Effects of the Scrap Steel Ratio and Bottom-Blowing Process Parameters on the Fluid Flow Characteristics in a Physical Model of a Steelmaking Converter

Abstract

The amount of scrap steel and selection of blowing process parameters are known to influence the fluid flow characteristics of the melt pool in converter steelmaking. However, few studies have considered the effects of scrap steel and blowing process parameters together. In this study, a physical model of a converter is established to investigate the influences of the amount of scrap steel and bottom-blowing process parameters on the fluid flow characteristics of the melt pool. Particle image velocimetry is used to measure the velocity distribution in the melt pool, and the stimulus–response method is used to measure the mixing time of the melt pool under different operating conditions. The results show that increasing the scrap steel ratio worsens the dynamic conditions of the melt pool. The best of the explored combinations is achieved at a scrap steel ratio of 20% and with six nozzles. The mixing time decreases as the gas flow rate increases, but the rate of decrease also decreases. Based on the results, the mixing time can be predicted from the gas flow rate and the number of nozzles. A relationship between the stirring power and mixing time of a converter using the bottom-blowing process is established.

1. Introduction

Converter steelmaking is the main method used around the world to produce high-quality steel owing to its advantages of high production efficiency and wide smelting rang [1,2,3]. The melt pool needs to be stirred to increase the reaction area of the slag, promote the floating of inclusions, and reduce weak flow areas, which helps shorten the mixing time [4,5]. Stirring is usually accomplished by a bottom-blowing, top-blowing, or combined blowing process [6,7,8]. The blowing process parameters (e.g., the number, placement, diameter, gas flow rate, and gas supply method of nozzles) are considered to have a significant impact on the mixing time of the melt pool [9,10,11,12,13]. Scrap steel is an important raw material that helps guarantee low-carbon development during the converter steelmaking process [14,15] and the amount of scrap steel added also affects the flow field and mixing characteristics of the melt pool [16,17,18,19].

Because of the high temperatures involved (1500–1600 °C), physical simulations such as water models are often used to study the fluid flow characteristics of the melt pool [20,21,22,23,24]. Nigmatulin and Lahey [13] used a water model to show that the mixing time of the melt pool is proportional to the one-third power of the number of nozzles for the bottom-blowing process. Zhou et al. [25] and Choudhary and Ajmani [26] also used water models to show that an asymmetric arrangement of bottom-blowing nozzles [25,26] facilitates mixing of the melt pool. However, Ballal and Ghosh [27] suggested that such an asymmetric arrangement will generate stronger shear forces and thereby accelerate the wear of the bottom-blowing nozzles and surrounding refractory material. Lai et al. [28] used a water model to show that the mixing time of the melt pool mainly depends on the gas flow rate of the bottom-blowing nozzles. Ajmani and Chatterjee [29] reported that the rate of decrease in the mixing time gradually decreases as the gas flow rate of the bottom-blowing nozzles increases and can even reverse. Xi et al. [16] and Liu et al. [18] used water models to study the effects of the amount and distribution of scrap steel, as well as the ratio of light and heavy scrap steel, on the mixing time of the melt pool. Their results show that the amount of scrap steel can be optimized to reduce the mixing time of the melt pool. Wu et al. [30] used a water model to show that the mass transfer of the top-blowing process is about 1/10 that of the bottom-blowing process. Given that the mass transfer rate is directly determined by the stirring intensity derived from gas energy, this finding indirectly confirms the significantly lower efficiency of top blowing in transferring energy into practical bath agitation compared to bottom blowing. Cai et al. [31] used water models and particle image velocimetry to study the fluid flow characteristics and mixing time of a melt pool under a combined blowing process. They obtained an empirical formula expressing a nonlinear relationship between the mixing time and stirring power.

Numerical simulations have also been used to study the fluid flow characteristics of melt pools [32,33,34]. Liu et al. [6] used the volume-of-fluid (VOF) method and discrete-phase model (DPM) in Fluent to study the influence of the bottom-blowing process on the fluid flow characteristics of a melt pool. They showed that the arrangement of bottom-blowing nozzles has a significant impact on the uniformity of the velocity distribution and dead zone areas in the melt pool. Yao et al. [35] used an eddy dissipation model to study the influence of the furnace gas composition on the characteristics of supersonic oxygen jets and showed that carbon monoxide affected the velocity and turbulent energy distribution of the jets. Sun et al. [36] and Zhou et al. [37] used the VOF method and DPM, respectively, to study the fluid flow characteristics of a melt pool using the combined blowing process. They showed that the top-blowing process made a substantially smaller contribution than the bottom-blowing process to the mixing of the melt pool. In addition, positioning the bottom-blowing nozzles at 0.3–0.4D, where D corresponds to the melt pool diameter, minimized the low-velocity area of the melt pool. Zhang et al. [19] explored the optimal proportioning method of scrap for converters using an optimization mathematical model. Through the optimization model, it is possible to obtain the lowest cost per ton of molten steel in the converter smelting process by determining the optimal proportions of various types of scrap.

