Application of a Swirling Flow Producer in a Conventional Tundish during Continuous Casting of Steel

Abstract

A swirling flow producer was designed for a conventional tundish in order to produce a swirling flow in the SEN driven by the steel flow potential. CFD simulations were carried out to investigate the flow phenomena in the new tundish system. The results show that a swirling flow in the tundish SEN was successfully obtained. The swirl number of the obtained steel flow inside the SEN can reach a value of 1.34, with a tangential velocity of around 2.8 m/s. The possibility of slag entrainment at the top of the tundish was estimated by analyzing the steel flow characteristics near the top surface. The calculated Weber Number is around 0.3 outside the cylinder, which indicates a low possibility of slag entrainment. A high value of shear stress was found on the SEN wall. This is due to the rotational steel flow in SEN. Also, non-metallic inclusions were tracked in the fully developed steel flow field. It was found that the number of inclusions that touch the top surface increases with an increased inclusion size. Small size inclusions mainly move into the cylinder from the left side of tangential inlet. Therefore, methods like installing a dam at the tundish bottom may be helpful to change the inclusion trajectories to move towards the top of the tundish.

1. Introduction

During continuous casting, steel flow characteristics are very important both for the quality of steel products and for the productivity. This is due to the fact that some important issues during continuous casting, e.g. slag entrainment, refractory erosion, inclusion removal and nozzle clogging, are closely related to the steel flow phenomena. Furthermore, the steel flow pattern is also very important for the steel solidification in the casting mold. This, in turn, affects the steel product quality.

In recent years, the use of swirling flows in steel castings has received a lot of interest. M-EMS (Mold-ElectroMagnetic Stirring) is one of the ways to realize a swirling or a rotational flow in the mold to improve the steel product quality.^1,2,3,4,5) However, this technology requires the cost of an electromagnetic stirrer and the cost of electricity. In addition, it is important to modify the flow in the SEN (Submerged Entry Nozzle) as a root measure to control the flow in a mold. For this aim, the reliable, easy-to-use and cost-saving technologies are required to produce a swirling flow inside nozzle or at a nozzle outlet for a swirling flow steel casting process. The concept of a swirling flow nozzle for steel casting is possibly first proposed by Yokoya et al.⁶⁾ in 1994. Table 1 shows the summary of the contributions on the development of the swirling flow nozzle technology.^{6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35)} It was found that a quite stable outlet-flow pattern of the immersion nozzle can be obtained with a swirling flow nozzle¹⁰⁾ and that the penetration depth of the nozzle outlet flow is remarkably decreased in mold.⁸⁾ Industrial experimental results^22,23,30) show that the swirling flow SEN effectively improved the steel product quality. In addition, the clogging problem of the SEN outlet port is effectively reduced.²³⁾ Therefore, the swirling flow SEN has shown its advantages for a good quality of steel product and an efficient production process.

Table 1. Summary on the studies on swirling flow nozzles for steel castings.

Year	Author	Swirling Flow Producing Method					CFD	Turbulent Model	PM	PT	Casting
		Swirl Blade	EMS	TS	TD	SEND
1994	Yokoya et al.6)	●	–	–	–	–	–	–	water	–	CC
	Yokoya et al.7)	●	●	–	–	–	●	k-ε	–	–	CC
1998	Yokoya et al.8)	●	–	–	–	–	●	standard k-ε	water	–	CC
2000	Yokoya et al.9)	●	–	–	–	–	●	standard k-ε	water	–	CC
	Yokoya et al.10)	●	–	–	–	–	–	–	water	–	CC
2001	Yokoya et al.11)	●	–	–	–	–	–	–	water	–	CC
	Yokoya et al.12)	●	–	–	–	–	●	standard k-ε	water	–	CC
	Yokoya et al.13)	●	–	–	–	–	–	RNG k-ε and RSM	water	–	CC
	Yokoya et al.14)	●	–	–	–	–	●	realizable k-ε	water	–	CC
2003	Yokoya et al.15)	●	–	–	–	–	●	standard k-ε	water	–	CC
2004	Yokoya et al.16)	●	–	–	–	–	●	RSM k-ε	water	–	CC
	Tsukaguchi et al.17)	●	–	–	–	–	–	–	wood metal	–	CC
2007	Tsukaguchi et al.18)	●	–	–	–	–	–	–	water	–	CC
	Kholmatov et al.19)	●	–	–	–	–	●	standard k-ε	water	–	CC
2008	Kholmatov et al.20)	●	–	–	–	–	●	standard k-ε	water	–	CC
	Kholmatov et al.21)	●	–	–	–	–	●	standard k-ε	water	–	CC
2010	Hallgren et al.22)	●	–	–	–	–	●	k-ε	–	●	IC
	Tsukaguchi et al.23)	●	–	–	–	–	–	–	Water	●	CC
2011	Sun and Zhang24)	–	–	–	–	●	●	k-ε	–	–	CC
2012	Geng et al.25)	–	●	–	–	–	●	standard k-ε	–	–	CC
	Wondrak et al.26)	–	●	–	–	–	–	–	Ga-In-Sn alloy	–	CC
	Tan et al.27)	●	–	–	–	–	●	–	–	–	IC
2013	Yang et al.28)	–	●	–	–	–	●	–	–	–	CC
	Li et al.29)		●	–	–	–	●	standard k-ε	Pb-Sn-Bi	–	CC
2014	Sun and Zhang30)	–	–	–	–	●	●	–	–	●	CC
	Li et al.31)	–	●	–	–	–	●	standard k-ε	–	–	CC
2015	Yang et al.32)	–	●	–	–	–	●	k-ε	–	–	CC
	Tan et al.33)	–	–	●	–	–	●	realizable k-ε	–	–	IC
	Bai et al.34)	–	–	●	–	–	●	standard k-ε	–	–	IC
2016	Bai et al.35)	–	–	●	–	–	●	standard k-ε realizable k-ε, RSM	water	–	IC
	Bai et al.36)	–	–	●	–	–	●	realizable k-ε, RSM, DES	water	–	CC
	Ni et al.37)	–	–	–	●	–	●	realizable k-ε	–	–	CC
	Ni et al.38)	–	–	–	●	–	●	realizable k-ε	–	–	CC
2017	Present Study	–	–	–	●	–	●	RSM	–	–	CC

