# Numerical Modeling of Open-Eye Formation and Mixing Time in Argon Stirred Industrial Ladle

^{1}

^{2}

^{3}

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## Abstract

**:**

^{2}when the flow rate of argon was varied from 100 to 500 NL/min. The mixing time (95% criterion) of tracer addition into the metal bath decreased from 139 s to 96 s, when the argon flow rate was increased from 100 to 500 NL/min. The model validation was verified by comparing with measured experimental results.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Description

#### 2.2. Experimental Details

#### 2.3. Numerical Details

^{−5}for the residuals of dependent variables.

## 3. Results and Discussion

#### 3.1. Effect of Gas Flow Rate on Open-Eye Formation

^{2}, 2.09 m

^{2}, and 3.17 m

^{2}, respectively. The respective time-averaged values for the constant level of the open-eye area were 0.66 m

^{2}, 1.37 m

^{2}, and 2.36 m

^{2}. The predicted trend of enlargement of the open-eye area with argon flow rate was in good agreement with the measurements of Valentin et al. [7].

#### 3.2. Flow Field Distribution

#### 3.3. Mixing Behavior

## 4. Conclusions

- The flow patterns of the molten steel inside the ladle furnace are largely dependent on the argon flow rate. The flow velocity is very high at heights near to the bottom of the ladle furnace, and it tends to decrease as the flow moves upwards.
- The increase in the flow rate of argon gas from 100 to 500 NL/min enlarges the open-eye size from 0.66 to 2.36 m
^{2}. - The simulated mixing time (95% criterion) of tracer addition into the metal bath decreased from 139 s to 96 s when the argon flow rate was increased from 100 to 500 NL/min.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Open-eye size in the ladle from experimental results (Z = 3.37 m): (

**a**) Q = 100 NL/min, (

**b**) Q = 300 NL/min, and (

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

**Figure 3.**Open-eye size in the ladle from simulation results (Z = 3.37 m): (

**a**) Q = 100 NL/min, (

**b**) Q = 300 NL/min, and (

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

**Figure 5.**Velocity distribution profiles for different gas flow rates from the ladle bottom: (

**a**) 1.5 m (

**b**) 3.0 m.

**Figure 6.**Turbulent kinetic energy profiles for different gas flow rates from the ladle bottom: (

**a**) 1.5 m (

**b**) 3.0 m.

**Figure 7.**Turbulent dissipation rate profiles for different gas flow rates from the ladle bottom: (

**a**) 1.5 m (

**b**) 3.0 m.

**Figure 9.**Tracer concentration profiles for different gas flow rates of 100 (left), 300 (middle), and 500 (right) NL/min with different time intervals: (

**a**) 0 s (

**b**) 5 s (

**c**) 10 s (

**d**) 20 s (

**e**) 40 s (

**f**) 60 s.

**Figure 10.**Tracer concentration change for different gas flow rates of (

**a**) 100 NL/min (

**b**) 300 NL/min and (

**c**) 500 NL/min. (

**d**) Comparison of simulated average mixing time for different gas flow rate with the experimental values.

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

Density of liquid steel [30] | 6913 | kg/m^{3} |

Viscosity of liquid steel [30] | 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 | 100, 300 and 500 | NL/min |

Slag layer height | 35 | cm |

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**MDPI and ACS Style**

Ramasetti, E.K.; Visuri, V.-V.; Sulasalmi, P.; Fabritius, T.; Saatio, T.; Li, M.; Shao, L. Numerical Modeling of Open-Eye Formation and Mixing Time in Argon Stirred Industrial Ladle. *Metals* **2019**, *9*, 829.
https://doi.org/10.3390/met9080829

**AMA Style**

Ramasetti EK, Visuri V-V, Sulasalmi P, Fabritius T, Saatio T, Li M, Shao L. Numerical Modeling of Open-Eye Formation and Mixing Time in Argon Stirred Industrial Ladle. *Metals*. 2019; 9(8):829.
https://doi.org/10.3390/met9080829

**Chicago/Turabian Style**

Ramasetti, Eshwar Kumar, Ville-Valtteri Visuri, Petri Sulasalmi, Timo Fabritius, Tommi Saatio, Mingming Li, and Lei Shao. 2019. "Numerical Modeling of Open-Eye Formation and Mixing Time in Argon Stirred Industrial Ladle" *Metals* 9, no. 8: 829.
https://doi.org/10.3390/met9080829