In summary, the studies discussed above provide methodological references for investigating the fluid flow characteristics of the converter bath, including both physical modeling and numerical simulation. They also offer several quantitative conclusions. For example, the energy transfer efficiency of top blowing is much lower than that of bottom blowing, while factors such as the number of bottom-blowing nozzles, their positions, the gas flow rate, and the gas supply method all influence the mixing effectiveness of the converter. However, existing studies focusing on bottom-blowing process parameters have not accounted for the effect of scrap steel addition, while studies examining the impact of scrap steel on bath fluid flow characteristics have not considered the influence of bottom-blowing process parameters. Therefore, there is currently no detailed research on the coupled effects of scrap steel addition and bottom-blowing process parameters on the fluid flow characteristics of the converter bath.

In this study, a 300-ton converter prototype was taken as the research object, and a 1:8.8 physical model of a steel–scrap–gas three-phase flow furnace was established to investigate the combined effects of the scrap steel ratio and bottom-blowing process parameters on the fluid flow characteristics of the melt pool. This study is expected to provide supporting data and theoretical guidance for the rational use of scrap steel in converters.

2. Materials and Methods

Principle: This study was based on the principle of similarity, where compressed air was used to simulate argon gas, and water was used to simulate molten steel.

Table 1. The physical properties of fluid.

Physical Parameters	Prototype		Model
	Steel	Argon	Water	Air
Density, kg m−3	7000.00	1.63	1000.00	1.29
Viscosity, kg m−1 s−1	6.400 × 10−3	2.125 × 10−5	0.001	1.789 × 10−5
Surface tension, N m−1	1.500	/	0.071	/
Thermal conductivity, W m−1 K−1	15.0000	0.0158	0.6000	0.0242
Specific heat, J kg−1 K−1	670.00	520.64	4182.00	1006.43
Temperature, K	1873	300	300	300

Note: This isothermal physical model is based on the Froude number similarity criterion, for which density is the only property required in the core calculations. The values of parameters such as surface tension (as part of the complete thermophysical dataset for reference) are provided for completeness.

lists the physical properties of the fluids. The physical model was established by using the approximate modeling method and cold modeling method [38,39]. In addition to the geometric dimensions and the modified Froude number mentioned above, the selection of the simulated solid scrap steel, with the scrap ratio as a premise, was primarily based on the volume ratio between the actual scrap steel and the simulated scrap steel. The density of actual scrap steel from a steel plant was measured, and polyurethane with a density of 1.25 g cm⁻³ was used to simulate the scrap steel and maintain similarity with the converter prototype.

It should also be noted that this stage of the work is focused on revealing the flow and mixing patterns within the molten bath itself, which serves as a foundation for subsequent, more complex models incorporating multiple phases (e.g., slag).

To simulate the fluid flow characteristics of the melt pool while ensuring geometric similarity between the converter prototype and model, it is only necessary to ensure that the modified Froude numbers are equal:

$$\lambda ={\displaystyle \frac{L_{\mathrm{p}}}{L_{\mathrm{m}}}}$$

(1)

$$F{r}_{\mathrm{m}}^{\prime }=F{r}_{\mathrm{p}}^{\prime }$$

(2)

$${\displaystyle \frac{u_{\mathrm{gm}}^2}{g{L}_{\mathrm{m}}}}\cdot {\displaystyle \frac{{\rho }_{\mathrm{gm}}}{{\rho }_{\mathrm{l}\mathrm{m}}-{\rho }_{\mathrm{gm}}}}={\displaystyle \frac{u_{\mathrm{gp}}^2}{g{L}_{\mathrm{p}}}}\cdot {\displaystyle \frac{{\rho }_{\mathrm{gp}}}{{\rho }_{\mathrm{l}\mathrm{p}}-{\rho }_{\mathrm{gp}}}}$$

(3)

$$Q_{\mathrm{m}}=Q_{\mathrm{p}}{\left({\displaystyle \frac{L_{\mathrm{m}}}{L_{\mathrm{p}}}}\right)}^{{\displaystyle \frac{5}{2}}}\cdot {\left({\displaystyle \frac{{\rho }_{\mathrm{gp}}}{{\rho }_{\mathrm{gm}}}}\right)}^{{\displaystyle \frac{1}{2}}}\cdot {\left({\displaystyle \frac{{\rho }_{\mathrm{l}\mathrm{m}}-{\rho }_{\mathrm{gm}}}{{\rho }_{\mathrm{l}\mathrm{p}}-{\rho }_{\mathrm{gp}}}}\right)}^{{\displaystyle \frac{1}{2}}}$$

(4)

where $L_{\mathrm{m}}$ and $L_{\mathrm{p}}$ are the feature dimensions (m) of the model and prototype, respectively; $\lambda$ is the similarity ratio; $F{r}_m^{\prime }$ and $F{r}_p^{\prime }$ are the modified Froude numbers of the model and prototype, respectively; $u_{\mathrm{g}\mathrm{m}}$ and $u_{\mathrm{g}\mathrm{p}}$ are the gas velocity (m·s⁻¹) of the model and prototype, respectively; ${\rho }_{\mathrm{g}\mathrm{m}}$ and ${\rho }_{\mathrm{g}\mathrm{p}}$ are the gas densities (kg·m⁻³) of the model and prototype, respectively; ${\rho }_{\mathrm{l}\mathrm{m}}$ and ${\rho }_{\mathrm{l}\mathrm{p}}$ are the liquid densities (kg·m⁻³) of the model and prototype, respectively; $Q_{\mathrm{m}}$ and $Q_{\mathrm{p}}$ are the gas flow rates (Nm³·h⁻¹) of the model and prototype, respectively; and $g$ is the gravitational acceleration (m·s⁻²).

