Structural optimisation of three-strand asymmetric tundish for super large round bloom continuous casting

Abstract

In recent years, there has been significant development in the large-scale utilisation of round bloom continuous casting, which has led to an increase in the strand spacing of the tundish. However, this increase often accompanies issues such as poor consistency among each strand. This study focuses on the three-strand asymmetric tundish used in super-large round bloom continuous casting and uses a combination of numerical simulation and physical experiment to investigate the impact of different dam and retaining wall structures on the flow, temperature and removal of inclusions in the super-large round bloom tundish. The reliability of the model is verified through isothermal Water model experiments. The results indicate that by employing an optimised flow control structure with a U-shaped retaining wall featuring small diversion holes and a dam near each of strands No.1 and No.3, several improvements are achieved compared to the prototype tundish. The dead zone ratio of the tundish is reduced by 16.33%, the standard deviation of average residence time decreases by 167.07 s, the volume of the tundish's low temperature zone decreases by 7.79% and the total inclusion removal ratio increases by 14.44%. By appropriately incorporating dams, reducing the area of diversion holes and modifying the retaining wall structure in the tundish, the flow, temperature and inclusion removal consistency of each strand can be effectively improved. This enhances the overall metallurgical efficiency of the tundish. Even when encountering strand blocking operation, the dead zone ratio can be further reduced to 22.44% using the optimised structure proposed in this study. This demonstrates that the optimised structure not only improves the steady-state metallurgical behaviour of the asymmetric three-strand tundish with large strand spacing for super-large round bloom but is also suitable for addressing unsteady-state metallurgical behaviour caused by on-site working conditions, such as production scheduling or high casting speed. By implementing the findings of this study, it is expected that the efficiency and effectiveness of the super-large round bloom continuous casting process will be significantly enhanced.

Keywords

Super large round bloom asymmetric tundish consistency for each strand inclusions escape ratio

Introduction

The tundish is a vital component in continuous casting, influencing the cleanliness and quality of molten steel and the final product.^1,2 To enhance steel flow and improve cleanliness, various approaches have been explored, including the addition of flow control devices,^3–5 redesigning the tundish structure^6–8 and utilising electromagnetic flow control equipment.^9–11 While redesigning the tundish structure can be effective in enhancing flow behaviour and increasing inclusion removal efficiency, it often necessitates costly replacement and results in more complex structures. Similarly, using electromagnetic flow control equipment incurs higher equipment costs and requires multiple trial runs. In contrast, adding flow control devices offers a direct and efficient method that involves minimal changes to refractory materials, resulting in lower costs and improved metallurgical outcomes in the tundish.^12,13

Flow control devices in tundish, such as turbulence inhibitors, retaining walls and gas-permeable barriers, are critical for refining molten steel.^14,15 Lin et al.¹⁶ employed fluid–structure interaction simulations to examine the forces on turbulence inhibitors at casting onset, identifying height and brim width as vital to stress distribution. They noted that square inhibitors exhibit stress concentrations at corners, where erosion by molten steel is most severe. Chattopadhyay et al.^17,18 explored the efficacy of impact pads and dams on inclusion removal in delta-shaped tundish through Particle Image Velocimetry and simulations. The study revealed that such devices are instrumental in modulating steel flow and extracting inclusions. Liu et al.^19,20 demonstrated through simulations that retaining walls, coupled with filtration, can regulate flow and capture inclusions, with retaining walls additionally aiding in the contact and removal of inclusions at the steel-slag interface. Ramirez et al.²¹ analyzed a five-strand asymmetric tundish using multiphase flow simulations to uncover that dam design optimisation leads to better molten steel flow patterns and inclusion flotation. In summary, integrating targeted flow control devices enhances flow behaviour and inclusion removal in tundish. These devices must be customised for the tundish shape and specific casting conditions, suggesting that design considerations are as crucial as the devices’ functional implementations.

However, with the increasing market demand for large shaft-type cast-forged components and the constant enlargement of strand sizes, the spacing between strands in the tundish has also increased. This leads to issues such as poor consistency between edge strands and central strands. Moreover, production trials have identified that the structures of multi-strand asymmetric tundishes and the instability of steel cleanliness during non-steady-state casting are major constraints in the production of high-quality steel.^22,23 Therefore, this study aims to optimise the structure of a super-large round bloom casting three-strand asymmetric tundish at a certain steel plant. By employing a combination of physical experiment and numerical simulation methods, the research enhances the flow field and temperature field distribution within the tundish. This is achieved by introducing control devices such as dam combinations, diversion hole design and optimised retaining wall structures, on top of using turbulence inhibitors with brims. The study not only improves the efficiency of inclusion removal but also provides a theoretical basis for the application of asymmetric tundish with super-large inter-strand spacing.

Model description

This study focuses on the super-large round bloom continuous casting three-strand asymmetric tundish used in the production of 42CrMo4 wind turbine bearing steel. Figure 1 provides a three-dimensional view and cross-sectional view of the prototype tundish. The tundish includes flow control devices such as turbulence inhibitor and dam or retaining wall. The inter-strand spacing measures 3000 mm, and the height of the tundish shell is 1298 mm. The outlets, defined from left to right as Out1, Out2 and Out3, have different distances with Out2 being closer to the steel ladle's long nozzle, which can potentially cause short-circuiting flows. The structure and specific dimensions of the turbulence inhibitors are shown in Figure 1(c) and 1(d). The key dimensions and process parameters of the tundish are listed in Table 1. This study intends to optimise the tundish structure through two stages of structural design, namely dam and retaining wall optimisation. It is expected to reduce the short-circuit flow condition of the Strand No.2 and thereby improve the consistency of the flow field and temperature field within the tundish.