Note: EMS-Electromagnetic Stirring, TS-TurboSwirl, TD-Tundish Design, SEND-SEN Design, CFD-Computational Fluid Dynamics, PM-Physical Model, PT-Plant Trial, CC-Continuous Casting, IC-Ingot Casting

As shown in Table 1, various technologies have been investigated to produce a swirling flow inside a nozzle. Specifically, Yokoya et al.^{6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)} investigated the use of the swirl blade to produce a swirling flow inside SEN. This is a method by installing a swirl blade inside a SEN to produce a swirling flow. The driving force for the swirling flow is the head difference between the tundish and the mold. Therefore, it is a cost-saving method. The swirl blade method has shown to be an effective way to produce a swirling flow and plant trials have shown that it is possible to improve the steel product quality.²³⁾ However, the lifespan of the swirl blade and the inclusion attachment on its surface, which may lead to nozzle clogging, restrict its application for longer casting times. The electromagnetic stirring method is another method to produce a swirling flow in SEN, which has received a lot of attention in recent years.^{25,26,28,29,31,32)} The swirling flow is obtained by installing the electromagnetic stirring equipment outside the SEN. Simulation results^25,29,31,32) showed that it can produce a good swirling flow inside the SEN. However, it requires an equipment cost and an electricity cost. Therefore, its application increases the steel product cost. Some other methods to produce a swirling flow in a nozzle or at nozzle outlet have also been investigated. Tan et al.³³⁾ and Bai et al.^34,35) investigated the use of a turboswirl to obtain a swirling flow in ingot casting. Turboswirl is a cylindrical box with a tangential inlet and an outlet located at the round bottom. Later, Bai et al.³⁶⁾ used a turboswirl in continuous casting to produce a swirling flow in the SEN. This method could be a promising method in ingot casting. However, its application in a conventional tundish during continuous casting may be difficult regarding its installation. Also, Sun et al.^24,30) investigated the method to produce a swirling flow by changing the SEN outlet direction. Four tangential outlets at the end of the circular SEN pipe were used. However, this solution still needs to be coupled with M-EMS. This is possibly due to its limited ability to produce a strong enough swirling flow in mold. In a summary, a simple, reliable and cost-saving technology for a swirling flow SEN is still required for the steel production which be confronted with an increased competition and an increased quality requirement.

Recently, Ni et al.^37,38) proposed a new method to produce a swirling flow in SEN by using a cylindrical tundish design. It is a simple design based on the change of the shape of the tundish to control the steel flow path. The swirling flow in SEN is then obtained due to the rotational steel flow inside the cylindrical tundish. Therefore, this is a simple and cost-saving method to realize a swirling flow in SEN. However, the geometry change still means that either a large change of a conventional tundish is necessary or that a newly produced tundish has to be made. This is especially true for multi-SEN tundish. In order to easily produce a swirling flow in a conventional tundish, a new method is proposed in this paper which is achieved by installing a cylinder in a conventional tundish without the need to replace a conventional tundish. In addition, the swirling flow was found asymmetrical in the swirling flow space in previous research,^37,38) where one tangential inlet was used. In the current study, two tangential inlets were used in the new design, which is expected to improve the swirling flow symmetry. A RSM (Reynolds Stress Model) model coupled with the Stress-Omega sub-model was used to simulate the new setup. This is due to that this model has shown a good performance to simulate the swirling steel flow, when compared to water model validations.³⁵⁾ Using this model, the steel flow characteristics and inclusion motion in the new setup were investigated and the results were critically analyzed.

2. Model Description

2.1. Tundish Model

A three-dimensional model of the new tundish design was developed. The geometry and parameters of the tundish are shown in Fig. 1.

Fig. 1.

Geometry of the new tundish setup, (a) tundish side view, (b) tundish bottom view, (c) A-A cross section, (d) SEN inlet geometry.