Equation (4) was used to obtain the following relationship between the gas flow rates of the model and prototype:

$$Q_{\mathrm{m}}=0.00182Q_{\mathrm{p}}$$

(5)

Table 2. The gas flow rates of the prototype and model.

Scheme	Prototype/Nm3·h−1	Model/Nm3·h−1
1	350	0.6
2	500	0.9
3	650	1.2
4	750	1.4
5	1100	2.0

lists the gas flow rates of the prototype and model. The gas flow rate for the prototype was set based on literature review and steel plant smelting data, while the gas flow rate for the model was calculated according to Equation (5).

Table 3. The stages of gas flow rates.

Stage	The Variation Range of Gas Flow Rates/m3·h−1
1	350–500
2	500–650
3	500–750
4	650–750
5	750–1100

divides the gas flow rates into stages. The gas flow rate was divided into five stages: 350–500 Nm³·h⁻¹, 500–650 Nm³·h⁻¹, 500–750 Nm³·h⁻¹, 650–750 Nm³·h⁻¹, and 750–1100 Nm³·h⁻¹. This division aims to more clearly describe the influence pattern of the bottom-blowing gas flow rate on the mixing homogeneity of the converter bath.

Setup: Figure 1 shows the experimental setup, which included a gas supply system, the physical model of the converter (the physical model was made from organic glass), a PIV system, and a DJ-800 data acquisition system. The experimental setup listed here in sequence: (1) air compressor (Jiangsu Dailuo Medical Technology Co., Ltd., Suzhou, China), (2) gas storage tank (Jiangsu Dailuo Medical Technology Co., Ltd., Suzhou, China), (3) scrap steel (Baoshan Iron & Steel Co., Ltd., Shanghai, China), (4) bottom-blowing nozzles (Tianchang Nanfang Organic Glass Factory, Tianchang, China), (5) physical model (Tianchang Nanfang Organic Glass Factory, Tianchang, China), (6) monitored area (shaded), (7) electrode probes (Shanghai Yidian Scientific Instrument Co., Ltd., Shanghai, China), (8) charge-coupled device (high-speed CMOS) cameras (Hefei Zhongke Junda Shijie Technology Co., Ltd., Hefei, China), (9) lasers (Hefei Zhongke Junda Shijie Technology Co., Ltd., Hefei, China), (10) conductivity meter (China Institute of Water Resources and Hydropower Research, Beijing, China), (11) DJ-800 data acquisition system (China Institute of Water Resources and Hydropower Research, Beijing, China), (12) synchronizer (Hefei Zhongke Junda Shijie Technology Co., Ltd., Hefei, China), and (13) computer (Dell (China) Co., Ltd., Xiamen, China).

Figure 2 shows a schematic of the converter model and three arrangements of six, eight, or ten bottom-blowing nozzles. For the six-nozzle arrangement, the nozzles formed a 45° angle with the ear axis and a 45° angle with the centerline perpendicular to the ear axis. The nozzles were positioned at 0.45D, 0.55D, and 0.65D (respectively, represented by A6-0.45D, A6-0.55D, and A6-0.65D), where D represents the diameter of the melt pool. For the eight-nozzle arrangement, the nozzles formed a 30° angle with the ear axis and a 30° angle with the centerline perpendicular to the ear axis. The nozzles were positioned at 0.45D, 0.55D, and 0.65D (respectively, represented by B8-0.45D, B8-0.55D, and B8-0.65D). For the 10-nozzle arrangement, the nozzles formed a 45° angle with the ear axis and a 45° angle with the centerline perpendicular to the ear axis. The nozzles were positioned at both 0.4D and 0.6D (represented by C10-0.4D & 0.6D). The following gas flow rates were tested: 350, 500, 650, 750, and 1100 m³·h⁻¹. The following scrap steel ratios were tested: 0%, 10%, 15%, 20%, 25%, 30%, and 40%. It should also be noted that the monitoring planes for the velocity contour, turbulent kinetic energy contour, and turbulent kinetic energy dissipation rate contour are the NG section, as shown in Figure 2a, b, and c, respectively. This NG section corresponds to the shaded area in Figure 1.

Table 4. Experimental Scheme.

Number	Scheme
1	Bottom blowing gas flow rates/Nm3·h−1	350
		500
		650
		750
		1100
2	Number of bottom-blowing nozzles	6
		8
		10
3	Layout position of bottom-blowing nozzle	0.40D
		0.45D
		0.55D
		0.60D
		0.65D
4	Scrap steel ratio/%	0
		10
		15
		20
		25
		30
		40

presents the detailed experimental scheme, and

Table 5. The key geometric parameters of prototype and model.

Parameter	Converter
	Prototype	Model
Converter capacity/tons	300	/
D1/mm	3600.0	409.1
D2/mm	2912.4	331.0
H/mm	11,500.0	1306.8
D/mm	6472.0	735.5
Molten bath depth/mm	1865	212

lists the key geometric parameters of the converter prototype and physical model.

