Optimization of the Liquid Steel Flow Behavior in the Tundish through Water Model Experiment, Numerical Simulation and Industrial Trial

Abstract

A reasonable tundish flow behavior could improve liquid steel cleanliness by promoting floating and removal of the inclusions. The flow behaviors of the tundish could be obtained by water model experiments and numerical simulations, respectively. However, the difference in density between the tracer and water in the experiment can contribute to notable errors. A new type of tracer, which is a mixture of potassium chloride (KCl) and ethanol, was proposed in this study to reduce the errors. The numerical simulation model was validated by the experimental data and its error was below 2%. By comparing the flow behaviors in seven tundishes with different inner structures obtained by simulation, it is found that the C1 can significantly reduce the dead volume ratio and C4 can improve the uniformity of liquid steel charged though each outlet. The structural strength of the baffle in C1 scheme was not considered, resulting in a crack of the baffle in the industrial trial. Industrial trials of the molten steel flow in the C4-based tundish were conducted and reported a reduction of 43.81% in the inclusions over the prototype.

1. Introduction

The tundish is the equipment between the ladle and the continuous caster. As a buffer and the last container of the liquid steel in the process of steelmaking, it plays a critical role in reducing the content of the non-metallic inclusion. Different measures were taken to optimize the flow behavior of the liquid steel to enhance the floatation of the inclusion, and the most common one is the usage of the flow control device.

To obtain the flow behaviors, the water model experiment and numerical simulation are widely used. The former could reproduce the flow field of the liquid steel through monitoring the flow characteristics of water in a scaled tundish. The latter could provide comprehensive information on the steel flow in a practical tundish. To analyze the behaviors, the residence time distribution (RTD) is extensively used in the experiment and numerical simulation as an indicator of liquid mixing degree.

To obtain the RTD curve, the flow field in the experimental tundish is usually measured through injecting an electrolyte tracer [1]. The RTD curve of the outlet can be drawn by the stimulus-response technique. The decisive factor in the experiment is whether the influence of the tracer flow behavior on the water can be neglected or not. Therefore, the properties of the tracer [2] and the way the tracer is added [3] are the keys to the experiment. Chen [4] and Ding [5] found that the concentration, volume, and types of the tracer can affect the experiment results, and less tracer with a lower concentration was suggested. However, limited by the resolution of the measurement device, a small amount of low-concentrated tracer is prone to result in a large measurement error.

Accurate simulation results, including the RTD curve, rely on the accuracy of the turbulence model of the liquid flow. The verification of the model is usually conducted by comparing simulation results to the water model experiment data. Previous studies reported that the k-ε model [6,7,8], SST model [7], SST k-ω model, and the realizable k-ε model [9] were reliable for different single-strand tundishes, and therefore these models were used for the optimization of the tundishes, including symmetric [10] and asymmetric [11]. For the multi-strand tundish, the inner flow field would be more complex due to multiple outlets [10]. In previous studies, the model was qualitatively validated by comparing the tracer concentration contour with the dye tracer outlines from the water model experiment [12,13]. The RTD curve and the dead zone ratio were also used as flow characteristics to compare [14].

As a straightforward method, an industrial trial was also carried out to check the feasibility of modified structures by measuring the content of the inclusion in the sampled billets [15]. However, the expense of the industrial trial is much higher than the water model experiment and especially the numerical simulation. Additionally, previous trials were conducted based on one tundish. The trials merely focused on the performance of the new one, which means the trial based on the original one was not conducted simultaneously [16,17]. If the trials of the old tundish and the new tundish are not conducted at the same time, the charged liquid steel from the ladle would be different because the content of the inclusion varies with charging time. When the liquid steel charged into the original and new tundish, they had different inclusion numbers; this could contribute to unreliable trial results at the outlet and further affect the evaluation of tundish performance.

To optimize the flow field of an asymmetry five-strand tundish, a water model experiment with a novel tracer applied was carried out. The flow model in the numerical simulation was validated and then used to investigate the effects of the inner structure of the tundish on the liquid steel flow field. Two schemes with an improved inner structure of the tundish were proposed, and the corresponding industrial trials were conducted to investigate the effectiveness of the scheme.

2. Geometry Model

The schematic of the five-strand tundish structure is shown in Figure 1. The tundish consists of a lashed zone and a casting zone, and they act as a receiver and discharger of the liquid steel. The two zones are separated by a baffle where two orifices (Orifices I and II) are set on one side and the last one (Orifice III) on the other side. The lashed zone includes a ladle shroud and a turbulence inhibitor, while the casting zone contains a dam, five stoppers, and five submerged entry nozzles (marked as S1–S5). The height, diameter, and elevation angle are marked as h, d, and α. The operating parameters of the five-strand tundish are listed in

Table 1. Operating parameters of the five-strand tundish.