2.2. Mathematical Model for Steel Flow

The three-dimensional mathematical model for the new tundish setup is based on the following assumptions:

(1) Steel behave as an incompressible Newtonian fluid, the steel density and viscosity are 7000 kg/m³ and 0.0064 kg/(m s), respectively;

(2) Solidification and heat transfer do not occur;

(3) The tundish wall was assumed to be a smooth wall;

(4) The slag phase at the top surface outside the cylinder and the argon gas phase inside the cylinder was not considered;

(5) The liquid steel flow velocity, 1.1 m/s, was fixed at the inlet of the tundish;

(6) The pressure at the SEN outlet was constant and equal to the atmospheric pressure;

(7) The boundary condition at the tundish wall, cylinder wall, stopper-rod wall and top surface was a no-slip wall boundary condition.

2.2.1. Transport Equations

The conservation of a general variable ϕ within a finite control volume can be expressed as a balance among the various processes, which tends to increase or decrease the variable values. The conservation equations, e.g. continuity, momentum and turbulence equations can be expressed by the following general equation:³⁹⁾   

$$\frac{\partial }{\partial t}\left(\rho \varphi \right)+\frac{\partial }{\partial x_i}\left(\rho \varphi u_i\right)=\frac{\partial }{\partial x_i}\left({\mathrm{\Gamma }}_{\varphi }\frac{\partial \varphi }{\partial x_i}\right)+S_{\varphi }$$(1)

where the first term on the left-hand side is the change of ϕ with time, the second term on the left-hand side represents the transport due to convection, the first term on the right-hand side expresses the transport due to diffusion where Γ_ϕ is the diffusion coefficient and it is different in different turbulence models.^40,41,42,43) Furthermore, the second term on the right-hand side is the source term.

2.2.2. Turbulence Modelling

The realizable k-ε turbulence model⁴⁰⁾ coupled with the Enhanced Wall Treatment model⁴¹⁾ was first used to produce an initial flow field. Then, with this flow initialization, the RSM model^41,42,43) combined with the Stress-Omega sub-model^41,44) was used to simulate the steel flow. The Stress-Omega sub-model is good for modeling flows over the curved surfaces and swirling flows.⁴¹⁾ The exact equation for solving the Reynolds stresses in the RSM model is as follows:   

$$\begin{array}{l}\underset{local\mathrm{\hspace{0.17em} }time\mathrm{\hspace{0.17em} }derivative}{\underbrace{\frac{\partial }{\partial t}\left(\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)}}+\underset{convection}{\underbrace{\frac{\partial }{\partial x_k}\left(\rho u_k\overline{u_i^{\prime }{u}_j^{\prime }}\right)}}\\ =\underset{turbulent\mathrm{\hspace{0.17em} }diffusion}{\underbrace{\frac{\partial }{\partial x_{\text{k}}}\left(\frac{{\mu }_t}{{\sigma }_k}\frac{\partial \overline{u_i^{\prime }{u}_j^{\prime }}}{\partial x_k}\right)}}+\underset{molecular\mathrm{\hspace{0.17em} }diffusion}{\underbrace{\frac{\partial }{\partial x_k}\left[\mu \frac{\partial }{\partial x_k}\left(\overline{u_i^{\prime }{u}_j^{\prime }}\right)\right]}}\underset{stress\mathrm{\hspace{0.17em} }production}{\underbrace{-\rho \left(\overline{u_i^{\prime }{u}_k^{\prime }}\frac{\partial u_j}{\partial x_k}+\overline{u_j^{\prime }{u}_k^{\prime }}\frac{\partial u_i}{\partial x_k}\right)}}\\ +\underset{pressure\mathrm{\hspace{0.17em} }strain}{\underbrace{\overline{p^{\prime }\left(\frac{\partial u_i^{\prime }}{\partial x_j}+\frac{\partial u_j^{\prime }}{\partial x_i}\right)}}}\underset{dissipation}{\underbrace{-\text{2}\mu \overline{\frac{\partial u_i^{\prime }}{\partial x_k}\frac{\partial u_j^{\prime }}{\partial x_k}}}}\underset{production\mathrm{\hspace{0.17em} }by\mathrm{\hspace{0.17em} }system\mathrm{\hspace{0.17em} }rotation}{\underbrace{-\text{2}\rho {\mathrm{\Omega }}_k\left(\overline{u_j^{\prime }{u}_m^{\prime }}{\epsilon }_{ikm}+\overline{u_i^{\prime }{u}_m^{\prime }}{\epsilon }_{jkm}\right)}}\\ +\underset{user\mathrm{\hspace{0.17em} }defined\mathrm{\hspace{0.17em} }source\mathrm{\hspace{0.17em} }term}{\underbrace{S_{user}}}\end{array}$$(2)

