1.   Introduction

Ruhrstahl-Heraeus, namely RH furnace, is one of the most important refining equipment in steel production, mainly used for some high-quality steel production such as ultra-low carbon steel, electrical steel, bearing steel, pipeline steel, and so on. The structure of a RH furnace is shown in Fig. 1. At present, RH furnace has been developed into multifunctional refining equipment with decarburization, degassing, desulfurization, the removal of inclusions, and the adjustment of steel temperature and compositions.

Figure  1.  Schematic diagram of a RH furnace.

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Mixing time and circulation flow rate are the key characteristics to evaluate the refining efficiency of RH furnace, which are significantly influenced by steel flow behaviors. Due to the limitation of the high steel temperature, a direct investigation on multiphase flow behaviors during a RH refining process is very difficult. Therefore, numerical simulations have been widely used. Initially, the flow phenomena during a RH refining were simulated to be simplified into a single-phase flow [1–6]. Therefore, it cannot properly describe the multi-phase flow phenomena which happen in a real RH reactor. Then, the Eulerian-Lagrangian [7] and Eulerian-Eulerian [8–9] approach were used to simulate the RH refining process. These two methods can generally depict the flow phenomena, which is validated by water model experiments. In above studies, the vacuum chamber and the top surface of the ladle were assumed to be flat, ignoring the existence of top gas or top slag phase. In order to track the interface behavior, a combined discrete phase model (DPM)–volume of fluid (VOF) approach was used to simulate the RH refining process [10–11]. Recently, a new model called the particle-free surface coupled model was used to investigate the argon-steel-slag flow in the vacuum chamber [12], where the size change of gas bubbles was considered. Chen et al. [13] and Shao et al. [14] established a coupled model of computational fluid dynamics model and population balance model to simulate the multiphase flow during RH refining process. Numerical simulations are usually validated either by water model experiments or by industrial measurements to show its reliability [6,10].

The circulation flow rate and mixing time of a RH refining process depend on many variables. Gas blowing nozzle number is an important factor that affects the circulation flow rate. Generally, an increased number of gas plumes in the up-snorkel leads to an increased steel volume influenced by the injected gas, and an improved decarburization efficiency [15–17]. However, the circulation flow rate can be decreased when too many nozzles are used [10]. This is due to that each nozzle plume coalesces into a large plume. Gas blowing flow rate is another important factor that affect the circulation flow rate, which has been extensively studied [10,15,18–20]. It was found that the circulation flow rate can be improved by an increased gas flow rate until a ‘saturated level’ was reached. In addition, a lower vacuum chamber pressure can obtain a larger circulation flow rate [21–24]. However, the increase in the gas blowing flow rate is supposed to be more efficient than a low vacuum degree [25]. The multi-leg design and an oval or arched shape of the snorkel cross section was found to be effective to enhance the circulation flow rate [26–30]. Also, a ladle bottom gas injection can shorten the mixing time and improve the refining efficiency [31–34]. However, an excessive gas flow rate can lead to the formation of a slag eye in the ladle and the accelerate erosion on the up-snorkel [35–36].

The circulation flow in a RH system was driven by the gas injection, resulting from the effect of gravity and buoyancy force. The velocities of both liquid and gas in the up-snorkel are mainly in the vertical direction. An additional horizontal velocity may help to improve the mixing of the liquid during passing by the up-snorkel. Li et al. [37] investigated the rotational flow phenomena generated by using a mechanical stirring impeller inside the up-snorkel. Water model experiments showed that this technique can increase the circulation flow rate by about 25%. In addition, electromagnetic stirring method was used to produce a rotational flow in the up-snorkel [38–39]. The results showed that a large circulation flow rate can be obtained with the effect of swirling flow. Qi et al. [40] found that the generation of a rotational flow can increase the residence time of bubbles. In addition, Wang et al. [41] applied a forward-reverse rotational electromagnetic field to suppress the central vortex formation and to enhance the bubble refinement.

