Removal of Inclusions using Swirling Flow in a Single-Strand Tundish

Abstract

Swirling flow tundish was developed to enhance the coalescence of inclusions, so as to deeply clean the liquid steel. Inclusions would gather to the center of the swirling flow by centripetal force, due to the density difference between inclusions and liquid steel. Thus, small inclusions can coalesce into larger ones, and then float to the free surface by their self-buoyance. Physical experiments were carried out in a 1/2.5 scale single strand tundish to study the flow characteristics of tundish with swirling chamber. Numerical modeling was developed to simulate the movements of small inclusions in swirling flow. Discrete phase model was employed together with the O’Rourke algorithm to characterize the coalescence of the inclusions in the swirling flow. The removal of inclusions was investigated, considering the absorption by upper slag and trapping by outside wall of ladle shroud. Compared with a turbulence inhibitor, a swirling chamber shows a similar effect on flow improvement, while performs better in inclusion removal, owing to the inclusion coalescence caused by centripetal force. The results revealed that swirling chamber in diameter of 450 mm is an optimized scheme for deep cleaning of liquid steel, with only 1.66% of the inclusions flowing out of the tundish nozzle.

1. Introduction

The removal of inclusions in liquid steel is a major concern of steel making, due to the increasing requirement of clean steel. Non-metallic inclusions have detrimental influence on mechanical properties of steel product, including tensile strength, impact strength and fracture toughness.^1,2,3) Tundish, as the last container before the solidification of the liquid steel, largely determines the amount of residual inclusions in final steel products. Besides, tundish is also an appropriate place for inclusion removal, owing to its long residence time and stable flow field.

The flow control devices can improve flow characteristics of the molten steel and forming an upward flow in the tundish, so as to promote the floatation of inclusions. Plenty of studies were carried out to analyze the inclusion removal by flow control devices, considering the effects of the inclusion size, inclusions density and the configuration of flow control device.^4,5,6) Fan et al.⁷⁾ investigated motion behaviors of inclusions in a one-strand tundish with four flow control devices. They reported that the tundish with pouring pad can enhance the opportunity for the inclusions to float by slowing down the flow of molten steel, achieving the highest removal rate of inclusions. Yazdi et al.⁸⁾ established a 1/2.5 scale tundish model to evaluate the effects of dams on the removal of inclusions, using four different water levels. According to their results, the tundish with tall dam and 22.5 cm water level exhibits an optimum inclusion separation performance, leading to a 29.4% drop of 595 μm output inclusions. However, the inclusions less than 50 μm are hard to reach the slag layer by Stokes floatation due to their weak self-buoyancy force, corresponding to a terminal floating velocity of 10⁻⁴−10⁻³ m/s.⁹⁾ Besides, these inclusions smaller than 50 μm flow firmly with the steel flow due to their small sizes, which has a Stokes number much smaller than 1.¹⁰⁾ In conclusion, the flow control devices have great advantages on the elimination of larger inclusions but seems to be difficult to promote the removal of small inclusions.

Inert Gas bubbling method was employed to promote the removal of small inclusions by bubble surface absorption and bubble wake capture. Chang et al.¹¹⁾ developed a full-scale four-strand tundish model to investigate the removal of inclusions using micro-bubble swarms produced by gas injection from a ladle shroud. They reported that the highest inclusions removal rate was up to 79.56%, when gas was injected through the four ports closed to the slide gate, at a gas flow rate of 0.2 L/min. However, the floating bubbles would impact the slag-metal interface, potentially leading to some molten steel being exposed to the atmosphere. Therefore, the slag entrapment and heat loss of liquid steel caused by gas bubbling cannot be neglected. Multi-hole ceramic filter, made by microporous refractory, can distort the flow streamlines when liquid steel travels through the filter holes, resulting in the separation of inclusions from the liquid steel. Wang et al.¹²⁾ developed a numerical model to study the effects of ceramic filter on the flow pattern and elimination of inclusions in a full-scale two-strand tundish, with the slenderness ratio of ceramic filter ranges from 3 to 5. Their results showed that the 5 slenderness ratio is the optimum scheme, which can remove 72% of inclusions in 1 μm. Nevertheless, these holes of filter are easily clogged by trapped inclusions, so that the filter would play as a dam. This potentially worsens the flow characteristics.

Swirling flow is widely used in chemical engineering to concentrate particles with lower density by centrifugal force. A centrifugal flow tundish (CFT), as a contactless methodology, was proposed to produce swirling flow by outside rotating magnetic field. Owing to the difference of densities between inclusions and liquid steel, inclusions could gather to the center of the swirling flow that enhances the coalescence of inclusion. As such, these newborn large inclusions can float up by their self-buoyancy, so as to be absorbed by the top slag. Miki et al.¹³⁾ carried out extensive plant trials to investigate the promoting effects of CFT on the separation of inclusions. According to their results, the centripetal force and large turbulence energy caused by swirling flow in CFT can accelerate inclusion separation. However, CFT dramatically change the configuration of the tundish that would potentially influence the tundish flow characteristics. Besides, the rotating magnetic brings the huge energy cost. In view of these problems, the swirling flow tundish (SFT) was developed to generate swirling flow by the gravitational potential energy of entry liquid steel. After departing from the heterotype ladle shroud, the entry liquid steel would rotate along the cylindrical wall of the swirling chamber. Furthermore, the swirling chamber can effectively dissipate the turbulence kinetic energy of the entry flow, which also achieves the functions of the turbulence inhibitor. Hou et al.¹⁴⁾ investigated the movements of inclusions in a 1/2.5 scale SFT, using discrete phase method approach. Their results showed that the SFT can promote the floatation of inclusions, with an 89.85% separation ratio for 20 μm inclusions.

