Numerical Investigation of Gas Flow Rate Optimization for Enhanced Mixing in RH Degassing

Abstract

Optimizing the operational parameters of an RH degasser is essential for increasing the production of high-quality steel while reducing energy and resource consumption. This paper presents a study on the impact of different injection gas flow rates on the mixing characteristics of an industrial-scale RH degasser and evaluates the optimal flow rate for achieving the lowest mixing time. A 3D simulation model was developed using a VOF–DPM framework, with gas flow rates being varied from 18 to 72 SCFM to assess mixing time and associated flow behavior. The results indicate that the mixing time has a non-linear relationship with the gas flow rate, and increasing the flow rate does not always lead to a reduced mixing time. A flow rate of 45 SCFM (a 1.5-fold increase from 18 SCFM) provided the best mixing efficiency, reducing the mixing time by 52%. Additionally, beyond 36 SCFM, a saturation limit was observed in the circulation rate, where further increases in the gas flow rate resulted in a less than 5% improvement in steel flowing through the snorkels. These findings highlight the need for careful evaluation of injection gas flow rates in RH operations to identify the optimal value that maximizes mixing efficiency, minimizes resource consumption, and enhances productivity by enabling greater steel output in less time.

1. Introduction

The Ruhrstahl–Heraeus (RH) reactor is widely used in the steel refining process to produce low-carbon steel. Originally designed to remove gaseous impurities, the RH system has since been enhanced to perform decarburization, alloying, and inclusion removal and to promote homogeneous mixing [1,2,3]; these enhancements have increased its adoption across steel industries in recent years.

An industrial-scale RH degasser consists of three parts, namely a ladle, two snorkels (up-snorkel and down-snorkel) and a vacuum chamber. In the beginning, the steel from the ladle rises and partly fills the vacuum chamber due to the induced pressure difference. This is followed by circulation of the liquid steel within the system due to the high-velocity gas injections administered at the inlets on the up-snorkel walls.

One of the earliest references to the RH degassing process was by Messing et al. [4] in 1971, who highlighted the challenges of constructing and operating an efficient vacuum setup. In 1981, Shirabe et al. [5] identified the principal fluid flow patterns, mixing characteristics, and inclusion removal mechanisms within the RH system. In the recent years, these factors have been studied in detail with the help of experimental and mathematical models [6,7,8].

Studying the full-scale RH degasser through practical experiments is not always feasible due to the operational constraints. Hence, Computational Fluid Dynamics (CFD) have been commonly employed to understand the complex mechanisms within the system. The review study conducted by Chen et al. [8] describes the different types of CFD methodologies employed for studying the multiphase flow inside the RH degasser over the past 20 years. These strategies include the Volume of Fluid–Discrete Phase Model (VOF–DPM), the Eulerian Model, and the Homogeneous Fluid Model. In the Homogeneous Fluid Model, the liquid gas mixture is treated as a single homogeneous fluid, and density difference drives the fluid flow. However, as it employs several empirical parameters, it cannot be easily implemented in CFD codes. In the Eulerian Model, the liquid and gas phases act as interpenetrating fluids, making this model suited for modeling the flow, especially in the snorkels. On the other hand, the Eulerian Model is not suitable for the simulation of free surface flows due to the numerical diffusion at the interface. In the VOF–DPM, the interfaces between the continuous phases are tracked through the VOF model, and the gas bubble trajectories are modeled with the DPM. Still, the DPM assumes that the bubble volume fraction on the liquid flow could be neglected, which might impact the simulation results in cases where the gas concentration is significant. According to Chen et al. [8], the selection of the one among the three approaches depends on the parameters of interest, and, irrespective of the modeling methods, the results should be validated with practical or industrial experiments to enhance reliability. For the studies involving flow characteristics in an RH degasser, the VOF–DPM is a more preferred approach as the impact of the bubble volume fraction could be integrated by adding an additional equation to calculate the time-averaged bubble volume fraction. Additionally, in comparison with the other methods, the interaction between the steel, slag, and air could be easily captured and helps in achieving numerical convergence [9,10].