Table 1.

Relevant structural dimensions and process parameters of the tundish.

Parameters	Value
Liquid depth	950 mm
Casting speed	0.10 m·min⁻¹
Number of strand	3
Section size of round bloom	1200 mm
Capacity	36 t
Ladle shroud diameter	75 mm
Submerged entry nozzle diameter	50 mm

Assumptions

In the numerical simulation process, in order to reasonably reproduce the complex and interacting metallurgical-physical processes during the continuous casting process and improve computational efficiency, the following basic assumptions were made for the model:

The molten steel is treated as a steady-state, viscous and incompressible Newtonian fluid. To accurately analyze the influence of the thermal state of the molten steel on its flow, the density of the molten steel is set as a function of temperature. Within the tundish, the temperature of the molten steel remains mostly above the liquidus line, with its viscosity, specific heat capacity and thermal conductivity exhibiting minimal variation with temperature, thus are assumed to be constant.

The turbulent model adopts the standard Reynolds-averaged Navier-Stokes (RANS) k-ε model. The influence of the slag layer on the flow of molten steel is neglected. The heat losses caused by heat dissipation from all walls and the upper surface are treated as constant values.²⁴

Inclusions are assumed to be spherical particles, and the interaction forces between particles are neglected. The impact of inclusions on the fluid flow is also neglected. Inclusion particles enter the tundish from the inlet.

Control equations

Fluid Flow Model

\frac{\partial (ρ u_{i})}{\partial x_{i}} = 0

(1)

\begin{aligned} \frac{\partial (ρ u_{i})}{\partial t} + ρ \frac{\partial (u_{i} u_{j})}{\partial x_{j}} = - \frac{\partial p}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} \\ [μ_{eff} (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}})] + ρ g \end{aligned}

(2)

where $ρ$ is the density of molten steel, kg·m⁻³; $\vec{u}$ is the velocity of molten steel, m·s⁻¹; p is the pressure, Pa; $\vec{g}$ is the acceleration of gravity, m·s⁻²; $μ_{eff}$ is the effective viscosity coefficient, kg·m⁻¹·s⁻¹, determined by the standard $k - ε$ turbulence model²⁵:

\frac{\partial (ρ k u_{i})}{\partial x_{i}} = \frac{\partial}{\partial x_{i}} (\frac{μ_{eff}}{σ_{k}} \times \frac{\partial k}{\partial x_{j}}) + G_{k} - ρ ε

(3)

\frac{\partial (ρ ε u_{i})}{\partial x_{i}} = \frac{\partial}{\partial x_{i}} (\frac{μ_{eff}}{σ_{ε}} \times \frac{\partial ε}{\partial x_{i}}) + C_{1 ε} \frac{ε}{k} G_{k} - C_{2 ε} ρ \frac{ε^{2}}{k}

(4)

G_{k} = μ_{t} \frac{\partial u_{j}}{\partial x_{i}} (\frac{\partial u_{i}}{\partial u_{j}} + \frac{\partial u_{j}}{\partial u_{i}})

(5)

where

σ_{k}

σ_{ε}

C_{1 ε}

and

C_{2 ε}

from Launder,²⁶ is 1.0, 1.3, 1.44 and 1.92.

Heat Transfer Model

\frac{\partial (c_{p} ρ T)}{\partial t} + \frac{\partial (c_{p} ρ u_{i} T)}{\partial x_{i}} = \frac{\partial}{\partial x_{i}} (λ_{eff} \frac{\partial T}{\partial x_{i}})

(6)

where

c_{p}

is the specific heat capacity of molten steel at constant pressure, J·kg⁻¹·K⁻¹; T is the temperature, K;

λ_{eff}

is the effective heat transfer coefficient, W·m⁻¹·K⁻¹.

Species Transport Model

\frac{\partial (C ρ)}{\partial t} + \frac{\partial (C ρ u_{i})}{\partial x_{i}} = \frac{\partial}{\partial x_{i}} (ρ D_{eff} \frac{\partial C}{\partial x_{i}})

(7)

where C is the component volume concentration and

D_{eff}

is the component diffusion coefficient, m⁻²·s⁻¹.

Inclusion motion model

The Lagrangian discrete phase model (DPM) predicts the trajectory of the discrete phase by performing a force balance analysis on the particles. This force balance can be written as:

\frac{d {\vec{u}}_{p}}{d t} = \frac{\vec{u} - {\vec{u}}_{p}}{τ_{r}} + \frac{\vec{g} (ρ_{p} - ρ)}{ρ_{p}} + \vec{F}

(8)

where

\frac{\vec{μ} - \vec{μ_{p}}}{τ_{r}}

is the drag force per unit particle mass and

τ_{r} = \frac{ρ_{p} d_{p}^{2}}{18 μ} \frac{24}{C_{d} Re}

(9)

where

τ_{r}

is the particle relaxation time, s;

\vec{μ_{p}}

is the velocity of particle, m·s⁻¹;

μ

is the molecular viscosity of the molten steel, Pa·s;

ρ_{p}

is the density of particle, kg·m⁻³;

d_{p}

is the diameter of particle, m;

C_{d}

is drag force coefficient;

Re

is the relative Reynolds number; and

\vec{F}

is an additional acceleration term, including virtual mass force and pressure gradient force.