In the present paper, water model experiments were performed in a 1/2.5 single strand tundish to rotate liquid steel using a novel swirling chamber. Corresponding numerical modeling was developed to investigate the motion behaviors of small inclusions in the swirling flow. Reynolds Stress Model (RSM) coupled with a Stress-Omega sub model was employed to simulate the swirling flow field in the tundish, considering possible anisotropic fluctuations. The trajectories of inclusions were calculated in a Euler-Lagrange framework. The coalescence of inclusions was simulated using O’Rourke algorithm. The inclusions being absorbed by free surface, trapped by central shroud wall and flowing out of the nozzles were collected by post-processing, in order to evaluate the promotion of inclusion removal by swirling flow. Furthermore, the influence of swirling chamber diameter on the inclusion removal was taken into consideration as well.

2. Physical Model

A 1/2.5 scaled water model (as shown in Fig. 1) was established on the basis of a 40 t single strand tundish. Flow characteristics in the swirling flow tundish were investigated, and compared with that in the tundish using a conventional turbulence inhibitor. The model configurations with key dimensions in this study are shown in Fig. 2. The Reynolds numbers of prototype and model tundish are both in the same self-modeling domain, above 8000. Therefore, the criterion of dynamic similarity is independent of the Reynolds number in the present study. Only the Froude number, Fr, needs to be kept equal in two systems, in order to guarantee the dynamic similarity between model and prototype.¹⁵⁾   

$$F{r}_{\mathrm{m}}=\frac{u_{\mathrm{m}}^2}{g{L}_{\mathrm{m}}}=\frac{u_{\mathrm{p}}^2}{g{L}_{\mathrm{p}}}=F{r}_{\mathrm{p}}$$(1)

where, L expresses the characteristic length (m), the subscript m and p denote the model and prototype, respectively. According to the Froude Criterion, the volume flow rate in model tundish, Q_fm, can be calculated as follow:   

$$Q_{\mathrm{f}\mathrm{m}}={\left(\frac{L_{\mathrm{m}}}{L_{\mathrm{p}}}\right)}^{\frac{5}{2}}\cdot Q_{\mathrm{f}\mathrm{p}}$$(2)

Fig. 1.

The water model of swirling flow tundish. (Online version in color.)

Fig. 2.

The configurations with key dimensions of the: (a) tundish, (b) turbulence inhibitor, (c) swirling system (mm).

At the beginning of the water model experiment, a stable 390 mm water level was maintained by adjusting digital gate valves. The “pulse-response”¹⁶⁾ method was employed to obtain the residence time distribution (RTD) curves with different flow controllers. According to the influence of tracer amount on RTD measurement,¹⁷⁾ 70 mL saturated NaCl solution was employed in the present work. Once the flow field reaching steady, the tracer was injected into ladle shroud, meanwhile the tracer concentration was measured using conductivity probe located at tundish outlet. Detailed parameters of prototype and water model are listed in Table 1.

Table 1. Operation parameters in the prototype and model tundish.

Parameter	Prototype tundish	Water model
Fluid	Molten Steel	Water
Density [kg/m3]	7038	998.2
Viscosity [Pa·s]	0.0064	0.0009
Flow rate [L/min]	401	40
Depth of liquid [mm]	976	390
Diameter of shroud [mm]	62.5	25
Temperature [K]	1823	298

3. Mathematical Model

In order to investigate the effect of swirling flow on the removal of small inclusions in liquid steel, a full-scale numerical model was developed by ANSYS 18.1 package. The computational domain was discretized into 850000 hexahedral grids, on the basis of mesh independence test. The continuous phase was assumed to be an incompressible liquid and has Newtonian behavior. The entry liquid steel came into the ladle shroud through a velocity inlet with an initial velocity of 2.18 m/s. The outlets were set as pressure-outlet with a zero gauge pressure. Non-slip wall condition was used for all the solid walls in the tundish. The top surface of liquid steel was regarded as free surface by assigning a zero shear stress. An isothermal condition of liquid steel was assumed in tundish operations, with a temperature of 1823 K.