Velocity Measurement: PIV is a noncontact, transient, and full-field velocity measurement method. In this study, the PIV system comprised a high-frequency laser, high-speed CMOS camera, synchronizer, computer, and light guide arm. Before measurement, tiny tracer particles with a density matched to the fluid were uniformly seeded into the physical model. For the PIV measurement, a synchronizer (timing controller) was employed to precisely coordinate the pulsed laser sheet illumination and the high-speed CMOS camera’s exposure. The laser illuminated the monitored area (shaded in Figure 1) at precise intervals. Operating in double-frame mode, the high-speed CMOS camera captured sequential image pairs of the tracer particles at a frequency of 1.92 Hz, resulting in 48 image pairs over a period of 25 s for each experimental condition. These image pairs were transferred to the computer via a high-speed interface. The velocity distribution/fields of the flow field under different operating conditions were finally calculated through cross-correlation analysis of the sequential image pairs using dedicated PIV software (PIV-3D3C-STD520). The software Tecplot360 (2024R1) was used for postprocessing of the images to obtain the velocity distribution. The turbulent kinetic energy and turbulent energy dissipation rate of the melt pool were, respectively, calculated as follows:

$$k={\displaystyle \frac{1}{2}}({u_{\mathrm{r}}^{\prime }}^2+{u_{\mathrm{v}}^{\prime }}^2)$$

(6)

$$\epsilon =\left|{\displaystyle \frac{dk}{dt}}\right|$$

(7)

where $k$ is the turbulent kinetic energy (m²·s⁻²), $\epsilon$ is the turbulent energy dissipation rate (m²·s⁻³), $t$ is the time (s), and $u_{\mathrm{r}}^{\prime }$ and $u_{\mathrm{v}}^{\prime }$ are the radial and vertical fluctuating velocities, respectively (m·s⁻¹). These are calculated as follows:

$$u_{\mathrm{r}}^{\prime }=u_{\mathrm{r}}-\overline{u_{\mathrm{r}}}$$

(8)

$$u_{\mathrm{v}}^{\prime }=u_{\mathrm{v}}-\overline{u_{\mathrm{v}}}$$

(9)

where $\overline{u}$ is the average velocity (m·s⁻¹). The subscripts r and v represent the radial and vertical directions, respectively. $u_{\mathrm{r}}$ and $u_{\mathrm{v}}$ are the instantaneous velocity components in the radial and vertical directions, respectively (m·s⁻¹).

Mixing Time Measurement: The mixing time of the melt pool was measured by using the stimulus–response method. Measurements were taken by using the physical model, gas supply system, flow meter, electrode probes, conductivity meter, DJ-800 data acquisition system, and computer (Figure 1). After the gas supply to the melt pool was stabilized, a tracer solution was quickly added to the melt pool. The electrode probes measured the concentration of the tracer solution, which was converted into conductivity by the conductivity meter, and transmitted to the DJ-800 data acquisition system, where it was converted into a digital signal. In this study, 35 mL of saturated NaCl solution (Shanghai Bohr Chemical Reagent Co., Ltd., Shanghai, China) was used as the tracer solution. The NaCl solution was introduced using the pulse addition method. At the beginning of the experiment, it was rapidly injected in a single dose through a feed funnel located at the top center region of the converter model’s bath. The specific injection location can be found in Figure 2b. When the conductivity curve stabilized within an error range of ±5% of the final value, the melt pool was considered to have reached a mixed state. The mixing time was defined as the difference from the time when the tracer was added to the melt pool to the time when the mixed state was reached. Each experiment was repeated three times to reduce the influence of human error. The mixing time at the position of an electrode probe was obtained by taking the average value:

$$t={\displaystyle \frac{t_1+t_2+t_3}{3}}$$

(10)

The final mixing time was defined as the average of the mixing times for both electrode probes. Figure 3 shows the changes in conductivity measured by the two electrode probes.

3. Results and Discussion

3.1. Effects of the Scrap Steel Ratio

To evaluate the effects of the scrap steel ratio on the fluid flow characteristics of the melt pool, the eight-nozzle arrangement was used with the bottom-blowing nozzles positioned at 0.45D (i.e., B8-0.45D). B8-0.45D is the actual bottom-blowing nozzle arrangement used in a 300-ton converter at a steel plant.

3.1.1. Mixing Time

Figure 4 shows the relationship between the mixing time, scrap steel ratio, and gas flow rate. Increasing the scrap steel ratio caused the mixing time to initially increase and then decrease before finally increasing again. When investigating the effect of scrap steel ratio, the best of the explored conditions was obtained at a scrap steel ratio of 20%, which resulted in mixing times of 93.2, 76.0, and 67.8 s at gas flow rates of 500, 750, and 1100 m³·h⁻¹, respectively.

Increasing the scrap steel ratio to 40% caused the mixing times at the same gas flow rates to increase by 18%, 40.4%, and 54.9%, respectively. When the total volume of molten steel and scrap steel in the melt pool was fixed, increasing the scrap steel ratio not only reduced the volume of molten steel but also blocked the molten steel from being stirred by the gas flow, which lengthened the mixing time. When only the volume of molten steel was fixed, adding moderate amount of scrap steel changed the path of the gas flow into the melt pool, which actually increased the stirred area and reduced the mixing time to some extent.

Table 6. The percentage decrease in mixing time at different stages of gas flow rates.