Boundary conditions

The inlet boundary condition is given by the velocity inlet, which is calculated from the mass conservation law based on the casting speed and the section size of bloom, and the inlet temperature is set to a constant value of 1791 K. The turbulent kinetic energy and turbulent energy dissipation rate at the inlet were calculated using the semi-empirical formula²⁷:

k = 0.01 v^{2}

(10)

ε = 2 \times \frac{k^{1.5}}{D}

(11)

where v is the inlet velocity, m·s⁻¹, its value can be determined by the law of mass conservation; D is the diameter of the long nozzle, m;

The outlet boundary condition is set as outflow.

The free surface of the tundish is zero shear stress. The other walls are set as a no-slip boundary condition.

When inclusions collide with the tundish wall surface, they will be reflected. If they contact with the top surface they are trapped. The boundary condition of the DPM model at the outlet is set as escape.

The relevant calculation parameters of the model are shown in Table 2.^24,28

Table 2.

Parameters related to the computational model.

Parameters	Value
Steel:
Density	8405.88–0.8046 T kg·m⁻³
Thermal conductivity	34 W·m⁻¹·K⁻¹
Viscosity	0.0062 kg·m⁻¹·s⁻¹
Specific heat	819 J·kg⁻¹·K⁻¹
Heat flux of bottom surface	4000 W·m⁻²
Heat flux of transversal wall	3200 W·m⁻²
Heat flux of top surface	15000 W·m⁻²
Heat flux of longitudinal wall	3800 W·m⁻²
Inclusion:
Density	3960 kg·m⁻³
Diameter	10/20/30/40/50 μm

Water model experiment

The water model experiment followed similar principles and built a tundish water model experiment platform with a similar ratio of 1:3. The physical picture of the tundish plexiglass model is shown in Figure 2(a). The overall Water model experiment platform and the equipment used are shown in Figure 2(a) and (b). According to the similar ratio, it can be seen that:

λ = \frac{L_{m}}{L_{P}} = \frac{1}{3}

(12)

where $λ$ is the scale factor; $L_{m}$ is the model geometry; and $L_{P}$ is the prototype geometry.

Based on the equality of Froude number for the tundish model and the prototype,²⁹ leads to:

u_{m} = \sqrt{λ} u_{P}

(13)

Q_{m} = λ^{\frac{5}{2}} Q_{P}

(14)

t_{m} = λ^{\frac{1}{2}} t_{P}

(15)

where

u_{m}

and

u_{P}

are model and prototype velocity,

Q_{m}

and

Q_{P}

are model and prototype flow rates,

t_{m}

and

t_{P}

are model and prototype time.

During the water model experiment, the duration of the experiment was related to the casting speed. To compress the experimental time, a condition of 0.13 m·min⁻¹ was selected for conducting the experiment. The main parameters of the water model experiment are shown in Table 3. The experimental process involved filling the ladle with water using a pump and maintaining a continuous outflow through the overflow pipe, while also achieving a target liquid level within the tundish by adjusting the inflow and outflow rates to maintain a steady target liquid level. After the water system had been operating stably for 3 min, 100 ml of saturated potassium chloride solution was injected as a tracer into the tundish. Concurrently, the conductivity of the solution was measured at the outlet using a conductivity meter, with values recorded over time by a computer. The collection duration was three times the theoretical mean residence time ( $t_{i} = \frac{V}{Q}$ ). To minimise experimental error, conductivity measurements for each scheme were repeated three times. Ultimately, the relationship curve between the dimensionless concentration and dimensionless time, that is, the Residence Time Distribution (RTD) curve, was obtained through conversion. Additionally, flow field tracing experiments employed black ink as the tracer. Post-conductivity data collection, we introduced 50 ml of ink into the tundish and documented the ink's dispersion with a camera, providing a visual analysis of the mixing process.

Table 3.

Main parameters of the water model experiment.

Parameters	Water model
Liquid depth of water	317 mm
Ladle shroud flow rate	1.697 m³·h⁻¹
Ladle shroud diameter	25 mm
Submerged entry nozzle diameter	16.7 mm
Flow rate of each submerged entry nozzle	0.566 m³·h⁻¹

Description of the solution process and the case

The numerical simulations were carried out using Fluent 2023 R1 software. The grid was generated using ICEM, with approximately 1,600,000 cells. The solver process commenced with solving for steady-state flow and temperature fields. The coupling of pressure and velocity was achieved using the Semi-Implicit Method for Pressure-Linked Equations algorithm, with the pressure equation discretised using the standard algorithm, and the remaining equations discretised using a second-order upwind implicit scheme. The initialisation utilised the standard method, starting calculations from the inlet region. The convergence criteria were set to a residual of 10⁻⁴ for all variables and 10⁻⁶ for energy. Subsequently, with the steady-state flow and temperature fields as initial solutions, the three-dimensional turbulent diffusion equation for the tracer was solved. For this stage, the velocity and pressure coupling changed to the Pressure-Implicit with Splitting of Operators method, the pressure equation to the PRESTO! algorithm and the other equations to a first-order upwind implicit discretisation scheme. A pulse of the tracer lasting 1 s was instantaneously injected at the tundish inlet, followed by a transient computation for 5000 s to derive the concentration versus time curve (RTD) of the molten steel at the outlet. Additionally, the DPM was applied based on the steady-state results to calculate the removal of non-metallic inclusions. Considering the influence of turbulence on particle motion, a random walk mold is used. The same number and size of inclusion particles are released at the inlet in each case, with the number of inclusions of different diameters evenly distributed. Extended combined models were employed for the treatment and analysis of the RTD curves, providing calculations for the mean residence time, the proportion of dead zones, piston flow and mixed flow. The computational formulas are illustrated in Table 4.^30,31

Table 4.

Formulas for calculating flow characteristic parameters.