3.1. Governing Equations

Based on the above assumptions, a series of governing equations were solved simultaneously in the Cartesian coordinate system to predict the tundish flow behaviors. The continuous equation and the momentum conservation of the continuous phase can be described as:   

$$\frac{\partial \rho }{\partial t}+\frac{\partial (\rho u_i)}{\partial x_i}=0$$(3)

  

$$\begin{array}{l}\frac{\partial (\rho u_i)}{\partial t}+\frac{\partial (\rho u_j{u}_i)}{\partial x_j}=\\ -\frac{\partial P}{\partial x_i}+\frac{\partial }{\partial x_j}\left[\mu \left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)\right]-\frac{\partial (\rho \overline{u_i^{\prime }{u}_j^{\prime }})}{\partial x_j}+\rho g_i+F\end{array}$$(4)

where, $\rho \overline{u_i^{\prime }{u}_j^{\prime }}$ represents the Reynolds stresses, (kg/m·s²), F represents the momentum exchange, caused by the interaction between the continuous phase and discrete phase, (kg/m²·s²).   

$$F=\sum \left[-\frac{3\mu C_{D}Re}{4{\rho }_{\mathrm{p}}{d}_{\mathrm{p}}^2}(u-u_{\mathrm{p}})+F_{\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}\right]\mathrm{\hspace{0.17em} }{\dot{m}}_{\mathrm{p}}\mathrm{\Delta }t$$(5)

where, ${\dot{m}}_{\mathrm{p}}$ represents the mass flow rate of inclusions through each control volume, (kg/m³·s), Δt is the time step of calculation for the discrete phase, which was set to 0.01 s in this study. The first term in the bracket is the drag force of inclusions, F_other is the other force caused by the inclusion movements, including pressure gradient force and virtual mass force.

In order to close the Eq. (4), the Reynolds stresses term need to be modeled for considering the effects of turbulence. As an elaborate turbulence model, RSM accounts the effects of streamline curvature, swirl, rotation, and rapid changes in strain rate, which is suitable to accurately predict swirling flows in this study.¹⁸⁾ The transport equations for Reynolds stresses can be written by:   

$$\begin{array}{l}\frac{\partial }{\partial t}(\rho \overline{u_i^{\prime }{u}_j^{\prime }})+\underset{C_{ij}}{\frac{\partial }{\partial x_k}(\rho u_k\overline{u_i^{\prime }{u}_j^{\prime }})}=\\ -\frac{\partial }{\partial x_k}\underset{D_{T,ij}}{\left[\rho \overline{u_i^{\prime }{u}_j^{\prime }{u}_k^{\prime }}+\overline{p^{\prime }({\delta }_{kj}{u}_i^{\prime }+{\delta }_{ik}{u}_j^{\prime })}\right]}\underset{P_{ij}}{-\rho \left(\overline{u_i^{\prime }{u}_k^{\prime }}\frac{\partial u_j}{\partial x_k}+\overline{u_j^{\prime }{u}_k^{\prime }}\frac{\partial u_j}{\partial x_k}\right)}\\ +\underset{{\phi }_{ij}}{\overline{p^{\prime }\left(\frac{\partial u_i^{\prime }}{\partial x_j}+\frac{\partial u_j^{\prime }}{\partial x_i}\right)}}-\underset{{\epsilon }_{ij}}{2\mu \overline{\frac{\partial u_i^{\prime }}{\partial x_k}\frac{\partial u_j^{\prime }}{\partial x_k}}}+\underset{{\phi }_{ij}}{\overline{p^{\prime }\left(\frac{\partial u_i^{\prime }}{\partial x_j}+\frac{\partial u_j^{\prime }}{\partial x_i}\right)}}\end{array}$$(6)

The pressure strain term (P_ij), turbulent diffusion term (D_T,ij) and viscosity dissipation term (ε_ij) need to be modeled to close the equation. In this study, Stress-Omega sub-model was used to simulate the pressure strain term.¹⁹⁾ The turbulent diffusion term was evaluated using the gradient diffusion model.²⁰⁾ The viscosity term was predicted using the Wilcox model.²¹⁾

To calculate the RTD curves, a passive scalar equation was used to simulate the movement of the tracer during the numerical simulation.²²⁾   

$$\frac{\partial }{\partial t}(\rho c)+\frac{\partial }{\partial x_i}(\rho u_{i}c)=\frac{\partial }{\partial x_i}\left(\rho D_{\mathrm{e}\mathrm{f}\mathrm{f}}\frac{\partial c}{\partial x_i}\right)$$(7)

where, c is the mass concentration of the tracer, (kg/m³), and the property of tracer is the same as the fluid during the calculation, D_eff is the effective diffusion coefficient, (m²/s), which is the sum of molecular diffusion coefficient and turbulent diffusion coefficient.

