**2. Water Model**

In order to uniform the composition and temperature of metal bath in the ladle, a 1:5 downscale water model was established, with the geometrical similarity of the actual ladle in a Chinese steel mill. Water and air were chosen to simulate molten steel and argon, the dimension data of the water model and prototype were shown in Table 1, and a schematic diagram of the prototype was in Figure 1.


**Table 1.** The dimension data of the water model and prototype.

**Figure 1.** Schematic diagram of the ladle prototype; (**a**) vertical section; (**b**) porous plug arrangement.

The major forces affecting the flow of molten steel in the ladle include float force, viscous force and gravity. According to similarity rules, modified Freud number can characterize the kinetic similarity of the argon blowing system in the ladle with bottom blowing of argon. In our study work, the water model should have the same modified Freud number as the prototype, as Equation (1):

$$(Fr')\_m = (Fr')\_p \tag{1}$$

That is,

$$\frac{\rho\_{air} \cdot \mathbf{u}\_{water}^2}{(\rho\_{water} - \rho\_{air}) \cdot \mathbf{g} \cdot H\_m} = \frac{\rho\_{Ar} \cdot \mathbf{u}\_{steel}^2}{(\rho\_{steel} - \rho\_{Ar}) \cdot \mathbf{g} \cdot H\_p} \tag{2}$$

where, ρ*air*, ρ*water*, ρ*Ar*, ρ*steel* are the densities of air, water, argon and molten steel respectively, kg/m3; *g* is the acceleration of gravity, m/s2; *uwater*, *usteel* are the characteristic velocities of air and argon respectively, m/s; *H* is the height of steel bath in the ladle, m.

The characteristic velocity *u* can be expressed with Equation (3):

$$
\mu = \frac{4Q}{\pi \cdot d^2} \tag{3}
$$

where, *Q* is the gas flow rate, m3/h; *d* is the equivalent diameter of the porous plug, m.

Based on the data of Table 1, Equations (2) and (3), the relation between gas flow rates in the water model and in the actual teeming ladle, i.e., *Qm* and *Qp*, was derived as Equation (4).

$$Q\_m = 0.00794 Q\_p \tag{4}$$

According to the range of flow rate of argon blown in the prototype ladle, that is 12–50 m3/h, the air flow rates were calculated from Equation (4) and listed in Table 2.

**Table 2.** The flow rate of bottom gas in the water model and prototype ladle.


As the flow behaviour of molten steel-slag was influenced by interfacial tension of molten steel and slag, the weber numbers of the model should be equivalent to that of the prototype to insure the kinetic similarity at the interface between the molten steel and slag, Equation (5).

$$\mathcal{W}e\_m = \mathcal{W}e\_p\tag{5}$$

That is,

$$\frac{\rho\_{\text{water}} \cdot \mathbf{u}\_{\text{water}}^2}{\left[\mathcal{S}^{\circ \sigma\_{\text{water}} - \text{oil}^{\circ}} (\rho\_{\text{water}} - \rho\_{\text{air}})\right]^{1/2}} = \frac{\rho\_{\text{steel}} \cdot \mathbf{u}\_{\text{steel}}^2}{\left[\mathcal{S}^{\circ} \sigma\_{\text{steel}} - \text{slag} \cdot \left(\rho\_{\text{steel}} - \rho\_{\text{slag}}\right)\right]^{1/2}}\tag{6}$$

where, σ*water*-oil is the interfacial tension between the water and oil, N/m; σ*seel*-slag is the interfacial tension between the steel and slag, N/m.

In the water model experiment, aviation kerosene and vacuum pump oil were mixed in a certain proportion to obtain a mixture oil with the same kinematic viscosity of the top slag.

The slag layer thickness of the prototype ladle is 60–100 mm, and the oil layer thickness (OLT) in the water model experiment is 12–20 mm according to the similarity ratio of 1:5. Five oil layer thicknesses were selected in the experiment, as shown in Table 3, to study the effect of the slag layer thickness to level fluctuation and slag entrapment of steel bath in the ladle.

**Table 3.** The thicknesses of the top oil layer.


There were two methods of eccentric bottom blowing in the prototype ladle: One is a single porous plug with eccentric distance of 0.6 R, in which the eccentric distance is the distance between the centers of the porous plug and ladle; the other is a double porous plug with an intersection angle of 100◦ and eccentric distance of 0.6 R.

The schematic diagram of the water model experiment setup was shown in Figure 2. In the experiments, the mixing time of the model was measured through the stimulus-response method with a tracer of KCl solution, flow field, level fluctuation and slag entrapment of steel bath in the model ladle was recorded by high speed digital camera.

