# Numerical Modelling of the Influence of Argon Flow Rate and Slag Layer Height on Open-Eye Formation in a 150 Ton Steelmaking Ladle

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## Abstract

**:**

^{2}with the increment of argon flow rate from 200 to 500 NL/min for slag layer thickness of 40 cm. Furthermore, the influence of slag layer height on the open-eye area was investigated. An argon flow rate of 200 NL/min was able to break the slag layer for slag layer height of 40 cm, and the open-eye formation was not possible for the same flow rate when the slag layer height was elevated from 40 to 55 cm. The numerical simulation results were validated against industrial measurements carried out at Outokumpu Stainless located in Tornio, Finland. The numerical simulation results of dynamics and time-averages of the slag area showed a good agreement when compared to the industrial measurements. To conclude, it is necessary to define gas flow rate based on the slag layer height to have an open-eye suitable for alloying.

## 1. Introduction

## 2. Mathematical Model

#### 2.1. Governing Equations

#### 2.2. Physical Properties and Operating Condictions

#### 2.3. Execution of the Experiments

#### 2.4. Initial and Boundary Conditions

#### 2.5. Employed Physical Properties of Slag

_{2}O

_{3}, Ni, S and P) was 61.3 wt% CaO, 26.0 wt% SiO

_{2}, 7.8 wt% MgO, 0.2 wt% MnO, 4.3 wt% Al

_{2}O

_{3}and 0.4 wt% Fe

_{2}O

_{3}. The composition was determined based on four slag samples taken from the process studied, while the employed average slag temperature represents an average of the temperatures measured during the validation experiments. For the sake of simplicity, the top slag was assumed to be liquid. The viscosity of the slag was calculated using the viscosity module of FactSage ver. 7.2. [33]. The viscosity module relates the dynamic viscosity of the slag to the structure of the slag melt, which is calculated using the modified quasichemical model [30]. The density of the slag was calculated using the partial molar volume method using Equations (6) and (7) [34].

#### 2.6. Numerical Details

## 3. Results and Discussion

#### 3.1. Influence of Argon Flow Rate on Open-Eye Formation for Slag Layer Thickness of 40 cm

^{2}(relative area of 10.3%) in experiments (Figure 4a) and 0.69 m

^{2}(relative area of 10.2%) through simulations (Figure 5a). The open-eye formation did not appear when the industrial scale ladle operated with a flow rate lesser than 200 NL/min. For a flow rate of 400 NL/min, the open-eye area generated was approximately 1.58 m

^{2}(relative area of 23.3%) in experiments (Figure 4b) and 1.59 m

^{2}(relative area of 23.5%) through simulations. At a flow rate of 500 NL/min, the area of the open-eye was 2.24 m

^{2}(relative area of 33.1%) in experiments (Figure 4c) and 2.3 m

^{2}(relative area of 34.0%) through simulations (Figure 5c). At higher flow rates, the edge of the open-eye moves closer to the ladle wall, resulting in an increase of fluid flow adjacent to the ladle wall. This may increase refractory wear and thus diminish the ladle life. The predicted trend of increase in the open-eye area with argon flow rate were in acceptable agreement with the industrial observations of Valentin et al. [24]. The simulation results of the open-eye area accorded well with the simulations of Li et al. [25] and Liu et al. [26]. This information can be used to select the optimal argon flow rates to achieve a sufficient-sized open-eye for alloying purposes.

^{2}, 3.2 m

^{2}and 5.0 m

^{2}, respectively. The time-averaged values of the open-eye area were 0.69 m

^{2}, 1.6 m

^{2}and 2.24 m

^{2}.

#### 3.2. Influence of Increasing Slag Layer Height to 55 cm from 40 cm on Open-Eye Formation

^{2}(relative area of 23.3%) to 1.32 m

^{2}(relative area of 19.5%) in experimental results, and from 1.59 m

^{2}(relative area of 23.5%) to 1.44 m

^{2}(relative area of 21.1%) through simulation results. At 500 NL/min, the open-eye area reduces from 2.24 m

^{2}(relative area of 33.1%) to 1.81 m

^{2}(relative area of 26.7%) in experimental results, and from 2.29 m

^{2}(relative area of 34.0%) to 1.95 m

^{2}(relative area of 28.8%) through simulation results.