Although the RH system is known for its higher refining capacity, the decarburization tends to decline when processing molten steel with low carbon content due to thermodynamic and kinetic limitations [11]. Under such conditions, efficient circulation and thorough mixing become critical to maintaining the reaction rates. These aspects are in turn strongly influenced by factors such as geometry of the RH system, flow rate of the gas injected, immersion depth of the snorkel in the ladle, and the vacuum chamber pressure [12,13,14]. Among these, the gas injection rate is one the most practical parameters to modify, as it requires minimal infrastructural changes and only a marginal increase in operational costs. As per current industry operations, the associated rise in argon consumption and energy usage is relatively small, and the potential reduction in mixing time can also shorten the overall cycle time, leading to net cost savings in large-scale steel plant operations.

Although prior research has provided valuable insights into RH degassing, some important gaps remain. Suraj et al. [14] used a Eulerian–Eulerian CFD model to analyze circulation rates at higher gas flow rates (80 to 160 Nm³/h), but the influence of lower flow rates and their effect on mixing time were not considered. Similarly, Chang et al. [6] employed a physical water model and observed that mixing time decreases with an increasing circulation rate, but their experiments could not reach circulation saturation, making industrial-scale study necessary. Zhenming et al. [15] also reported that circulation increases with the gas flow rate until reaching a saturation point, yet the impact on mixing efficiency was not examined. Rudong et al. [13] focused on ladle bottom stirring, showing circulation rate improvements with higher gas flow rates but without evaluating mixing times. Finally, Wang et al. [16] demonstrated that increasing the gas flow rate raises the steel level in the vacuum chamber, but the combined effects on circulation rate and mixing efficiency remain unexplored. In this context, the present study advances the literature by simultaneously evaluating the circulation rate and mixing time across both typical industrial operating ranges (18–45 SCFM) and extended conditions (72 SCFM). By doing so, it provides new insights into the trade-offs between the gas flow rate, circulation rate saturation, and mixing efficiency at an industrial scale.

In this study, a VOF–DPM methodology was developed to simulate the RH degasser and investigate its flow characteristics. First, the methodology was validated with the help of a reference experiment conducted by Wang et al. [17]. This was followed by the development of a full-scale CFD model of an industrial RH degasser currently in operation. To evaluate the mixing efficiency across different flow rates, a commonly used metric known as the mixing time was utilized, where a shorter mixing time typically indicates a higher mixing efficiency [18]. In addition, the circulation flow rate was evaluated for different gas flow rates to gain further insight into the system’s performance. A mesh convergence study was performed to eliminate variations caused by element size. Subsequently, the velocity of the injected gas was varied, and its impact on the mixing time was analyzed. Finally, the optimal gas flow rate for achieving the shortest mixing time was identified, along with an investigation into the underlying reasons for the observed trend in the mixing time with respect to the flow rate.

The primary objectives of this work are therefore: (i) to establish and validate a methodology for RH degasser simulation; (ii) to investigate the influence of the gas flow rate on circulation and mixing performance; and (iii) to identify the optimal gas injection rate that balances mixing efficiency with practical industrial considerations.

2. Methodology

To simulate the complex flow behavior inside an RH degasser, a three-dimensional multiphase flow model was developed using the widely adopted commercial software ANSYS Fluent 2023 R1 Commercial software. The model captured the interaction between molten steel, slag, and air using the Volume of Fluid (VOF) approach, while argon gas injection was modeled through the Discrete Phase Model (DPM).

Turbulent flow within the system was modeled using the realizable k-ε turbulence model. This is a widely used closure model within the Reynolds-averaged Navier–Stokes (RANS) framework. This model improves upon the standard k-ε formulation and provides better accuracy in capturing the recirculating and rotational flows, which has made it a popular choice in ladle flow simulations [19]. While more advanced approaches, such as LES, can provide finer resolution of transient eddies, they are computationally more expensive due to the requirement of very fine meshes and small time steps [18]. For an industrial-scale RH system involving large domain sizes and long operational times, such approaches would require high computational resources, including a much finer mesh and substantially smaller time steps. In comparison, the realizable k-ε turbulence model offers a good compromise between accuracy and computational efficiency, capturing the key flow features relevant to the mixing time and circulation rate while maintaining a feasible simulation cost and time.

To accurately represent the behavior of bubbles, a user-defined function (UDF) was integrated to account for coalescence and breakup phenomena, with bubbles being removed from the domain once the air-phase volume fraction exceeded 0.9. For pressure–velocity coupling, the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) scheme was employed, completing the numerical framework of the simulation.

