Effect of cavity shape caused by jet impact of swirl-type oxygen lance on molten bath mixing efficiency

Abstract

In top-blowing steelmaking, the shape and size of the cavity formed by a supersonic jet have impacts on the molten bath, which is crucial for the refining process. This study used physical experiments to explore the influences that the operation and structural parameters of swirl-type oxygen lance have on cavity shape and mixing time. The results demonstrate that the lance height has a greater influence on cavity shape than flow rate, and the influence that the inclination angle has on cavity shape is greater than that of the swirl angle. Compared to the traditional oxygen lance, the mixing efficiency of the swirl-type oxygen lance increased by 5%–13.3%. When the cavity shape index of the swirl-type oxygen lance for the 260 t converter is in the range of 0.46–0.5, the mixing effect of the molten bath is the best. Additionally, an improved cavity depth prediction model of the swirl-type oxygen lance was proposed using the previous studies.

Keywords

Converter swirl-type oxygen lance cavity depth mixing time physical experiment

Introduction

In modern steelmaking, high-pressure oxygen is transformed into a supersonic jet through a nozzle, and it is transported to the converter for oxidation. During this process, there is a series of fundamental flow phenomena, including the production of the cavity, circulation, splashing, oscillation of molten bath and slag-metal emulsification.^1–4 The cavity is an important part of the interaction between the jet and the molten bath. Many critical refining reactions occur in the cavity; for example, 55% of the total carbon is removed during the entire blowing process.⁵ Therefore, it is necessary to have an in-depth understanding of the impact characteristics of the supersonic oxygen jet on the molten bath.

Due to a harsh environment and insufficient measurement methods, it is impossible to directly observe the cavity shape under actual operation conditions. Therefore, physical experiments and computational fluid dynamics simulation are commonly used to investigate the cavity size and the mixing efficiency of the molten bath. Molloy⁶ analysed the oscillation behaviour of the liquid surface when the jet impinged on the molten bath, and three different modes (dimpling, splashing and penetrating) were proposed. Solórzano-López et al.⁷ used mathematical and physical simulations to analyse the interaction between the jet and liquid surface and compared different formulas of cavity depth. Li et al.⁸ used theoretical analysis and physical experiments to establish a theoretical model, which predicted the cavity depth when the multiple jets impacted two layers of liquid in the converter. Dong et al.⁹ used numerical simulation to analyse the influence that the lance height has on the penetration depth, and the penetration depth was fitted mathematically. Wei et al.¹⁰ combined a theoretical model and numerical simulation to establish a hybrid model for predicting the penetration depth of a coherent supersonic jet, and the error is < 3.92%. Wu et al.¹¹ used a theoretical model and numerical simulation to establish an improved model for the penetration depth of an inclined coherent jet. Cao et al.¹² proposed a cavity shape index to quantitatively characterise the cavity shape, and it was found that there is an exponential relationship between the index and the splashing rate of molten steel. Sun et al.¹³ used the volume of fluid model to investigate how a supersonic jet impacts molten steel, and it was found that the lance height had a greater effect on the cavity dimensions than oxygen pressure; also, a modified cavity shape index was proposed. The above studies have made a significant contribution to the development of converter steelmaking, but most studies are limited to traditional single or multi-hole oxygen lance.

In recent decades, with the development of converters and an increase in demand for steel production, various new oxygen lances have been designed. For example, such lances include the central subsonic oxygen lance,¹⁴ double-parameter oxygen lance,^15,16 single-flow post-combustion oxygen lance¹⁷ and post-combustion oxygen lance.¹⁸ In addition, a swirl-type oxygen lance has been developed, as shown in Figure 1. Higuchi and Tago¹⁹ used physical experiments to study the jet behaviour and splashing of swirl-type oxygen lance, and it was found that a swirl angle of 11.4° was most effective for reducing the splashing rate. Lv et al.^20,21 used physical experiments and numerical simulations to analyse the influence that the swirl angle has on the emulsification of gas–slag–metal phases and the stirring efficiency. Liu et al.²² used numerical simulation to discuss the stirring efficiency that swirl-type oxygen lance has on the molten bath, and it was determined that a swirl angle of 8° was optimal for a 120 t dephosphorisation converter. Li et al.²³ used numerical simulations to investigate the dynamic characteristics of swirl-type oxygen lance jet, and the results indicated that the impact area was maximum at a swirl angle of 5°. Li et al.²⁴ conducted physical experiments and found that swirl-type oxygen lance with a swirl angle of 20° was more advantageous for reducing splashing and stirring the molten bath. Although the above works have made great contributions to the development and popularisation of the swirl-type oxygen lance, the influences that the cavity shape that is formed by swirling jets has on the mixing efficiency of the molten bath have rarely been studied, and there is no a theoretical model that is suitable for the swirl-type oxygen lance to predict the cavity depth.