	Liquid Steel Level/mm	Billet Section/mm × mm	Casting Speed/M·s−1
Value	850	180 × 180	1.3

.

3. Water Model Experiment

3.1. Experimental Equipment

The Froude similarity criterion was used for dynamic similarity analysis. The water model experiment was carried out in a 1/3 scaled tundish, and therefore, the velocity of the liquid at the inlet (the ladle shroud) of the water model can be determined as follows:

$$\frac{u_m}{u_r}={\lambda }^{0.5}$$

(1)

where, u_m and u_r are the velocity in the experimental and industrial tundish, respectively. $\lambda$ is the similar factor, which is 1/3 in this study. The system of the water model is described in Figure 2. It includes a water supply system, a tracer injector, a tundish model built by polymethyl methacrylate (PMMA), and a data collection system.

3.2. Experimental Procedure

The stimulus-response technique was applied in the experiment. The tracer was injected through the ladle shroud, and its concentration at each outlet was monitored continuously. As shown in Figure 2, the conductivity of the mixed fluid was measured to obtain the tracer concentration. The conductivity detectors were calibrated before conducting the experiment. Saturated potassium chloride (KCl) was firstly used in the experiment as the tracer. However, we observed that the tracer was sinking fast instead of flowing along the centerline of orifices after passing through the orifices (it was unable to be captured due to the limitation of the resolution of the camera, but it was notable due to light refraction). The sinking phenomenon is caused by the difference in the density and would deviate from the original water flow field under buoyant force and induce a significant experiment error [18]. Therefore, to reproduce the flow field with a small error, an unsaturated tracer with a density of 964.05 kg/m³ (1174 kg/m³ for saturated KCl solution) was prepared by mixing 800 mL water, 225 mL ethanol, and 47.34 g crystal KCl.

4. Mathematical Model

4.1. Model Assumptions

To simplify the simulation, the following assumptions were made. (1) The liquid steel in the tundish is assumed incompressible, and its flow is steady. (2) The flow field is assumed isothermal. (3) The effect of inclusion to flow field is ignored.(4) The chemical reaction is neglected.

4.2. Governing Equation and Boundary Condition

The Continuity and Navier-Stokes Equations at the steady state are expressed as follows,

$$\nabla \cdot \left(\rho \mathit{U}\right)=0$$

(2)

$$\nabla \cdot \left(\rho \mathit{U}\mathit{U}\right)=-\nabla p+\nabla \cdot \left[\left(\mu +{\mu }_t\right)\nabla \mathit{U}\right]$$

(3)

where, ρ is the density of liquid; U is the velocity vector, m/s; p is pressure, Pa; μ is the molecular viscosity; μ_t is the turbulence viscosity, which is solved by the SST k-ω model [19]:

$${\mu }_t=\frac{\rho a_{1}k}{\max \left(a_1\omega ,\mathit{S}\cdot {\mathit{F}}_2\right)}$$

(4)

The transient motion of the tracer in the tundish is described by the scalar transport equation:

$$\frac{\partial \left(\rho Y\right)}{\partial \tau }+\nabla \cdot \left(\rho \mathit{U}Y\right)=\nabla \cdot \left(\rho D\nabla Y\right)$$

(5)

where, Y is the tracer mass concentration; D is the turbulence diffusion coefficient, m²/s.

The flow behavior of the liquid and the tracer were simulated separately. The steady flow of the liquid was firstly solved, and the obtained flow field was the basis of the unsteady simulation of tracer flow. When the effects of the tracer on the flow behaviors of the liquid steel could be ignored, the combination of the steady simulation of liquid flow and transient simulation of tracer flow can contribute to a reliable result. The solver program simpleFOAM and scalarTransportFOAM in OpenFOAM v8 (released by OpenFOAM Foundation, OpenCFD Ltd., Bracknell, UK) were used in this study for solving the steady flow field and transient tracer behavior, respectively. The boundary conditions for steady flow simulation are listed in Equation (6).

