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Three lance designs for argon bubbling in molten steel are presented. Bottom bubbling is considered too. Geometries considered are straight-shaped, T-shaped, and disk-shaped. The bubbling behavior of these lances is analyzed using Computational Fluid Dynamics, so transient three dimensional, isothermal, two-phase, numerical simulations were carried out. Using the numerical results, the bubble distribution and the open eye area are analyzed for the considered lance geometries. The plume volume is calculated from the open eye area and the lance immersion depth using geometrical considerations. Among the three lance designs considered, disk-shaped lance has the bigger plume volume and the smaller mixing time. As the injection lance is deeper immersed , the power stirring is increased and the mixing time is de creased.

Homogenization of temperature and composition of molten steel requires proper stirring, which is frequently achieved by means of argon gas bubbling given that momentum transfer occurs from argon bubbles to molten steel [

Open eye formation, plume characteristics, fluid dynamics of molten steel and slag behavior are topics that are frequently addressed by researchers in the last two decades. Cold physical modeling and Computational Fluid Dynamics simulations are commonly employed as tools for the analysis [

Related to plume structure and characteristics, in [

Recent papers have been published on fluid dynamics in gas stirred ladles, e.g. [

In [

Unfortunately, few works have been published related to lance design. In this work three lance configurations for argon bubbling in molten steel are designed and presented. Bottom bubbling is considered too. Geometries considered are straight-shaped, T-shaped, and disk-shaped. The bubbling behavior of these lances is analyzed using Computational Fluid Dynamics, and transient three dimensional, isothermal, two-phase, numerical simulations were carried out. The open eye area, the volume plume and the plume volume fraction are quantified and compared maintaining constant the gas flow rate.

Computational Fluid Dynamics (CFD) [

v in = 4 Q g π d n 2 N n (1)

where v_{i} is the inlet velocity, Q_{g} is the gas flow rate, d_{n} is nozzle diameter, and N_{n} is the number of nozzles in the lance head. Q_{g} was kept constant irrespective of the lance design.

Stirring power can be determined using the empirical correlation reported in [

ε ˙ = 14.23 ( Q g T m W m ) log ( 1 + H 1.48 P 0 ) (2)

where ε ˙ is the stirring power (W tonne^{−1}), Q_{g} is the gas flow rate (Nm^{3}·min^{−1}), T_{m} is the molten steel temperature (˚K), W_{m} is the molten steel weight (tonne), H is the lance immersion depth (m), and P_{0} is the gas pressure at the bath surface (atm). Besides, for the above lance, the mixing time is determined from [

τ m = 116 ( ε ˙ ) − 1 / 3 D 5 / 3 H − 1 (3)

where τ_{m} is the mixing time (s), and D is the ladle diameter (m).

Residence time of the bubbles in the molten steel bath can be roughly estimated considering that bubbles have a vertical ascending trajectory:

τ r = H v b (4)

where τ_{r} is the residence time, and v_{b} is the bubble rise velocity. This last variable is estimated from the Stoke’s Law [

v b = g ( ρ m − ρ g ) d b 2 18 μ m (5)

where g is the gravity acceleration, ρ_{m} and ρ_{g} are the densities of molten steel and injection gas, respectively, d_{b} is the bubble diameter, and μ_{m} is the molten steel viscosity. The bubble diameter depends, among others, on the nozzle diameter, the gas flow rate, and the physical properties of molten steel. At low gas flow rates the bubble diameter can be estimated from the expression [

d b = ( 6 d n σ m g ( ρ m − ρ g ) ) 1 / 3 (6)

where σ_{m} is the surface tension of molten steel.

It can be assumed that the plume is a two-phase (molten steel and gas bubbles) region in the form of an inverted cone, being its height the lance immersion depth (H) and being its top diameter the diameter of the open eye. Then the plume volume (V_{p}) can be estimated as the volume of a truncated cone:

V p = ( 1 12 ) π H ( d 1 2 + d 2 2 + d 1 d 2 ) (7)

where d_{1} is the plume diameter at the injection point, and d_{2} is the diameter of the open eye at the molten steel surface. The first one is obtained here from trigonometry and lance immersion depth, and the second one is determined from CFD simulations. For bottom injection d_{1} = 0.

As the plume is composed of molten steel and gas bubbles, the gas content of the plume depends on the bubble diameter and the number of bubbles in the plume. The volume fraction of the plume (x_{p}) is the quotient between the plume volume and the molten steel volume:

x p = V p V m (8)

The volume fraction of the plume plays an important role in the gas stirring efficiency given that, generally speaking, as x_{p} is increased the momentum transfer is increased, the stirring power is increased, and the mixing time is decreased [

To numerically solve the momentum, continuity, turbulence and VOF model, CFD software was employed. Transient, isothermal, two-phase (molten steel and argon) three-dimensional computer simulations were carried out using a time step of 0.001 s. Slag was not considered. The geometric model of the ladle was meshed in 99,000 trilateral cells and the ladle physical dimensions are shown in