Therefore, this work established a physical experimental model of a 260 t converter with a ratio of 1:7. Then, the influences that the operation parameters (the lance height and ﬂow rate) and structural parameters (the inclination angle and swirl angle) of the swirl-type oxygen lance have on the depth and width of the cavity and the mixing time were analysed. Also, the relationship between the cavity shape and mixing time was discussed. Finally, based on the previous studies, an improved model of the swirl-type oxygen lance for predicting cavity depth was proposed.

Experimental apparatus and method

Based on geometric similarities, a physical experimental model of the 260 t converter with a ratio of 1:7 was established, as shown in Figure 2. The apparatus included a converter model, lifting platform, air compressor, air tank, conductivity meter, computer, high-speed camera, oxygen lance nozzle etc. The converter model is made of organic glass, and a 3D printer was used to make the nozzle from the resin material. Oxygen and molten steel were replaced by compressed air and water, respectively. The bottom-blowing arrangement of the model is the same as that of the prototype, which had eight evenly arranged holes. The prototype and model parameters of the nozzle are shown in Table 1.

Table 1.

Geometric parameters of the nozzle.

Parameters	Prototype	Model
Throat diameter, d_t (mm)	45.7	6.53
Outlet diameter, d_e (mm)	61.1	8.73
Inclination angle, α (°)	15	13, 14, 15
Swirl angle, β (°)	0	0, 5, 8, 10, 12, 15
Mach number, Ma (–)	2.07	2.07

Without considering the chemical reaction, there are four forces in the interaction between the jet and the molten bath in the top-blowing process. These four forces are gravitational force, inertial force, viscous force and surface tension. Considering the major influence of gravitational force and inertial force on the physical model, the modiﬁed Froude number was adopted in this study to calculate the experimental parameters.^8,16 Froude number is modiﬁed as follows:

F r^{'} = \frac{ρ_{g} V_{g}^{2}}{g H ρ_{l}},

(1)

where V_g is the gas velocity (m/s), ρ_g is the gas density (kg/m3), ρ_l is the liquid density (kg/m3), g is the gravitational acceleration (m/s²) and H is the lance height (m). The model and prototype parameters were calculated based on the geometric and dynamic similarities, and the values of the parameters are listed in Table 2.

Table 2.

Geometric and operation parameters of converter.

Parameters	Prototype	Model
Molten bath diameter, D (mm)	6120	875
Molten bath depth, h (mm)	1833	262
Lance height, H (mm)	1833–3055	262–436
Top blowing rate, Q_t (Nm³/h)	45 000–57 000	70–90
Bottom blowing rate, Q_b (Nm³/h)	480	1.6

As shown in Figure 3, a high-speed camera was used to capture the shape of the cavity, and Image J software was employed to measure the size of the cavity. In this study, the maximum depth of the jet that penetrates the molten bath was defined as the cavity depth, denoted by h₀. The splash diameter at the edge of the cavity was used as the cavity diameter, denoted by d₀.¹⁵ The liquid fluctuations caused by the jet’s impact on the molten bath made the shape of the cavity unstable. Therefore, to minimise measurement error, the average value of five images was calculated under each operation condition.

As shown in Figure 2, saturated KCl solution (200 mL) was added to the converter when the fluid in the converter approached stability. A conductance probe was installed in the position, which is opposite to the direction of the additional position and on the side wall 200 mm away from the bottom of the converter. The conductance probe was used to monitor the conductivity of the liquid at 1 s intervals. The time when the conductivity of the monitoring point was within ± 2.5% of the final value of liquid is deﬁned as the mixing time. To eliminate errors of other factors, each operating condition was repeated three times, and the average value was taken as the ﬁnal mixing time.

Results and discussion

Cavity size

In the steelmaking process, the impact characteristics of the jet on the molten bath are closely related to the slagging reaction and the stirring strength of the converter. Therefore, a reasonable cavity shape is significant for improving the refining efficiency.²⁴ Figure 4 shows a comparison of the cavity morphologies of traditional oxygen lance and swirl-type oxygen lance at Q = 80 Nm³/h and H = 30d_e. The results show that the cavity distribution of the swirl-type oxygen lance is more dispersed than that of the traditional oxygen lance; this indicates that swirl-type oxygen lance has a larger contact area between slag and metal and improves the dephosphorisation efficiency in the early stage of smelting. Liu et al.²² and Li et al.²³ supported this finding. In addition, the cavity position of the swirl-type oxygen lance rotates significantly because of the swirl angle, and this means that the tangential force of the jet improves the mixing efficiency of the molten bath and promotes the decarbonisation reaction.