2.1. Assumptions in Modeling

The following assumptions were made in the current model to reduce the complexity and improve solving time:

• Air, steel, and slag are incompressible Newtonian fluids with constant viscosity.
• The flow is fully turbulent.
• The steel temperature is assumed to be constant throughout the process [20,21], as heat loss during the RH treatment is negligible compared with the short refining time. Accordingly, the system is treated isothermal with no chemical reactions, focusing solely on the flow-induced mixing behavior.
• The vacuum chamber is pre-filled with molten steel at the start.
• The properties of the mixing tracer used for calculating the mixing time are identical to those of the molten steel inside the ladle.

While these assumptions simplify the computational efforts, they also introduce certain limitations. The pre-filled steel level in the vacuum chamber does not capture the transient filling process observed in industrial operations. Similarly, assuming constant fluid properties and neglecting heat transfer effects may lead to slightly underpredicted mixing times. Hence, these limitations need to be considered when interpreting the results.

2.2. Governing Equations

Conservation of mass equation:

$${\displaystyle \frac{\delta \rho }{\delta t}}+\nabla ·(\rho \overrightarrow{u})=0$$

(1)

Conservation of momentum equation:

$${\displaystyle \frac{\delta \left(\rho \overrightarrow{u}\right)}{\delta t}}+\nabla ·\left(\rho \overrightarrow{u}\overrightarrow{u}\right)=-\nabla p+\nabla ·\left[\mu \left(\nabla \overrightarrow{u}+{\left(\nabla \overrightarrow{u}\right)}^T\right)\right]+\rho \overrightarrow{g}+{\overrightarrow{F}}_b$$

(2)

Here, $\overrightarrow{u}$ is the velocity of the continuum phase, ρ is the fluid density, $\overrightarrow{g}$ is the local gravity acceleration, μ is the effective viscosity, and ${\overrightarrow{F}}_b$ is the force from the bubble.

The Volume of Fluid model (VOF) is widely used in calculating interface behavior between two or more non-mixing fluids. The continuity equation of the VOF model is given as:

$${\displaystyle \frac{\partial {\alpha }_m}{\partial t}}+\overrightarrow{u}\cdot ▽{\alpha }_i=0$$

(3)

$$\sum {\alpha }_m=1$$

(4)

Here, ${\alpha }_m$ is the volume fraction from each phase in every mesh cell, and subscript ‘i’ refers to the individual substances within the simulation.

The bubbles injected to the snorkels were simulated using the Discrete Phase Model (DPM). The trajectory followed by each bubble is governed by Newton’s second law, described as follows:

$${\displaystyle \frac{d{\overrightarrow{u}}_b}{dt}}=F_D\left(\overrightarrow{u}-{\overrightarrow{u}}_p\right)+{\displaystyle \frac{\overrightarrow{g}\left({\rho }_p-\rho \right)}{{\rho }_p}}+{\overrightarrow{F}}_{VM}+{\overrightarrow{F}}_{pressure}$$

(5)

The terms on the right of the equation correspond to the drag force, buoyant force, virtual mass force, and pressure gradient force, respectively.

The turbulence in the system was modeled using the widely used realizable k-ε turbulence approach, which offered higher accuracy in predicting the spreading rate of round jets. The transportation equations for the model are as follows:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+▽\cdot \left(\rho k\overrightarrow{u}\right)=▽\cdot \left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right)▽k\right]+G_k+G_b-\rho \epsilon$$

(6)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \epsilon \right)+▽\cdot \left(\rho \epsilon \overrightarrow{u}\right)=▽\cdot \left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right)▽\epsilon \right]+\rho C_1{S}_{\epsilon }-\rho C_2{\displaystyle \frac{{\epsilon }^2}{k+\sqrt{\nu \epsilon }}}+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}{C}_{3\epsilon }{C}_b$$

(7)

where $G_b$ and $G_k$ depict the turbulent kinetic energy due to the buoyancy and velocity gradients. ${\sigma }_{\epsilon }$ and ${\sigma }_k$ are turbulence Prandtl numbers and equal 1.2 and 1.0, respectively.