  

$${\mu }_t={\alpha }^{*}\frac{\rho k}{\omega }$$(3)

where σ_k is equal to 2.0, α^* is the coefficient which damps the turbulent viscosity causing a low-Reynolds number correction, k is the turbulent kinetic energy per unit mass, ω is the specific dissipation rate, μ is the dynamic viscosity, μ_t is the turbulent viscosity, and Ω_k is the rotation vector. Furthermore, ε_ijk is the alternating symbol, with the value equal to 1 if i, j and k are different and in cyclic order, equal to 1 if i, j and k are different and in anti-cyclic order, and equal to 0 if any two indices are the same.^41,42) The turbulent diffusion term, the pressure strain term and the dissipation term are required to be modeled to close the equation. The detailed information for modeling of these terms can be found in the work of Launder, Reece and Rodi⁴³⁾ and the ANSYS FLUENT Theory Guide.⁴¹⁾ In order to close the equation sets, the equation for the specific dissipation rate ω should be solved. In the Stress-Omega sub-model, this is computed in the same way as when using the standard k-ω model as follows:⁴¹⁾   

$$\frac{\partial }{\partial t}\left(\rho \omega \right)+\frac{\partial }{\partial x_i}\left(\rho \omega u_i\right)=\frac{\partial }{\partial x_j}\left({\mathrm{\Gamma }}_{\omega }\frac{\partial \omega }{\partial x_j}\right)+G_{\omega }-Y_{\omega }+S_{\omega }$$(4)

where G_ω represents the generation of ω, Γ_ω represents the effective diffusivity of ω, Y_ω represents the dissipation of ω due to turbulence, S_ω is the user defined source term which is zero in this paper. The method to calculate these terms can be found in the work of Wilcox⁴⁵⁾ and in the ANSYS FLUENT Theory Guide.⁴¹⁾

For the RSM model with the Stress-Omega sub-model, a near-wall treatment is automatically used to perform a blending between the viscous sublayer and the logarithmic region.⁴¹⁾ A very fine grid with the y⁺ value of the first grid smaller than 1, was used to solve the flow and its turbulent properties in the swirling flow SEN.

2.2.3. Solution Method

The steel flow field in the new tundish design was solved by using the commercial software ANSYS FLUENT 18.0^®. The PISO scheme was used for the pressure-velocity coupling. Furthermore, the PRESTO method was adopted to discretize the pressure. The governing equations were discretized using a second order upwind scheme. The convergence criteria were as follows: the residuals of all dependent variables were smaller than 1×10⁻³ at each time step.

2.3. Inclusion Tracking Model

Non-metallic inclusions were tracked in the previously solved steel flow field in the new tundish design. The density of the Al₂O₃ inclusions were assumed to be 3500 kg/m³, based on the data from reference.⁴⁶⁾ The inclusion tracking was done using the DPM (Discrete Phase Model) model, which is available and described in the reference manual in the commercial software ANSYS FLUENT 18.0^®.

2.3.1. Model Assumption for Particle Tracking

(1) Inclusions were assumed to be spherical;

(2) Inclusions escaped from the domain when they exited from the SEN outlet;

(3) Inclusions were assumed to stick to the top surface outside the cylinder once they touched it; a “reflect” boundary condition was used for all the other boundaries if not otherwise specifically mentioned;

(4) Interactions between inclusions were not considered;

(5) A one-way coupling between steel and inclusions was used, i.e. the influence that inclusions have on the steel flow was not considered.

2.3.2. Lagrangian Particle Tracking Model

The locations of inclusions were obtained by solving the following equation:   

$${\mathit{u}}_p=\frac{d{\mathit{x}}_p}{dt}$$(5)

where x_p is the inclusion position and u_p is the inclusion velocity. The inclusion velocity was obtained by solving the following inclusion momentum equation:   

$$\begin{array}{c}\frac{d{\mathit{u}}_p}{dt}=\frac{\left(\mathit{u}-{\mathit{u}}_p\right)}{{\tau }_r}+\mathit{g}\left(1-\frac{{\rho }_f}{{\rho }_p}\right)+\frac{1}{2}\frac{{\rho }_f}{{\rho }_p}\left({\mathit{u}}_p\nabla \mathit{u}-\frac{d{\mathit{u}}_p}{dt}\right)\\ +\frac{{\rho }_f}{{\rho }_p}{\mathit{u}}_p\nabla \mathit{u}+\frac{2K{v}^{\frac{1}{2}}{\rho }_f{S}_{ij}}{{\rho }_p{d}_p{\left(S_{lk}{S}_{kl}\right)}^{\frac{1}{4}}}\left(\mathit{u}-{\mathit{u}}_p\right)\end{array}$$(6)

where the first term on the right-hand side is the drag force per unit inclusion mass, the second term on the right-hand side is the force per unit inclusion mass due to gravity and buoyancy, the third term on the right-hand side is the virtual mass force per unit inclusion mass, and the fourth term on the right-hand side is the pressure gradient force per unit inclusion mass. The fifth term on the right-hand side is the Saffman’s lift force,^47,48) where S_ij and S_lk are the deformation tensors, and K is a constant which is equal to 2.59.⁴⁸⁾ In addition, τ_r is the particle relaxation time and Re_d is the relative Reynolds number. They are expressed by Eqs. (7) and (8), separately. The particle relaxation time represents the time required for the particle to respond to a change in the velocity. Therefore, it reflects its ability to follow a flow change.   

$${\tau }_r=\frac{{\rho }_p{d}_p^2}{\text{18}\mu }\frac{\text{24}}{C_{D}R{e}_d}$$(7)

  

$$R{e}_d=\frac{{\rho }_f{d}_p\left|\mathit{u}-{\mathit{u}}_p\right|}{\mu }$$(8)

where u is the continuous-phase velocity, μ is the molecular viscosity of the fluid, v is the kinematic viscosity of the fluid, d_p is the diameter of an inclusion, ρ_f and ρ_p are the densities of the fluid and the inclusion, respectively. Furthermore, the drag coefficient, C_D, for spherical particles from Morsi and Alexander⁴⁹⁾ was used.