#### 3.3. Influence of Decreasing Slag Layer Thickness to 25 cm from 40 cm on Open-Eye Formation

^{2}(relative area of 15.9%) in experimental results and to 0.95 m

^{2}(relative area of 14.0%) through simulations when the slag layer height was decreased from 40 cm to 25 cm. In addition, at a flow rate of 400 NL/min, the open-eye area increases to 1.82 m

^{2}(relative area of 26.8%) in experimental results to 1.89 m

^{2}(relative area of 27.9%) through simulations. At a higher argon flow rate of 500 NL/min, the open-eye formation follows the same trend as in the case with a slag layer height of 40 cm, but the open-eye size is very large and there is a large deformation of the slag layer both near the open-eye position and far from it. The size of the open-eye is almost half of the ladle surface cross-sectional area. The results indicate that, the higher argon flow rates leads to the formation of larger open-eyes, and at high flow rates if the slag layer thickness is lower it may result in the generation of a fluctuating open-eye. Emulsification of slag into steel was found to be more aggressive compared to cases with gas flow rates of 200 and 400 NL/min.

#### 3.4. Summary of Open-Eye Area for Different Argon Flow Rates and Slag Layer Heights

## 4. Conclusions

- (1)
- The injected argon flow rate has a significant influence on the fluid flow velocities and the open-eye size generated in the ladle.
- (2)
- The elevation in flow rate of argon gas, the open-eye size and the spreading area of molten steel increases. The open-eye increases from 10.3% to 33.1% of the ladle’s free top surface area with an increase of flow rate from 200 to 500 NL/min and a 40 cm slag layer thickness.
- (3)
- The velocity of the fluid flow developed due to the injection of argon gas through the nozzle was very high adjacent to the nozzle inlet and reduces as the flow reaches the argon/steel/slag interface.
- (4)
- The slag layer height has a great effect on the formation of the open-eye. The reduction of the slag layer thickness from 40 to 25 cm resulted in a much larger deformation of slag layer and a more rapidly fluctuating open-eye at a high flow rate of 500 NL/min. The increase of the slag layer thickness from 40 to 55 cm resulted in non-formation of an open-eye at 200 NL/min.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Open-eye size in the ladle from experimental results for a slag layer thickness of 40 cm: (

**a**) Q = 200 NL/min, (

**b**) Q = 400 NL/min, and (

**c**) Q = 500 NL/min.

**Figure 5.**Open-eye size in the ladle from simulation results for a slag layer thickness of 40 cm: (

**a**) Q = 200 NL/min, (

**b**) Q = 400 NL/min, and (

**c**) Q = 500 NL/min.

**Figure 7.**Simulation results of time-averaged flow velocity profiles in the ladle furnace for different gas flow rates at different heights: (

**a**) Z = 0.5 m, (

**b**) Z = 1.5 m, (

**c**) Z = 2.5 m, and (

**d**) Z = 3.5 m.

**Figure 8.**Comparison of non-dimensional open-eye area ratio with the literature (K & I: Krishnapisharody and Irons [6]; Yonezawa and Schwerdtfeger [5]; Han et al. [37]; E. Ramasetti et al. [36]: (${A}_{e}^{\ast}/{A}_{p}^{\ast})\text{}vs.\text{}{({Q}^{\ast})}^{\frac{1}{3}}\text{}{\left(\frac{H}{h}\right)}^{\frac{1}{2}}$).

