Lance Design for Argon Bubbling in Molten Steel

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 decreased.


Introduction
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 [1]. Besides, argon bubbling is employed to degassing of molten steel, desulphurization, removal of undesirable nonmetallic inclusions, change of inclusion morphology, enhancement of chemical reaction rate and mass transfer, and so on [2]. Argon injection in molten steel is carried out by submerged lance injection or bottom injection methods [3], as is depicted in Figure 1. When argon is injected in molten steel through a submerged lance or a porous plug located at the bottom of the ladle, the gas jet breaks up into bubbles. The rising bubbles break the up-to the injected gas flow rate and inversely proportional to the immersion depth.
In [10] an expression for estimating the plume rise velocity in bubble-stirred ladle systems was derived. It is shown that the plume velocity in such systems is related to the ladle operating parameters: molten steel depth, ladle radius, and gas flow rate. A Large-Eddy Simulation model is employed in [11] to quantify the impact of the bubble size, the nozzle diameter and the gas flow rate on the properties of bubble plumes, such as the plume's width, centerline velocity, and mass flux.
Recent papers have been published on fluid dynamics in gas stirred ladles, e.g. [12]. In [13] flow structures of molten steel during stirring operations with argon injection are studied through physical and mathematical models. Emphasis is made on the turbulent conditions near the metal-slag interface since this region is important for mass transfer and inclusions capture by the slag. In [14] [15] the Euler-Euler and Euler-Lagrange modeling approaches were applied to simulate the multiphase flow in gas-stirred ladles. A multi-scale mathematical model to simulate the multiphase flow in ladles, which captures large phase interfaces and eddies is presented in [16]. In [17] a rotary lance is proposed and tested using a cold water model. The mixing time of the water bath stirred by gas injection was determined by an electrical conductivity method. Effects of the gas flow rate, the rotation speed and the bath depth on the mixing time were examined. It is reported that the effect of the gas flow rate on the mixing time becomes significant for high lance immersion depths and low rotation speeds. In [18] seven different lance configurations were proposed to determine the most efficient design using physical and mathematical modeling approach. A new curved port lance was designed by the authors, and this lance yields uniform and swirling flow profile inside the ladle without rotating the lance. Injection through the new lance increased the residence time of the particles and reduced the dead zones in the molten steel volume. A physical and mathematical study on gas injection in water using convergent-divergent nozzles is presented in [19]. Different geometries were em-

Mathematical Model
Computational Fluid Dynamics (CFD) [21] was employed to study the fluid flow in the multiphase system formed by molten steel and argon. Slag is not considered. The injection process is here considered isothermal. The equations of continuity and momentum [22], the Volume of Fluid (VOF) model for multiphase flow [23] and the classical K-ε model for turbulence [24] were employed in the CFD simulations. The boundary conditions for K and ε in the lance nozzles were determined in accordance with those suggested in [25] using the inlet velocity as parameter, which was determined from the expression 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 [26] for gas injection through a straight-shaped lance: World Journal of Engineering and Technology 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 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: 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 [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 [27] ( ) 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: 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: 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 [5].

Numerical Solution and Simulations
To numerically solve the momentum, continuity, turbulence and VOF model,  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 Table 1. Besides, Table 1 shows the values of the operational parameters employed in the numerical simulations, which approximately correspond to an industrial ladle, as it is reported in [1] and [5].

Results and Comments
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.  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 straightshaped lance bubbles ascend vertically almost stuck to the lance with low lateral dispersion, as is seen in Figure 4(a) and Figure 4(c). This causes a reduced open eye area, as is observed in Figure 8(a) and Table 2. A comparison between Figure 4(a) and Figure 5(a) suggests that the T-shaped lance causes a lateral dispersion greater than that caused by the straight-shaped lance. Then a larger open eye area it would be expected for the T-shaped lance, as is corroborated in Figure 8(b) and Table 2.  Results for the bottom injection method are presented in Figure 7. This method has a similar behavior to that of the T-shaped design in terms of the open eye area, as is seen in Table 2. In accordance with Figure 6(a) and Figure 6(c), among the designs considered here, the disk-shaped lance exhibits the widest bubble dispersion. This is due to the large number of nozzles and its circular distribution along the lance head. According to the above, the disk-shaped lance presents the largest open eye area, the largest plume volume, and the largest plume volume fraction, as is shown in Table 2. As the plume volume and the plume volume fraction are related to large stirring power and small mixing time, then the disk-shaped lance presents, among the considered designs, the best performance. The stirring power and the mixing times for the straight-shaped lance as function of the lance immersion depth are shown in Figure 9 and Figure 10. It is appreciated that the lance immersion depth increases the stirring power and decreases the mixing time, as is reported in [1]. The bottom injection method minimizes the mixing time due to its large immersion depth, however this method, in accordance to Table 2, yields a lower plume volume and a lower plume volume fraction than the disk-shaped lance.   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.