2.3.3. Particle Stochastic Turbulence Model

In order to simulate the effect of the turbulent fluctuations on the inclusion motion, a stochastic turbulent model can be used. The fluctuating velocity components are discrete piecewise constant functions of time. Their random value is kept constant over an interval of time given by the characteristic lifetime of the eddies or, if shorter, the transit time of the particle through the eddy.^50,51) Therefore, the continuous-phase velocity can be expressed by using the following equation:   

$$\mathit{u}=\overline{\mathit{u}}+\acute{\mathit{u}}$$(9)

where u and ú are the continuous-phase averaged velocity and the fluctuating component, respectively. The parameter u can be obtained by solving the Eulerian equations for the continuous-phase. Moreover, ú is calculated by using the following equation:   

$$\acute{\mathit{u}}=\zeta \sqrt{\overline{u_{\text{i}}^{\prime }{}^{\text{2}}}}$$(10)

where ζ is a zero mean value, which has a unit variance and a normally distributed random number. The expression $\sqrt{\overline{u_{\text{i}}^{\prime }{}^{\text{2}}}}$ is the root mean-square local fluctuation velocity in the i direction. The latter is directly solved by using the RSM model. Therefore, the anisotropic turbulent fluctuations can be taken into account in the calculations.

3. Results

The new tundish model was solved based on around 3 million grid cells to obtain a grid-independent solution. The realizable k-ε model with an Enhanced Wall Treatment was firstly used to solve the flow field during the first 57 s. After that, this solution was used as the initial condition for the RSM model calculation. Figure 2 shows the velocity change over time at location 1 (shown in Fig. 1(c)) in the SEN. It can be seen that the tangential velocity fluctuates in the range of 2.1 m/s to 2.6 m/s, with an average value of around 2.3 m/s. This kind of velocity fluctuation is also found in some other swirling flow situations.³⁶⁾ Therefore, this swirling flow shows a periodic characteristic, and a steady state calculation will not accurately describe this kind of dynamic swirling flow phenomena. Since the velocity profile shows only a little change from 93 s to 105 s, this illustrates that a developed steel flow was obtained. In the following, the developed steel flow at 105 s was used to show the steel flow phenomena and to track the inclusion behavior.

Fig. 2.

Tangential velocity change over time at Location 1 in the SEN.

3.1. Steel Flow in the New Tundish

Figure 3 shows the streamlines of the steel flow in the new tundish. The steel flows into the tundish from the tundish inlet. After that, the flow stream hits the turbostopper and the flow direction changes to an upwards direction towards the tundish top surface. After it arrives at the top surface, the steel flow changes its direction and moves towards the vertical tundish wall (shown as red arrows in Fig. 3(b)) and thereafter go deep into the steel metal bath. The horizontal flows indicated with red arrows in Fig. 3(b) give inclusions a chance to move from molten steel up to the top slag layer. At the tundish bottom, steel flows into the cylinder from its two tangential inlets. Then, a rotational steel flow is produced inside it, as shown in Fig. 3(b). Thereafter, a swirling flow in the tundish SEN is formed which can be seen in Fig. 3(a).

Fig. 3.

Streamlines of the steel flow in new tundish, (a) front view, (b) top view.

In order to present the steel flow characteristics in the tunidish, Fig. 4 shows the velocity magnitude and turbulent kinetic energy contour in the middle XZ plane of the new tundish. It can be seen that the regions with a high steel flow velocity and turbulence kinetic energy are located near the tundish inlet, turbostopper and inside the cylinder and SEN. For the other regions, both the steel flow velocities and the turbulent kinetic energies are very small, with values smaller than 0.1 m/s and 0.003 m²/s², respectively. Inside the cylinder, it can be seen that the steel flow velocity is generally in the range of 1.0 to 1.6 m/s. In addition, a high turbulent kinetic energy exists at the location close to the top surface, with the value of around 0.018 m²/s². After the steel flows into the SEN through a narrow gap between the stopper-rod and the tundish bottom, the velocity reach levels higher than 2 m/s. In addition, a high turbulent kinetic energy region exists on the top of the SEN, which gives rise to a chaotic flow. Figure 5 shows the velocity vectors and turbulence kinetic energies at different XY planes of the new tundish. The velocity vectors in Fig. 5(a) and turbulent kinetic energies in Fig. 5(b), at the XY plane which is located at 0.02 m below the top surface, show that outside the cylinder, both the steel flow velocity and the turbulent kinetic energy are very small near the whole top-surface of the tundish, with the maximum value lower than 0.1 m/s and 0.003 m²/s², respectively. This is due to that the newly installed cylinder does not largely influence the flow situation outside it, compared to the conventional tundish without the new cylinder.

Fig. 4.

