# Physical Simulation on Molten Steel Flow Characteristics of RH Vacuum Chamber with Arched Snorkels

Authors: Zhi-Feng Ren; Zhi-Guo Luo; Fan-Xia Meng; Zong-Shu Zou; Yi-Hong Li; Ai-Chun Zhao; Hai-Lian Gui
Journal: Advances in Materials Science and Engineering
 (2020)

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## Abstract

The RH vacuum refining technology is a vitally powerful method of producing clean steel. The inner diameter of traditional circular snorkel is very difficult to be increased owing to the metallurgical refractory thickness around the snorkels and the limitation of the area under the vacuum chamber, limiting the increase in refining efficiency. In order to improve the refining efficiency of the RH reactor, a new designed RH degasser with an optimized arched snorkel is established. This design replaces the traditional two circular snorkels structure with the two arched snorkels and greatly enhances the cross-sectional area of snorkel. In this study, the flow characteristics of this new type RH were studied and analyzed by establishing a 1 : 5.5 physical model of RH with arched snorkels. Results show that the circulation flow rate of RH with arched snorkels can increase by 100% ∼ 180% and the mixing time approximately decreases by 35% compared with RH with circular snorkels under actual production conditions. The circulation flow rate of RH with arched snorkels continues to increase obviously when gas flow rate exceeds the saturated value of RH with circular snorkels. The RH with arched snorkels can increase the refining efficiency significantly and has important application prospect.


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## Body

## 1. Introduction

As a tool for molten steel secondary refining, the Ruhrstahl–Heraeus (RH) processing has wide applications owing to its multiple metallurgical functions, such vacuum degassing, decarburization, inclusion removal, denitrogenation, and inclusion removal. It is widely used for the production of ultralow carbon steels, bearing steels, pipeline steels, spring steels, silicon steels, etc. The RH vacuum steel degassing process depends on sucking the liquid steel from the ladle to the vacuum chamber equipped with two snorkels (up-leg and down-leg) [1]. When the inert gas is blown to the liquid steel, then the circulation flow of steel between vacuum chamber and ladle is forced. The degassing process mainly occurs in liquid internal [1], at splashed metals in vacuum chamber and bubble surfaces [2, 3], which involves complex chemical reactions and transport phenomena [4]. Thus, to improve the degassing and decarburization rate and promote the inclusion removal rate in the RH systems, it is important to illustrate liquid steel flow characteristics. Nevertheless, the RH system can hardly be observed directly because of its complex physical and pyrometallurgical process, which involves thermodynamics, kinetics, and multiphase flow and mass transfer [4]. The problem was suddenly thrown into sharp focus. In order to reduce costs, many researchers are very concerned about improving the refining efficiency of RH equipment. It is generally considered that the circulation flow rate [5–10] and the mixing time [11–16] are two significant parameters during the RH process. Thus, many researchers have developed physical [10, 11, 17–21] or mathematical models [5, 13, 22–27] to simulate the multiphase flow [13, 22, 26–29], mixing phenomena [10–16, 28–31], behavior of bubble and inclusion removal [22, 30, 32], and decarburization process [1, 2, 8, 20, 23, 25, 33, 34] during the RH treatment. Based on the physical simulation experiment work of predecessors on circulation flow rate of RH, some empirical formulas are listed in Table 1, which includes the formulas put forward at the first time and excludes similar equations reported later. It is generally accepted that the circulation flow rate of RH is related to the injected gas flow rate and the section size of snorkel. From process parameter improvement view, many researches have proved that a higher gas flow rate [5, 7, 29, 30, 34], a lower vacuum pressure [18, 19, 28], a deeper insertion depth of snorkel [3, 14] would favor to optimize the fluid flow of RH. However, the circulation rate will reach a saturated value with the gas flow rate increasing [14, 36]. From equipment improvement view, many investigations have proved that a larger snorkel sectional area [24, 26, 29, 38]blowing from the bottom of the vacuum chamber [15] or ladle [39] would favor to optimize the fluid flow of RH. Recently, many researchers have tried to increase the refining efficiency by using single-leg [12, 28, 31, 40], multilegs [38, 41], and magnetic field [42] imposed around the up-leg. However, the single-leg was hardly used in the actual industrial manufacture considering technical immaturity; meanwhile, multilegs and imposing magnetic field around snorkel were also hardly used in the actual industrial manufacture considering the cost issue. All of the equations in Table 1 imply that the arched snorkels with greater sectional area would bring a larger circulation flow rate. Additionally, the stimulus-response was the general method used to measure the mixing time [7, 10], another important parameter for the RH treatment. In the physical simulation experiments of this paper, this method will continue to observe the mixing of molten steel.Table 1
Equations for circulation flow rate.
AuthorEquationsVariablesReferenceWatanabe et al.Q=0.020D1.5G0.33Q: circulation flow rate, t·min−1;G: gas flow rate, NL·min−1; D: diameter of snorkel, m[35]Tokio et al.Q=K⋅D1.5G0.33K: constant[11]Seshadri and CostaQ=ρ⋅S⋅0.74GlnP2/P11/3ρ: liquid density, g·cm−3; S: section area of snorkel, m2P1: pressure at top level, Pa; P2: pressure at injection point, Pa[36]Kuwabara et al.Q=K⋅G1/3D4/3lnP1/P24/3P1: pressure at blowing point, atmP2: pressure at vacuum vessel, atm[15]Kamata et al.Q=11.4Qg1/3dp4/3ln1+ρ1gh/Pv1/3Qg: gas flow rate, NL·min−1; dp: diameter of snorkel, m; ρl: liquid density, g·cm3; g: gravitational acceleration, m·s−2; h: gas inject depth, cm; PV: vacuum chamber pressure, Pa[37]However, little results [38, 42] were reported to study the shape of RH snorkels, which has always been circular until the oval snorkel was proposed by Kuwabara [15]. The oval snorkels were favored to enhance fluid flow of RH, but we want the refining efficiency to keep getting bigger, including a great increase in circulation flow rate and saturated value of gas flow rate. In the current study, a new vacuum degasser equipped with two snorkels of larger sectional area was designed. The two traditional circular snorkels were replaced with two arched snorkels, which was not reported in previous investigations. For the arched snorkel, the internal arc height is equal to the radius of traditional circular snorkel and the internal diameter is 3 to 4 times of the circular snorkel. Hence, the sectional area of arched snorkel is much larger than that of circular snorkel. Water modeling was performed according to similarity criterion. The flow velocity of the RH water model down-on leg-outlet plane was captured by electronic tachometer, and the stimulus-response method was used to measure the mixing time. The results provided the experimental basis for promoting and improving this new RH vacuum refining equipment.