$$\{\begin{array}{l}\mathit{U}{|}_{\hspace{0.17em}\mathrm{in}}=(0,-\frac{4Q_V}{\pi d_{in}^2},0),\hspace{0.17em}\hspace{0.17em}\\ p{|}_{\mathrm{out}}=0\\ u_n{|}_{\mathrm{liquid}\hspace{0.17em}\mathrm{surface}}=0,\hspace{0.17em}\hspace{0.17em}\frac{\partial \phi }{\partial \mathit{n}}{|}_{\mathrm{liquid}\hspace{0.17em}\mathrm{surface}}=0\\ \mathit{U}{|}_{\hspace{0.17em}\mathrm{wall}}=(0,0,0)\end{array}$$

(6)

The boundary conditions for unsteady simulation are given below:

$$\{\begin{array}{l}Y{|}_{\hspace{0.17em}\mathrm{in},t<1}=0.2647,Y{|}_{\hspace{0.17em}\mathrm{in},\mathrm{t}>1}=0\\ \frac{\partial Y}{\partial \mathit{n}}{|}_{\mathrm{out}}=0\\ \frac{\partial Y}{\partial \mathit{n}}{|}_{\mathrm{liquid}\hspace{0.17em}\mathrm{surface}}=0\\ \frac{\partial Y}{\partial \mathit{n}}{|}_{\mathrm{wall}}=0\end{array}$$

(7)

4.3. Validation of Numerical Simulation Model to Experiment Data

The RTD curve of each outlet was used to characterize the liquid flow behavior in the tundish. It represents the variation of the concentration $E\left(\theta \right)$ with the time at the outlet, and it is defined as follows:

$$E\left(\theta \right)=\frac{{\displaystyle \sum _{i=1}^5{E}_i\left(\theta \right)Q_{V_i}}}{Q_V}$$

(8)

$$E_i\left(\theta \right)=\frac{Y_i\left(\theta \right)}{{\displaystyle {\int }_0^{\infty }{Y}_i\left(\theta \right)\mathrm{d}\theta }}$$

(9)

$$\theta =\frac{t}{V/Q_V}$$

(10)

where $E_i\left(\theta \right)$ and $E\left(\theta \right)$ are the dimensionless concentration at each outlet and total concentration; t is the time, s; V is the volume of tundish, m³; Q_V is the total flow rate, m³/s; $Y_i\left(\theta \right)$ is the KCl mass concentration at the dimensionless time θ at the ith outlet. $Q_{V_i}$ is the flow rate at the ith outlet, m³/s, which is controlled by the valve with the help of the flow meter in the experiment. The upper limit of the integration in Equation (9) is 3. The total RTD curves obtained through the water model experiment and simulation are compared in Figure 3.

Figure 3 exhibits a good agreement between the numerical simulation results and the experimental data, especially in the range of 1.0 < θ < 3.0. When θ is less than 1, the difference between the two curves is obvious, which might be attributed to the sharp increase in the flow rate of the tracer (about 1.5~1.8 times than steady water flow rate) when it was injected.

The dead zone ratio is an important indicator of the reasonability of the flow field in the tundish, which indicates the degree of the inclusion floatation in the tundish. The smaller the dead zone ratio is, the more inclusions could be removed. The dead zone ratio is calculated as follows:

$$\frac{V_d}{V}=1-{\displaystyle {\int }_0^3\theta E_{total}\left(\theta \right)}\mathrm{d}\theta$$

(11)

The dead zone ratios provided by the simulation and water model experiment are shown in

Table 2. The dead zone ratio provided by the simulation and water model experiment.

	Numerical Simulation	Water Model Experiment	Error
Dead zone ratio/%	12.77	11.46	1.31

. The absolute error is 1.31%, proving the reliability of the simulation model.

5. Simulation Result and Discussion

The orifice on the baffle and the dam in the casting zone have a significant influence on the flow pattern of liquid steel in the tundish. Structural parameters of the orifice and the dam were therefore investigated in this study regarding their influence on the flow behaviors. A total number of seven cases were investigated with seven factors considered. The factors are the inner diameter of the ladle shroud and three orifices, the inclination angle and height of Orifice II h_II, and the existence of the dam, as shown in Figure 1 and given in

Table 3. Structural parameters of all cases.

Case No.	dLD/mm	dI/mm	dII/mm	dIII/mm	hII/mm	αII/°	Dam
C0(prototype)	30	150	150	150	220	10	No
C1	30	150	200	200	220	30	Yes
C2	60	100	200	150	220	10	Yes
C3	60	125	200	150	220	10	Yes
C4	60	150	200	150	190	10	Yes
C5	60	150	190	150	190	10	Yes
C6	60	150	180	150	190	10	Yes

.