Contours of the steel flow at XZ middle plane in the new tundish, (a) velocity magnitude, (b) turbulence kinetic energy.

Fig. 5.

Steel flow vector and turbulence kinetic energy at XY plane of 0.02 m blow the steel-slag interface (a) flow vector and (b) turbulent kinetic energy.

Figure 6 shows the velocity vector and turbulent kinetic energy at XY plane located 0.34 m under the top surface. It can be seen that the steel flow pattern in Fig. 6(a) is different from that in Fig. 5(a), where the steel flows upwards and flows from the tundish middle to the wall, rather than a horizontal flow observed in Fig. 5(a). This is due to that a rotational steel flow exists in tundish and this rotational steel flow path can be seen from Fig. 3(a). Furthermore, the influence region of the rotational steel flow is shown in Figs. 5(a) and 6(a) with red lines. After steel flows out of this region, it simply flows towards the tangential inlets of the cylinder, without giving rise complex rotational swirl flow structures any more. In addition, with an increased depth from Figs. 5 to 6, it can be seen that the turbulent kinetic energy has a similar level with a value around 0.0005 m²/s². However, it is slightly higher in a small region at the tundish inlet due to the inlet steel stream.

Fig. 6.

Steel flow vector and turbulence kinetic energy at XY plane of 0.34 m blow the steel-slag interface (a) flow vector and (b) turbulent kinetic energy.

3.2. Steel Flow Characteristics in the SEN

In order to understand the swirling flow characteristics in the SEN, Fig. 7 shows the tangential velocity distributions on different cross sections of the SEN. The locations of these cross sections are shown in Fig. 1(c). Overall, it can be seen that a good swirling flow was obtained in the SEN. In Fig. 7(a), it shows that the tangential velocity was asymmetrical in the swirling flow space in a cross section located 0.1 m below the SEN inlet. The maximum tangential velocity magnitude can reach a value of 2.83 m/s, as shown in the region with a red circle in Fig. 7(a). However, at the opposite side of the swirling flow center, its value is only around 2.2 m/s as shown inside the black circle. With the swirling flow moving downwards in Figs. 7(b) to 7(d), the distribution of the tangential velocity tends to be more symmetrical in swirling space due to the flow development, compared to the values in Fig. 7(a). In addition, the maximum magnitude of the tangential velocity decreases from 2.81 m/s in Cross Section 1 to 2.31 m/s in Cross Section 4.

Fig. 7.

Tangential velocity distribution in different cross sections of the SEN.

Figure 8 shows the velocity profile along different lines in the SEN. The locations of these lines are shown in Fig. 7 and are also shown in Fig. 1(c). From the SEN center to the SEN wall, it can be seen that the steel flow velocity magnitude first rapidly increases to a peak value region and then decrease to zero at the wall. This is a typical velocity distribution in a swirl flow.⁵²⁾ The two peak values of the flow velocity magnitude along Line 1 show some differences, as illustrated in Fig. 8(a). Furthermore, these two peak values tend to become alike as the steel flows downwards in the vertical SEN. A similar situation was observed in Fig. 8(b) for the tangential velocity magnitude. This illustrates that the initial uneven velocity peak is due to the uneven rotational steel flow velocity and due to that the swirl flow is underdeveloped in this region. From Figs. 8(a) and 8(b), it can be seen that the magnitudes of both the total velocity and the tangential velocity decrease with an increased distance from SEN inlet. Specifically, the maximum velocity magnitude (averaged by two peak values) decreases from around 2.8 m/s at Line 1 to around 2.3 m/s at Line 4. The maximum tangential velocity magnitude (averaged by two peak values) also decreases from around 2.5 m/s at Line 1 to around 2.1 m/s at Line 4. Since a constant steel flow was maintained, the axial velocity in Fig. 8(c) shows no large difference in magnitude from Line 1 to Line 4. Here, a completely similar velocity distribution is not observed at different Lines as shown in Fig. 8(c). This is due to that the velocity profile changes over time which can be seen from the swirling flow characteristics previously shown in Fig. 2. By comparing Figs. 8(a) to 8(c), it can be concluded that the velocity magnitude decrease is due to the loss of the rotational steel flow momentum which is reflected by the decrease of the tangential velocity.

Fig. 8.

Velocity profiles along different lines (shown in Fig. 1(b)) in SEN, (a) the total velocity distribution; (b) the tangential velocity distribution; (c) the axial (Z direction) velocity distribution.

In order to present the dissipation of the tangential momentum, Fig. 9(a) shows the total shear stress on the SEN wall. It can be seen that the values of the wall shear stress are mostly in the range of 50 Pa to 260 Pa. Figure 9(b) shows the shear stress component in the vertical direction. It can be seen that the magnitude of the shear stress resulting from the vertical steel flow is mostly in the range of 0 to 100 Pa. Here, the negative value of the shear stress in Fig. 9(b) is due to the steel flow direction, which is in the negative Z direction. This means that the other contributions to the wall shear stress in Fig. 9(a) are due to the rotational steel flow in the SEN. This rotational component of the shear stress leads to the dissipation of the rotational momentum of the swirling steel flow. Therefore, the tangential velocity as well as the total velocity was found to decrease as the steel flows downwards, which was previously shown in Figs. 7 and 8(a) and 8(b).