## 2. Experiment

### 2.1. Model Design

The prototype is one RH vacuum chamber with two circular snorkels from a steel plant in China. According to the empirical formulas listed in Table1, we have determined the kernel idea of this design is to increase the cross-sectional area of snorkel as much as possible. The scale of water model and prototype is 1 : 5.5. Figure 1(a) shows the model size of circular snorkel. The circular snorkel diameter is very difficult to be increased owing to the metallurgical refractory thickness around the snorkels and the limitation of the area under the vacuum chamber. In order to increase the cross-sectional area of the snorkel as much as possible, two snorkels are changed to arched structures in this research. So as to make full use of the space under the vacuum chamber, the inner diameter of the vacuum chamber is determined as the diameter of arched snorkel and the arc height is same as the inner diameter of circular snorkel, utilizing the bottom space of the vacuum chamber optimized. Figure 1(b) exhibits the top view of the arched snorkel water model. Compared with circular snorkel, this arched structure increases the equivalent inner diameter by approximately 70% and the cross-sectional area by 193% in this design.Figure 1
Model schematic of the RH vacuum chamber with (a) circular and (b) arched snorkels (top view).
(a)(b)


### 2.2. Similarity Theory

A 1 : 5.5 scale water model of 170t RH was built according to the similarity principle. Table 2 shows the main parameters of the prototype and physical model. The lifting gas flow rate of model Qm is calculated from the actual gas flow rate on-site Qp with the modified Froude criterion according to the following equation:(1)Qm=0.01448Qp.Table 2
Parameters of the prototype and water model.
ItemPrototype (mm)Water model for circular snorkels (mm)Water model for arched snorkels (mm)Diameter of ladle top3077564564Diameter of ladle bottom2666489489Height of ladle3806692692Inner diameter of vacuum chamber1800330330Height of vacuum chamber1035010001000Internal diameter of circular snorkel5009292Internal diameter of arched snorkel1800330330Internal arc height of arched snorkel5009292Length of snorkels1500275275Inner diameter of gas injection nozzles61.11.1Distance between nozzles and bottom of vacuum chamber550100100


### 2.3. Experimental Device and Parameters

The water model experimental devices consist of vacuum chamber and ladle made of plexiglass. Two snorkels are equipped at the bottom of the vacuum chamber. To the RH with two circular snorkels, compressed air is used as the lifting gas through six evenly distributed gas injection nozzles in one horizontal plane of circular up-leg. To the RH with two arched snorkels, four nozzles are distributed evenly in the arc of the arched up-leg, two others are distributed evenly in the chord, and these six nozzles are in one horizontal plane of arched up-leg. This model also includes the gas source system, gas distributor and transmission pipeline, vacuuming system, metering system, and detection system. Figure2 shows the schematic of the main apparatus of the water model.Figure 2
Schematic of water modeling.The gas flow rate is 60 ∼ 130 Nm3·h−1, the pressure in the vacuum chamber is 67 Pa, and insertion depth of snorkel is 627 mm in the production site. Table 3 shows the corresponding parameters of the prototype and water model.Table 3
Parameters of the prototype and water model.
Main parametersVacuum degree (Pa)Gas flow rate (Nm3·h−1)Insertion depth of snorkel (mm)Prototype673569104138173193382545710818Model977090.511.522.52.870100130150


### 2.4. Experimental Index

#### 2.4.1. Circulation Flow Rate

The circulation flow rateGm was obtained by measuring the fluid velocity, which was 20 mm above the outlet of the down-leg. Five measuring points were horizontally and longitudinally set at the cross-sectional center of down-leg. The fluid velocity at the measuring point was obtained with an electronic tachometer (XC-LSB-1, XINGLIANCHEN Technology Co., Ltd., China). Each measurement was repeated three times, and the cross-sectional velocity was obtained by the average value of all measuring points. The circulation flow rate was the product of the measured velocity and cross-sectional area of the down-leg.


#### 2.4.2. Mixing Time

The mixing timeTmix was measured by an electrical conductivity meter [18, 36]. The saturated NaCl aqueous solution was used as the tracer. When the fluid flow in the model was stable, the saturated NaCl aqueous solution was injected into the water through the spare nozzle on top of up-leg. Meanwhile, the conductivity instrument (DDS-307A, INESA Scientific Instrument Co., Ltd., China) was employed to measure the conductivity until a stable value (C∞) was reached. The time for reaching the stable value is called mixing time. The conductivity probe was placed 60 mm below the ladle liquid level in the center between the up-leg and down-leg.