The cavity depth values of the traditional oxygen lance and swirl-type oxygen lance under different flow rates and lance heights are shown in Figure 5. h₀ and h represent the depth of the cavity and the molten bath, respectively. H and d_e are defined as the lance height and the outlet diameter of the nozzle, respectively. H/d_e is a dimensionless quantity that represents the distance between the oxygen lance and the molten bath. As seen, the cavity depth increases with an increase in the flow rate or a decrease in the lance height; also, the cavity depth of the swirl-type oxygen lance is lower than that of the traditional oxygen lance, and this is consistent with the previous research.²⁵ Under the same operation conditions, the swirling jet has a lower axial velocity because of the tangential component, and this reduces the impact strength on the molten bath. This is one of the reasons why the swirl-type oxygen lance is not currently widely used in steelmaking plants.

The width of the cavity represents the size of the impact area; this is an important indicator for determining the degree of contact between the jet and the surface of the molten bath. Figure 6 shows the cavity width of the traditional oxygen lance and swirl-type oxygen lance under different flow rates and lance heights. d₀ and D represent the width of the cavity and the diameter of the molten bath, respectively. As observed, the cavity width increases with an increase in the flow rate and the lance height, and the cavity width of the swirl-type oxygen lance is greater than that of the traditional oxygen lance. Li's research provides an explanation that the influence of jet coalescence is reduced due to the swirl angle; this improves the independence of the jet and causes the positions of the cavity to be more dispersed.²³ That is to say, the impact area of the swirl-type oxygen lance is higher than that of the traditional oxygen lance, indicating that it has a stronger slagging ability in the steelmaking process. Figures 5 and 6 illustrate a phenomenon that when the swirl angle increases, the lance height of the swirl-type oxygen lance can be appropriately reduced to obtain a cavity shape that meets the melting requirements.

Further analysis shown in Figures 5 and 6 demonstrates that when the flow rate was increased from 70 to 90 Nm³/h, the average depth of the cavity increased by 12.2 mm and the average width increased by 25.9 mm. With an increase in the lance height from 30d_e to 50d_e, the average depth of the cavity decreased by 22.6 mm and the average width increased by 32.1 mm. The above analysis indicates that the influence that the lance height has on the cavity shape is higher than that of the flow rate. Therefore, more attention should be given to controlling the lance height in actual operation because this affects the degree of slag drying and foaming.

The shape of the cavity is related to the lance height and flow rate as well as to the geometric parameters of the nozzle. The angle is an important parameter in designing an oxygen lance nozzle.^26,27 Because of the unique nozzle structure of the swirl-type oxygen lance, changes in the inclination angle and swirl angle can affect interactions between the swirling jet and molten bath. Therefore, it is significant to explore the relationship between the angle and the cavity shape for designing a swirl-type oxygen lance.

Figure 7 shows the relationship between the inclination angle and swirl angle with respect to the depth and width of the cavity at Q = 80 Nm³/h and H = 30d_e. As seen, with increases in the inclination angle and swirl angle, the depth and width of the cavity decrease or increase, respectively. The results demonstrate that an increase in the inclination angle or swirl angle increases the contact area between the jet and the molten bath, and this promotes mixing between slag and metal. However, it may reduce how much the jet impacts the molten bath and aggravates how the jet scours the converter wall.²⁸ It can also be observed from Figure 7 that for every 1° increase in the inclination angle, the average depth of the cavity decreases by 1.86 mm and the width increases by 10 mm. For every 5° increase in swirl angle, the average depth and width of the cavity decreases by 2 mm and increases by 8 mm, respectively. The above analysis indicates that the influence that the inclination angle has on the cavity shape is greater than that of the swirl angle.

Mixing time

Mixing time is a key indicator for estimating the stirring efficiency of the molten bath, and thus, mixing time is used in most studies to determine the performance of the oxygen lance. Figure 8 shows the mixing time of the molten bath under different flow rates and lance heights. The results show that the mixing time decreased and then increased with increases in the flow rate and lance height; the mixing time was lowest at Q = 80 Nm³/h and H = 40d_e. The results of this study are similar to those of physical experiments reported by Lv et al.²⁰ The reason for this phenomenon is that when the flow rate is high or the lance height is low, the exorbitant momentum of the jet collides with the bottom-blowing gas, causing energy dissipation. Furthermore, when the flow rate is low or the lance height is high, the energy of the jet that reaches the liquid surface is too small to stir the molten bath, and this results in an increase in the mixing time.