Fig. 9.

Shear stress on the SEN wall.

In a swirl flow, the rotational flow intensity is generally characterized by Swirl Number. The definition of the Swirl Number from Yokoja et al.⁹⁾ used in this paper is a ratio of the rotational momentum to the axial flow momentum in a cross section of the SEN. Figure 10 shows the Swirl Number at different cross sections (shown in Fig. 7) in the SEN. It can be seen that the swirl number can reach a value of 1.34 at cross section 1. Moreover, it decreases to around 1.14 at cross section 4 due to the dissipation of tangential momentum of the steel flow. In addition, the dissipation rate generally shows the following linear relationship with the distance from SEN inlet:   

$$S_{\text{n}}=\text{1}\text{.34}-\text{0}\text{.467}\left(Z_{\text{n}}-Z_{\text{1}}\right)$$(11)

where Z₁ is the distance of cross section 1 to the SEN inlet and it is equal to 0.1 m in this investigation, Z_n is the distance to the SEN inlet.

Fig. 10.

Swirl Number at different cross sections of the SEN.

In a swirling flow, a rotational flow momentum exists. Due to the influence of the centrifugal phenomena, the pressure distribution inside the SEN may significantly change compared to a non-swirl flow SEN. Figure 11 shows the pressure distribution in the SEN in the current study. It can be seen that a high pressure, around 30 kPa larger than the atmospheric pressure, was observed in the regions near the SEN wall. This may be good to prevent air from being sucked into the SEN. However, in the swirling flow center, the pressure drops to around 20 kPa below the atmospheric pressure. Therefore, a large pressure gradient exists in the radial direction of a SEN cross section. This is different from a conventional SEN, where no large pressure gradient appears from the SEN wall to the SEN center.

Fig. 11.

Pressure distribution inside a SEN.

3.3. Inclusion Behavior in the New Tundish System

In order to understand the behavior of inclusions in the new tundish, 140 inclusions of 1 μm, 10 μm, 30 μm and 100 μm, which are released from the tundish inlet, were individually tracked. Figure 12 shows the trajectories of different sizes of inclusions in the new tundish. It can be seen that many 1 μm, 10 μm and 30 μm inclusions move to the bottom of the tundish. They enter the cylinder mainly from the left side cylinder inlet. With an increased inclusion size, the number of inclusions which reaches the right end of the tundish is decreased. 100 μm inclusions moved to the top part of the tundish and only one inclusion moved into the cylinder. After it moves into the SEN, it follows the rotation inside the SEN due to the swirling flow. Furthermore, it is mainly located at the center of the SEN due to the effect of the centripetal force or the high pressure gradient shown in Fig. 11. This has also been found in the previous research where inclusions in a swirling flow SEN was investigated.³⁸⁾ Figure 13 shows the ratio of the inclusions that touch the top surface. It can be seen that the number of inclusions that touch the top surface increases with an increased inclusion size. Specifically, the ratio is 36.40% for 1 μm inclusions, while the value is 99.3% for 100 μm inclusions. The different behavior of different inclusion sizes is mainly due to the effect of the buoyancy. Specifically, large size inclusions get a much larger buoyancy than small size inclusions. This makes the large inclusions move towards the top tundish as shown in Fig. 12(d).

Fig. 12.

Inclusion trajectories in the new tundish.

Fig. 13.

Ratio of inclusions that touch the top surface of the tundish.

4. Discussion

A new design of a swirling flow producer in a conventional tundish was investigated with the purpose to obtain a swirling flow in the SEN by using the steel flow potential. This design is easily realized by adding a cylinder on the top of a SEN in a conventional tundish, without the need of a significant change of the original tundish structure. It can not only be used in a single SEN tundish, but also can be easily used in the tundish with multiple SENs. Therefore, the method proposed in this paper is a promising method to produce a swirling flow in a convenient way. The RSM turbulence model with stress-omega sub-model was used to simulate the casting process when using the new tundish, since the RSM model has previously been validated and shown to accurately capture the swirling flow phenomena.³⁵⁾ The simulation results show that the swirling flow in tundish SEN was successfully obtained by using the new design. With two tangential inlets in the cylinder, the obtained steel flow velocity distribution (shown in Fig. 8) is more symmetrical than that with one tangential inlet used in previous research.³⁷⁾ This can easily be seen by comparing two peak values along a radial line. Therefore, it is good to use two or even more tangential inlets to obtain a symmetrical swirling flow.