### 2.5. RH Work Principle and Bubble Behavior

The lifting gas is injected into the molten steel through the nozzles, and discrete spherical bubbles are formed at the nozzle exit. The bubbles with initial horizontal velocity enter into up-leg from the nozzles, and then the bubbles float upward and drive the molten steel up. Figure3 shows the schematic of the bubble formation and motion path.Figure 3
Schematic of the formation and path of bubbles in up-leg.The molten steel circulation process between the vacuum chamber and the ladle in RH vacuum degasser is similar to the “bubble pump” mechanism. A certain height difference between the liquid levels in the vacuum chamber and ladle is created in the vacuum degree of the vacuum chamber. The lifting gas first enters into molten steel in the form of bubbles, floats upward, and then expands with the temperature increase and pressure decrease. Accordingly, the density of gas-liquid two-phase in the up-leg reduces. The molten steel in the ladle is driven to the up-leg and then flows out through the down-leg due to gravity after entering the vacuum chamber. Thereafter, a circulation flow is formed, and the following equation is achieved [8, 14, 17]:(2)Agas=Asteel+Aloss,where Agas is the gas expansion work, J; Asteel is the work for lifting molten steel, J; and Aloss is the lost work, J.ConsideringAloss is small, equation (2) can be expressed as(3)Agas=Asteel=MHg=MP0−Pρg−1P0−Pρ1,where M is the quality of lifting liquid steel, kg; H is the lifting height of liquid steel, m; P0 is the atmospheric pressure, Pa; g is the acceleration of gravity, m·s−2; P is vacuum chamber pressure, Pa; ρg-l is the density of gas-liquid two-phase, kg·m−3; and ρl is the density of liquid, kg·m−3. The density of the gas-liquid two-phase is the weighted value of the gas and liquid phases and obtained from equation (4) [17] as follows:(4)ρg−1=α⋅ρg+1−α⋅ρ1,where α is the gas holdup.


## 2.1. Model Design

The prototype is one RH vacuum chamber with two circular snorkels from a steel plant in China. According to the empirical formulas listed in Table1, we have determined the kernel idea of this design is to increase the cross-sectional area of snorkel as much as possible. The scale of water model and prototype is 1 : 5.5. Figure 1(a) shows the model size of circular snorkel. The circular snorkel diameter is very difficult to be increased owing to the metallurgical refractory thickness around the snorkels and the limitation of the area under the vacuum chamber. In order to increase the cross-sectional area of the snorkel as much as possible, two snorkels are changed to arched structures in this research. So as to make full use of the space under the vacuum chamber, the inner diameter of the vacuum chamber is determined as the diameter of arched snorkel and the arc height is same as the inner diameter of circular snorkel, utilizing the bottom space of the vacuum chamber optimized. Figure 1(b) exhibits the top view of the arched snorkel water model. Compared with circular snorkel, this arched structure increases the equivalent inner diameter by approximately 70% and the cross-sectional area by 193% in this design.Figure 1
Model schematic of the RH vacuum chamber with (a) circular and (b) arched snorkels (top view).
(a)(b)


## 2.2. Similarity Theory

A 1 : 5.5 scale water model of 170t RH was built according to the similarity principle. Table 2 shows the main parameters of the prototype and physical model. The lifting gas flow rate of model Qm is calculated from the actual gas flow rate on-site Qp with the modified Froude criterion according to the following equation:(1)Qm=0.01448Qp.Table 2
Parameters of the prototype and water model.
ItemPrototype (mm)Water model for circular snorkels (mm)Water model for arched snorkels (mm)Diameter of ladle top3077564564Diameter of ladle bottom2666489489Height of ladle3806692692Inner diameter of vacuum chamber1800330330Height of vacuum chamber1035010001000Internal diameter of circular snorkel5009292Internal diameter of arched snorkel1800330330Internal arc height of arched snorkel5009292Length of snorkels1500275275Inner diameter of gas injection nozzles61.11.1Distance between nozzles and bottom of vacuum chamber550100100


## 2.3. Experimental Device and Parameters

The water model experimental devices consist of vacuum chamber and ladle made of plexiglass. Two snorkels are equipped at the bottom of the vacuum chamber. To the RH with two circular snorkels, compressed air is used as the lifting gas through six evenly distributed gas injection nozzles in one horizontal plane of circular up-leg. To the RH with two arched snorkels, four nozzles are distributed evenly in the arc of the arched up-leg, two others are distributed evenly in the chord, and these six nozzles are in one horizontal plane of arched up-leg. This model also includes the gas source system, gas distributor and transmission pipeline, vacuuming system, metering system, and detection system. Figure2 shows the schematic of the main apparatus of the water model.Figure 2
Schematic of water modeling.The gas flow rate is 60 ∼ 130 Nm3·h−1, the pressure in the vacuum chamber is 67 Pa, and insertion depth of snorkel is 627 mm in the production site. Table 3 shows the corresponding parameters of the prototype and water model.Table 3
Parameters of the prototype and water model.
Main parametersVacuum degree (Pa)Gas flow rate (Nm3·h−1)Insertion depth of snorkel (mm)Prototype673569104138173193382545710818Model977090.511.522.52.870100130150


## 2.4. Experimental Index

### 2.4.1. Circulation Flow Rate

The circulation flow rateGm was obtained by measuring the fluid velocity, which was 20 mm above the outlet of the down-leg. Five measuring points were horizontally and longitudinally set at the cross-sectional center of down-leg. The fluid velocity at the measuring point was obtained with an electronic tachometer (XC-LSB-1, XINGLIANCHEN Technology Co., Ltd., China). Each measurement was repeated three times, and the cross-sectional velocity was obtained by the average value of all measuring points. The circulation flow rate was the product of the measured velocity and cross-sectional area of the down-leg.


### 2.4.2. Mixing Time

The mixing timeTmix was measured by an electrical conductivity meter [18, 36]. The saturated NaCl aqueous solution was used as the tracer. When the fluid flow in the model was stable, the saturated NaCl aqueous solution was injected into the water through the spare nozzle on top of up-leg. Meanwhile, the conductivity instrument (DDS-307A, INESA Scientific Instrument Co., Ltd., China) was employed to measure the conductivity until a stable value (C∞) was reached. The time for reaching the stable value is called mixing time. The conductivity probe was placed 60 mm below the ladle liquid level in the center between the up-leg and down-leg.


## 2.4.1. Circulation Flow Rate

The circulation flow rateGm was obtained by measuring the fluid velocity, which was 20 mm above the outlet of the down-leg. Five measuring points were horizontally and longitudinally set at the cross-sectional center of down-leg. The fluid velocity at the measuring point was obtained with an electronic tachometer (XC-LSB-1, XINGLIANCHEN Technology Co., Ltd., China). Each measurement was repeated three times, and the cross-sectional velocity was obtained by the average value of all measuring points. The circulation flow rate was the product of the measured velocity and cross-sectional area of the down-leg.