3.2. Inclusion Tracking Model

The trajectories of non-metallic inclusions were tracked in the flow field by Euler-Lagrange approach. Inclusions were assumed to be escaped once they reach the outlet of the tundish. Inclusions adhered to the outside surface of ladle shroud was considered by assigning a trapped boundary. The inclusion (alumina) density was assigned as 3500 kg/m³. Inclusions were injected from top surface of the ladle shroud at a flow rate of 9900/s, considering the time step of inclusion release and grids of the inlet. For the exact location of inclusions, it can be obtained by solving the following equation:   

$$\frac{d{u}_{\mathrm{p}}}{dt}=\frac{g({\rho }_{\mathrm{p}}-\rho )}{{\rho }_{\mathrm{p}}}+F_{\mathrm{D}}+F_{\mathrm{v}\mathrm{m}}+F_{\mathrm{p}}$$(8)

  

$$F_{\mathrm{D}}=\frac{3\mu C_{D}Re}{4{\rho }_{\mathrm{p}}{d}_{\mathrm{p}}^2}(u-u_{\mathrm{p}})$$(9)

  

$$F_{\mathrm{v}\mathrm{m}}=\frac{1}{2}\frac{\rho }{{\rho }_{\mathrm{p}}}\frac{d}{dt}(u-u_{\mathrm{p}})$$(10)

  

$$F_{\mathrm{P}}=\left(\frac{\rho }{{\rho }_{\mathrm{p}}}\right)u_{\mathrm{p}}\frac{\partial u}{\partial x}$$(11)

where F_D is the drag force per unit inclusions mass, (N).²³⁾ F_vm is the virtual mass force per unit mass, (N), which is considered due to the large density of liquid steel. F_P is the pressure gradient force per unit mass, (N). Besides, the influence of other hydrodynamic forces is neglected for that they are much smaller than the drag force. The drag coefficient (C_D) can be calculated based on spherical drag law, which can be given as follow:   

$$C_{\mathrm{D}}=n_1+\frac{n_2}{Re}+n_3$$(12)

where, n₁, n₂ and n₃ are the model constants recommended by Morsi and Alexander.²⁴⁾ In order to consider the effects of turbulent fluctuations in the swirling flow field, a stochastic model was applied, with a default 0.15 time scale constant.²⁵⁾

3.3. Collision and Coalescence Model

The algorithm of O’Rourke²⁶⁾ was used to model the collision and coalescence phenomenon of the inclusions, being assumed as spherical particles. A collision volume is employed to calculate the probability of collision in this algorithm, assuming that the probability distribution of the collisions number is Poisson distributed. Two inclusions are considered to coalesce if they collide head-on, or to bounce if the collision is more oblique.²⁷⁾ The probability of coalescence depends on the offset of the collector particle center and the trajectory of the smaller particle. According to O’Rourke algorithm, the critical offset can be described as a function of the Weber number and the relative radius of the two particles:   

$$b_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}=(r_1+r_2)\sqrt{min\left(1.0,\frac{2.4f}{We}\right)}$$(13)

where, r₁ and r₂ are the relative radii of collector and smaller particle, (m), respectively, f is a function of r₁/r₂, can be expressed as:   

$$f\left(\frac{r_1}{r_2}\right)={\left(\frac{r_1}{r_2}\right)}^3-2.4{\left(\frac{r_1}{r_2}\right)}^2+2.7\left(\frac{r_1}{r_2}\right)$$(14)

The actual collision parameter, b, can be calculated as:   

$$b=(r_1+r_2)\sqrt{Y}$$(15)

where, Y is a random number locates 0 or 1. The collision result depends on the comparison between b and b_crit. If b < b_cirt, the two particles would be coalesced (the smaller particle would coalesce with the bigger one). If b ≥ b_cirt, the collision is treated as a grazing collision that parts of the kinetic energy of the inclusions is lost to viscous dissipation and angular momentum generation. The mass and the momentum of the coalesced particles follow the conservation laws.

3.4. Solution Procedure

The Pressure-Implicit with Splitting of Operators (PISO) algorithm was applied to couple of pressure and velocity during solving process.²⁸⁾ In order to guarantee the computation precision, the value of the under-relaxation factors was remained as defaults, with 0.3 and 0.7 for the pressure and momentum terms, respectively. The standard wall function was employed to describe the flow characteristics in the boundary layer. For each time step (0.001 s), the computation was judged to be convergent when the residuals of all variables were less than 10⁻⁴. The scalar transport equation was solved after the fluid flow reached stable condition. The computational RTD curves were obtained by post-processing the mass fractions of tracer measured at outlets. Inclusions in 50 μm were continuously released from the inlet face following with the entry flow. Inclusions were regarded as escaping once reaching the free surface and the outlet, and were deemed as being trapped when they attach to the ladle shroud. The inclusion detection started after the distribution of inclusions in tundish bath became stable, lasting for 15 s, in order to evaluate the effects of the swirling chamber and turbulence inhibitor.

4. Results and Discussion

4.1. The Effects of Swirling Chamber on the Flow Pattern

In this study, water experiments were carried out to study the flow characteristics in the tundish with swirling chambers in diameter ranged from 180 mm to 280 mm, compared with those in the tundish using a conventional turbulence inhibitor. Figure 3 shows the RTD curves obtained from the water modeling. It is notable that the tundishes with swirling chambers and turbulence inhibitor have similar response times. However, the peak concentration of RTD curves obtained from the conventional tundish is higher and occurs earlier than that of SFT, indicating a smaller volume fraction of plug flow. Besides, the RTD curves obtained with swirling chambers are similar, that means the diameter of swirling chamber has a little influence on the flow characteristics.