In this work, a new method to produce a rotational flow in the up-snorkel was investigated and it could realize by simply changing the gas blowing nozzle direction. Both water model experiments and numerical simulations were carried out to investigate the multiphase flow behavior in the new design. The effect of the gas blowing nozzle angle on the multiphase flow, mixing time, and circulation flow rate were investigated.

2.   Water model experiment

A water model with a geometric scale of 1:4 from a 260 t industrial RH furnace was built up. The dimensions of the water model are given in Table 1. Both the water model and the prototype have 16 nozzles, where 8 nozzles are uniformly distributed on the circumference of an up-snorkel cross section. The specific layout of the nozzles is shown in Fig. 2. The snorkels are immersed 110 mm beneath the free surface in ladle. The similarity of the two systems was guaranteed by the same value of Froude number in Eqs. (1) and (2). The gas flow rate in the water model can be obtained by using Eq. (3) [43], with the value of 40 L·min^–1. The pressure in the vacuum chamber is around 97.7 kPa.

Table  1.  Parameters of water model geometry and fluid physical properties

Height of ladle / mm	Diameter of ladle top / mm	Diameter of ladle bottom / mm	Liquid level of ladle / mm	Diameter of snorkel / mm	Length of snorkel / mm	Distance between snorkel / mm
1035	978	929	800	180	412.5	394.5
Diameter of vacuum chamber / mm	Number of nozzles	Diameter of nozzles / mm	Lower layer nozzle height from the bottom of snorkel / mm	Distance between two rows of nozzles / mm	Density of water / (kg·m–3)	Viscosity of water / (10–3 Pa·s)
574.5	16	2	50	50	1000	1.003
Density of air / (kg·m–3)	Viscosity of air / (10–5 Pa·s)	Density of the saturated NaCl solution / (kg·m–3) [42]	Molar concentration of the saturated NaCl solution / (mol·L–1) [42]	Interfacial tension of water and air / (N·m–1)
1.225	1.79	1197.2	5.326	0.07197

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Figure  2.  Top view of nozzle arrangements (a) conventional nozzle and (b) rotated nozzle.

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The tracer addition position and the monitoring points in the water model are shown in Fig. 3. The stimulus-response approach was used to measure the mixing time in the bath. When the flow in the whole system is fully developed (about 270 s after the start of the gas blowing), 200 mL NaCl saturated solution was poured into the vacuum chamber as the tracer. Then, the changes of the electrical conductivity with time at different locations were measured to determine the bath mixing time.

Figure  3.  Locations of monitor points, tracer addition, and different cross sections.

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where Fr is the Froude number; ρ_g is gas density, kg·m^–3; ρ_l is liquid density, kg·m^–3; g is the gravitational acceleration rate, m·s^–2; L is a feature length, m; v_g is gas velocity, m·s^–1; λ is the geometric similarity ratio; Q is gas flow rate, m³·s^–1; P is gas pressure, Pa; T is temperature, K; the subscript m and p represents the water model and prototype, respectively.

3.   Mathematical model description

3.1   Model assumptions

The mathematical model was built up based on the following assumptions: (1) Water and air are incompressible Newtonian fluids. (2) The heat and mass transfer between the gas and liquid phases were not considered, and the two-phase flow was assumed to be an isothermal flow. (3) Both the top slag in the ladle and the gas phase in the vacuum chamber were not considered. The liquid surface at the top of both the ladle and the vacuum chamber were assumed to be flat. (4) The gas bubble shape was assumed to be spherical, and their expansion, coalescence and breaking up were not considered. (5) A two-way coupling between water and air bubbles was used.

3.2   Governing equations

The liquid flow field was obtained by solving the continuity equation, momentum equation, and turbulence model equations, as follows [44]:

Continuity equation

Momentum equation

where u is liquid velocity, m·s^–1; μ_eff is effective viscosity, Pa·s, which is the sum of laminar viscosity (μ_l) and turbulence viscosity (μ_t); F is the momentum transfer term exerted by the discrete phase, N·m^–3; g is the gravitational acceleration rate, m·s⁻².