## 2.4.2. Mixing Time

The mixing timeTmix was measured by an electrical conductivity meter [18, 36]. The saturated NaCl aqueous solution was used as the tracer. When the fluid flow in the model was stable, the saturated NaCl aqueous solution was injected into the water through the spare nozzle on top of up-leg. Meanwhile, the conductivity instrument (DDS-307A, INESA Scientific Instrument Co., Ltd., China) was employed to measure the conductivity until a stable value (C∞) was reached. The time for reaching the stable value is called mixing time. The conductivity probe was placed 60 mm below the ladle liquid level in the center between the up-leg and down-leg.


## 2.5. RH Work Principle and Bubble Behavior

The lifting gas is injected into the molten steel through the nozzles, and discrete spherical bubbles are formed at the nozzle exit. The bubbles with initial horizontal velocity enter into up-leg from the nozzles, and then the bubbles float upward and drive the molten steel up. Figure3 shows the schematic of the bubble formation and motion path.Figure 3
Schematic of the formation and path of bubbles in up-leg.The molten steel circulation process between the vacuum chamber and the ladle in RH vacuum degasser is similar to the “bubble pump” mechanism. A certain height difference between the liquid levels in the vacuum chamber and ladle is created in the vacuum degree of the vacuum chamber. The lifting gas first enters into molten steel in the form of bubbles, floats upward, and then expands with the temperature increase and pressure decrease. Accordingly, the density of gas-liquid two-phase in the up-leg reduces. The molten steel in the ladle is driven to the up-leg and then flows out through the down-leg due to gravity after entering the vacuum chamber. Thereafter, a circulation flow is formed, and the following equation is achieved [8, 14, 17]:(2)Agas=Asteel+Aloss,where Agas is the gas expansion work, J; Asteel is the work for lifting molten steel, J; and Aloss is the lost work, J.ConsideringAloss is small, equation (2) can be expressed as(3)Agas=Asteel=MHg=MP0−Pρg−1P0−Pρ1,where M is the quality of lifting liquid steel, kg; H is the lifting height of liquid steel, m; P0 is the atmospheric pressure, Pa; g is the acceleration of gravity, m·s−2; P is vacuum chamber pressure, Pa; ρg-l is the density of gas-liquid two-phase, kg·m−3; and ρl is the density of liquid, kg·m−3. The density of the gas-liquid two-phase is the weighted value of the gas and liquid phases and obtained from equation (4) [17] as follows:(4)ρg−1=α⋅ρg+1−α⋅ρ1,where α is the gas holdup.


## 3. Results and Discussion

### 3.1. Comparison of RH with Circular Snorkels and RH with Arched Snorkels

#### 3.1.1. Flow Field

Under the condition of vacuum chamber pressure (P = 97709 Pa), insertion depth of snorkel (Himm = 100 mm), gas flow rate (Qm = 1.0 Nm3·h−1), and flow field using the black ink as tracer is shown in Figure 4. The ink was injected into up-leg through the spare nozzle on the top of up-leg. A high-speed camera was used to record the flow field. As shown in the flow fields from the water models, the molten steel driven by lifting gas flowed into the vacuum chamber through the up-leg, and violent mixing occurred in the vacuum chamber. Then, the molten steel flowed downward the ladle through down-leg, reached the ladle bottom, and rose upward again. The time of tracer in RH with arched snorkels to complete the mixing in the vacuum chamber, reaching the ladle bottom and complete one cycle, was, respectively, 3 s, 12 s, and 18 s and that of RH with circular snorkels was 3 s, 18 s, and 44 s. Compared with RH with circular snorkels, the quantity of the flowing molten steel through down-leg increases with the increase of the cross-sectional area and has a better diffusion capacity in the ladle while flowing to the bottom of the ladle in RH with arched snorkels. The mixing capacity of RH with arched snorkels was stronger than that of RH with circular snorkels.Figure 4
Flow field of (a) RH with circular snorkels and (a) RH with arched snorkels in one circulation.
(a)(b)