Parameters	Formulas
Mean residence time	${\bar{t}}_{c} = \frac{\int_{0}^{\infty} C t d t}{\int_{0}^{\infty} C d t}$ (16)
Plug flow volume fraction	$V_{p} = \frac{t_{min} + t_{peak}}{2 t_{i}}$ (17)
Dead volume fraction	$V_{d} = 1 - \frac{{\bar{t}}_{c}}{t_{i}}$ (18)
Well-mixed flow volume fraction	$V_{m} = 1 - V_{p} - V_{d}$ (19)

Note: $t_{min}$ and $t_{p e a k}$ are response time and peak concentration time, respectively.

Figure 3 shows the description of this research programme with eight tundish structures. Figure 3(a) presents a schematic diagram of the fluid computational domain under a Y-shaped retaining wall structure, marking the position and height parameters of the dam. Figure 3(b) shows the basic structure and key parameters of different schemes, while Figure 3(c) illustrates the fluid computational domain of the tundish under a U-shaped retaining wall structure. Initially, Cases A1-A4 analyze the effects of varying the number and position of dams on the flow field and temperature distribution of molten steel within the tundish under a fixed Y-shaped retaining wall structure. Subsequently, based on the preferred dam number and position, the structure of the retaining wall is optimised (Cases B, C, D and E). Variables include the size, number and position of the openings in the retaining wall, as well as the shape of the retaining wall itself.

Model validation

The Water model experiments are isothermal experiments conducted at room temperature, whereas the numerical simulations, as mentioned earlier, take into account the effects of temperature variation. Consequently, to align with the conditions of isothermal water model experiments, the density of molten steel in the numerical simulations for model verification is set as a constant value of 6965 kg·m⁻³. The scheme used for model verification is marked as Case C*. The height of Dam No.1 in Case C* is 200 mm. Other than that, other structural features of Case C* are the same as Case C. Figure 4 compares the isothermal water simulation results to the isothermal numerical simulation outcomes, including the RTD curves, the minimum response times ( $t_{min}$ ), the peak times ( $t_{peak}$ ), the dimensionless peak concentrations E(θ)_peak and the diffusion of the tracer. As can be seen from Figure 4(a), the overall agreement between the RTD curves from the physical experiments and the numerical calculations is quite good, demonstrating a high degree of overlap. Figure 4(b) provides a statistical comparison of the $t_{min}$ , $t_{peak}$ and E(θ)_peak from three repetitions of the physical experiments against the numerical simulation results, finding that the numerical simulation outcomes fall within the range of variability of the physical experimental results. The mean values of E(θ)_peak obtained in the physical simulation experiments are 0.80, 0.94 and 0.95 for each strand, respectively, whereas those obtained from the numerical simulation computations are 0.81, 0.97 and 0.95, respectively. The errors of E(θ)_peak for each strand are within 5%. Figure 4(c) shows the time-evolution of tracer distribution in both physical and numerical simulations, capturing images at 17 s, 35 s and 52 s of the physical experiment using ink as a tracer; 17 s after the start of the tracer experiment, the ink first flows through the hole and reaches dams No. 1 and No. 3. At 35 s, the ink moves upwards and forms a backflow after hitting the liquid's surface due to the obstruction from the dams. At 52 s, the regions near Out1, in the area of stopper No. 2, and behind Dam No. 3 exhibit uneven ink mixing. The corresponding times in the numerical simulations can be calculated using equation (15), corresponding to 30 s, 60 s and 90 s. It is apparent from the figures that the diffusion patterns of the tracer in both the physical.

Results and discussion

Optimisation of dam structures

Figure 5 presents three-dimensional streamline diagrams of the molten steel in the tundish for different dam quantity schemes. As shown in Figure 5(a), when there are no dams within the tundish, the molten steel flows out from the diversion holes and forms a large circulation at the bottom to the sides of the tundish. Notably, the proximity of Strand No.2 to the diversion hole results in higher fluid velocities in that area, which may lead to a short-circuiting flow. In Figure 5(b), it is observed that when Dam No.3 is added to the tundish, the steel outflow from the right diversion hole divides into two backflows. Some of the molten steel crosses over Dam No.3 and forms a smaller recirculation on the right side of the dam, while the rest is redirected by the barrier of the dam back towards the vicinity of Strand No.2. Figure 5(c) demonstrates that when Dams No.1 and No.3 are simultaneously added to the tundish, the molten steel flowing out from the left diversion hole is also somewhat obstructed, which allows the molten steel to cross over the dam and approach Strand No.1, effectively prolonging the time it takes for the steel to reach the outlet. From Figure 5(d), it is evident that when Dam No.1, No.2 and No.3 are all added, a recirculation zone can be distinctly seen forming between the retaining wall and Dam No.2. Another major recirculation occurs after the steel flows over Dam No.2, and there is almost no flow observed between Dams No.2 and No.3, indicating a stagnant flow region. This suggests that adding Dam No.2 reduces the effective volume of the tundish.