Fig. 3.

Comparison between experimental RTD curves in the tundishes with swirling chambers and turbulence inhibitor. (Online version in color.)

RTD curves were analyzed by combined model,²⁹⁾ in order to calculate the volume fractions of dead region, plug flow and well-mixed flow. The volume fraction of dead region can be given by:   

$$\frac{V_{\mathrm{d}}}{V}=1-\frac{Q}{Q_{\mathrm{a}}}\cdot \frac{\sum _{\theta =0}^{2}E(\theta )\cdot \theta }{\sum _{\theta =0}^{2}E(\theta )}$$(16)

where, Q_a is the flow rate passing through active zone, (L/min). The volume fraction of plug flow can be given as:   

$$\frac{V_{\mathrm{p}}}{V}=\frac{1}{2}({\theta }_{min}+{\theta }_{max})$$(17)

where, θ_min is the dimensionless time when the tracer concentration first appears, (−), θ_max is the dimensionless time when the maximum tracer concentration appears, (−). The volume fraction of mixing flow can be calculated as follow:   

$$\frac{V_{\mathrm{m}}}{V}=1-\frac{V_{\mathrm{d}}}{V}-\frac{V_{\mathrm{p}}}{V}$$(18)

Table 2 lists the experimental RTD curves of tundish with different flow controllers. The volume fraction of plug flow in the tundish with turbulence inhibitor is 23.92%, which is 34.59% smaller than that in the tundish with swirling chamber in diameter of 280 mm. The plug flow volume fraction of SFT reduces from 36.57% to 28.41% when the diameter of chamber decreases from 280 mm to 180 mm. Compared with turbulence inhibitor, swirling chamber has an advantage in flow control.

Table 2. Flow characteristics of the tundish with turbulence inhibitor and swirling chambers with different diameter.

Case	Vp/V [%]	Vd/V [%]	Vm/V [%]
Turbulence Inhibitor	23.92	23.10	52.98
180 mm Swirling Chamber	28.41	22.72	48.87
230 mm Swirling Chamber	34.46	20.02	45.52
280 mm Swirling Chamber	36.57	19.01	44.42

The mixing flow volume fraction decreases from 52.98% to 44.42%, when replaced the turbulence inhibitor by a swirling chamber in diameter of 280 mm. Correspondingly, the dead region in the SFT is 17.71% smaller than that in the tundish with turbulence inhibitor. These results revealed that the swirling chamber can improve the flow characteristics of tundish, which is beneficial for the flotation of inclusions. This is due to that the kinetic energy dissipation in the pouring region of SFT is promoted by swirling flow, stabilizing the flow field out of the pouring region.

In order to further investigate the tundish flow patterns, numerical model was developed on the basis of the prototype with a 450 mm swirling chamber, corresponding to 180 mm in the water model. The RTD curves in the tundish with 450 mm diameter swirling chamber and turbulence inhibitor were calculated by the scalar equation, as shown in Fig. 4. It can be seen that the RTD curves predicted by the numerical simulation are in good agreements with those obtained from water modeling, validating the result of the numerical simulation.

Fig. 4.

Comparison between experimental and computational RTD curves in the tundish: (a) with a square inhibitor, (b) with the swirling chamber in diameter of 180 mm. (Online version in color.)

Figure 5(a) shows the streamlines of molten steel in the tundish with a square turbulence inhibitor. The entry flow at an initial velocity of 2.18 m/s is mixed intensively in the turbulence inhibitor, leading to the dissipation of turbulence kinetic energy and significant decrease of the flow velocity. As a result, the molten steel reverses vertically at a velocity of 0.28 m/s.

Fig. 5.

The streamlines in the tundish: (a) with a turbulence inhibitor, (b) with a swirling chamber in diameter of 450 mm. (Online version in color.)

As shown in Fig. 5(b), it is obvious that a large vortex was formed in the swirling chamber. After that, the liquid steel flows out of the swirling chamber along with the tangential direction of swirling flow, at a residual velocity of 0.61 m/s. The contours of dissipation rate of kinetic energy in two tundishes are shown in the Fig. 6. In SFT, the fluid keeps a high tangential velocity after moving out of the swirling chamber, leading to a strong mixed flow not only in the swirling chamber but also at the upper part of the pouring region. In the tundish with turbulence inhibitor, the dissipation of turbulent kinetic energy only concentrates within the turbulence inhibitor, and no significant dissipation of turbulent kinetic energy is appeared at the upper part of the pouring region. For the two typical planes in Fig. 6, it is obvious that SFT has a global higher kinetic energy dissipation rate in the pouring region, compared with the tundish with turbulence inhibitor. The swirling chamber is beneficial to stabilize the fluid flow out of the pouring region. This is consistent with the analysis of RTD curves. Besides, the inclusions with smaller density would gather to the center of swirling flow by the centripetal force that makes small inclusions coalesce into a larger one. As such, small inclusions have more chances to float up and be absorbed by slag layer.