#### 3.1.2. Saturated Gas Flow Rate

In water model experiment, the circulation flow rate increases with the gas flow rate. After reaching a certain value, the circulation flow rate tends to be saturated. The circulation flow rate at this time is called saturated circulation flow rateGm,max, and the minimum gas flow rate corresponding to the Gm,max is called saturated gas flow rate Qm,max [14, 36].The horizontal section and horizontal trajectory of the bubbles in gas-liquid plume observed schematically at the outlet of the up-leg are shown schematically in Figure5. For the two RH models, the bubbles in the gas-liquid plume formed at the exit of each nozzle are individually close to the wall of up-leg at small gas flow rate. With the increase of the gas flow rate, the diameter and horizontal penetrating depth of bubbles in gas-liquid plume increase. When the gas flow rate tends to be Qm,max, the bubbles in gas-liquid plume will collide with each other for RH with circular snorkels as shown in Figure 5(a), and bubbles from nozzle 2 and 3 will collide the opposite wall lastly for RH with arched snorkels as shown in Figure 5(b). If the gas flow rate continues to increase and the bubbles are in the state of ejection, the gas driving power will be greatly reduced and the circulation flow rate will tend to be saturated. Therefore, it can be considered that the gas flow rate corresponding to the contact of bubbles from different nozzles with each other or the contact of bubbles and opposite wall is Qm,max. The bubble is simulated by a complete sphere, and the geometric conditions of this contact state of RH with circular snorkels and RH with arched snorkels are expressed by equations (5) and (6) [10]. Equations (7)–(9) [37] show the calculation formulas of diameter and horizontal penetrating depth of bubble; by combining equations (5) and (6), the Qm,max of the two RH water models can be calculated:(5)dB=dp2−LB+dB2∗2sinθN2,(6)dp/2−HscosθN/2+LB=dp2,where dB is the bubble diameter, m; dp is the diameter of up-leg, m; LB is the horizontal penetrating depth of bubble, m; Hs is internal arc height; and θN is the angle between adjacent nozzles; for circular snorkel,θN=2π/nc (nc is the nozzle number); for arched snorkel, θN=arccos0.5dp−Hs/0.5dp/2.5:(7)dB=6σd0ρ1g2+0.54Qg4nd00.50.28961/6,(8)LBd0=3.7ρgρ1−ρgVg2gd01/3,(9)Vg=Qg/nπd02/4,where d0 is the nozzle diameter, m; σ is the surface tension in the liquid phase, N·m−1; ρ1 and ρgare the density of liquid and phase, kg·m−3; n is the nozzle number; Vg is the orifice gas velocity, m·s−1; gis the acceleration of gravity, m·s−2; and Qg is the gas flow rate, Nm3·s−1.Figure 5
Illustration of bubble dispersion behavior in up-leg observed from the bath bottom. RH with (a) circular snorkels and (b) arched snorkels.
(a)(b)TheQm,max of RH with circular snorkels calculated from above is 2.52 Nm3·h−1. And, this is 5.03 Nm3·h−1 to RH with arched snorkels. The Qm,max of RH with arched snorkels is approximately 99.6% higher than that of the RH with circular snorkels from theoretical calculations.Figure6(a) shows the variation of circulation flow rate Gm and gas flow rate Qm under the conditions that insertion depth of snorkel Himm is 70, 100, 130, and 150 mm, respectively. The Gm increased with the increase of Himm, and the Gm of RH with circular snorkels showed saturation tendency at about 2.50 Nm3·h−1 of Qm even at different Himm, which was very consistent with the calculated value (2.52 Nm3·h−1). The Qm,max is the result of the horizontal movement of the bubbles and is independent of the insertion depth of snorkel. Therefore, Figure 6(b) only shows the variation of the Gm and Qm under the condition of Himm 70 mm; the Gm kept increasing with the increase of Qm, because the Qm,max of RH with arched snorkels was 5.03 Nm3·h−1.Figure 6
Variation of circulation flow rateGm as a function of gas flow rate Qm. (a) RH with circular snorkels. (b) RH with arched snorkels.
(a)(b)According to equation (1), the Qp,max of RH with arched snorkels is 347 Nm3·h−1 on-site, which is far beyond the gas flow rate (60 ∼ 130 Nm3·h−1) in the production site. Excessive gas flow rate will result in mismatching of vacuum pump and other equipment. Therefore, it is not necessary to extend the gas flow rate to its Qm,max of RH with arched snorkels in this physical simulation.


#### 3.1.3. Circulation Flow Rate and Mixing Time

Under the condition of vacuum chamber pressure (P = 97709 Pa) and insertion depth of snorkel (Himm = 100 mm), the relationship between the circulation flow rate Gm and gas flow rate Qm in RH with arched snorkels and RH with circular snorkels is compared in Figure 7. It can be seen that the Gm of RH with arched snorkels was much larger than that of RH with circular snorkels in the whole Qm. Under the same experimental conditions, the Gm of RH with arched snorkels was 2.0 ∼ 2.8 times that of RH with circular snorkels. This result indicated that the Gm increases with the cross-sectional area increase of the arched snorkel; such result verified the previous studies that the circulation flow rate increases with the increase of cross-sectional area of the snorkel [3, 24, 38].Figure 7
Relationship betweenGm and Qm in RH with arched snorkels and RH with circular snorkels.Under the condition ofP = 97709 Pa and Himm = 100 mm, the relationship between mixing time Tmix and Qm in RH with arched snorkels and RH with circular snorkels is compared in Figure 8. It can be seen that the Tmix decreased with the increase in Qm. When the Qm was 2.0 Nm3·h−1, the Tmix of RH with arched snorkels was 74 s, whereas that of RH with circular snorkels was 118 s. Under the experimental condition, the Tmix of RH with arched snorkels was 63% ∼ 70% that of RH with circular snorkels.Figure 8
Relationship betweenQm and Tmix in RH with arched snorkels and RH with circular snorkel.


### 3.2. Effect of Gas Flow Rate and Insertion Depth of Snorkel on RH with Arched Snorkels

TheGm increases with the increase of Qm and Himm. Equations (7)–(9) demonstrate that the bubble number, diameter, and horizontal penetrating depth increase with the increase in Qm, the work conducted by bubble floatage increase. Accordingly, the “drove efficiency” to molten steel of the lifting gas and the Gm increase. When other parameters are fixed, the liquid level in vacuum chamber increases with the Himm. The rising distance of the bubble increases and the contact time with the molten steel is longer, and the “drove efficiency” to molten steel of lifting gas increases, so the Gm increases.However,Himm should be controlled; otherwise, the gas lifting efficiency will be inefficient. The experimental results showed that the Gm rapidly increases with the Himm increase when the Qm was small. The Himm influence on the Gm gradually decreased with the Qm increase. Figure 9(a) shows when the Himm exceeded 100 mm, especially when the Qm was greater than 2.3 Nm3·h−1, the Himm increasing had little significance to Gm. With Himm increase, the travel of bubbles increases, Aloss increases when the Qm is fixed, and Asteel will decrease according to equation (2). The Himm should be  ≤100 mm and ≤550 mm on-site, which will improve the production efficiency of RH with arched snorkels.Figure 9
Effect ofQm and Himm on the Gm and Tmix of RH with arched snorkels.
(a)(b)TheTmix decreased with the increase of the Qm and Himm as shown in Figure 9(b). The mixing time was obviously shortened with the increase of Qm. The Gm increases with the increase of the Qm, and the downflow of molten steel into the ladle from the vacuum chamber increases, which increases the stirring of molten steel and reduces the Tmix. The Tmix decreased with the Himm increase at a certain vacuum degree as shown in Figure 9(b). When the Himm was greater than 100 mm, the trend of Tmix decreasing was weakened. This finding indicates that the Himm of the arched snorkels should be ≤ 550 mm on-site. The result of immersion depth control in the mixing time experiment is consistent with that in the circulation flow rate experiment.Compared with then RH with circular snorkels, the RH with arched snorkels greatly improves the circulation flow rate, reduces the mixing time, and improves the mixing capacity. However, the refractory building is highly demanded. The RH with arched snorkels is seldom applied on-site because the complex structure of arched snorkels. The ability of the refractory building to resist molten steel erosion of RH with arched snorkels needs be studied in the future.