2.3. Industrial-Scale Model

A full-scale numerical model was built based on a 195 metric ton RH degasser system used by United States Steel Corporation (USA), following the discussed methodology and as shown in Figure 1a. The model was discretized into 1.1 million-cell polyhedral mesh in ANSYS Fluent 2023 R1, ensuring refined mesh around critical areas for better accuracy. The slag layer was not considered in this study, as observations of industrial-scale RH degassing operations showed that the snorkels are immersed below the slag layer and that only a minimal amount of slag passes through the snorkels and vacuum chamber. Like the reference methodology, a part of the vacuum chamber was pre-filled with steel, as depicted in Figure 1b.

The simulations were performed in ANSYS Fluent 2023 R1, with a time step size of 0.002 s, and the boundary conditions were set to replicate industrial operating conditions. The vacuum chamber was modeled by defining the top surface as a pressure outlet boundary with a gauge pressure of −101,058 Pa (equivalent to 2 Torr or 266 Pa absolute) to represent the vacuum degree during operation. This setup allows the steel circulation and gas behavior to respond naturally to the imposed pressure differential between the ladle and the vacuum chamber. The ladle steel layer top was modeled as a zero-shear stress boundary condition, and the combined flow rate of the argon gas injected through the top and bottom gas inlets was maintained at 36 SCFM.

The properties of air and steel were derived from the reference literature [22] and are shown in

Table 1. Properties of steel and air.

Material	Density (kg m−3)	Viscosity (kg/ms)
Steel	7000	6.20 × 10−3
Air	1.2	1.789 × 10−5

. The surface tension between the air and steel phases was taken as 1.82 N/m, and the argon density was calculated through a user-defined function, accounting for its variation with absolute pressure as it rose through the snorkels to the vacuum chamber. Although air density and viscosity increase with temperature, their influence on overall flow behavior is negligible since it is several orders of magnitude smaller than that of molten steel [20].

2.4. Mesh Convergence Analysis

To make sure the element size did not significantly influence the results, a mesh convergence study was performed. Three models were created: one with 2.2 million cells, another with 1.1 million cells, and a coarser mesh model with 0.5 million cells. The plane-averaged velocities at the center of the snorkels were compared among all three models to understand how results changed with the number of elements. To help visualize the data, an exponential moving average of the velocity values was calculated using a smoothing factor of 0.001 and plotted, as shown in Figure 2.

The comparison indicates that all three meshes exhibit similar flow behavior. The velocities increased steadily during the first 10 s and then approached a quasi-steady state, with minor fluctuations after approximately 40 s. The time-averaged velocities were 1.23 m/s, 1.38 m/s, and 1.32 m/s for the 0.5, 1.1, and 2.2 million-cell models, respectively. Since the difference between the 1.1 and 2.2 million-cell cases was only 4%, further mesh refinement had a negligible impact on the results. Therefore, to balance accuracy and computational time, the model with 1.1 million cells was chosen as the baseline model.

3. Validation of Methodology

To validate the proposed methodology, a CFD-based water model was built using the parameters obtained from the relevant literature [17,18,22], and the results were compared with the reference study conducted by Wang et al. [17].

3.1. Water Model and Boundary Conditions

As described in the reference study, a scaled model of a ladle was created, as shown in Figure 3a. The steel and slag were replaced with water and oil, respectively, to create the ‘water model’. Gas inlets were defined at the up-snorkel wall, and the snorkels, ladle, and the bottom region of the vacuum chamber were filled with water. The geometry was meshed with 2.5 million cells, as shown in Figure 3b.

The ladle, snorkel, and the vacuum chamber walls were given a no-slipping condition to constrain the fluid motion. The top of the vacuum chamber was set as a pressure outlet with −3626 Pa (gauge pressure), and the lifting gas was injected at an overall flow rate of 30.42 NL/min at the top and bottom gas inlet. To simulate argon bubble coalescence and breakup, a user-defined function was incorporated into the DPM. Convergence was deemed achieved when the residuals for turbulence, continuity, and momentum reached a value less than 10⁻³.

3.2. Velocity Analysis of Water Model

To verify the pseudo-steady state, four planes were defined within the system, as shown in Figure 4a. The plane-averaged velocity of the liquid was recorded over time for each of these planes, as shown in Figure 4b.

An initial fluctuation of velocity was observed across all the planes for the first 1.8 s, followed by a gradual increase that reached a steady state after 40 s, indicating a pseudo-steady condition. The highest velocity occurred at the snorkel mid-plane due to the high-velocity argon gas injection in the up-snorkel. However, very minimal velocity changes were observed in the mid-planes within the ladle, indicating that significant fluid motion occurred primarily within the snorkels and the vacuum chamber.