5.1. Flow Field

The flow fields in a plane cross the centerline of the orifices of different cases and are shown in Figure 4. There are two large vortices on each side of the baffle. The vortex located in the receiving chamber is the result of the combined effects of the upward liquid steel from the turbulence inhibitor and the downward liquid steel from the surface. The other vertex in the discharger chamber is induced by the backflow of two jets of liquid steel from orifices I and II.

The inclination angle of the orifice affects the jet flow behavior in the discharging zone. Comparing Figure 4b with Figure 4c, it can be found that an increase in the inclination angle makes the jets from Orifices I and II mix at a short distance from the baffle. Furthermore, as d_II increases, the velocity of the jet from Orifice II slows down, letting the vertex near the orifice in the discharging zone move upward.

The dam plays a crucial role in the flow field distribution nearby. Comparing Figure 4b with Figure 4c–h, when the dam is applied, a part of the backflow from the mixed jet is redistributed with more liquid flowing to S4 instead of S3. As a result, the short-circuit flow through S3 is improved, but the flow through S4 is worsened.

By adjusting the diameter of the orifice, the jet behaviors can be regulated. In Figure 4d,e, the velocity of the jet from Orifice I in C2 is slower than that in C3, which makes the liquid steel spend more time reaching S4 and S5. Additionally, the upward deflection degree of the jet from the centerline of Orifice II is weakened when d_II decreases, as shown in Figure 4f–h. The reason is that the decrease of d_II accelerates the liquid steel flow in Orifice II and reduces the momentum of the jet so that it becomes easier to change jet flow behavior.

5.2. Tracer Behavior at Outlets

The variation of the tracer concentration with the time is extracted from the simulation results, and three dimensionless indicators were extracted to investigate the influence of the structure parameter on the flow behavior of the liquid steel. The three indicators are the minimum residence time and the mean residence time.

The minimum residence time is the shortest time for the liquid steel to flow from the inlet to the outlet, and a small value indicates a high probability of the short-circuit flow in the tundish. As shown in Figure 5a, among all the outlets, the one with the smallest value in each case is S2. This is because it is at the downstream location of the jet from Orifice III and the distance from it to all orifices is the shortest. In the original tundish, the minimum residence time of S2 is below 0.026, which suggests an extremely high probability of the existence of the short-circuit flow. By contrast, the short-circuit flow of the other cases is suppressed with the smallest value over 0.05. This indicates that any change in the inner structure in this study can prolong the residence time to promote the floatation of the inclusion.

Similar to the minimum residence time, a larger dimensionless mean residence time suggests a better performance of the tundish. However, the mean residence time is a mass-averaged residence time, which indicates a large mean residence time for one outlet is at the cost of the cleanness of another outlet. Since the shortest mean residence time indicates the poorest cleanness, the outlet with the smallest value is the weak point of the tundish. Therefore, an optimal tundish should have a balanced mean residence time to some degree and guarantee a relatively large value for its weak point. As shown in Figure 5b, the weak point of the original tundish is S3. The order of the mean residence time of S3 for the investigated cases is C1(0.72) > C4(0.71) > C6(0.70) > C3(0.69) > C5(0.66) > C2(0.54) > C0(0.39). Furthermore, the order of the largest mean residence time for all cases is C1(1.79) > C4(1.56) > C5(1.48) > C2(1.47) > C6(1.42) > C3(1.35) > C0(1.20). The orders above show that C1 is the optimal case either in the best-performed outlet or the poorest-performed outlet.

5.3. Dead Zone Ratio and Uniformity

The equation for calculating dead zone ratio has given in Section 4.3. The average of the standard deviations of the tracer concentration for the five outlets during the whole flow time was used to evaluate the uniformity, which is calculated as follows (Equation (12)):

$${\overline{S}}_N=\frac{1}{Z}{\displaystyle {\sum }_{j=1}^Z\sqrt{{{\displaystyle {\sum }_{i=1}^N\left[E_i\left({\theta }_j\right)-\overline{E}\left({\theta }_j\right)\right]}}^2/\left(N-1\right)}}$$

(12)

where, Z is the number of time step; N is the number of outlets; the subscript i indicates the outlet i; the subscript j indicates time step j; $\overline{E}\left({\theta }_j\right)=\frac{1}{N}{\displaystyle \sum _{i=1}^N{E}_i\left({\theta }_j\right)}$ is the mean dimensionless concentration at time step j.

The calculated dead zone ratio and flow uniformity of different cases are given in

Table 4. Dead zone ratio and uniformity of different cases.