In addition, Figure 8 shows that the mixing time of the swirl-type oxygen lance is lower than that of the traditional oxygen lance. The reason is that the unique tangential force of the swirl-type oxygen lance promotes the circumferential flow of molten steel, thereby promoting the mixing of the molten bath.²⁴ More specifically, the above results suggest that swirl-type oxygen lance has better performance in mixing efﬁciency under the same operation conditions. In other words, the lance height of the swirl-type oxygen lance can be increased higher than that of the traditional oxygen lance if the stirring is intense. This results in a lower erosion rate of the lance tip and thus prolongs its life span.

Figure 9 shows the mixing time of different inclination angles and swirl angles at Q = 80 Nm³/h and H = 40d_e. As seen, the mixing time decreased and then increased with an increase in the swirl angle, and the mixing time was lowest at a swirl angle of 10°. The reason for this is that the tangential force of the swirling jet promotes the mixing of the molten bath and improves the stirring efficiency. Nevertheless, the larger swirl angle accelerates the decay of the jet axial velocity, and this has a negative influence on the mixing of the molten bath. According to statistics, the mixing efficiency of the swirl-type oxygen lance improved by 5%–13.3% compared to that of the traditional oxygen lance. It is noteworthy that the optimal values of the swirl angle in previous studies were in the range of 5°–11.4°.^19–23 The reasons for the deviation are that the size of a converter in previous research was between 120 t and 150 t and that the number of nozzle holes was different. Tago and Higuchi²⁹ considered that the number of nozzle holes changes the jet characteristics, thereby influencing the cavity shape and the flow field distribution of the molten bath. With increases in the inclination angle, the mixing time tended to decrease, and the lowest mixing time was at an inclination angle of 15°. This is because the increase in the range of jet impact improves the flow of molten steel at the furnace wall, which is the inactive zone of the molten bath in most studies.^13,17

Relationship between cavity shape and mixing time

In the top-blowing process, the cavity is generated when the oxygen jet impacts the molten bath, the shape and size of the cavity are crucial factors in refining the reaction rate.¹⁷ In top-blowing physics experiments, the different shapes of the cavity (disc, bowl and cone) were observed by Zhang et al.³⁰ and Liu et al.,¹⁵ and these correspond to the different splashing modes (dimpling, splashing and penetrating) that were proposed by Molloy,⁶ as shown in Figure 10. Cao et al.¹² proposed a dimensionless number to quantitatively characterise the shape of the cavity, this number is called the cavity shape index I₀. Moreover, it was also found that the shape of the cavity changed from disc shape to cone shape with an increase in I₀. The expression for I₀ expression is as follows:

I_{0} = \frac{h_{0}}{d_{0}} .

(2)

To explore the relationship between the cavity shape index and mixing time, the cavity shape index and the mixing time of different oxygen lances are compared at Q = 80 Nm³/h and H = 40d_e, and the results are shown in Figure 11. The results suggest that when the cavity shape index is small or large, the mixing time of the molten bath is relatively long. The specific explanation for this is that a smaller shape index corresponds to a cavity with a disc shape. At this moment, the velocity attenuation of the jet above the molten bath increases, and this indicates that the lower energy transfer efficiency of the jet to the molten bath causes less stirring. As the shape index increases, the cavity gradually approaches the bowl shape, and more energy of the jet is transferred into the molten bath, improving the stirring of the molten bath. Moreover, a larger shape index corresponds to a cavity with a cone shape, and this demonstrates that the energy of the jet is mainly used to penetrate the molten bath and oscillate the liquid surface. Also, there is dissipation through collisions with bottom-blowing gas. In other words, an appropriate cavity shape is conducive to stirring the molten bath, and this observation is similar to the research results reported by Cao et al.¹² In this study, the swirl-type oxygen lance jet has the best stirring effect on the molten bath when the cavity shape index is in the range of 0.46–0.5.

An improved cavity depth model

The phenomenon of the gas jet impacting the molten bath occurs widely in metallurgical refining processes. Other studies have conducted extensive work on the phenomenon and quantitatively normalised cavity depth, but most studies focused on single or multiple jets.^8,13,17 Studies on the prediction of cavity depth by a swirling jet have not been reported, and thus this study, which provides an in-depth discussion of this topic, fills a needed area of information.