To understand the velocity field inside the system, the velocity vectors were generated on a vertical plane passing through the vacuum chamber, snorkels, and ladle, as shown in Figure 5.

From the contours, it can be inferred that as time progressed, water from the ladle flowed into the vacuum chamber through the up-snorkel and returned to the ladle through the down-snorkel, aligning with the normal RH system operation. In addition, consistent with the plane-averaged velocity analysis, the highest velocity was observed in the snorkels near the gas inlets. Moreover, internal flow circulations could be observed within both the ladle and the water layer in the vacuum chamber.

3.3. Mixing Time Calculation

Mixing time can be defined as the duration for an introduced substance to achieve a uniform concentration throughout the ladle volume, indicating uniform homogenization. Accordingly, a lower mixing time reflects a system with a higher mixing efficiency [18].

To evaluate the mixing efficiency, once the system reached a steady state (60 s), a tracer species with properties identical to steel was injected at the top of the water level in the vacuum chamber, and its concentration was recorded at predefined monitor points inside the ladle. Since the amount of tracer injected and the location of monitor points were not specified in the reference study [17], two different tracer quantities (10% and 5% of total water volume) and two monitor points (Pt 1 and Pt 2) were selected to minimize the influence of these parameters.

The mixing time was calculated using a dimensionless concentration parameter, defined as the ratio between the instantaneous tracer mass fraction and the tracer mass fraction at saturation. Physically, it represents the degree of homogenization achieved once the system reaches a steady state, with values closer to 1 indicating a higher level of mixing. The mixing time was evaluated when the dimensionless concentration reached ±3% of 1.

The variation of dimensionless concentration for different cases in the current study is plotted alongside the reference experiment and simulation conducted by Wang et al. [17] in Figure 6. Additionally, the location of monitor points and the tracer injection locations are also indicated.

From the plot, it is evident that the amount of tracer injected plays a minimal role, whereas the location of monitor points significantly affects the results during the initial time intervals. However, after 35 s, the results from both the current study and the reference study converges within a similar range. The mixing time calculated from the current model was 42 s, while the reference experiment reported a value of 39.8 s, showing only a 5.5% deviation. This indicates that the developed methodology is in good agreement with the water model experiments and can be reliably used to simulate a full-scale RH degasser model.

4. Results

The velocity characteristics, mixing efficiency, and the circulation flow rate was analyzed for the industrial model setup, which was then treated as the baseline model. Afterwards, a parametric analysis was carried out by varying the injection gas flow rate to understand its impact on the mixing time and circulation flow rate.

4.1. Velocity Analysis of Molten Steel

To understand the flow circulations inside the ladle, a velocity vector analysis was conducted. The velocity vectors were extracted for a middle plane passing through the center of the ladle, snorkels, and vacuum chamber at a time of 60 s, as indicated in Figure 7a.

The vector directions show that steel moves from the ladle to the vacuum chamber through the up-snorkel and returns through the down-snorkel, indicating that the flow direction resembles that of industrial operations. Two main flow circulations, one clockwise and the other counterclockwise, were observed inside the ladle, complementing the steel flow. Additionally, the highest velocity was observed inside the up-snorkel due to the momentum imparted by the high-velocity argon gas injections administered through the gas inlets.

To study the plane-averaged velocity variations of steel, four planes were defined within the system. Two planes were positioned inside the ladle, another plane passed through the center of the snorkels, and the topmost plane was located at the center of the steel layer inside the vacuum chamber, as shown in Figure 7b. The plane-averaged velocity across these planes was plotted over a duration of 60 s, as shown in Figure 7c.

The average velocity across different planes indicates a rapid increase during the first 4 s, followed by an oscillating pattern. Like the velocity vector results, the highest plane-averaged velocity was observed at the middle plane of the snorkel. It was also noted that the largest velocity fluctuations occurred at the vacuum chamber and snorkel planes, compared with the planes inside the ladle. This behavior can be attributed to the injection of argon gas through the up-snorkel, which travels toward the vacuum chamber and results in stronger interactions between steel and argon gas in these regions.