Turbulent properties of the flow field were solved by using standard k–ε turbulence model. The turbulence viscosity is related to the turbulent kinetic energy k (m²·s^–2) and the dissipation rate ε (m²·s^–3) as follows [44]:

where k and ε can be obtained by solving the following equations [44]:

where C_μ, C_ε1, C_ε2, σ_k, and σ_ε are the constants in the turbulence model, with the value of 0.09, 1.44, 1.92, 1.0, and 1.3, respectively [44–45]. The production rate of turbulence kinetic energy P_k is expressed as follows [44]:

3.3   Discrete phase model

Air gas is injected into the liquid through the nozzles. The movement of air bubbles can be obtained by solving the following equation [46]:

where x_p is the bubble position and v_b is the bubble velocity. The velocity of air bubbles can be computed by the following equation:

where m_b is the mass of bubbles, ${\overrightarrow{F}}_{\text{ D}}$ is the drag force, ${\overrightarrow{F}}_{\text{ L}}$ is the lift force, ${\overrightarrow{F}}_{\text{ VM}}$ is the virtual mass force, ${\overrightarrow{F}}_{\text{ P}}$ is the pressure gradient force, ${\overrightarrow{F}}_{\text{ G}}$ and ${\overrightarrow{F}}_{\text{ B}}$ are the gravity and buoyancy force, respectively. These forces are usually considered to investigate the circulation flow rate and mixing time in a RH refining process [10,47].

3.3.1   Drag force

The drag force plays a decisive role in the momentum transfer between the gas and liquid phase. It can be expressed by the following equation [46]:

where τ_b is the particle relaxation time, which can be calculated by the following equation [46]:

where d_b is bubble diameter, Re_b is the Reynolds number of air bubbles, C_D is the drag coefficient, where Schiller and Naumann’s [48] drag law was used to calculate this value as follows:

The bubble diameter was calculated through the empirical formula derived by Sano et al. [49] as follows:

where σ_gl is the surface tension between air and water, N·m^–1; v_b,0 is the initial bubble velocity at the entrance which can be calculated by the following equation:

where A_nozzle is the total area of all the blowing nozzles, m².

3.3.2   Lift force

The Saffman lift force can be expressed by the following equation [46]:

where r_b is the radius of the bubble, m; L_v is relative velocity gradient, which is computed by the following equation [46]:

3.3.3   Virtual mass force

The virtual mass force is proportional to the relative acceleration of the discrete phase, which can be calculated by the following equation [46]:

3.3.4   Pressure gradient force

The pressure gradient force can be expressed by the following equation [46]:

3.3.5   Gravity and buoyancy force

The gravity and buoyancy forces are given by the following equation [46]:

3.4   Turbulent dispersion model

In order to consider the effect of turbulent fluctuations on bubble motion, the DRW (Discrete random walk) model was used. The instantaneous velocity can be expressed by the following equation:

where $\bar {\boldsymbol{u}}$ is the averaged velocity of the continuous phase, ${\boldsymbol{\acute{u}}}$ is velocity fluctuation component, which is expressed as follows:

where ζ is a zero mean, which has a unit variance and normally distributed random number.

3.5   Tracer transport

Tracer transport was solved by using the following equation [44]:

where C is tracer concentration; D_eff is effective diffusion coefficient, m²·s^–1, which is the sum of molecule diffusion coefficient (D₀) and turbulent diffusion coefficient (D_t). D₀ value is 0.551 × 10^–9 m²·s^–1 for NaCl solution at 25°C [50]. D_t can be expressed as the following equation:

where Sc_t is the turbulent Schmidt number, which is equal to 1 in this study.

3.6   Boundary condition and initial condition

A constant velocity was used as the inlet condition for gas blowing. The vacuum chamber pressure is fixed at 97.7 kPa. A non-slip wall boundary condition was used. A reflect boundary condition was used for bubbles once they touch a wall, and they escaped from the calculation domain after they pass by the liquid surface in the vacuum chamber. It was considered to be a fully developed flow at 270 s after gas blowing, which can be seen from the velocity changes at monitoring positions in Fig. 4. Then, 200 mL tracer was released at the same location as that in water model experiment to investigate its transport and the bath mixing behavior.

Figure  4.  Predicted velocity changes at monitoring points for different nozzle angles: (a) 0°; (b) 30°; (c) 45°.