## 3.1. Comparison of RH with Circular Snorkels and RH with Arched Snorkels

### 3.1.1. Flow Field

Under the condition of vacuum chamber pressure (P = 97709 Pa), insertion depth of snorkel (Himm = 100 mm), gas flow rate (Qm = 1.0 Nm3·h−1), and flow field using the black ink as tracer is shown in Figure 4. The ink was injected into up-leg through the spare nozzle on the top of up-leg. A high-speed camera was used to record the flow field. As shown in the flow fields from the water models, the molten steel driven by lifting gas flowed into the vacuum chamber through the up-leg, and violent mixing occurred in the vacuum chamber. Then, the molten steel flowed downward the ladle through down-leg, reached the ladle bottom, and rose upward again. The time of tracer in RH with arched snorkels to complete the mixing in the vacuum chamber, reaching the ladle bottom and complete one cycle, was, respectively, 3 s, 12 s, and 18 s and that of RH with circular snorkels was 3 s, 18 s, and 44 s. Compared with RH with circular snorkels, the quantity of the flowing molten steel through down-leg increases with the increase of the cross-sectional area and has a better diffusion capacity in the ladle while flowing to the bottom of the ladle in RH with arched snorkels. The mixing capacity of RH with arched snorkels was stronger than that of RH with circular snorkels.Figure 4
Flow field of (a) RH with circular snorkels and (a) RH with arched snorkels in one circulation.
(a)(b)


### 3.1.2. Saturated Gas Flow Rate

In water model experiment, the circulation flow rate increases with the gas flow rate. After reaching a certain value, the circulation flow rate tends to be saturated. The circulation flow rate at this time is called saturated circulation flow rateGm,max, and the minimum gas flow rate corresponding to the Gm,max is called saturated gas flow rate Qm,max [14, 36].The horizontal section and horizontal trajectory of the bubbles in gas-liquid plume observed schematically at the outlet of the up-leg are shown schematically in Figure5. For the two RH models, the bubbles in the gas-liquid plume formed at the exit of each nozzle are individually close to the wall of up-leg at small gas flow rate. With the increase of the gas flow rate, the diameter and horizontal penetrating depth of bubbles in gas-liquid plume increase. When the gas flow rate tends to be Qm,max, the bubbles in gas-liquid plume will collide with each other for RH with circular snorkels as shown in Figure 5(a), and bubbles from nozzle 2 and 3 will collide the opposite wall lastly for RH with arched snorkels as shown in Figure 5(b). If the gas flow rate continues to increase and the bubbles are in the state of ejection, the gas driving power will be greatly reduced and the circulation flow rate will tend to be saturated. Therefore, it can be considered that the gas flow rate corresponding to the contact of bubbles from different nozzles with each other or the contact of bubbles and opposite wall is Qm,max. The bubble is simulated by a complete sphere, and the geometric conditions of this contact state of RH with circular snorkels and RH with arched snorkels are expressed by equations (5) and (6) [10]. Equations (7)–(9) [37] show the calculation formulas of diameter and horizontal penetrating depth of bubble; by combining equations (5) and (6), the Qm,max of the two RH water models can be calculated:(5)dB=dp2−LB+dB2∗2sinθN2,(6)dp/2−HscosθN/2+LB=dp2,where dB is the bubble diameter, m; dp is the diameter of up-leg, m; LB is the horizontal penetrating depth of bubble, m; Hs is internal arc height; and θN is the angle between adjacent nozzles; for circular snorkel,θN=2π/nc (nc is the nozzle number); for arched snorkel, θN=arccos0.5dp−Hs/0.5dp/2.5:(7)dB=6σd0ρ1g2+0.54Qg4nd00.50.28961/6,(8)LBd0=3.7ρgρ1−ρgVg2gd01/3,(9)Vg=Qg/nπd02/4,where d0 is the nozzle diameter, m; σ is the surface tension in the liquid phase, N·m−1; ρ1 and ρgare the density of liquid and phase, kg·m−3; n is the nozzle number; Vg is the orifice gas velocity, m·s−1; gis the acceleration of gravity, m·s−2; and Qg is the gas flow rate, Nm3·s−1.Figure 5
Illustration of bubble dispersion behavior in up-leg observed from the bath bottom. RH with (a) circular snorkels and (b) arched snorkels.
(a)(b)TheQm,max of RH with circular snorkels calculated from above is 2.52 Nm3·h−1. And, this is 5.03 Nm3·h−1 to RH with arched snorkels. The Qm,max of RH with arched snorkels is approximately 99.6% higher than that of the RH with circular snorkels from theoretical calculations.Figure6(a) shows the variation of circulation flow rate Gm and gas flow rate Qm under the conditions that insertion depth of snorkel Himm is 70, 100, 130, and 150 mm, respectively. The Gm increased with the increase of Himm, and the Gm of RH with circular snorkels showed saturation tendency at about 2.50 Nm3·h−1 of Qm even at different Himm, which was very consistent with the calculated value (2.52 Nm3·h−1). The Qm,max is the result of the horizontal movement of the bubbles and is independent of the insertion depth of snorkel. Therefore, Figure 6(b) only shows the variation of the Gm and Qm under the condition of Himm 70 mm; the Gm kept increasing with the increase of Qm, because the Qm,max of RH with arched snorkels was 5.03 Nm3·h−1.Figure 6
Variation of circulation flow rateGm as a function of gas flow rate Qm. (a) RH with circular snorkels. (b) RH with arched snorkels.
(a)(b)According to equation (1), the Qp,max of RH with arched snorkels is 347 Nm3·h−1 on-site, which is far beyond the gas flow rate (60 ∼ 130 Nm3·h−1) in the production site. Excessive gas flow rate will result in mismatching of vacuum pump and other equipment. Therefore, it is not necessary to extend the gas flow rate to its Qm,max of RH with arched snorkels in this physical simulation.