Gas Flow Rate Change Stage	Percentage Reduction in Mixing Time per 100 m3·h−1/%
	S0	S10 (a)	S15	S20	S25	S30	S40
3	3.3	5.3	4.6	7.4	4.2	1.6	1.2
5	1.6	2.9	2.5	3.1	1.7	0.7	0.5

^(a) (scrap steel ratio is 10%).

presents the percentage decrease in mixing time at different stages of gas flow rates. Increasing the gas flow rate gradually decreased the percentage decrease in mixing time. At a scrap steel ratio of greater than or equal to 30%, the percentage decrease in mixing time is smaller. For example, at a scrap steel ratio of 10%, increasing the gas flow rate from 500 to 750 m³·h⁻¹ resulted in a percentage decrease in mixing time of 5.3% for every increment of 100 m³·h⁻¹. However, increasing the gas flow rate from 750 to 1100 m³·h⁻¹ resulted in a percentage decrease in mixing time of only 2.9%. At a scrap steel ratio of 30%, the corresponding percentage decreases in mixing time were 1.6% and 0.7%, respectively. Therefore, increasing the gas flow rate improves the mixed state of the melt pool at scrap steel ratios of less than or equal to 25%.

3.1.2. Velocity Distribution

Figure 5 shows contour maps of the velocity distribution in the melt pool at scrap steel ratios of 0% and 20% (Figure 5(b) NG cross-section). The colors and arrow lengths represent the magnitude of the velocity. The velocity was highest above the nozzles and had a positive correlation with the gas flow rate. The presence of scrap steel in the melt pool reduced the area stirred by the gas flow and the flow velocity of the melt pool.

Figure 6 shows the average velocity of the melt pool at different scrap steel ratios. At a scrap steel ratio of 0%, increasing the gas flow rate from 500 to 750 m³·h⁻¹ increased the average velocity from 0.092 to 0.123 m·s⁻¹, respectively, for a percentage increase of 1.24% for every 100 m³·h⁻¹ increment. Increasing the gas flow rate from 750 to 1100 m³·h⁻¹ increased the average velocity from 0.123 to 0.128 m·s⁻¹, respectively, for a percentage increase in only 0.14% for every 100 m³·h⁻¹ increment. This is consistent with the trend of changes observed for the mixing time.

Table 7. The percentage increase in average velocity of the melt pool at other scrap steel ratios.

Gas Flow Rate Change Stage	Percentage Increase in Average Speed per 100 m3·h−1/%
	S10	S15	S20	S25	S30	S40
3	0.59	0.41	0.84	0.69	0.52	0.45
5	0.23	0.35	0.42	0.44	0.28	0.18

lists the percentage increase in average velocity for every 100 m³·h⁻¹ increment in the gas flow rate at other scrap steel ratios. At a scrap steel ratio of 20%, the average velocity reaches its maximum value of 0.116 m·s⁻¹. At gas flow rates of 500, 750, and 1100 m³·h⁻¹, increasing the scrap steel ratio from 20% to 40% decreased the average velocity of the melt pool by 24.3%, 28.9%, and 32.6%, respectively.

3.1.3. Turbulent Characteristics

Figure 7 and Figure 8 show contour maps of the distributions of the turbulent kinetic energy and turbulent energy dissipation rate in the melt pool at scrap steel ratios of 0% and 20%. The distributions are consistent with that of the velocity. The turbulent energy and turbulent energy dissipation rate were highest above the nozzles and had positive correlations with the gas flow rate.

Figure 9 shows the average turbulent energy dissipation rate of the melt pool at different scrap steel ratios. The average turbulent energy dissipation rate had a negative correlation with the mixing time: in other words, a higher average turbulent energy dissipation rate corresponded with a shorter mixing time.

The average turbulent energy dissipation rate was minimized at a scrap steel ratio of 40% compared with a scrap steel ratio of 20%; the average turbulent energy dissipation rates decreased by 22.1%, 34.4%, and 39.8% at gas flow rates of 500, 750, and 1100 m³·h⁻¹, respectively.

3.2. Effects of Bottom-Blowing Process Parameters

According to the results of Section 3.1, it can be concluded that if scrap steel is added to the converter, among the explored combinations, a scrap steel ratio of 20% yields the best kinetic conditions for the melt pool. Therefore, to explore the influence of the bottom-blowing process parameters on the fluid flow characteristics of the melt pool, the scrap steel ratio was set to 20%.

3.2.1. Mixing Time

Figure 10 shows the statistical results of mixing time for the 6-nozzle arrangement.

In Figure 10a, samples were labeled according to the following system: if A6-S20-045D is taken as an example, then A6 corresponds to six nozzles, S20 corresponds to a scrap steel ratio of 20%, and 0.45D corresponds to the nozzle position. The fitting degrees of the four fitting curves were $R_{\mathrm{A}6\text{-}\mathrm{S}20\text{-}0.45\mathrm{D}}^2$ = 0.97, $R_{\mathrm{A}6\text{-}\mathrm{S}20\text{-}0.55\mathrm{D}}^2$ = 0.96, $R_{\mathrm{A}6\text{-}\mathrm{S}20\text{-}0.65\mathrm{D}}^2$ = 0.97, and $R_{\mathrm{A}6\text{-}\mathrm{S}0\text{-}0.55\mathrm{D}}^2$ = 0.91, indicating a clear relationship between the total gas flow rate and the mixing time. First, the mixing time was minimized at a nozzle position of 0.55D, followed by 0.45D and then 0.65D. Second, the presence of scrap steel greatly degraded the mixing conditions of the melt pool. At a gas flow rate of 350 m³·h⁻¹, the mixing time increased by 21.8 s at a scrap steel ratio of 20% compared with a scrap steel ratio of 0%. However, at a gas flow rate of 1100 m³·h⁻¹, the increase in mixing time with a scrap steel ratio of 20% was only 3.5 s. Therefore, the effects of the scrap steel ratio on the mixing condition can be reduced by increasing the gas flow rate.

