Numerical Model of Dephosphorization Reaction Kinetics in Top Blown Converter Coupled with Flow Field

Physics model

The simulated domain is the space just below the oxygen lance tip (including lance nozzles). The capacity of the converter is 80 ton and the hot metal surface height is 1,130 mm, and the lance height is 1,700 mm. The domain is central symmetry and can be simplified into 1/8 for calculation efficiency. Note that the details of geometry size are taken into consideration. The 3D model was then built (on the scale of 1:1) and meshed up with certain mesh distribution and geometric parameters, see Figure 1 and Table 1.

The designed stagnation oxygen pressure is 0.8 MPa, and once the lance parameters are given, the gas flow rate is a function of oxygen pressure. In order to investigate the influence of oxygen pressure, the flow field in converter was simulated under oxygen pressure of 0.7, 0.8 and 0.9 MPa respectively.

Figure 1:

Geometric parameters of converter and mesh distribution.

CFD model

The CFD model was built up based on the method that described in a previous report [13] in detail. The governing equations are continuity, volume fraction (VOF) and standard k−ε.

Dephosphorization kinetics model

Hypothesis

In order to simplify the model, some assumptions must be made as follows:

1. The mass transfer in the steel is faster than that at interface;

2. The mass transfer of phosphorus between bath metal and slag interface obeys the penetration theory and the velocity of slag at the interface equals to that in steel;

3. The droplets are supposed to be spherical with uniform size;

4. The area of bath metal and slag interface is calculated from the mesh area approximately;

5. The oxygen blowing time is set to be 800 s and during this time the lance height, oxygen pressure or L_p remain no change;

6. The effects of other reactions on dephosphorization are negligible in this model.

The equation of dephosphorization is as:

The reaction has no gas attend or produced. The reactants of de-P reaction are from steel and slag and then the products go to slag and steel respectively. This means the reaction can only happen at steel-slag interface. There are two interfaces at the top blown converter and in this model the mixed control theory is applied.

For the bath metal–slag interface, if the resistance from reaction is neglected, the dephosphorization rate can be expressed as below:

where vp1 is the dephosphorization rate at bath metal–slag interface, %/s; F is the interface area, m²; W_m is the mass of total molten steel, which is supposed to be constant during refining; ρm and ρs are density of molten steel and slag respectively, kg/m³; k[p] and k(p) are mass transfer coefficient of phosphorus in steel and slag boundary respectively, m/s; L_p is the equilibrium phosphorus distribution between slag and steel.

Given that the mass transfer of phosphorus in the steel and slag sides obeys penetration theory [11], the mass transfer coefficients can be calculated by the following equations:

where D_m and D_s are diffusion coefficient of phosphorus in steel and slag, m²/s; u_m and u_s are velocity of steel and slag around the interface, m/s; l is cycle length of steel flow, and in this model it is the radius of converter, 2.02 m.

For the droplet metal–slag interface dephosphorization, the rate is described as:

where [%P]is mass concentration of phosphorus at steel and [%P]eqis the equilibrium concentration, [%P]eq=(%P)/Lp; f is the surface area of one droplet, which is calculated from droplet size, m²; W_d is the mass of one droplet, kg.

Since the droplet keeps moving in the slag and can be considered as a sphere, the mass transfer of phosphorus in the surrounding slag is [15]:

where d is the diameter of droplet; Sh is Sherwood number:

In which Re is Reynolds number and Sc is Schmitt number：

In the equation above, v is the velocity of droplet moving in the slag, and in the converter condition with high viscosity slag, it is supposed to be Stokes flow. So v here can be calculated as follows:

where μ is the viscosity of slag, Pa · s.

In eq. (4), if

And after integration, eq. (4) becomes:

where [%P]0is the phosphorus content when the droplet leave the bath, and [%P]t is the content when the droplet move back to the bath.

So by some mathematical transformations:

Equation (10) means dephosphorization amount of one droplet and thus for all the droplets above, the reaction rate is

where vp2 is the dephosphorization rate at droplet metal–slag interface, %/s; m is droplet generation rate, kg/(kg steel)/s.

At initial stage of oxygen blowing, the droplets generate but not fall back to the bath. Once the droplets begin to fall (reach the resistance time of the first droplet, t), the amount of droplets that suspending in slag reaches an equilibrium state, in which M represents the mass fraction of these droplets in total steel, kg/(kg steel).

In the converter, the whole dephosphorization rate is

Coupling of models

Considering that the dephosphorization reaction has little effect on the flow field, the two models are coupled by adopting one direction method. That means firstly the CFD model computes stable flow field results in converter and then some parameters from the CFD results, such as interface area, fluid velocity and droplet mass fraction, will be transferred to the kinetics model to simulate the dephosphorization process. The flow sheet is as shown in Figure 2. The relation between models is as shown in Table 2.

Figure 2:

Flow sheet of coupling dephosphorization kinetics and CFD model.

Table 2:

Coupling relations of models.

Dephosphorization rate

Figure 3:

Comparison of dephosphorization rates at different interfaces.

There are two interfaces in top blown converter and at both of them dephosphorization reaction happens. As is shown in Figure 3, V_p1 and V_p2 are dephosphorization rates and they both decline with time, which is caused by the decreasing phosphorus content. Besides, V_p1 is two magnitudes larger than V_p2, which is consistent with the results of Molloseau [16], who has reported that the decarbonation rate with emulsion is two magnitudes bigger than that without droplets generated. This means that the dephosphorization reaction mainly happens at the droplet metal–slag interface and is governed by the droplet generation parameters. Although the size of single droplet is small, the big specific surface area leads to a large total area.

Effect of oxygen lance pressure

Figure 4 is velocity contour map of converter vertical section. It can be seen that with the oxygen pressure getting higher, the velocity of steel increase, the area with relatively high velocity expands.

Figure 4:

Converter’s velocity contour map of vertical section at different oxygen pressure.

Figure 5:

Phosphorus content in steel changing with time at different oxygen pressure.

Figure 5 shows the relationship between phosphorus content and time under different oxygen pressure, and the slope of the curve represents the dephosphorization rate. It is indicated that when the pressure gets higher, the rate decreases. As is shown, the dephosphorization rate has an obvious increase with the pressure rising from 0.7 to 0.8 MPa, and the end phosphorus content decreases 19 %. However, when the pressure increases from 0.8 to 0.9 MPa, the change of end phosphorus content is almost negligible.

The dephosphorization rate is related to many factors, such as droplet fraction, bath metal–slag interface area and steel flow velocity. For investigating the influence of different factors on end phosphorus content, their values were monitored under different pressure, see Figure 6. The drop fraction seems to be inversely correlated with the end phosphorus content, while the others do not show any obvious relationship.

Figure 6:

Parameters related to dephosphorization kinetics at different oxygen pressure.

Effect of oxygen lance height

Figure 7 illustrates that the flow field is better at highest (2.0 m) and lowest (1.2 m) lance height, while at 1.5 m the high speed area of the flow field is smallest and the low speed area is the biggest. However, in Figure 8, the trends are different, which shows that the dephosphorization rate increases continuously with the lance height getting higher. In fact, dephosphorization has nothing to do with the flow field, but is influenced by the droplet fraction. As is shown in Figure 9, the end phosphorus content is nearly in linear relationship with lance height, and the droplet mass faction shows an inverse correlation with the end phosphorus content.

Figure 7:

Converter’s velocity contour map of vertical section at different lance height.

Figure 8:

Phosphorus content in steel changing with time at different lance height.

Figure 9:

Droplet mass fraction vs end phosphorus content at different lance height.