Figure 6 provides the RTD curves for the tundish under different dam quantities. Flow characteristic parameters derived from the RTD curves are listed in Figure 7, including the minimum response time (t_min) and its standard deviation (S_min), the dimensionless peak concentration (E(θ)_peak) and its standard deviation (S_E_(θ)peak), the mean residence time (t_mean) and its standard deviation (S_mean), as well as the dead zone volume fraction (V_d) and the plug flow volume fraction (V_plug). The figures indicate that, within the Y-shaped retaining wall structure, the response time for the Strand No.2 is consistently the shortest regardless of the number of dams. As the number of dams in the tundish increases, the degree of overlap of the RTD curves initially improves and then deteriorates, with both E(θ)_peak and S_mean showing a trend of first decreasing and then increasing. As illustrated in Figure 7(d), with an increasing number of dams, the V_d also decreases and then grows. Specifically, when there are two dams in the tundish (Case A3), the overlap of the RTD is optimal, the E(θ)_peak of the Strand No. 2 is the lowest, and the V_d and V_plug are 26.46% and 22.89%, respectively. This represents a decrease of 2.46% and an increase of 3.47% compared to the no-dam case. This indicates that introducing Dam No. 1 and No. 3 into the tundish not only mitigates short-circuiting issues in the Strand No. 2 but also enhances the flow uniformity among the different strands and increases the effective volume of the tundish.

Figure 8 depicts the temperature distribution contour on the vertical cross-sections (Y = 0 mm) of the outlets under different dam configurations in the tundish. It can be observed that in the absence of dams, the tundish shell experiences varying degrees of heat loss, which results in the uniform presence of low-temperature zones below 1785 K along with the shell. The introduction of Dam No.3 reduces the low-temperature area on the left side of the dam, yet a significant low-temperature zone still forms behind the dam. When both Dam No.1 and Dam No.3 are added, the low-temperature region near Dam No.3 is further reduced, but it increases near Dam No.1. With all three dams present, there is a distinct high-temperature region to the left of Dam No.2, while a substantial low-temperature area develops on its right side. Figure 9 presents a statistical analysis of the temperatures and temperature differences (ΔT_MAX) at the outlets for each case. As the number of dams increases, the outlet temperature for Strand No.2 initially decreases and then rises. The ΔT_MAX for Cases A1, A2, A3 and A4 are 3.00 K, 1.48 K, 1.31 K and 4.37 K, respectively. When there are two dams present (Case A3), the ΔT_MAX among the strands is the smallest, indicating the best uniformity in the temperatures of the different strands.

Production practice has shown that low-temperature areas within the tundish often experience solidification of the molten steel towards the end of casting, significantly reducing the utilisation rate of the molten steel.³² Taking Case A1 as an example, the area of the low-temperature region across each outlet section (Y = 0 mm) and the volume of the overall low-temperature region within the tundish are quantified. Figure 10(a) illustrates the area of low-temperature regions (colored in blue) where the temperature is below 1785 K at the vertical cross section of each outlet (Y = 0 mm), obtained by employing CFD-POST software to calculate the proportion of the low-temperature area to the total cross-sectional area at Y = 0 mm. Figure 10(b) displays an isosurface of the tundish at T = 1785 K, with the volume of regions below 1785 K also quantified to derive the percentage of the low-temperature volume relative to the total volume of the tundish. An evaluation of the percentage of cross-sectional low-temperature area and the tundish low-temperature volume under different dam configurations is presented in Figure 10(c). The distribution of both the cross-sectional low-temperature area percentage and the tundish low-temperature volume percentage trends downward before increasing. The largest low-temperature region within the tundish is observed in Case A4, with the cross-sectional low-temperature area at the outlet (Y = 0 mm) and the tundish low-temperature volume percentage reaching as high as 28.16% and 17.99%, respectively. The results for Cases A2 and A3 are quite similar, with cross-sectional low-temperature area percentages at 5.72% and 6.59%, and tundish low-temperature volumes at 3.36% and 3.40%, respectively.

Figure 11 presents the information on inclusions under different dam configurations. The maximum difference in the inclusion escape ratios of each outlet is defined as ΔER. As shown in Figure 11(a), within the tundish of any structural design, large-sized inclusion particles are likely to rise to the steel-slag interface due to greater buoyant forces, leading to their removal. Consequently, the inclusion removal ratio increases with the size of the inclusions. Moreover, as the number of dams increases, the total inclusion removal ratio first increases and then decreases. Notably, when there are two dams within the tundish (Case A3), the overall inclusion removal ratio is highest at 73.66%, an 8.46% improvement over the scenario with no dams (Case A1). Under Case A1, the removal ratio for inclusions with a diameter of 10 µm is only 60.67%, whereas Case A3 sees an increase of 10.24%, suggesting that adding two dams in the tundish also enhances the chance of collision between inclusions, facilitating the removal of smaller-sized inclusions. Production considerations indicate that a higher ratio of inclusion escape from the tundish or greater variance between outflows detrimentally affects the stability and improvement of subsequent strand quality.³³ According to Figure 11(b), regardless of the number of dams, the highest inclusion escape ratio is always at Out2. However, this ratio decreases before increasing with a rising number of dams, and the ΔER among various Cases also shows a trend of first decreasing and then increasing. The maximum inclusion escape ratio in Case A1 is 20.11%, while in Case A3, it is only 9.77%, a drop of 10.34%, with a ΔER of just 1.77%. It is evident that the consistency of inclusion removal aligns with the uniformity of flow and temperature.

Optimisation of retaining wall structures

A comparison of the flow field, temperature field, RTD curves, mixing characteristics and inclusion removal performance under scenarios with different numbers of dams within the tundish reveals that adding Dam No.1 and Dam No.3 can mitigate short-circuiting in Strand No.2, while also improving the uniformity of the flow, temperature and inclusion removal performance across different strands and reduce the low-temperature regions in the tundish. Therefore, subsequent optimisation of the retaining wall structure will be conducted on the premise of simultaneously incorporating Dam No.1 and No.3 within the tundish. Cases B, C and D are Y-type dam configurations, differing from one another in the opening area and number of openings, with the opening area gradually decreasing from Case B to Case D. Case E is a U-type retaining wall.