### 3.1.3. Circulation Flow Rate and Mixing Time

Under the condition of vacuum chamber pressure (P = 97709 Pa) and insertion depth of snorkel (Himm = 100 mm), the relationship between the circulation flow rate Gm and gas flow rate Qm in RH with arched snorkels and RH with circular snorkels is compared in Figure 7. It can be seen that the Gm of RH with arched snorkels was much larger than that of RH with circular snorkels in the whole Qm. Under the same experimental conditions, the Gm of RH with arched snorkels was 2.0 ∼ 2.8 times that of RH with circular snorkels. This result indicated that the Gm increases with the cross-sectional area increase of the arched snorkel; such result verified the previous studies that the circulation flow rate increases with the increase of cross-sectional area of the snorkel [3, 24, 38].Figure 7
Relationship betweenGm and Qm in RH with arched snorkels and RH with circular snorkels.Under the condition ofP = 97709 Pa and Himm = 100 mm, the relationship between mixing time Tmix and Qm in RH with arched snorkels and RH with circular snorkels is compared in Figure 8. It can be seen that the Tmix decreased with the increase in Qm. When the Qm was 2.0 Nm3·h−1, the Tmix of RH with arched snorkels was 74 s, whereas that of RH with circular snorkels was 118 s. Under the experimental condition, the Tmix of RH with arched snorkels was 63% ∼ 70% that of RH with circular snorkels.Figure 8
Relationship betweenQm and Tmix in RH with arched snorkels and RH with circular snorkel.


## 3.1.1. Flow Field

Under the condition of vacuum chamber pressure (P = 97709 Pa), insertion depth of snorkel (Himm = 100 mm), gas flow rate (Qm = 1.0 Nm3·h−1), and flow field using the black ink as tracer is shown in Figure 4. The ink was injected into up-leg through the spare nozzle on the top of up-leg. A high-speed camera was used to record the flow field. As shown in the flow fields from the water models, the molten steel driven by lifting gas flowed into the vacuum chamber through the up-leg, and violent mixing occurred in the vacuum chamber. Then, the molten steel flowed downward the ladle through down-leg, reached the ladle bottom, and rose upward again. The time of tracer in RH with arched snorkels to complete the mixing in the vacuum chamber, reaching the ladle bottom and complete one cycle, was, respectively, 3 s, 12 s, and 18 s and that of RH with circular snorkels was 3 s, 18 s, and 44 s. Compared with RH with circular snorkels, the quantity of the flowing molten steel through down-leg increases with the increase of the cross-sectional area and has a better diffusion capacity in the ladle while flowing to the bottom of the ladle in RH with arched snorkels. The mixing capacity of RH with arched snorkels was stronger than that of RH with circular snorkels.Figure 4
Flow field of (a) RH with circular snorkels and (a) RH with arched snorkels in one circulation.
(a)(b)


## 3.1.2. Saturated Gas Flow Rate

In water model experiment, the circulation flow rate increases with the gas flow rate. After reaching a certain value, the circulation flow rate tends to be saturated. The circulation flow rate at this time is called saturated circulation flow rateGm,max, and the minimum gas flow rate corresponding to the Gm,max is called saturated gas flow rate Qm,max [14, 36].The horizontal section and horizontal trajectory of the bubbles in gas-liquid plume observed schematically at the outlet of the up-leg are shown schematically in Figure5. For the two RH models, the bubbles in the gas-liquid plume formed at the exit of each nozzle are individually close to the wall of up-leg at small gas flow rate. With the increase of the gas flow rate, the diameter and horizontal penetrating depth of bubbles in gas-liquid plume increase. When the gas flow rate tends to be Qm,max, the bubbles in gas-liquid plume will collide with each other for RH with circular snorkels as shown in Figure 5(a), and bubbles from nozzle 2 and 3 will collide the opposite wall lastly for RH with arched snorkels as shown in Figure 5(b). If the gas flow rate continues to increase and the bubbles are in the state of ejection, the gas driving power will be greatly reduced and the circulation flow rate will tend to be saturated. Therefore, it can be considered that the gas flow rate corresponding to the contact of bubbles from different nozzles with each other or the contact of bubbles and opposite wall is Qm,max. The bubble is simulated by a complete sphere, and the geometric conditions of this contact state of RH with circular snorkels and RH with arched snorkels are expressed by equations (5) and (6) [10]. Equations (7)–(9) [37] show the calculation formulas of diameter and horizontal penetrating depth of bubble; by combining equations (5) and (6), the Qm,max of the two RH water models can be calculated:(5)dB=dp2−LB+dB2∗2sinθN2,(6)dp/2−HscosθN/2+LB=dp2,where dB is the bubble diameter, m; dp is the diameter of up-leg, m; LB is the horizontal penetrating depth of bubble, m; Hs is internal arc height; and θN is the angle between adjacent nozzles; for circular snorkel,θN=2π/nc (nc is the nozzle number); for arched snorkel, θN=arccos0.5dp−Hs/0.5dp/2.5:(7)dB=6σd0ρ1g2+0.54Qg4nd00.50.28961/6,(8)LBd0=3.7ρgρ1−ρgVg2gd01/3,(9)Vg=Qg/nπd02/4,where d0 is the nozzle diameter, m; σ is the surface tension in the liquid phase, N·m−1; ρ1 and ρgare the density of liquid and phase, kg·m−3; n is the nozzle number; Vg is the orifice gas velocity, m·s−1; gis the acceleration of gravity, m·s−2; and Qg is the gas flow rate, Nm3·s−1.Figure 5
Illustration of bubble dispersion behavior in up-leg observed from the bath bottom. RH with (a) circular snorkels and (b) arched snorkels.
(a)(b)TheQm,max of RH with circular snorkels calculated from above is 2.52 Nm3·h−1. And, this is 5.03 Nm3·h−1 to RH with arched snorkels. The Qm,max of RH with arched snorkels is approximately 99.6% higher than that of the RH with circular snorkels from theoretical calculations.Figure6(a) shows the variation of circulation flow rate Gm and gas flow rate Qm under the conditions that insertion depth of snorkel Himm is 70, 100, 130, and 150 mm, respectively. The Gm increased with the increase of Himm, and the Gm of RH with circular snorkels showed saturation tendency at about 2.50 Nm3·h−1 of Qm even at different Himm, which was very consistent with the calculated value (2.52 Nm3·h−1). The Qm,max is the result of the horizontal movement of the bubbles and is independent of the insertion depth of snorkel. Therefore, Figure 6(b) only shows the variation of the Gm and Qm under the condition of Himm 70 mm; the Gm kept increasing with the increase of Qm, because the Qm,max of RH with arched snorkels was 5.03 Nm3·h−1.Figure 6
Variation of circulation flow rateGm as a function of gas flow rate Qm. (a) RH with circular snorkels. (b) RH with arched snorkels.
(a)(b)According to equation (1), the Qp,max of RH with arched snorkels is 347 Nm3·h−1 on-site, which is far beyond the gas flow rate (60 ∼ 130 Nm3·h−1) in the production site. Excessive gas flow rate will result in mismatching of vacuum pump and other equipment. Therefore, it is not necessary to extend the gas flow rate to its Qm,max of RH with arched snorkels in this physical simulation.