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3.7   Numerical procedure

The numerical model was solved by the commercial software COMSOL Multiphysics 5.6. The mesh with 550,000 grid number was used, as shown in Fig. 5. A fine grid with the size of 1 mm was used at the gas blowing inlet area. The separated constant (Newton) nonlinear method in COMSOL Multiphysics was used to treat non-linear equations. The backward difference formula was firstly used to deal with the convection term. Then, the generalized-alpha method was further used to obtain the final solution. These two methods are all second order scheme. The initial time step was set to 0.0001 s, and the maximum step size was 0.02 s. The convergence criteria were as follows: the residuals of all dependent variables were smaller than 1 × 10^–3.

Figure  5.  Grid configuration of the RH model.

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4.   Results and discussion

4.1   Model validation

Experimental measurements and numerical simulation were carried out to investigate the mixing time in the RH water model with a conventional nozzle. The mixing time measurements were repeated 10 times to obtain the mean value. Fig. 6 shows the comparison between the model predictions and the measured values. It can be seen from that the deviations at point 1, 2, and 3 were 7.3%, 1.3%, and 7.3%, respectively. Here, the mixing time was defined as the time when a dimensionless concentration was within 3% deviation from the averaged value. With a 5% deviation standard, the mixing time deviations at point 1, 2, and 3 were 15.3%, 4.0%, and 3.1%, respectively. Therefore, the model can generally catch the mixing behavior inside the bath. In the following, the 3% deviation criterion was used to evaluate the bath mixing time.

Figure  6.  Comparison of predicted and measured concentration change: (a) point 1; (b) point 2; (c) point 3.

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4.2   Effect of rotated gas blowing nozzle on RH multiphase flow

4.2.1   Mixing time and circulation flow rate

Fig. 7 shows the mixing times at point 1, 2, and 3 under different nozzle blowing angles. It can be seen from that the mixing time at each monitoring point was decreased after either 30° or 45° rotated nozzle. Specifically, when the nozzle rotated from a conventional 0° to 30°, the mixing time at monitoring point 1, 2, and 3 was shortened by 16.2, 24.7, and 9.3 s, respectively, which corresponds to a decrease of 21.3%, 28.2%, and 12.3%. Therefore, a rotated nozzle can effectively reduce the mixing time. With the nozzle angle changed from 30° to 45°, the mixing time change is very small, as shown in Fig. 7(d).

Figure  7.  Effect of nozzle angle on predicted concentration change and mixing time: (a) point 1; (b) point 2; (c) point 3; (d) mixing time at different points and nozzle angles.

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In order to have a good observation on the mass transfer behavior induced by different nozzle angles, tracer was added at the lower part of the up-snorkel (Z = 690 mm cross section as shown in Fig. 3). Fig. 8 shows the variation of tracer concentration with time in the snorkels and the vacuum chamber under different nozzle angles. Compared to a conventional nozzle angle with 0°, the high tracer concentration region seems to move faster towards the down-snorkel when both 30° and 40° rotated nozzles were used. Furthermore, the tracer concentration is more uniform on the cross section of the up-snorkel.

Figure  8.  Movement of the high tracer concentration region in the snorkels and vacuum chamber for different nozzle angles and times: (a) 0°; (b) 30°; (c) 45°.

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The mixing time and the refining efficiency are related to the circulation flow rate, which can be calculated by using the following equation:

where R is the circulation flow rate, kg·s^–1; u_i is the velocity perpendicular to the snorkel cross section, m·s^–1; A_i is each grid area on the cross section, m²; A₀ is the cross-section area, m².

The cross-section of the down-snorkel, located at 700 mm above the bottom of the ladle as shown in Fig. 3, was selected to calculate the circulation flow rate. Fig. 9 shows the calculated values of the circulation flow rate under different nozzle angles. It can be seen that the circulation flow rate increases from 9 to 10.3 kg·s^–1 when the nozzle angle increases from 0° to 30°. With a further increase to 45°, the circulation flow rate increases by only 0.1 kg·s^–1. Therefore, the rotated nozzle injection can increase the circulation flow rate during RH refining. This also explains the faster movement of the high tracer concentration region in the vacuum chamber as shown in Fig. 8.