Third, increasing the gas flow rate gradually decreased the mixing time, but the rate of decrease in the mixing time initially increased and then decreased before increasing again. For example, In Figure 10b, at the nozzle position of 0.55D, the changes in mixing time for the first, second, third, and fourth stages of the gas flow rate were 7.6, 11.7, 4.5, and 6.2 s, respectively, which correspond to percentage changes of 5.1%, 7.8%, 4.5%, and 1.8%, respectively, for every 1 m³·h⁻¹ increment in the gas flow rate. Therefore, the optimal bottom-blowing process parameters for a scrap steel ratio of 20% and a six-nozzle arrangement were a nozzle position of 0.55D and a gas flow rate of 650 m³·h⁻¹, which resulted in the shortest mixing time and highest utilization rate of the gas flow.

Figure 11 shows the statistical results of mixing time for the 8-nozzle arrangement.

In Figure 11a, the fitting degrees of the fitting curves were $R_{\mathrm{B}8\text{-}\mathrm{S}20\text{-}0.45\mathrm{D}}^2$ = 0.92, $R_{\mathrm{B}8\text{-}\mathrm{S}20\text{-}0.55\mathrm{D}}^2$ = 0.94, $R_{\mathrm{B}8\text{-}\mathrm{S}20\text{-}0.65\mathrm{D}}^2$ = 0.93, and $R_{\mathrm{B}8\text{-}\mathrm{S}0\text{-}0.45\mathrm{D}}^2$ = 0.92, indicating a clear relationship between the total gas flow rate and mixing time.

First, the mixing time was minimized at the nozzle position of 0.45D, followed by 0.65D and then 0.55D. The results differ from those when the number of bottom-blowing nozzles is six, the specific explanation is as follows: “as can be seen from the vector diagram in Figure 5, the regions between the converter central axis and the bottom-blowing nozzles, as well as between the bottom-blowing nozzles and the furnace wall, constitute two primary inner/outer bottom-blowing jet stirring bath circulation zones. When the bottom-blowing nozzles are positioned at 0.55D, they lie closer to the intermediate region between the converter central axis and the furnace wall, thereby exerting a greater overall influence on the stirring effects within both the inner and outer circulation zones. As the number of bottom-blowing nozzles increases from 6 to 8, the gas flow rate per individual nozzle decreases. Compared to the positions at 0.45D and 0.65D, this reduction has a more pronounced weakening effect on the stirring efficiency at 0.55D, which is situated closer to the “intermediate position.” Consequently, comparing Figure 10 and Figure 11, when the total bottom-blowing flow rate remains constant, the increase in mixing time is relatively smaller for the 0.45D and 0.65D positions, whereas the increase is more substantial for the 0.55D position as the number of nozzles rises from 6 to 8. This leads to the observed phenomenon where “with 6 nozzles, the mixing time follows 0.55D < 0.45D < 0.65D, while with 8 nozzles, it follows 0.45D < 0.65D < 0.55D”.

Second, increasing the gas flow rate improved the mixing conditions of the melt pool in the presence of scrap steel. At a gas flow rate of 350 m³·h⁻¹, the mixing time was increased by 21 s at a scrap steel ratio of 20% compared to a scrap steel ratio of 0%. However, increasing the gas flow rate to 1100 m³·h⁻¹ decreased the increase in mixing time to 2.8 s. Third, the gas flow rate was inversely proportional to the mixing time, but the change in mixing time initially increased, followed by a decrease before it increased again. For example, In Figure 11b, at the nozzle position of 0.45D, the changes in the mixing time for the four stages of the gas flow rate were 4, 9.4, 7.8, and 8.2 s, respectively, which correspond to percentage changes of 2.7%, 6.3%, 7.8%, and 2.3%, respectively, for every 1 m³·h⁻¹ increment in the gas flow rate. Therefore, the optimal bottom-blowing process parameters for a scrap steel ratio of 20% and an eight-nozzle arrangement were a nozzle position of 0.45D and a gas flow rate of 750 m³·h⁻¹.

Figure 12 shows the statistical results of mixing time for the 10-nozzle arrangement.

In Figure 12a, the fitting degrees of the two curves were $R_{\mathrm{C}10\text{-}\mathrm{S}20\text{-}0.4\mathrm{D}\text{\&}0.6\mathrm{D}}^2$ = 0.86 and $R_{\mathrm{C}10\text{-}\mathrm{S}0\text{-}0.4\mathrm{D}\text{\&}0.6\mathrm{D}}^2$ = 0.87, indicating a clear functional relationship between the total gas flow rate and mixing time.

