Modeling of Droplet Generation in a Top Blowing Steelmaking Process

Abstract

Quantification of metal droplets ejected due to impinging gas jet on the surface of liquid metal is an important parameter for the understanding and for the modeling of the refining kinetics of reactions in slag-metal emulsion zone. In the present work, a numerical study has been carried out to critically examine the applicability of droplet generation rate correlation previously proposed by Subagyo et al. on the basis of dimensionless blowing number (N _B). The blowing number was re-evaluated at the impingement point of jet with taking into account the temperature effect of change in density and velocity of the gas jet. The result obtained from the work shows that the modified blowing number N _B,T at the furnace temperature of 1873 K (1600 °C) is approximately double in magnitude compared to N _B calculated by Subagyo and co-workers. When N _B,T has been employed to the Subagyo’s empirical correlation for droplet generation, a wide mismatch is observed between the experimental data obtained from cold model and hot model experiments. The reason for this large deviation has been investigated in the current study, and a theoretical approach to estimate the droplet generation rate has been proposed. The suitability of the proposed model has been tested by numerically calculating the amount of metals in slag. The study shows that the weight of metals in emulsion falls in the range of 0 to 21 wt pct of hot metal weight when droplet generation rate has been calculated at ambient furnace temperature of 1873 K (1600 °C).

Appendices

Appendix I: Algorithm for Calculation of Metal in Emulsion

Modeling of Metals in Emulsion

In the present work, residence time of the droplets was calculated based on the theory of bloated droplet given by Brooks et al.[27] The total blowing time was divided into small time steps, ∆t. At each time step, a set of droplet generated and their residence time were calculated from the residence time model. Thus, the amount of metals in the emulsion phase at a given time is calculated by adding all the metal droplets present in the emulsion. It is to be noted that the droplets present in the emulsion at a particular time are different in their size mass and density due to the bloating phenomena caused by decarburization reaction. Here, it is assumed that the number of droplet remains same in the emulsion. Computational methodology to calculate the metal in emulsion is shown in Figure A1.

Fig. A1

Algorithm to calculate the amount of metal in emulsion

A matrix W _em is constructed to keep the track of the change in droplet mass due to decarburization reaction at a given time step and time of residence in emulsion phase.

$$ W_{em} = \left( {\begin{array}{ccccc} {n_{1} w_{{m}_{1,1}} } & {n_{2} w_{{m}_{2,1}} } & \cdots & {n_{k} w_{{m}_{k,1}} } \\ {n_{1} w_{{m}_{1,2}} } & {n_{2} w_{{m}_{2,2}} } & \cdots & \vdots \\ \vdots & \vdots & \cdots & \vdots \\ {n_{1} w_{{m}_{1,j}} } & {n_{2} w_{{m}_{2,j}} } & \cdots & {n_{k} w_{{m}_{k,j}} } \\ \end{array} } \right), $$

where w _m is the mass of the single droplet at the time of ejection and n _k is the number of droplet generated at each calculation time. W _em is a j × k matrix and j, k values are calculated as

$$ j = {\text{Residence time}} (k)/\Delta t,k = {\text{ Blowing time}}/\Delta t. $$

The instantaneous value of total metal in emulsion at each time of blowing has been calculated from the matrix W _em by summing up the diagonal elements (both off diagonal and main diagonal), which is shown below:

Appendix II: Sample Calculation for Droplet Generation for Steelmaking Conditions

The modified blowing number is calculated according to Eq. [13] and the density of the gas and velocity of the jet at the impingement have been corrected by applying Eq. [12]. At ambient temperature of the furnace of 1873 K (1600 °C), T _h is estimated to be 1060 K (787 °C).

At lance height h = 1.8 m, ambient temperature T = 1873 K (1600 °C), Pa = 101325 Pa, P₀ = 1180436.3 Pa, Q _O2 = 10.33 Nm³/s, the density and jet velocity of the gas have been estimated to be

$$ \rho_{\text{g,h}} = 0.36 \;{\text{kg}}/{\text{m}}^{3} \; {\text{and}} \; u_{j} = 373 {\text{m}}/{\text{s}}. $$

Substituting η = 0.4421, ρ _l = 7000 Kg/m³, σ _l = 1.7 N/m, the modified blowing number is

$$ N_{\text{B,T}} = 1 5 $$

The modified droplet generation rate is calculated based on Eq. [16] by applying temperature effect on volumetric expansion of the gas. Assuming pressure of the gas jet remains constant, the volume expansion of the gas at furnace environment is calculated as

$$ F_{\text{G,T}} = \frac{1060}{298} \times 10.33 = 36.75 \;{\text{m}}^{3} /{\text{s}}. $$

Substituting $F_{\text{G,T}}$ and $N_{\text{B,T}}$ values in Eq. [16], R _B,T can be estimated to be ~1783 kg/s.