Figure 12 displays three-dimensional streamline of the molten steel within the tundish under different retaining wall structures, as well as streamline across the vertical section at each outlet (Y = 0 mm). When both Dam No.1 and Dam No.3 are added in the tundish, regardless of the retaining wall structure employed, there are four significant recirculation zones within the casting area of the tundish. When the diversion hole has larger opening sizes (Case B), the flow velocity on the Y = 0 mm section is relatively small, and the recirculation near Dam No.3 is minor. This is because the molten steel exiting the diversion hole flows slowly with lower turbulence energy and cannot reach Dam No.3 while most of the molten steel exits through Out2. As the size of the diversion hole decreases, the velocity of the steel flowing out of the diversion hole correspondingly increases, and the outflow on the right side of the dam forms a recirculation only after reaching Dam No.3. Compared to Y-type retaining wall structures, the U-type retaining wall has a larger recirculation zone near Out2.

The RTD curves for each case are shown in Figure 13, and the flow characteristic parameters derived from the analysis of the RTD curves are listed in Figure 14. As indicated by Figure 13, except for Case B, RTD curves for the other cases do not exhibit noticeable peaks, suggesting that the short-circuiting condition at Out2 has been alleviated. The response times for Strand No.2 in Case B, C and D are 53 s, 70 s and 117 s, respectively, indicating that reducing the retaining wall opening area can prolong the response time for Strand No.2. It is also found that the response times for Strand No.1 and Strand No.3 have been shortened, and the standard deviation of the response times has decreased progressively. The mean residence times for Strand No.2 in Cases B, C and D are 381 s, 697 s and 715 s, respectively, with standard deviations for the mean residence time of 242.56 s, 34.38 s and 44.34 s. Compared to Case B, Cases D and E have, respectively, reduced the dead zone ratio by 5.8% and 5.65% and increased the plug flow ratio by 18.62% and 18.94%. This suggests that reducing the size of the diversion hole opening area to a certain extent, thereby increasing the outflow velocity of the steel from the diversion hole, can improve the flow behaviour of the steel in the tundish. On this basis, when the Y-type retaining wall is replaced with a U-type retaining wall (Case E), the standard deviation of the response time is only 4.58 s, the mean residence time is extended, and the standard deviation for the mean residence time is significantly reduced, even to as low as 5.99 s. The RTD curves for the different strands also overlap more closely, which could further enhance the flow behaviour of the molten steel within the tundish.

Figure 15 presents the temperature distribution contours and temperature information at each outlet of the vertical section (Y = 0 mm) for the different retaining wall structures. It can be seen from the figure that in Case B, there is a large area of low temperature near Out3, with the temperature at Out3 being 1783.86 K, whereas the temperature at Out2 is higher at 1788.36 K, reaching a temperature difference of 4.49 K. Cases C and D have certain low-temperature regions behind Dam No.1, with the maximum temperature difference across the strands in the two cases being only 0.97 K and 1.43 K, respectively. The temperature distribution on the vertical section at the outlets of case E is very uniform, with the maximum temperature difference among the flows reaching as low as 0.06 K. An evaluation of the low-temperature area (T ≤ 1785 K) at the Y = 0 mm section and the percentage volume of the low-temperature region in the tundish for different retaining wall structures are shown in Figure 16. It can also be seen that the volume of the low-temperature region in Case B is significantly higher than that of the other three cases, with the sectional low-temperature area and low-temperature volume in the tundish for Cases C, D and E all below 3%, among which Case E has the smallest volume of the low-temperature region in the tundish, lowering to just 1.30%.

Figure 17 shows the information on inclusions under different retaining wall structures. As can be deduced from Figure 17(a), the overall inclusion removal ratio for each case, which is based on the structure with the addition of two dams in the tundish, is above 70%. In addition, the area of the diversion holes does not have a significant impact on the overall removal effectiveness of the inclusions, but replacing the Y-type retaining wall with a U-type retaining wall can enhance the inclusion removal ratio. Among them, Case D has the lowest total inclusion removal ratio at 72.80%, while Case E has the highest at 79.64%. Under Case E, when the inclusion diameters are 10 μm, 20 μm, 30 μm, 40 μm and 50 μm, the respective removal ratios are 76.40%, 78.88%, 80.22%, 80.22% and 82.47%. Figure 17(b) shows that when the diversion hole area is too large (Case B), the ΔER reaches 10.17%, while for the other dam configurations, the respective ΔER is 1.71%, 2.83% and 2.29%, all maintained at a lower level. This demonstrates that the U-type retaining wall (Case E) is more conducive to reducing the overall escape ratio of inclusions and ensuring the consistency of the escape ratio of inclusions in each strand, which is beneficial for improving the cleanliness effect of the tundish.

The comprehensive analysis above indicates that the low-temperature zones in the tundish do not merely result from heat dissipation near the walls but also reflect areas within the tundish where flow is less active. It is also noted that the percentage of the low-temperature area on the outlet longitudinal section (Y = 0 mm) is significantly higher than the volume percentage of the low-temperature zone in the tundish, suggesting that while this cross section has a certain representativeness in characterising the distribution of low-temperature zones between different cases, its numerical value tends to be larger. Therefore, the volume percentage of the low-temperature zone in the tundish proposed in this study is a more accurate indicator. Consequently, in the process of optimising the tundish structure, one should not only rely on empirical design based on the interpretation of RTD curves but also clearly identify the location of less active flow areas within the tundish to enable more targeted structural optimisation. In this research, Case E (which employs a U-type retaining wall, small diversion holes and with one dam each near the Strand No.1 and Strand No.3) can achieve good metallurgical effects under steady-state casting conditions for super-large round bloom in the three-strand asymmetric tundish.