The bottom injection has just one nozzle. The straight-shaped and the T-shaped lance have two nozzles, whereas the disk-shaped lance has six nozzles. The diameter of the lance nozzles was 0.02 m. The molten steel depth was kept at 2.8 m, and a lance immersion depth of 2.5 m was considered. The inlet velocity in each nozzle was adjusted in order to keep constant the gas flow rate at 0.377 Nm^{3}·min^{−1}. In this way, the inlet velocity for the bottom nozzle was 20 m·s^{−1}, for the straight-shaped and T-shaped nozzles were 10 m·s^{−1}, and for the disk-shaped was 3.33 m·s^{−1}. The physical properties of the involved phases are shown in

Numerical files obtained from CFD simulations were post-processed in order to analyze the characteristics of the flow dynamics for each of the lance design or bubbling method considered. Three aspects are reported: bubble distribution, streamlines of bubbles in molten steel, and phase distribution. Finer resolution of bubble geometry and size was not possible given the rather coarse mesh employed in the computer simulations. Working with a finer mesh was not possible for the present authors given the limitations of the available hardware. However, in spite of this disadvantage, some valuable information is obtained.

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

Molten steel density | 7100 kg·m^{−3 } |

Molten steel temperature | 1773.15 ˚K |

Molten steel viscosity | 0.0067 kg·m^{−1}·s^{−1} |

Molten steel surface tension | 1.69 N·m^{−1} |

Molten steel weight | 90 tonnes |

Molten steel volume | 12.63 m^{3} |

Molten steel depth | 2.8 m |

Gas density | 1.18 kg·m^{−3 } |

Gas pressure at the molten steel surface | 1 atm |

Nozzles diameter | 0.02 m |

Lance diameter | 0.1 m |

Lance immersion depth | 2.5 m |

Length of T head | 0.6 m |

Disk diameter | 0. 6 m |

Gas flow rate | 0.377 Nm^{3}·min^{−1} |

Nozzles in normal lance | 2 |

Nozzles in T lance | 2 |

Nozzles in disk lance | 6 |

Figures 4-7 show the bubble distribution, the streamlines in the molten metal, and the phase distribution for the straight-shaped, T-shaped, disk-shaped, and bottom injection configurations, respectively. These figures correspond to an immersion depth of 2.5 m. For the gas flow rate considered, in the straight-shaped lance bubbles ascend vertically almost stuck to the lance with low lateral dispersion, as is seen in

Lance design | Open eye area, m^{2 } | Plume volume, m^{3} | Plume volume fraction |
---|---|---|---|

Straight-shaped | 0.0619 | 0.0577 | 0.4568 × 10^{−2 } |

T-shaped | 0.1011 | 0.0942 | 0.7457 × 10^{−2} |

Disk-shaped | 0.1490 | 0.1389 | 1.0995 × 10^{−2 } |

Bottom injection | 0.1089 | 0.1017 | 0.8051 × 10^{−2 } |

Results for the bottom injection method are presented in

From a broad point of view, the flow patterns for the whole set of lances are similar, as is observed in Figures 4(b)-7(b). Generally speaking, recirculatory streamlines are formed in the bulk melt. However, more detailed studies are required to disclose the particularities of the flow patterns induced by each of the lance designs. Flow patterns were not an objective of the present work. It is important to recognize that the flow pattern and the interaction between molten steel and slag at the molten metal surface play an important role in the capture of non-metallic inclusions by the slag.

The stirring power and the mixing times for the straight-shaped lance as function of the lance immersion depth are shown in

Three lance designs were studied for stirring of molten steel by means of argon bubbling: straight-shaped, T-shaped and disk-shaped. Bottom injection was considered too. Three-dimensional transient and isothermal two-phase Computational Fluid Dynamics simulations were carried out to compare the lances performance in terms of bubble distribution, plume volume and open eye area.

Under the considered conditions (gas flow rate of 0.337 Nm^{3}·min^{−1}, immersion depth of 2.5 m, molten steel depth of 2.8 m, nozzle diameter of 0.02 m, weight of molten steel of 90 tonnes), and from the computer simulations results the following conclusions arise:

For argon bubbling, the lance configuration affects the bubble distribution, the plume volume and the open eye area in the molten steel. Under the considered conditions the plume volume and the open eye area of the T-shaped lance are similar to those of the bottom injection method. Among the three lance designs considered, disk-shaped lance has the bigger plume volume and the smaller mixing time. As the injection lance is deeper immersed the power stirring is increased and mixing time is decreased. Given that the mesh employed in the current simulations is relatively coarse, it is suggested that future work must be carried out considering finer meshing and cold model comparison.

The authors declare no conflicts of interest regarding the publication of this paper.

De la Cruz, S., Barron, M.A., Medina, D.Y. and Reyes, J. (2020) Lance Design for Argon Bubbling in Molten Steel. World Journal of Engineering and Technology, 8, 317-328. https://doi.org/10.4236/wjet.2020.83025