Fig. 6.

The distribution of turbulence dissipation rate in the tundish with a: (a) turbulence inhibitor at y = 0.2 m, (b) turbulence inhibitor at y = 0.8 m, (c) swirling chamber at y = 0.2 m, (d) swirling chamber at y = 0.8 m. (Online version in color.)

Theoretically, the vertical velocity of a surface should be as zero, otherwise, this surface would keep moving upward or downward. Indeed, the formation of slag eye is closely related to the vertical impact by the molten steel, which can be characterized by the potential upward liquid flow below the surface. According to the works of Krishnapisharody et al.³⁰⁾ and Thunman et al.,³¹⁾ the critical vertical velocity of liquid for the formation of slag eye is around 0.05 m/s, being measured at the plane below the free surface. Figure 7 shows the contours of vertical velocity components at the plane 20 mm below the free surface. In the tundish with a turbulence inhibitor, most of the reversed molten steel would impact the top surface with a high vertical velocity, which potentially leads to the formation of slag eye. The area with vertical flow velocity above 0.05 m/s accounts for 7.77% of the entire surface area in the tundish with the conventional turbulence inhibitor. In the SFT, momentum of molten steel flowing out of the swirling chamber is mainly in tangential direction, reducing the normal impact of reversed flow on the slag layer. Only 1.63% of the plane area is with a vertical velocity higher than 0.05 m/s. Therefore, swirling chamber has an advantage over turbulence inhibitor in maintaining a stable tundish slag layer.

Fig. 7.

The vertical velocity component at the plane 20 mm below the free surface in the tundish: (a) with a turbulence inhibitor, (b) with a swirling chamber in diameter of 450 mm. (Online version in color.)

4.2. The Concentration of Inclusions in the Swirling Chamber

Numerical simulations were developed to study the motion behaviors of inclusions in the SFT and the tundish with turbulence inhibitor, respectively. Figure 8 shows the process of 50 μm inclusions movements under the effects of swirling flow.

Fig. 8.

The concentration of inclusions in the swirling chamber. (Online version in color.)

It can be seen that the inclusions gather to the center of chamber, driven by the centripetal force, which leads to the increase in the local number density of inclusions. A higher inclusion number density is beneficial to the coalescence of small inclusions. According to the multiple size group model (MUSIG),³²⁾ the relationship between the birth rate of inclusions by coalescence and the number densities of inclusions can be given as:   

$$B_{\mathrm{C}}=\frac{1}{2}\sum _{j=1}^n\sum _{k=1}^n{\chi }_{ij}{n}_i{n}_j$$(19)

where, n_i and n_j represent the number of inclusions in unit volume, (−), χ_ij expresses the coalescence rate between two inclusion groups, (m³/s). The model predication indicates that a 50% rise of inclusion number density would result in a 125% increase of inclusion coalescence efficiency. In this study, the characteristic number density (−/m³) of inclusions inside the flow controller can be calculated by the following equation:   

$$n_{\mathrm{C}}=\frac{N}{V_{\mathrm{F}}}$$(20)

Where, V_F is the characteristic volume of the flow controller, (m³). As such, the characteristic number density of inclusions in the tundish with the turbulence inhibitor could be calculated as being 7.29 × 10⁵ m⁻³. When the turbulence inhibitor was replaced by the swirling chamber, this characteristic inclusion number density changes to 1.39 × 10⁶ m⁻³ a cylindrical region in 1/2 diameter of the swirling chamber, increased by 90.67%. This dramatically promotes the probability of inclusion coalescence, according to the MUSIG. Therefore, usage of swirling chamber can enhance the coalescence of inclusions in the tundish through rising the local number density of inclusions, which promotes the removal of inclusions.

4.3. The Removal of Inclusions

In order to investigate the effect of SFT on inclusion removal, numerical simulations were developed in the tundish with a 450 mm diameter swirling chamber and the conventional tundish using a turbulence inhibitor, considering the coalescence of inclusions. Figure 9 shows the amount of inclusions removed in the SFT and the tundish with turbulence inhibitor. It can be noted that inclusions are mainly removed at the free surface, in both the SFT and the tundish with turbulence inhibitor. When the turbulence inhibitor was replaced by swirling chamber, small inclusions would coalesce into larger ones in the swirling flow by centripetal force. These newborn large inclusions have more chances to reach the top surface, owing to their sufficient buoyancy force. Therefore, the number of inclusions removed on the free surface is increased by 6.55%. In addition, inclusions adhered on the ladle can also be removed during the change of ladle shroud. The number of the inclusions adhered to the shroud wall in the SFT is 115.88% larger than that in the tundish using turbulence inhibitor. This is owing to the centripetal movement of inclusions and the larger submerged surface of the ladle shroud in SFT. Table 3 lists the size distribution of inclusions removed in different cases. It can be noted that the number of inclusions above 80 μm removed in the tundish with a turbulence inhibitor is 1303, which is 67.05% less than that in the SFT. The swirling flow increases the local number density of inclusions, which enhances the inclusion coalescence.