First, the gas flow rate was inversely proportional to the mixing time. Increasing the gas flow rate improved the mixing effect in the presence of scrap steel. At a gas flow rate of 350 m³·h⁻¹, the mixing time increased by 29.8 s with a scrap steel ratio of 20% compared to a scrap steel ratio of 0%. However, at a gas flow rate of 1100 m³·h⁻¹, the increase in mixing time was only 9.7 s. Unlike the previous nozzle arrangements, the change in the mixing time with an increasing gas flow rate initially increased and then decreased. In Figure 12b, the changes in the mixing time for the four stages of the gas flow rate were 4.1, 9.3, 14.6, and 5.6 s, respectively, which correspond to percentage changes of 2.7%, 6.2%, 14.6%, and 1.6%, respectively, for every 1 m³·h⁻¹ increment in the gas flow rate. Therefore, the optimal bottom-blowing process parameter for a scrap steel ratio of 20% and a 10-nozzle arrangement was a gas flow rate of 750 m³·h⁻¹.

Figure 12a also shows that increasing the gas flow rate to 1100 m³·h⁻¹ resulted in a mixing time of 78.6 s, which is 12.8 and 10.8 s more than the mixing times of A6-S20-0.55D and B8-S20-0.45D, respectively. This is because an excessive number of nozzles resulted in a relatively small flow rate allocated to each nozzle, which reduced the stirring power. Therefore, the number of nozzles should be optimized to reduce the mixing time.

Figure 13 clarifies the effect of the number of nozzles and gas flow rate on the mixing time of the melt pool at a scrap steel ratio of 20%.

The mixing time was minimized with the 6-nozzle arrangement and nozzle position of 0.55D (orange bar). A review of the literature showed that countries such as Japan and South Korea generally use fewer nozzles in their converters than in China. In addition, Chinese steel mills have confirmed that reducing the number of bottom-blowing nozzles helps optimize the stirring effect of the melt pool and reduces the carbon-oxygen product of endpoint molten steel in BOF [40,41].

Figure 14 shows the relationship between the mixing time $\tau$, gas flow rate $Q$, and number of nozzles $N$, which can be expressed as

$$\tau =378.44Q^{-0.34}{N}^{0.34}$$

(11)

The fit yielded an R² of 0.91 with p < 0.0001, indicating a statistically significant relationship between the gas flow rate of a single nozzle and the mixing time. To improve the mixing effect, the gas flow rate of each nozzle should be increased.

The figure also shows the confidence and prediction bands at a 95% confidence level. The confidence band indicates that the mean mixing time can be estimated based on the flow rate of a single nozzle within the range of 35–180 m³·h⁻¹. The maximum estimation error and error percentage of the mean mixing times were 5.6% and 5.0%, respectively, which demonstrates the rationality of Equation (11). The prediction band indicates that the actual mixing time corresponding to the flow rate can be estimated. The maximum estimation error was 9.4 s, which indicates that Equation (11) can be used as a reference for predicting the mixing time of a melt pool.

Finally, it should be noted that this study found the shortest mixing time of the bath occurred at a scrap steel ratio of 20%. This result is consistent with the conclusions reported in water modeling studies [42], where an optimal scrap addition range (16~24%) for mixing efficiency was also identified and attributed to the enhancement of turbulence and energy dissipation by the solid scrap. This mutual confirmation from independent results obtained using similar physical modeling methods verifies the existence of a non-monotonic dependence between the scrap ratio and mixing efficiency. Beyond verifying this phenomenon, the further value of this work lies in elucidating that this optimal scrap ratio is coupled with bottom-blowing process parameters, and it provides a quantitative correlation model (Equation (11), Figure 14, R² = 0.91, p < 0.0001) for predicting mixing time under these conditions, which aligns with reports in Reference [43].

3.2.2. Velocity Distribution

Figure 15 shows contour maps of the velocity distribution in the melt pool with different combinations of the bottom-blowing process parameters at a scrap steel ratio of 20%.

The color and arrow length represent the magnitude of the velocity. The stirred area of the melt pool was shifted upward with a scrap steel ratio of 20% compared to a scrap steel ratio of 0%. The velocity was highest above a nozzle, and the highest velocity was achieved with A6-0.55D. Finally, the velocity had a positive correlation with the gas flow rate.

Figure 16 shows the average velocity of the melt pool with different combinations of the bottom-blowing process parameters. The fitting degrees of the curves were $R_{\mathrm{A}6\text{-}\mathrm{S}20\text{-}0.55\mathrm{D}}^2$ = 0.91, $R_{\mathrm{B}8\text{-}\mathrm{S}20\text{-}0.45\mathrm{D}}^2$ = 0.95, and $R_{\mathrm{C}10\text{-}\mathrm{S}20\text{-}0.4\mathrm{D}\text{\&}0.6\mathrm{D}}^2$ = 0.95, indicating a clear relationship between the total gas flow rate and average velocity of the melt pool. For A6-0.55D, gas flow rates of 350, 500, 650, 750, and 1100 m³·h⁻¹ corresponded to average velocities of 0.064, 0.088, 0.099, 0.115, and 0.125 m·s⁻¹, respectively. These are improvements of 6.7%, 10%, 17.9%, 13.9%, and 7.9%, respectively, compared with B8-045D and improvements of 14.3%, 25.7%, 25.9%, 17.3%, and 10.6%, respectively, compared with C10-0.4D&0.6D.