Figure  9.  Effect of nozzle angles on circulation flow rate.

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4.2.2   Flow phenomena in RH furnace

In order to better understand the reason for a high circulation flow rate and a low mixing time, flow phenomena under different nozzle conditions were studied. Fig. 10 shows the streamline of the liquid flow under different nozzle angles. It can be seen that the vertical movement of liquid was observed when a conventional nozzle was used, while a rotational movement was found for both 30° and 45°. This means that the gas momentum provides the force to produce a rotational liquid flow in the up-snorkel. Due to the symmetrical setup of the conventional nozzles, such phenomena were not produced. Fig. 11 shows the velocity distribution on the vertical middle plane of the whole system. As can be seen, the liquid flow velocity in the up-snorkel significantly increased and the velocity distribution became more uniform when 30° and 45° rotated nozzle were used. With a conventional 0°, the gas moves upwards along the wall of the up-snorkel. Therefore, its influence region on liquid is relatively smaller. In addition, with both 30° and 45° rotated nozzle, the liquid velocity in the down-snorkel was also increased. This can also explain the obtained high circulation flow rate in Fig. 9.

Figure  10.  Streamline of liquid flow under different nozzle angles: (a) 0°; (b) 30°; (c) 45°.

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Figure  11.  Velocity distribution on the vertical middle plane of the RH reactor under different nozzle angles: (a) 0°; (b) 30°; (c) 45°.

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To describe the bubble behavior in the RH system intuitively, Fig. 12 shows the trajectories and residence time of the bubbles under different nozzle angles. When the nozzle is not rotated, air bubbles move vertically into the vacuum chamber; when the nozzle was rotated, gas bubbles obtain a rotational movement and move upwards under the action of buoyancy effect. This can be clearly seen from Fig. 12(b) and (c). Under the effect of the considered force in Eq. (11), the spirally rising bubbles lead to the molten steel generating a rotational flow as shown in Fig. 10. In addition, the rotational flow makes bubbles moving towards the up-snorkel center. The average residence time of bubbles can be calculated using the following equation:

Figure  12.  Trajectories and residence time of the bubbles: (a) 0°; (b) 30°; (c) 45°.

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where t_b,i is the residence time of a bubble, $\bar t_{\text{b}}$ is the average residence time of bubbles, and n_b is the number of bubbles (with the value of 128 in this work). The average residence time is about 0.6 s in the conventional case. When the nozzle rotates 30° and 45°, the average residence time can reach around 0.8 s. In addition, the bubble trajectory length increases in the rotated nozzle cases. These should be beneficial for the refining process that happens at the bubble/steel interface.

In order to clearly understand the flow characteristics in the up-snorkel, Fig. 13 shows the velocity distribution on different cross sections of the up-snorkel under different nozzle angles. For the conventional nozzle case (Fig. 13(a)), the high velocity region was located at the near wall region, and the velocity is very small with the value of about 0.1 m·s^–1 in the center region. After the nozzle is horizontally rotated, the fluid in the up-snorkel has formed a good rotational flow. The tangential velocity distribution and its magnitude under different nozzle angles are similar. At the near wall region, the tangential velocity can reach 0.5 m·s^–1 as shown in Fig. 13(d)–(f). For the vertical velocity, it can be seen from Fig. 13(g)–(i) that a low velocity region was located at the snorkel center when a conventional nozzle was used. The velocity characteristics on the cross section at a top location can be found from Fig. 13(j)–(r). Generally, it can be seen that a high velocity region is still located at the near wall region for the conventional nozzle case, while it moves towards the snorkel center for rotated nozzle cases. The tangential velocity in Fig. 13(n)–(o) becomes more uniform compared to that of Fig. 13(e)–(f). For the vertical velocity, the near wall region shows a low value in Fig. 13(p)–(r) compared to that of Fig. 13(g)–(i). This is attributed to the gas plume moving towards the center region during it passing through the up-snorkel. Therefore, the rotated nozzle design significantly changed the flow behavior in the up-snorkel.