## 3.1.3. Circulation Flow Rate and Mixing Time

Under the condition of vacuum chamber pressure (P = 97709 Pa) and insertion depth of snorkel (Himm = 100 mm), the relationship between the circulation flow rate Gm and gas flow rate Qm in RH with arched snorkels and RH with circular snorkels is compared in Figure 7. It can be seen that the Gm of RH with arched snorkels was much larger than that of RH with circular snorkels in the whole Qm. Under the same experimental conditions, the Gm of RH with arched snorkels was 2.0 ∼ 2.8 times that of RH with circular snorkels. This result indicated that the Gm increases with the cross-sectional area increase of the arched snorkel; such result verified the previous studies that the circulation flow rate increases with the increase of cross-sectional area of the snorkel [3, 24, 38].Figure 7
Relationship betweenGm and Qm in RH with arched snorkels and RH with circular snorkels.Under the condition ofP = 97709 Pa and Himm = 100 mm, the relationship between mixing time Tmix and Qm in RH with arched snorkels and RH with circular snorkels is compared in Figure 8. It can be seen that the Tmix decreased with the increase in Qm. When the Qm was 2.0 Nm3·h−1, the Tmix of RH with arched snorkels was 74 s, whereas that of RH with circular snorkels was 118 s. Under the experimental condition, the Tmix of RH with arched snorkels was 63% ∼ 70% that of RH with circular snorkels.Figure 8
Relationship betweenQm and Tmix in RH with arched snorkels and RH with circular snorkel.


## 3.2. Effect of Gas Flow Rate and Insertion Depth of Snorkel on RH with Arched Snorkels

TheGm increases with the increase of Qm and Himm. Equations (7)–(9) demonstrate that the bubble number, diameter, and horizontal penetrating depth increase with the increase in Qm, the work conducted by bubble floatage increase. Accordingly, the “drove efficiency” to molten steel of the lifting gas and the Gm increase. When other parameters are fixed, the liquid level in vacuum chamber increases with the Himm. The rising distance of the bubble increases and the contact time with the molten steel is longer, and the “drove efficiency” to molten steel of lifting gas increases, so the Gm increases.However,Himm should be controlled; otherwise, the gas lifting efficiency will be inefficient. The experimental results showed that the Gm rapidly increases with the Himm increase when the Qm was small. The Himm influence on the Gm gradually decreased with the Qm increase. Figure 9(a) shows when the Himm exceeded 100 mm, especially when the Qm was greater than 2.3 Nm3·h−1, the Himm increasing had little significance to Gm. With Himm increase, the travel of bubbles increases, Aloss increases when the Qm is fixed, and Asteel will decrease according to equation (2). The Himm should be  ≤100 mm and ≤550 mm on-site, which will improve the production efficiency of RH with arched snorkels.Figure 9
Effect ofQm and Himm on the Gm and Tmix of RH with arched snorkels.
(a)(b)TheTmix decreased with the increase of the Qm and Himm as shown in Figure 9(b). The mixing time was obviously shortened with the increase of Qm. The Gm increases with the increase of the Qm, and the downflow of molten steel into the ladle from the vacuum chamber increases, which increases the stirring of molten steel and reduces the Tmix. The Tmix decreased with the Himm increase at a certain vacuum degree as shown in Figure 9(b). When the Himm was greater than 100 mm, the trend of Tmix decreasing was weakened. This finding indicates that the Himm of the arched snorkels should be ≤ 550 mm on-site. The result of immersion depth control in the mixing time experiment is consistent with that in the circulation flow rate experiment.Compared with then RH with circular snorkels, the RH with arched snorkels greatly improves the circulation flow rate, reduces the mixing time, and improves the mixing capacity. However, the refractory building is highly demanded. The RH with arched snorkels is seldom applied on-site because the complex structure of arched snorkels. The ability of the refractory building to resist molten steel erosion of RH with arched snorkels needs be studied in the future.


## 4. Conclusions

(1)
The circulation flow rate increases 100% ∼ 180%, and the mixing time decreases by approximately 35% compared with RH with circular snorkels in the whole range of the gas flow rate.(2)
The saturated gas flow rate of RH with arched snorkels is 99.6% more than that of RH with circular snorkels, which can greatly increase the gas flow rate range on-site.(3)
Compared with the RH with circular snorkels, the quantity of the flowing molten steel through down-leg increases with the increase of the cross-sectional area and has better diffusion in the ladle while flowing to the bottom of the ladle. The RH with arched snorkels has stronger mixing capacity.(4)
The circulation flow rate increases, and the mixing time decreases with the increase of the gas flow rate and insertion depth. The insertion depth of the arched snorkel should be ≤ 550 mm on-site to improve the production efficiency.



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*Source: 6525096-2020-08-30.xml*