**Figure 9.**Comparison of the anticipated non-dimensional open-eye area ratio with dimensionless groups for gas injection (K & I: Krishnapisharody and Irons [6]; Yonezawa and Schwerdtfeger [5]; Han et al. [37]; Ramasetti et al. [36]: $\left({A}_{e}^{\ast}/{A}_{p}^{\ast}\right)\text{}vs.\text{}{\left(1-{\rho}^{\ast}\right)}^{-\frac{1}{2}}\text{}\left({Q}^{\ast}{)}^{\frac{1}{3}}\text{}{\left(\frac{H}{h}\right)}^{\frac{1}{2}}\right)$.

**Figure 10.**Open-eye size in the ladle from experimental results for a slag layer thickness of 55 cm: (

**a**) Q = 200 NL/min, (

**b**) Q = 400 NL/min, and (

**c**) Q = 500 NL/min.

**Figure 11.**Open-eye size in the ladle from simulation results for a slag layer thickness of 55 cm: (

**a**) Q = 200 NL/min, (

**b**) Q = 400 NL/min, and (

**c**) Q = 500 NL/min.

**Figure 12.**Open-eye size in the ladle from experimental results for a slag layer thickness of 25 cm: (

**a**) Q = 200 NL/min, (

**b**) Q = 400 NL/min, and (

**c**) Q = 500 NL/min.

**Figure 13.**Open-eye size in the ladle from simulation results for a slag layer thickness of 25 cm: (

**a**) Q = 200 NL/min, (

**b**) Q = 400 NL/min, and (

**c**) Q = 500 NL/min.

Physical Properties at 1812 K | Value | Unit |
---|---|---|

Density of liquid steel [32] | 6913 | kg/m^{3} |

Viscosity of liquid steel [32] | 0.005281 | Pa·s |

Density of slag | 2746 | kg/m^{3} |

Viscosity of slag | 0.081 | Pa · s |

Density of argon gas | 0.8739 | kg/m^{3} |

Viscosity of argon gas | 2.2616 × 10^{−5} | Pa · s |

Temperature of bath | 1812 | K |

Flow rate of argon gas | 200, 400 and 500 | NL/min * |

Slag layer height | 25, 40 and 55 | cm |

**Table 2.**Summary of experimental and simulated values for open-eye area with various gas flow rates and slag layer height.

Slag Layer Height (cm) | 25 | 40 | 55 | |||
---|---|---|---|---|---|---|

Flow Rate (NL/min) | Exp. (m^{2}) | Sim. (m^{2}) | Exp. (m^{2}) | Sim. (m^{2}) | Exp.(m^{2}) | Sim. (m^{2}) |

200 | 1.08 | 0.95 | 0.72 | 0.69 | NA | NA |

400 | 1.82 | 1.89 | 1.58 | 1.59 | 1.32 | 1.44 |

500 | NA | NA | 2.24 | 2.30 | 1.81 | 1.95 |

Average Relative Error | 6.61% | |||||

R^{2} | 0.93 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Ramasetti, E.K.; Visuri, V.-V.; Sulasalmi, P.; Fabritius, T.; Savolainen, J.; Li, M.; Shao, L. Numerical Modelling of the Influence of Argon Flow Rate and Slag Layer Height on Open-Eye Formation in a 150 Ton Steelmaking Ladle. *Metals* **2019**, *9*, 1048.
https://doi.org/10.3390/met9101048

**AMA Style**

Ramasetti EK, Visuri V-V, Sulasalmi P, Fabritius T, Savolainen J, Li M, Shao L. Numerical Modelling of the Influence of Argon Flow Rate and Slag Layer Height on Open-Eye Formation in a 150 Ton Steelmaking Ladle. *Metals*. 2019; 9(10):1048.
https://doi.org/10.3390/met9101048

**Chicago/Turabian Style**

Ramasetti, Eshwar Kumar, Ville-Valtteri Visuri, Petri Sulasalmi, Timo Fabritius, Jari Savolainen, Mingming Li, and Lei Shao. 2019. "Numerical Modelling of the Influence of Argon Flow Rate and Slag Layer Height on Open-Eye Formation in a 150 Ton Steelmaking Ladle" *Metals* 9, no. 10: 1048.
https://doi.org/10.3390/met9101048