Influence of strand-blocking operation

Moreover, during the continuous casting production of super-large section strands, when increasing the casting speed, there are often problems such as insufficient molten steel supply or equipment scheduling, which may lead to strand-blocking operations.^34,35 The purpose of this section is to explore the metallurgical effects within the tundish during strand-blocking operations when increasing the casting speed (0.15 m·min⁻¹), under Case E. Figure 18(a) and (b) shows the three-dimensional molten steel streamline within the tundish and the streamline of the outlet longitudinal section, respectively. It can be seen from the figures that during strand-blocking operation, the flow pattern of the molten steel within the tundish is essentially the same as during normal casting conditions, with four recirculation regions existing on the outlet longitudinal section, and the combined area of regions 1 and 2 is roughly equivalent to that of regions 3 and 4. Figure 18(c) presents the RTD curves for Case E during strand-blocking operation, with RTD curves for Strand No.1 and No.3 still showing a good degree of overlap. A flow characteristic analysis of the RTD curves was performed, and its numerical values are shown in Table 5. Compared to normal casting conditions, the average residence times of Strand No.1 and No.3 during strand-blocking operation increased by 16 s and 25 s, respectively, and the standard deviation of the average residence time increased by 6.82 s, but its value remains relatively small at 12.81 s. Furthermore, under strand-blocking operation, the dead zone ratio is only 22.44%.

Table 5.

Mixing characteristics of Case E under strand-blocking operations.

Outlet	t_min (s)	t_peak (s)	t_mean (s)	S _min	S _mean
1	88	308	717	2.8	12.8
3	92	276	735	2.8	12.8

Figure 19 presents the temperature distribution contour of Case E's outlet longitudinal section (Y = 0 mm) under strand-blocking operation. The temperature distribution within the tundish is relatively uniform, with only very small low-temperature regions existing above the Out2 and behind the Dam No.3, other regions maintain a more uniform temperature distribution. Specifically, the temperatures at Out1 and Out3 are 1785.87 K and 1785.71 K, respectively, with a negligible temperature difference of only 0.1 K. This suggests that under the optimised structure of Case E, the strand-blocking operation does not have a significant impact on the temperature field within the tundish, and the temperature distribution remains relatively uniform.

Conclusions

This study employs a combination of numerical simulation and physical experiment to investigate the effects of different dam configurations and retaining wall structures on the metallurgical behaviour of asymmetrical three-strand tundish during the continuous casting of super-large round bloom. The accuracy and reliability of the models were qualitatively and quantitatively validated through isothermal water model experiments from multiple perspectives. The main conclusions are as follows:

Compared with the prototype tundish design (Y-type retaining wall, without dams), by adding the flow control combination of Dam No.1 and No.3 within the tundish can reduce the standard deviation of mean residence time from 173.06 s to 72.09 s. It also increases the effective volume of the tundish. The volume of low-temperature regions in the tundish can be reduced from 17.99% to 3.36%, and the extremal difference in escape ratio of inclusions across the strands can be decreased by 11.69%.

On the basis of a double-dam structure, comparing different retaining wall designs revealed that appropriately reducing the diversion hole area appropriately and changing the retaining wall structure to a U-type configuration can significantly improve the uniformity of flow, temperature and inclusion removal among the strands. With this case, the standard deviation of mean residence time is as low as 5.99 s, the dead zone ratio is at 24.86%. The maximum temperature difference between strands is only 0.06 K, the volume of low-temperature regions in the tundish is lowered to 1.30%, and the total removal ratio of inclusions can reach 79.64%.

The optimised strategy proposed by this study (utilising a U-type retaining wall, small diversion hole, with a dam near each of Out1 and Out3 for optimised flow control) remains applicable during the actual production process that requires strand-blockage operations for the casting of super-large round bloom. Under the strand-blockage operation, the standard deviation of mean residence time is 12.8 s, the dead zone ratio further decreases to 22.44% and the temperature difference between strands is just 0.1 K.

The indicator proposed in this study, the volume percentage of tundish low-temperature regions (T ≤ 1785 K), can more accurately characterise the location and volume of the inactive regions within the tundish. Compared to optimising tundish design empirically based on RTD curves, clearly identifying the location of inactive flow areas within the tundish can allow for more targeted optimisation of the flow control structures.

Footnotes

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The Science and Technology Talent Support Project of Hunan province in China, (grant number No. 2023TJ-Z14).

ORCID iD

Pu Wang

References

Qian

Liang

Song

, et al. Study on asymmetry and temperature difference between different strands in 7-outlets tundish. Ironmak Steelmak 2023; 50: 150–158.

Yao

Wang

Zhu

, et al. Mathematical study of realistic removal rates of non-metallic inclusions in continuous casting tundish using optimized criterion. Metall Mater Trans B 2023; 54: 1144–1158.

Wang

Chen

Xiao

, et al. Effect of flow control devices on the distribution of magnetic-flow-heat in the channel induction heating tundish. Ironmak Steelmak 2021; 48: 1200–1210.

Quan

Zhang

, et al. Physical and numerical investigation on fluid flow and inclusion removal behavior in a single-strand tundish. J Iron Steel Res Int 2023; 30: 1182–1198.

Chatterjee

Chattopadhyay

. Transient steel quality under non-isothermal conditions in a multi-strand billet caster tundish: part II effect of a flow-control device. Ironmak Steelmak 2017; 44: 413–420.