4.2. Mixing Efficiency and Mixing Time Evaluation

To calculate the mixing time for the given system, a tracer concentration study was performed [17,18]. An “alloy tracer” modeled as a species with properties identical to steel was initialized at the center of the vacuum chamber after 60 s, and 15 monitor points were defined inside the ladle, as shown in Figure 8a. Variations of the alloy tracer mass fraction over time at different monitor points are shown in Figure 8b. It could be noted that the tracer mass fraction across all points shows a sudden increase and subsequently stabilizes after 80 s, indicating near uniform mixing inside the ladle. To quantify the overall mixing, a parameter called “mixing ratio” was introduced, defined as the ratio of the minimum to the maximum tracer concentrations observed across all the 15 monitor points.

The variation of the mixing ratio over time is presented in Figure 8c. The mixing time was defined as the point at which the mixing ratio reached 95% of its final value and remained within ±5% of its final value, as achieving 100% homogenization might be practically challenging due to local fluctuations. Using 95% of the final mixing ratio is standard in mixing studies [18] and provides a reliable measure for engineering operations, since additional mixing beyond this point takes significantly more time while negligibly increasing homogeneity. The consistency of tracer concentrations across all the monitor points after stabilization demonstrates the reliability of the calculated mixing time. Additionally, the distribution of the alloy tracer at various time intervals is illustrated in Figure 9. While Figure 9 shows the tracer mass fraction throughout the system revealing how alloy spreads, Figure 8 shows the mixing ratio within the ladle, since mixing in the ladle is the slowest and therefore governs the overall homogenization rate. The scale in Figure 9 has been adjusted to improve visualization. The higher mass fraction observed in the snorkels can be attributed to steel flowing through the down-snorkel partially entering the up-snorkel without fully reaching the bottom of the ladle.

The mixing ratio remains close to zero for the first 20 s after the tracer is introduced, indicating the time required for the tracer to travel from the vacuum chamber to the monitoring points in the ladle. After 20 s, the mixing ratio increases steadily with minor fluctuations, eventually exceeding a value of 0.95 and transitioning into a near-steady state. Based on this behavior, the mixing time was determined to be 80.4 s after tracer injection. This calculated mixing time is comparable to the typical 120 s observed in industrial RH operations, suggesting that the simulation results align well with practical conditions and thereby enhance the credibility of the model.

4.3. Circulation Flow Rate

Circulation flow rate is defined as the mass of molten steel passing through the up-snorkel per second. As a key performance indicator of the degassing process, it must be measured at a location with minimal backflow or recirculation to avoid double counting. Therefore, based on the velocity vector results, the monitor plane for recording the flow rate was placed at the entrance of the up-snorkel, as shown in Figure 10a. The flow rate was recorded over time, as illustrated in Figure 10b. To aid visualization, an exponential moving average with a smoothing factor of 0.001 s was calculated and included in the plot.

The circulation flow rate was observed to rise rapidly during the first 3 s, reaching approximately 150 ton/min, followed by an oscillatory behavior between 120 and 160 ton/min. This initial 3 s period can be interpreted as the time required for steel to begin circulating through the degassing system, while the subsequent fluctuations suggest that the flow remains turbulent throughout the operation.

An average flow rate of 140 ton/min was calculated over the time span from tracer injection until complete homogenization, defined as the tracer injection time plus the calculated mixing time. Based on this average flow rate, the system would need to operate for more than 1.38 min for the entire molten steel volume to complete one full circulation through the vacuum chamber.

4.4. Parametric Analysis of Argon Gas Flow Rate

To study the impact of the injection gas flow rate on flow characteristics and mixing efficiency in RH degassing, five different flow rates were selected, as shown in

Table 2. Case matrix.

Case	Gas Flow Rate (SCFM)
1	18
2	27
3 (Baseline)	36
4	45
5	72

. All other operating parameters, including the vacuum chamber pressure, were kept constant across the cases. The gas flow rates investigated in this study (18–45 SCFM) cover the typical operational range reported by the industrial collaborators. An additional gas flow rate of 72 SCFM was included to understand the effect of an excessively high injection rate on the mixing efficiency. Since the initial studies were performed at 36 SCFM, Case 3 was chosen as the baseline.

4.4.1. Velocity Analysis

The velocity vector contours for all five cases were extracted at 60 s on the middle plane, as shown in Figure 11. The scales were adjusted to maintain a comparable magnitude, enabling effective comparison of flow direction, regions of high velocity, and flow circulation zones.