3.2.3. Turbulent Characteristics

Figure 17 and Figure 18 show contour maps of the distributions of the turbulent kinetic energy and turbulent energy dissipation rate, respectively, with different combinations of the bottom-blowing process parameters at a scrap steel ratio of 20%. The trends are consistent with those of the melt pool velocity. The turbulent kinetic energy and turbulent energy dissipation rate were highest with A6-0.55D. The turbulent energy and turbulent energy dissipation rate were also highest above the nozzles. Finally, the turbulent kinetic energy and turbulent energy dissipation rate increased with the gas flow rate.

Figure 19 shows the average turbulent energy dissipation rate of the melt pool with different combinations of the bottom-blowing process parameters at a scrap steel ratio of 20%. The fitting degrees of the curves were $R_{\mathrm{A}6\text{-}\mathrm{S}20\text{-}0.55\mathrm{D}}^2$ = 0.95, $R_{\mathrm{B}8\text{-}\mathrm{S}20\text{-}0.45\mathrm{D}}^2$ = 0.95, and $R_{\mathrm{C}10\text{-}\mathrm{S}20\text{-}0.4\mathrm{D}\text{\&}0.6\mathrm{D}}^2$ = 0.94, indicating a clear relationship between the total gas flow rate and turbulent energy dissipation rate. The regression equation has a good fitting effect.

The average turbulent energy dissipation rate was highest with A6-0.55D.

At gas flow rates of 350, 500, 650, 750, and 1100 m³·h⁻¹, the average turbulent energy dissipation rate was 1.5%, 2.6%, 6.6%, 3.2%, and 2.0% higher, respectively, compared with B8-0.45 and 8.8%, 13.7%, 15.5%, 9.7%, and 6.7% higher, respectively, compared with C10-0.4D&0.6D.

The above results indicated that the gas flow rate, number of nozzles, nozzle arrangement, and scrap steel ratio all affected the mixing time of the melt pool. The influence of these factors on the mixing time can be expressed by the stirring power. The following relationship was established between the stirring power ${\epsilon }_{\tau }$ (W ton⁻¹) and mixing time $\tau$ (s), as shown in Figure 20:

$$\tau =513{{\epsilon }_{\tau }}^{-0.62}$$

(12)

The curve had a fitting degree of $R^2$ = 0.91, which indicates a clear relationship between the stirring power and mixing time. The mixing time decreased as the stirring power increased, which can be obtained through dimensional conversion of the turbulent energy dissipation rate:

$${\epsilon }_{\tau }=1000\epsilon$$

(13)

Additionally, it should be pointed out that the quantitative relationship between stirring power and mixing time established in this study (Equation (11), Figure 20) is consistent with the general conclusions in classical metallurgical fluid dynamics regarding mixing behavior in gas-stirred systems. For instance, the work of Cai et al. [31] also asserts that mixing time is primarily determined by the stirring power input to the bath. The key finding of our work is that, at a specific and practically significant scrap ratio of 20%, this classical relationship is rigorously validated and given a concrete quantitative expression. This indicates that the effectiveness of stirring power as a core driving parameter can be reliably extended from a homogeneous bath system without scrap to a complex heterogeneous system containing a moderate amount of solid scrap. Therefore, this study not only verifies the applicability of the classical theory under conditions closer to actual production (fixed 20% scrap ratio) but, more importantly, provides a precise quantitative predictive model for this specific and crucial process scenario, transforming theoretical understanding into an engineering tool that can directly guide and optimize practical operations.

4. Conclusions

In this study, a 1:8.8 physical model of a converter prototype was established, and PIV and the stimulus–response method were used to measure the flow field distribution and mixing time of the melt pool, considering the effects of the scrap steel ratio and bottom-blowing process parameters. It should also be noted that this study did not simulate the melting and heat exchange processes of the scrap steel; therefore, the conclusions are confined to the scope of fluid stirring efficiency.

The following conclusions were obtained:

• Increasing the scrap steel ratio worsened the dynamic conditions of the melt pool. Increasing the scrap steel ratio from 20% to 40% increased the mixing time by 54.9%, decreased the average velocity by 32.6%, and decreased the average turbulent energy dissipation rate by 39.8%.
• At a scrap steel ratio of 20%, the best of the explored combination of bottom-blowing process parameters was the six-nozzle arrangement, 0.55D nozzle position, and gas flow rate of 650 m³·h⁻¹. This combination resulted in an average velocity of 0.099 m·s⁻¹, an average turbulent energy dissipation rate of 0.0194 m²·s⁻³, a mixing time of 76.5 s, and a stirring power of 19.4 W ton⁻¹. The relationship between the mixing time, gas flow rate, and number of nozzles was established in Equation (11): $\tau =378.44Q^{-0.34}{N}^{0.34}$. The presence of scrap steel in the melt pool necessitates increasing the gas flow rate of each nozzle to improve the mixing effect.
• The effects of the gas flow rate, number of nozzles, nozzle arrangement and scrap steel on the mixing time can be expressed by the stirring power. The relationship between the stirring power and mixing time was established in Equation (12): $\tau =513{{\epsilon }_{\tau }}^{-0.62}$. The mixing time decreases as the stirring power increases.