Fig. 9.

The number of inclusions trapped by surface and central shroud wall in tundishes with the turbulence inhibitor and the 450 mm swirling chamber. (Online version in color.)

Table 3. The diameter distribution of inclusions trapped at different places in tundish.

Diameter (μm)	Turbulence Inhibitor		Swirling Chamber (450 mm)
	Surface	Shroud Wall	Surface	Shroud Wall
d = 50	57777	3006	59064	4888
50 < d < = 70	13319	236	13187	1236
70 < d < = 80	5717	83	7348	747
80 < d < = 90	649	7	1316	138
90 < d < = 100	507	3	1581	149
100 < d	135	2	725	46
Average Diameter	54.66	51.67	56.17	56.74

The casting mold has a significant downward flow combined with strong boundary solidification, which is goes against to the removal of inclusions. Therefore, inclusion flowing out of the tundish determines the cleanness of the final casting slab, to a large extent. The size distribution of inclusions that escaped from tundish outlet in different tundishes is shown in Fig. 10. In the tundish with a turbulence inhibitor, there are 27416 inclusions escaped from the outlet. By contrast, only 1524 inclusions escaped from the outlet in the SFT, which is much less than that in the conventional tundish. The swirling chamber can effectively remove inclusions through improving flow characteristics and promoting inclusion coalescence. As shown in Fig. 11, there are some notable flow patterns in the right part of the tundish with a turbulence inhibitor, due to insufficient turbulent dissipation. This leads to some inclusions flowing out of the outlet directly. In the SFT, inclusions can pass through the weir smoothly, as kinetic energy of entry flow has been well consumed by swirling chamber, which is beneficial for inclusion flotation.

Fig. 10.

The size distribution of the inclusions escaped from the outlet in different tundishes. (Online version in color.)

Fig. 11.

The distribution of inclusions in the tundish with: (a) turbulence inhibitor, (b) swirling chamber. (Online version in color.)

The global coalesced rate of inclusions in the tundish was obtained by the following equation:   

$$R_{\mathrm{c}}=\frac{m_{\mathrm{c}}}{m_{\mathrm{c}}+m_{\mathrm{n}}}$$(21)

where, m_c represents the total mass of the inclusions larger than 50 μm, (kg); m_n denotes the total mass of those inclusions with an initial diameter of 50 μm, (kg). The inclusions in the SFT have a global coalesced rate of 56.45%, which is 27.08% larger than that in the tundish with turbulence inhibitor (with a global coalesced rate of 44.42%). Basically, small inclusions have a greater chance to coalesce in the SFT, which can result in the decrease of escaped inclusions. Although the SFT has a larger average inclusion diameter by promoting the coalescence of inclusions, owing to its higher removal rate, the number of large escaped inclusions in the SFT is less than that in the conventional tundish. The total number of escaped inclusions above 80 μm in the SFT with a 450 mm diameter swirling chamber is 18, which is 87.14% less than that in the traditional tundish (with 140 escaped inclusions above 80 μm). In conclusion, the use of SFT can not only promote the coalescence of inclusions but also inhibit the escape of big inclusions from the tundish outlet, which is beneficial to the cleanliness of the molten steel.

4.4. The Effects of Swirling Chamber Diameter on the Inclusion Removal

The effect of the swirling chamber diameter on the removal of inclusions was also considered by numerical simulations. Figure 12 shows the amount of inclusions measured at free surface in the tundishes with swirling chamber in diameter of 700, 575 and 450 mm. The inclusion detection in the conventional tundish using turbulence inhibitor was also included, as comparison.

Fig. 12.

The number of removed inclusions from free surface in tundishes with swirling chambers and the turbulence inhibitor. (Online version in color.)

The quantities of inclusions removed from the free surface in the swirling flow tundishes were all greater than that in the tundish with turbulence inhibitor. The swirling chamber in diameter of 700 mm performs better in the removal of inclusions by surface absorption. In order to evaluate the effect of the swirling chamber diameter on the swirling strength, a dimensionless swirling number was introduced to describe the swirling strength of the swirling flow, which can be given as:³³⁾   

$$Sw=\frac{G_{\theta }}{R{G}_{\mathrm{z}}}=\frac{{\int }_0^R\rho u_{\mathrm{z}}{u}_{\theta }{r}^{2}dr}{R{\int }_0^R\rho u_{\mathrm{z}}^{2}rdr}$$(22)

where, u_Z and u_θ are the axial velocity and tangential velocity of fluid, respectively. Equation (22) can be simplified to the following expression:   

$$Sw=\frac{{\overline{u}}_{\theta }}{{\overline{u}}_{\mathrm{Z}}}$$(23)

A greater swirling strength can promote the centripetal movement of inclusions in the swirling chamber. The characteristic swirling number of the swirling chamber is obtained by calculating the arithmetic mean of the swirling number on the selected horizontal planes in the swirling chamber. Three horizontal planes at the height of 200 mm, 400 mm and 600 mm were chosen to calculate the characteristic swirling number of the swirling chamber. The characteristic swirling number of the swirling chamber with 450 mm, 575 mm, and 700 mm diameter is 11.51, 13.21 and 14.68, respectively. Increasing the volume of swirling chamber can intensify the swirling strength that effectively dissipates the turbulence kinetic energy of the entry flow, so as to stabilize the liquid flow out of the swirling chamber. As such, the inclusions have more chances to float up to the top surface, which is consistent with the previous RTD analysis.