The velocity vector fields reveal that, across all five flow rates, steel flows from the ladle to the vacuum chamber through the snorkels, with the highest velocities consistently occurring near the exit of the up-snorkel. At 60 s, the steel velocity at the entrance of the up-snorkel remains nearly constant beyond 36 SCFM, indicating a saturation value for maximum steel inflow. A distinct clockwise circulation forms near the ladle bottom for flow rates between 36 and 45 SCFM, with only a slight displacement observed at 72 SCFM. Beyond 36 SCFM, the velocity at the ladle bottom, driven by the downward flow through the down-snorkel, shows minimal variation. Additionally, localized circulation within the up-snorkel is evident for the 72 SCFM case, which may slightly restrict the volume of steel passing through it.

To examine the steel velocity for different cases, the plane-averaged velocity was recorded over a 60 s period. Since the highest velocities were consistently observed at the snorkel mid-plane for all cases, these velocities were compared across the different gas flow rates, as shown in Figure 12. To facilitate comparison of the snorkel steel velocity, which exhibited significant fluctuations, an exponential moving average with a smoothing factor of 0.001 was applied to all cases.

The lowest plane-averaged velocity was observed for the 18 SCFM case, which is likely due to the lower momentum imparted by the argon gas compared with the other flow rates. The remaining gas flow rates exhibited similar steel velocities during the initial 40 s, after which a sudden decline was observed, particularly in the 27 SCFM case. This trend was absent in the 36 and 45 SCFM cases, which both maintained the highest plane-averaged velocities at the end of the 60 s period. Notably, the 45 SCFM case displayed a steadier velocity profile compared with the other cases.

4.4.2. Turbulent Kinetic Energy

Turbulent kinetic energy (TKE) serves as an indicator of the turbulence intensity within the system. Higher TKE values correspond to stronger turbulent motion, which generally enhances mixing and momentum transfer in the fluid. Figure 13 presents the TKE contours of the RH degasser system for the various cases at 60 s.

The highest turbulent kinetic energy (TKE) was observed in the snorkels and the vacuum chamber, resulting from the strong interaction between argon bubbles and molten steel in these regions. A slight decrease in TKE was noted at the center of the up-snorkel, except in the 36 and 45 SCFM cases, indicating a comparatively lower turbulence intensity at these locations. The primary source of turbulent kinetic energy imparted to the ladle was the downward motion of steel through the down-snorkel. At 60 s, this induced turbulence in the ladle was highest for the 27 and 36 SCFM cases compared with the other gas flow rates.

4.4.3. Circulation Flow Rate

To understand the variation in steel flow through the five different cases, the circulation flow rate was measured at the entrance of the up-snorkel. An exponential moving average was applied to the recorded values to facilitate visualization, as shown in Figure 14.

Significant fluctuations in the circulation flow rate were observed across all argon gas flow rates, reflecting the turbulent nature of the molten steel entering the up-snorkel. The 18 SCFM case exhibited the lowest circulation flow rate throughout the duration. The remaining cases, with flow rates ranging from 27 to 72 SCFM, displayed similar behavior during the first 40 s before diverging. At 60 s, the flow rates shown by the 36 and 72 SCFM cases were nearly identical, indicating that higher gas injection flow rates do not necessarily result in higher circulation flow rates.

4.4.4. Mixing Efficiency and Mixing Time

As with the baseline case, mixing efficiency is evaluated using the mixing ratio, with mixing time defined as the point at which the mixing ratio remains within ±5% of its final value. The mixing ratios for different gas flow rates are plotted in Figure 15. Cases with the shortest mixing times are considered to have the highest mixing efficiency, and vice versa.

The mixing efficiency plots show that during the initial few seconds after tracer injection, the 18 and 27 SCFM cases behaved similarly, while the remaining cases exhibited similar behavior among themselves. After this initial period, the values began to diverge.

The mixing time values exhibited a non-linear trend with increasing gas flow rates, as shown in Figure 16. The highest mixing time (116.5 s), corresponding to the lowest mixing efficiency, was observed for the 18 SCFM case. In contrast, the lowest mixing time (55.7 s), representing the highest mixing efficiency, was recorded for the 45 SCFM case. Notably, the 45 and 72 SCFM cases displayed very similar mixing times and mixing ratios despite the substantial difference in their injection gas flow rates, indicating that increasing the flow rate beyond 45 SCFM had a minimal impact on further improving mixing time and efficiency.