Wang

Tsukihashi

. Large eddy simulation on flow structure in centrifugal flow tundish. ISIJ Int 2007; 47: 568–573.

Qin

Cheng

, et al. Numerical study on a new swirling flow pocket brick for tundish upper nozzle during continuous casting of steel. Ironmak Steelmak 2023; 50: 1489–1501.

Xie

Nabeel

Ersson

, et al. A review on swirling flow casting technology in steel production. Steel Res Int 2022; 93: 2100410.

Chen

Wang

Xiao

, et al. Dual optimization of the geometric design and inductor parameters of the induction heating tundish based on numerical simulations. J Mater Res Tec 2023; 24: 1410–1428.

10.

Wang

Xiao

Chen

, et al. Influence of dual-channel induction heating coil parameters on the magnetic field and macroscopic transport behavior in T-type tundish. Metall Mater Trans B 2021; 52: 3447–3467.

11.

Chen

Xiao

Wang

, et al. Magnetic-flow-thermal characteristics of an innovative four-channel induction heating tundish. Steel Res Int 2022; 93: 2100839.

12.

Wang

Tie

Cai

, et al. Flow control to a T-shaped five-strand tundish for its overall enhanced metallurgical effects with an approachable identical products quality. ISIJ Int 2023; 63: 1351–1359.

13.

Sheng

. An integrated workflow for designing a single-strand tundish using CFD-Taguchi method and mean age theory. ISIJ Int 2023; 63: 1206–1216.

14.

Sahai

. Tundish technology for casting clean steel: a review. Metall Mater Trans B 2016; 47: 2095–2106.

15.

Singh

Ajmani

Pal

, et al. Single strand continuous caster tundish furniture comparison for optimal performance. Ironmak Steelmak 2012; 39: 171–179.

16.

Lin

Jin

Gan

, et al. Study of the impact of opening streams on turbulence inhibitors in tundishes. Metall Mater Trans B 2022; 53: 3159–3169.

17.

Chattopadhyay

Isac

Guthrie

RIL

. Effect of flow modifiers on liquid metal cleanliness in four-strand delta shaped billet caster tundish. Ironmak Steelmak 2012; 39: 454–462.

18.

Chattopadhyay

Isac

Guthrie

RIL

. Modelling of non-isothermal melt flows in a four strand delta shaped billet caster tundish validated by water model experiments. ISIJ Int 2012; 52: 2026–2035.

19.

Zhang

Zheng

Yan

, et al. Formation mechanism of interface reaction layer between microporous magnesia refractories and molten steel and its effect on steel cleanliness. J Iron Steel Res. Int 2023; 30: 1743–1754.

20.

Liu

Xiao

, et al. Numerical investigation on motion and removal of inclusions in continuous casting tundish with multiorifice filter. Steel Res Int 2022; 93: 2100818.

21.

Ramirez

OSD

Alonso

Banderas

JÁR

, et al. Thermal and fluid-dynamic optimization of a five strand asymmetric delta shaped billet caster tundish. Steel Res Int 2018; 89: 1700428.

22.

Tie

Tang

Wang

, et al. Effect of flow field optimization of an asymmetric multi-strand tundish on the quality consistency of cracking con-rod steel. Materials 2022; 15: 3698.

23.

Sarkar

Sambasivam

Ajmani

, et al. Numerical analysis of unsteady hydrodynamics and thermal transport in five-strand asymmetric tundish. Ironmak Steelmak 2012; 39: 540–549.

24.

Barreto

JDJ

BÓM

. Physical and mathematical modeling of steel flow and heat transfer in tundishes under non-isothermal and non-adiabatic conditions. ISIJ Int 1996; 36: 543–552.

25.

Siddiqui

MIH

Jha

. Assessment of turbulence models for prediction of intermixed amount with free surface variation using coupled level-set volume of fluid method. ISIJ Int 2014; 54: 2578–2587.

26.

Launder

Spalding

. The numerical computation of turbulent flows. Comput Method Appl M 1974; 3: 269–289.

27.

Lai

KYM

Salcudean

Tanaka

, et al. Mathematical modeling of flows in large tundish systems in steelmaking. Metall Mater Trans B 1986; 17: 449–459.

28.

Chakraborty

Sahai

. Mathematical modeling of melt flow and heat transfer in continuous casting tundishes. Tokyo: The Sixth International Iron and Steel Congress, 1990;3:189.

29.

Zhang

Yang

Cai

, et al. Investigation of fluid flow and steel cleanliness in the continuous casting strand. Metall Mater Trans B 2007; 38: 63–83.

30.

Ding

Lei

Niu

, et al. Effects of tracer solute buoyancy on flow behavior in a single-strand tundish. Metall Mater Trans B 2021; 52: 3788–3804.

31.

Sheng

. Mean age theory in continuous casting tundish. Metall Mater Trans B 2022; 53: 2735–2752.

32.

Manish

Tripathi

Hosahali

, et al. Reduction in skull loss in billet caster tundish through water modelling studies. Ironmak Steelmak 2021; 48: 803–810.

33.

Yang

Deng

Duan

, et al. Power curve” key factor affecting metallurgical effects of an induction heating tundish. J Iron Steel Res. Int 2022; 29: 151–164.

34.

Fan

Chen

, et al. Effect of uniform and non-uniform increasing casting flow rate on dispersion and outflow percentage of tracers in four strand tundishes under strand blockage conditions. Metals 2022; 12: 1016.

35.

Mishra

Jha

Sharma

, et al. Effect of blockage of outlet nozzle on fluid flow and heat transfer in continuously cast multistrand billet caster tundish. Can Metall Q 2012; 51: 170–183.