | 150 | 200 | 200 | 220 | 30 | Yes |

C2 | 60 | 100 | 200 | 150 | 220 | 10 | Yes |

C3 | 60 | 125 | 200 | 150 | 220 | 10 | Yes |

C4 | 60 | 150 | 200 | 150 | 190 | 10 | Yes |

C5 | 60 | 150 | 190 | 150 | 190 | 10 | Yes |

C6 | 60 | 150 | 180 | 150 | 190 | 10 | Yes |

Case No. | Dead Zone Ratio | Uniformity |
---|---|---|

C0 | 12.77% | 0.2371 |

C1 | 2.26% | 0.2689 |

C2 | 2.19% | 0.2468 |

C3 | 5.26% | 0.1952 |

C4 | 3.88% | 0.2100 |

C5 | 3.77% | 0.2238 |

C6 | 8.21% | 0.2084 |

Sample | O (wt.%) | N (wt.%) | H% (wt.%) | O&N (wt.%) | Relative Variation |
---|---|---|---|---|---|

Original S4 | 0.00002146 | 0.00003782 | 0.00000168 | 0.00005928 | - |

Case 4 S5 | 0.00001996 | 0.00003402 | 0.00000188 | 0.00005398 | 8.94% |

Sample | Mass Fraction of Inclusions | Number Density of Inclusions | ||
---|---|---|---|---|

Value (mg/10 kg) | Relative Variation | Value (/mm ^{2}) | Relative Variation | |

Original S4 | 2.99 | - | 17.83 | - |

C4-based S5 | 1.68 | 43.81% | 14.10 | 20.93% |

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**MDPI and ACS Style**

Liu, J.; Zhou, P.; Zuo, X.; Wu, D.; Wu, D.
Optimization of the Liquid Steel Flow Behavior in the Tundish through Water Model Experiment, Numerical Simulation and Industrial Trial. *Metals* **2022**, *12*, 1480.
https://doi.org/10.3390/met12091480

**AMA Style**

Liu J, Zhou P, Zuo X, Wu D, Wu D.
Optimization of the Liquid Steel Flow Behavior in the Tundish through Water Model Experiment, Numerical Simulation and Industrial Trial. *Metals*. 2022; 12(9):1480.
https://doi.org/10.3390/met12091480

**Chicago/Turabian Style**

Liu, Junda, Ping Zhou, Xiaotan Zuo, Di Wu, and Dongling Wu.
2022. "Optimization of the Liquid Steel Flow Behavior in the Tundish through Water Model Experiment, Numerical Simulation and Industrial Trial" *Metals* 12, no. 9: 1480.
https://doi.org/10.3390/met12091480