The adherence of inclusions on the outside wall of ladle shroud is another approach for inclusion removal. Figure 13 represents the quantities of inclusions collected at different places in the tundishes with swirling chambers and the turbulence inhibitor, respectively. Owing to the gathering effect of the swirling flow, the removal of inclusions by ladle shroud wall adherence in SFT is better than that in the tundish with turbulence inhibitor. Reducing the size of swirling chamber can shorten the distance of centripetal movements of inclusions, so that inclusions are more easily to reach the ladle shroud. In a tundish with a 450 mm swirling chamber, the number of inclusions adhered on the outside wall of the ladle shroud is up to 7204. By contrast, only 3335 inclusions adhered on the shroud wall in the tundish with 700 mm swirling chamber, reduced by 53.71%.

Fig. 13.

The quantities of inclusions collected at different places in the tundishes with swirling chambers and the turbulence inhibitor. (Online version in color.)

The global inclusion residual rate in the SFT was 1.66%, 1.67% and 2.08% for the 450 mm, 575 mm and 700 mm diameter swirling chamber, respectively. By contrast, 25.19% of inclusions would remain in final casting slab in the tundish with a turbulence inhibitor. Figure 14 shows the mass fractions of inclusions collected at different places in the tundishes with turbulence inhibitor and swirling chambers, respectively. It can be also noted that the the SFT also performs better than the tundish with turbulence inhibitor when comparing the mass of inclusions, which is similar to the trend obtained by comparing the number of inclusions. Only 1.37% of inclusion in weight can reach the nozzle of the tundish with 450 mm swirling chamber. In conclusion, the SFT performs much better than the tundish with the turbulence inhibitor in the removal of inclusions. In the present study, the 450 mm swirling chamber shows the highest inclusion removal rate, which is beneficial for deep cleaning the liquid steel.

Fig. 14.

The mass fractions of inclusions collected at different places in tundishes with swirling chambers and the turbulence inhibitor. (Online version in color.)

5. Conclusion

Water experiments were carried out to investigate the effects of the swirling chamber on flow field in a 1/2.5 scale single-strand tundish. The removal of inclusions by surface absorption and adherence on the ladle shroud wall in the SFT was predicted by numerical simulations, considering the coalescence of inclusions. As a comparison, numerical model was also carried out in a conventional tundish using a turbulence inhibitor. The major conclusions of this study are drawn as follows:

(1) The swirling flow in the SFT can improve the fluid characteristics of tundish. The dead volume fraction in the SFT with a 280 mm diameter swirling chamber is 17.71% smaller than that in the tundish with a turbulence inhibitor.

(2) Inclusions can gather to the center of the swirling chamber driven by centripetal force, which enhances the coalescence of inclusion. Under the effects of swirling flow, the global coalesced rate of inclusions in the SFT with a 450 mm swirling chamber is up to 56.45%.

(3) Increasing the diameter of swirling chamber can intensify the swirling strength and dissipate the turbulence kinetic energy of entry flow that promotes the removal of inclusion by surface absorption. However, a larger swirling chamber lengthens the distance of centripetal movements of inclusions, which goes against to the adherence of inclusions on the outside wall of the ladle shroud.

(4) The SFT with a 450 mm swirling chamber is an optimum scheme for deep cleaning of the molten steel, with only 1.66% of inclusions flowing out of the tundish nozzle.

Acknowledgements

The present work was financially supported by the National Natural Science Foundation of China (51904061), Fundamental Research Fund for the Central Universities (N182503029) and China Postdoctoral Science Foundation (2018M631702).

Nomenclature

L_m, L_f: characteristic length of model tundish and prototype tundish respectively, m

g: acceleration of gravity, m/s²

Q_f: volume flow rate, L/min

u, u_p: velocity of the fluid and inclusions respectively, m/s

ρ_l, ρ_p: density of liquid and inclusion respectively, kg/m³

d_p: diameter of the inclusions, m

μ: dynamic viscosity and turbulent viscosity, Pa·s

P: pressure, Pa

b: offset of the collector particle and the smaller particle, m

θ: dimensionless residence time, −

V: volume, m³

n_i: number density of the i_th particles, −/m³

B_c: birth rate of inclusions by coalescence, −/s

N: number of the particles in the flow controllers, −

G_θ: axial flux of angular momentum, kg·m²/s²

G_z: axial flux of axial momentum, kg·m/s²

R: diameter of the swirling chamber, m

r: distance between fluid and the rotating center, m

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