5. Discussion

The average values of the flow characteristics from the parametric analysis are summarized in

Table 3. Summary of flow parameters under different gas flow rates.

Injection Gas Flow Rate (SCFM)	Averaged Snorkel Plane Velocity (m/s)	Circulation Flow Rate (ton/min)	Mixing Time (s)	Average TKE (Inside Ladle) (m2/s2)
18	1.22	115	116.53	0.009
27	1.37	134	98.41	0.018
36	1.38	140	80.40	0.015
45	1.35	134	55.68	0.013
72	1.39	142	61.66	0.013

. The results reveal that increasing the injection gas flow rate in an RH degassing operation enhances the flow velocity and reduces the mixing time up to a certain threshold, beyond which the improvement becomes marginal and, in some cases, yields diminishing returns. For example, the mixing time increased by 11% when the gas flow rate was raised from 45 to 72 SCFM. A similar trend is observed for the circulation flow rate and snorkel plane velocity, which shows minimal improvement once the injection gas flow rate reaches 36 SCFM. Additionally, the average TKE values for the 45 and 72 SCFM cases were very close, despite a 60% increase in the gas flow rate, further supporting the inference that increasing the flow rate beyond a certain threshold (in this case, 45 SCFM) does not necessarily provide proportional improvements in the mixing efficiency.

The direction of steel motion within the system as well as the flow circulation that impacts the mixing time and the geometric constraints leading to the saturation of circulation rate are shown in Figure 17. Saturation of the circulation flow rate and snorkel plane velocity beyond 36 SCFM can be attributed to the fixed entrance diameter of the up-snorkel, which limits the maximum volume of steel passing through. At this flow rate, the driving force of the injected gas is balanced by the resistance of the snorkel geometry, restricting any significant increase in circulation rates. The mixing time reaches its optimum at 45 SCFM, where gas injection sufficiently enhances internal flow circulations, ensuring rapid tracer dispersions throughout the ladle without creating excessive turbulence or zones of low circulation. Beyond this point, at 72 SCFM, the increased gas velocity induces additional flow circulation within the up-snorkel, preventing molten steel from fully occupying the steel volume and creating localized circulation zones. As shown in Figure 11, the effective circulation at the bottom of the ladle is also reduced at this higher gas flow rate, and the average turbulent kinetic energy (TKE) inside the ladle slightly decreases. These factors reduce the effective mixing of the bulk steel, resulting in a minor increase in the mixing time. This behavior highlights the interplay between the gas flow rate, snorkel geometry, and internal flow patterns, indicating that an excessively higher injection gas flow rate can be counterproductive for increasing the mixing efficiency.

6. Conclusions

A detailed investigation was conducted to evaluate the impact of argon gas injection flow rates on the mixing behavior within an industrial-scale RH degasser. A VOF–DPM-based methodology was developed and validated against the reference literature, followed by the construction of a baseline model and a mesh convergence study. Subsequently, five gas flow rates, ranging from 18 to 72 SCFM, were simulated.

The results revealed that the mixing time decreased with an increasing gas flow rate up to a threshold value of 45 SCFM in the current model, beyond which further increases in the flow rate negatively affected the mixing time. A similar trend was observed for the circulation flow rate, where minimal improvement was noted beyond 36 SCFM in the rate of steel passing through the snorkels at any given instant. These findings indicate that selecting injection gas flow rates for an industrial-scale RH degasser requires careful optimization, as higher flow rates do not necessarily guarantee improved performance.

Furthermore, the developed VOF–DPM methodology is generalizable and can be extended to other industrial ladle and degasser configurations by adjusting the geometry parameters, operational conditions, and material properties. This approach provides a robust framework for evaluating flow behavior and mixing efficiency across different plant setups, supporting data-driven decisions for process optimization.

In future work, flow rates between 45 and 72 SCFM should be examined to confirm the observed trend. Furthermore, since the optimum gas flow rate is likely to depend on other geometric and operational parameters, such as snorkel diameter and vacuum chamber pressure, it should be investigated to develop a more generalized understanding of RH degasser performance.