Case No.	Dead Zone Ratio	Uniformity
C0	12.77%	0.2371
C1	2.26%	0.2689
C2	2.19%	0.2468
C3	5.26%	0.1952
C4	3.88%	0.2100
C5	3.77%	0.2238
C6	8.21%	0.2084

. The dead zone ratio of the cases from C1 to C6 was significantly reduced when compared with that of the original case. The minimum value is 2.19% from C2, but the uniformity of the case becomes deteriorated with a larger standard deviation than that of the original case. In contrast, the standard deviations of C3~C6 get decreased, and the best value is 0.1952 from C3.

6. Industrial Trials

6.1. Experiment Process

According to Table 4, the cases with a dead zone ratio below 5% are C1, C2, C4, and C5. Among the cases above, C4 has the smallest standard deviation, and therefore, it is selected for industrial trials. In addition, a small dead zone ratio is the primary consideration for the tundish operation. Therefore, although C1 and C2 have slightly larger standard deviations in uniformity, the dead zone ratios of the two cases are relatively small. C2 performs better than C1 in terms of the dead zone ratio and uniformity, but the mean residence time at the outlet of S3 did not significantly improve. Therefore, C1 is another case that was applied to the industrial trial. In the trial, two tundishes were used, as depicted in Figure 6, and the left one was the original, while the right one was C1 or C4. The two tundishes received liquid steel from the same ladle.

The liquid steel from different strands condensed to billet in the mold. To evaluate the performance of the new tundish, the content of the non-metallic inclusion in the billet was used as the evaluation indicator. Two 200 mm-long billets from the left and right tundish were sampled, as shown in Figure 7, and electrolysis was used to measure the content of the inclusion.

6.2. Trial Results

The baffle in the C1-based tundish cracked in the trial. The crack starts from Orifice II upward to the top of the baffle, as shown in Figure 8. The crack is caused by a sharp reduction in the distance between Orifice I and II when Orifice II gets enlarged and its elevation angle increases. Specifically, the distance between Orifice I and II decreases from 152 mm to 76 mm, which considerably reduces the strength of the baffle.

For the C4-based industrial trial, Orifice II also became enlarged, similar to C1, but no crack happened, as shown in Figure 9. This is because the orifice was moved down by 30 mm when enlarged, making the distance between Orifices I and II reach 157 mm, which guarantees the structural strength of the baffle.

The results of element analysis and electrolysis for the C4 trial are shown in

Table 5. Element content of strand sample of the industrial trial.

Sample	O (wt.%)	N (wt.%)	H% (wt.%)	O&N (wt.%)	Relative Variation
Original S4	0.00002146	0.00003782	0.00000168	0.00005928	-
Case 4 S5	0.00001996	0.00003402	0.00000188	0.00005398	8.94%

and

Table 6. Results of the electrolysis of the C4-based industrial trial.

Sample	Mass Fraction of Inclusions		Number Density of Inclusions
	Value (mg/10 kg)	Relative Variation	Value (/mm2)	Relative Variation
Original S4	2.99	-	17.83	-
C4-based S5	1.68	43.81%	14.10	20.93%

, respectively. When the C4-based tundish is applied, the total mass fraction of oxygen and nitrogen decreases by 8.94%. Furthermore, the mass fraction of the inclusions reduced from 2.99 mg/10 kg to 1.68 mg/10 kg, and the number density of the inclusion dropped from 17.83/mm² to 14.10/mm².

7. Conclusions

A water model experiment with a new tracer applied was carried out to validate the simulation model. The flow field characteristics of different tundish cases were obtained by simulation and compared. Two cases were selected and applied in the industrial trials. The main conclusions are drawn below:

• A recipe for a new tracer with a density close to that of water was proposed to reduce the buoyant effects of the tracer on the water flow behaviors. Based on the experimental data, a numerical simulation model was established and verified.
• The enlargement of Orifice II makes the vertex in the discharging chamber move upwards and the mean residence time at outlet S3 prolongs, which then promotes the floating of the inclusion in the tundish. Among all investigated cases, the C1 and C4 schemes provide a small dead volume ratio and great uniformity and were chosen for industrial trials.
• The crack of the baffle in the C1-based tundish industrial trial indicates that the structural strength of the baffle should be considered when the tundish structure changes.
• By enlarging the diameter of Orifice II to 200 mm and moving it down by 30 mm, the C4-based tundish industrial trial proved that it can reduce the mass fraction of inclusion by 43.81% and the number density of inclusion by 20.93%.