In the early 1960s, Banks and Chandrasekhar³¹ established an expression for the axisymmetric jet momentum and cavity depth based on the balance between the jet dynamic pressure and the static pressure at the impact point. The expressions are as follows:

\frac{M}{ρ_{l} g H^{3}} = \frac{π}{2 K^{2}} \frac{h_{0}}{H} {(1 + \frac{h_{0}}{H})}^{2},

(3)

M = \frac{π ρ_{g} d_{e}^{2} V_{e}^{2}}{4},

(4)

where M is the jet momentum (kg·m/s²), V_e is the jet velocity at the nozzle outlet (m/s), ρ_g is the gas density (kg/m³), ρ_l is the liquid density (kg/m³); g is gravitational acceleration (m/s²), d_e is the nozzle outlet diameter (m), H is the lance height (m) and h₀ is the cavity depth (m).

K represents the attenuation behaviour of the jet velocity along the axial direction. K is not a fixed constant, and differences between studies are because of different experimental conditions. The value of K in currently relevant research is in the range of 5.13–11.5.^32–35 In previous work, it was found that the velocity attenuation of the swirling jet is different from that of the traditional jet.²⁵ Accordingly, the value of K should be calculated for all schemes. The expression for K is as follows:

\frac{V_{m}}{V_{e}} = K \frac{d_{e}}{H},

(5)

where V_m is the jet centre velocity (m/s). The calculated values of K values for all schemes are shown in Table 3.

Table 3.

K values for all schemes.

	α = 13°	α = 14°	α = 15°
β = 0°	6.613	6.574	6.536
β = 5°	6.588	6.526	6.45
β = 8°	6.544	6.472	6.381
β = 10°	6.5	6.422	6.329
β = 12°	6.452	6.361	6.273
β = 15°	6.376	6.273	6.16

The K with α and β values for nonlinear surface fitting and the results are shown in Figure 12. The functional relationship between K and α and β is expressed as follows:

K = 7.54 - 0.37 α (0.186 + \frac{7.33 β^{1.62}}{10 000}) .

(6)

At the point of impact in the cavity, the following expression was obtained based on the relationship between the dynamic pressure of the jet and static pressure:

\frac{1}{2} ρ_{g} V_{m}^{2} = ρ_{l} g h_{0} .

(7)

Based on previous studies,^8,17 this study considered that the momentum of each single jet can be expressed as follows:

M = \frac{M_{n} \cos α \cos β}{n},

(8)

where M_n is the jet total momentum (kg·m/s²), M is the single jet momentum (kg·m/s²), and n is the number of holes. Then, equations (5) through (8) can be combined, and H can be substituted by (H + h₀) to establish a model of the swirl-type oxygen lance for predicting the cavity depth. However, previous studies neglected the coalescence effect between multiple jets,^8,17 and this may lead to deviations between experimental values and predicted values under higher lance height. In this study, a correction term (Δφ) was added to the model to represent the effect of multiple jets coalescence. Furthermore, a linear relationship between Δφ and lance height was revealed by further analysis, as shown in Figure 13.

Finally, the revised model is expressed as follows:

\frac{M_{n} \cos α \cos β}{ρ_{l} g n H^{3}} = \frac{\frac{π}{2} \frac{h_{0}}{H} {(1 + \frac{h_{0}}{H})}^{2}}{{(7.54 - 0.37 α (0.186 + \frac{7.33 β^{1.62}}{10000}))}^{2}} - 12 \frac{d_{e}}{H} + 0.4.

(9)

Figure 14 shows the experimental values and predicted values that result from equation (9) for a cavity depth under different lance heights. As seen, the predicted values are in good agreement with the experimental values, and the error range is between 0.8% and 4.7%. The results indicate the accuracy of the model, and this can provide theoretical guidance for the industrial application of the swirl-type oxygen lance.

Conclusions

How the swirl-type oxygen lance jet impacts the molten bath of the 260 t converter was studied using physical experiments. Also, the cavity shape and mixing time under different operation conditions were analysed. The results are summarised as follows:

Compared to the flow rate, the lance height has a greater influence on the cavity shape. The influence that the inclination angle has on the cavity shape is greater than that of the swirl angle. In addition, compared to the traditional oxygen lance, the mixing efficiency of the swirl-type oxygen lance increased by 5%–13.3%.

A smaller or larger cavity shape index results in an increase in the mixing time. For a swirl-type oxygen lance of the 260 t converter, the cavity shape index should be controlled to be within the range of 0.46–0.5 to achieve the best mixing effect.

Based on the previous studies, an improved model of the swirl-type oxygen lance for predicting the cavity depth is proposed.

Footnotes

Acknowledgements

The authors gratefully acknowledge the financial support from the Education Department Project of Liaoning Province (JYTMS20230932), the National Natural Science Foundation of China (U20A20272) and the National Natural Science Foundation of China (NSFC52074151).

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Xi Wang

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