**Figure 2.** Water model experiment setup: (**1**) Air compressor; (**2**) pressure gauge; (**3**) air flow rate controller; (**4**) porous plug; (**5**) model ladle; (**6**) conductivity probe; (**7**) computer; (**8**) conductivity meter; (**9**) high speed digital camera.

#### **3. Results and Discussion**

### *3.1. Mixing Time*

In the water model experiment, seven air flow rates, that is 0.095, 0.143, 0.191, 0.238, 0.286, 0.333, 0.381 m3/h, were used to bottom-blow into the model ladle with/without an oil layer covered through single or double porous plugs.

The influences of the bottom air flow rate, slag layer and the number of porous plugs to the mixing time were shown in Figure 3.

**Figure 3.** The relation between mixing time and air flow rate in the ladle with single porous plug and double porous plugs: (**1**) Single porous plug without oil layer; (**2**) single porous plug with 16 mm OLT; (**3**) double porous plugs without oil layer; (**4**) double porous plugs with 16 mm OLT.

From Figure 3, it was found that as the increase of the bottom air flow rate, the mixing time of the metal bath in ladle decreased. When the bottom blowing air flow rate was equal to 0.095 m3/h (corresponding 12 m3/h in prototype), the mixing time of the steel bath was relatively long, as stirring power produced by the dispersing small bubbles from porous plugs was too small and the circulating flow rate in steel bath was weak.

As the bottom blowing air flow rate was increased from 0.143 m3/h to 0.286 m3/h (corresponding from 18 m3/h to 36 m3/h in the prototype), the mixing time was reduced abundantly. When the bottom air flow rate was above 0.143 m3/h, the bubble group in water model was transferred from dispersing small bubbles to spherical bubbles or coronal bubbles group. The stirring energy by the bubble group increased abundantly, so was the circulating flow in the steel bath of the ladle, which decreased the mixing time markedly.

When the bottom blowing flow rate increased above 0.286 m3/h, the mixing time of the steel bath increased slowly with the bottom blowing flow rate. The reason was that when the flow rate exceeds 0.286 m3/h, the diameter of the plume caused by bubble groups did not increase further, more bubbles were blown into the plume, bubble coalescence and breaking were more frequent, and more energy was exhausted in bubble coalescence and breaking, instead of driving circulate flow in the bath. At the same time, there were more energy consumed by the surface rise and splashing, which were caused by the escaping of a large number of bubbles. Therefore, when the bottom blowing flow rate increased above 0.286 m3/h (i.e., 36 m3/h in prototype), the increase of the bottom blowing gas flow rate could not improve the mixing of the bath in the ladle, and there was an obvious inflection point on the mixing time curve.

The slag layer could influence the mixing time, Figure 3. It was shown that at the same bottom blowing flow rate, the mixing time without the oil layer was obviously shorter than the mixing time with OLT of 16 mm. The reason was that the horizontal flow at the surface was obstructed by the slag layer at the bath top, so was the circulating flow in the bath. It can also be seen from the figure that the air flow rate at mixing time inflection without the oil layer in the ladle was 0.286 m3/h, and the air flow rate at mixing time inflection point with the oil layer in the ladle was 0.333 m3/h.

As there were two plumes in the ladle with double porous plugs, the intersection area of bubble columns doubled, and the mixing of the bath improved obviously. From Figure 3, it was found that the mixing time of the bath in the ladle with double porous plugs shortened abundantly.

The relation between the mixing time and bottom blowing flow rate in the ladle with double porous plugs was shown in Figure 4. It was found that with the increase of the bottom gas flow rate, the mixing time of the bath in the ladle was decreased. When the flow rate is above 0.333 m3/h (i.e., 42 m3/h in prototype), the mixing time was reduced slowly as the increase of the flow rate, and the trend was similar to the ladle with a single porous plug. The slag layer obstructed the mixing in the ladle with double porous plugs, as the work by viscous force at the surface of the bath in the ladle consumed the kinetic energy of plumes driven by bubbles blown from double porous plugs. The thickness of the slag layer had a large influence to the mixing time of the bath in the ladle, as the mixing time of the bath in the ladle decreased with the increase of thickness of the slag layer.

In summary, for the actual operation of the prototype ladle, the best option of the bottom gas flow rate was 36–42 m3/h for the ladle. When the bottom flow rate in the actual ladle increased above that range, the mixing time could not be reduced effectively.

**Figure 4.** The relation of mixing time and air flow rate in the ladle with double porous plugs.