Figure  13.  Velocity distribution on different sections of the up-snorkel under different nozzle angles: (a–c) total velocity at Z = 890 mm; (d–f) tangential velocity at Z = 890 mm; (g–i) axial velocity at Z = 890 mm; (j–l) total velocity at Z = 990 mm; (m–o) tangential velocity at Z = 990 mm; (p–r) axial velocity at Z = 990 mm.

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Fig. 14 shows the distributions of the velocity and turbulent kinetic energy on the cross section of the vacuum chamber. It can be seen from Fig. 14(a)–(c) that a symmetrical distribution along the Line 1 was observed for the conventional nozzle case. However, the velocity did not show a symmetrical distribution for the rotated nozzle cases. This is due to the rotational direction of the flow in the up-snorkel. Fig. 14(d)–(f) shows the turbulent kinetic energy distribution on the cross section. Among the three cases, the highest turbulent kinetic energy was obtained when a conventional nozzle was used. With a rotated nozzle angle, a general uniform total turbulent kinetic energy distribution can be obtained, and the high turbulent kinetic energy region enlarged as shown in Fig. 14(d)–(f).

Figure  14.  Predicted properties of the flow field in the vacuum chamber: (a–c) total velocity; (d–f) turbulent kinetic energy.

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Fig. 15 shows the velocity distribution on different cross sections of the ladle under different nozzle angles. With a conventional nozzle, the velocity distribution on the ladle cross section shows a symmetrical distribution along the horizontal central line as shown in Fig. 15. However, the distribution is no longer symmetrical in the rotated nozzle cases. Due to the rotational flow in the up-snorkel, the velocity in the vacuum chamber was changed, as shown Fig. 14(a)–(c). This directly affects the flow behavior inside the down-snorkel and ladle. In addition, the velocity inside the ladle was large when a rotated nozzle angle was used. This is especially true for the near-wall region, and the velocity can reach 0.24 m·s^–1 on the cross section of Z = 200 mm, with an increase of 20%.

Figure  15.  Distribution of velocity on different cross sections of the ladle under different nozzle angles: (a–c) Z = 400 mm; (d–f) Z = 200 mm.

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Fig. 16 shows the predicted turbulent kinetic energy distribution on the Z = 400 mm plane of the ladle under different nozzle angles. With the rotated nozzles, a larger turbulent kinetic energy was found in the ladle, the maximum magnitude increased from 0.008 (conventional case) to 0.011 m²·s^–2 (rotated case) compared to the conventional nozzle case, resulting in a more efficient mixing inside the ladle as well as a reduced mixing time as predicted previously.

Figure  16.  Distribution of turbulent kinetic energy on the ladle cross section under different nozzle angles: (a) 0°; (b) 30°; (c) 45°.

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5.   Conclusions

Water model experiment and numerical simulation were carried out to investigate the effect of gas blowing nozzle angle on the mixing time, circulation flow rate, and fluid flow during RH refining process. The following conclusions were obtained:

(1) The numerical model predictions generally agree well with the measured values, which illustrates its reliability to describe the multiphase flow process in RH refining.

(2) With a rotated nozzle angle of 30° and 45°, the circulation flow rate increased by 14.4% and 15.6%, respectively, compared to a conventional nozzle. Furthermore, the mixing time at monitoring point 1, 2, and 3 were shortened by 21.3%, 28.2%, and 12.3%, respectively.

(3) When 30° and 45° rotated nozzles were used, a rotational movement of liquid was obtained. The liquid flow velocity in the snorkel was significantly increased and the velocity distribution is more uniform in the up-snorkel. The velocity inside the ladle increased especially at the near-wall region.

(4) The residence time of bubbles was increased by a rotated gas blowing nozzle, which was extended by around 33.3% for the nozzle angle of both 30° and 45° of 128 bubbles.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 51704062) and the Fundamental Research Funds for the Central Universities, China (No. N2025019). Jiahao Wang wishes to thank the comments and discussions on the mathematical model from Dr. Xiaobin Zhou from Anhui University of Technology, China.

Conflict of Interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.