Since the aim of the study is to investigate the new cylinder design to produce a swirling flow inside SEN, the slag phase on the top of the steel is ignored in the current CFD model. This is due to that the new design is not expected to significantly change the flow situation outside the cylinder in a conventional tundish. This can be seen from Figs. 4 and 5, where very low values of steel flow velocities and turbulent kinetic energies were found near the top surface outside the cylinder. Therefore, a similar situation of the slag behavior outside the cylinder would be expected as that in the original conventional tundish. In addition, the possibility of the slag entrainment problem can be estimated by analyzing the steel flow characteristics near the top surface. Therefore, the neglect of the slag phase does not significantly influence the quality of the results in the current study. According to previous research,^53,54) a slag entrainment into liquid steel may occur when the Weber number is greater than 12.3. The Weber number can be defined as:   

$$We=\frac{u_l^2{\rho }_l}{\sqrt{\sigma g\left({\rho }_l-{\rho }_s\right)}}$$(12)

where u_l is the steel velocity, g is gravitational acceleration and σ is the interfacial tension between steel and slag in the tundish. A slag density value of 2560 kg/m³ was used and the value of interfacial tension between steel and slag was set to 1.16 N/m.⁵⁵⁾ The maximum steel velocity, with the value of 0.1 m/s at the XY plane with 0.02 m under the top surface in Fig. 5(a) was used to calculate the Weber Number. The obtained maximum Weber Number outside the cylinder is 0.3. This illustrates that the risk of slag entrainment in tundish outside the cylinder away from the inlet region is very small. However, inside the cylinder, the steel flow velocity is very high, which has been shown in Fig. 5. The calculated Weber Number is around 80, which represent a high possibility of the slag entrainment if a top slag is used. Therefore, an argon protection instead of a slag protection might be required here to protect the steel from air reoxidation. The diameter of the cross section of the cylinder is only 0.3 m, which means that an application of argon protection should be easily realized for production conditions. Due to the rotational steel flow inside the cylinder, a declined argon gas-motel steel interface would be expected when an argon gas protection is used. However, this is not important any more for the concern of the slag entrainment due to the possible vortex formation, since no slag exists here. The calculated Weber Number in this study is only an indication of the slag entrainment possibility. In reality, the slag entrainment issue should be investigated experimentally in future, when a slag is used to protect the steel from air reoxidation.

Due to that it is very time consuming to simulate an unstable free surface, a wall boundary condition was used on the top of the tundish. However, this is not expected to negatively influence the main aim of this study to investigate the new application of tundish design to produce a swirling flow in the SEN. In addition, the pressure distribution can give a general understanding about the inclined interface due to the rotational steel flow. This can be evaluated by the pressure difference between the location close to the cylinder wall and the location close to the stopper-rod. Thus, the height difference of the inclined interface can be calculated by: ΔP=ρgh, where ΔP is the static pressure difference, ρ is the density of the steel, g is gravity acceleration rate and h is the height difference of the inclined interface. The calculated maximum height difference is around 0.16 m. However, the argon protection is planed to be used on the top surface and the steel height in the cylinder is around 0.74 m. Therefore, the whirlpool phenomena should not exist in the current design, which means that the open flow path for the top argon gas towards the SEN was not expected to exist in the current design. In addition, the height difference can also be reduced by a further cylinder design. This can be seen from the previous study where a small height difference, with the value of around 0.025 m, exists at the interface.³⁷⁾ A further study to optimize this issue may be carried out in the future.

Nozzle clogging is still a problem in the production of some steel grades, like Al-killed steel. This can also be a threat for some swirling flow technologies, i.e. due to an inclusion deposition on the surface of a swirl blade. Therefore, it is desirable that inclusions are removed from the molten steel to, for example, the top slag. In the current study, small inclusions were found to mainly move into the cylinder from its left entrance. These small inclusions normally have a small relaxation time (as easily can be seen from Eq. (7)), which means that they can generally follow the steel flow path in Fig. 3(a). Therefore, dams may be required at the tundish bottom (as shown in Fig. 12(a)) to change the inclusion path by changing the steel flow direction rather than the steel directly flowing into the left cylinder inlet as shown in Fig. 3(a). This might also be helpful to cause the inclusion to rise towards the top of the tundish. In the current cylinder design, the inclusion may deposit on the cylinder surface and especially at the tangential inlet. However, the cylinder diameter is around four times of the SEN diameter and the tangential inlet area is around 1.5 times of the SEN cross section. This means that the clogging influence on SEN may be larger than on the cylinder. In addition, the replacement of a clogged cylinder by a new cylinder might be done during production. However, the influence of the cylinder clogging on the swirling flow intensity should be investigated more in depth in the future.

The erosion of refractory due to steel flow is always a concern in steel production. This may arise from the shear stress on the SEN wall. In the current setup, the wall shear stress values, with the maximum value of around 300 Pa, are generally in the similar range as has been found in previous research.³⁷⁾ A high wall shear stress is expected in a swirling flow, since there is a rotational steel flow inside the flow channel in addition to an axial steel flow. The study from Sambasivam⁵⁶⁾ shows that the wall shear stress sometimes may be helpful to remove the non-metallic inclusions that touch the SEN wall. Therefore, concerns about steel flow erosion on different refractories, inclusion removal after an attachment and their relationship with shear stress should be experimentally evaluated.

5. Conclusions

A swirling flow device was designed to enable a use in any conventional tundish to produce a swirling flow in the SEN in an economical way. The steel flow phenomena in the tundish and the cylindrical swirling flow producer were investigated by using numerical simulations. The main obtained conclusions were the following:

(1) A swirling flow in the SEN was successfully obtained by putting a cylinder in a conventional tundish. The swirling flow characteristics show a dynamic change over time. The obtained swirl number inside the SEN can reach a value of 1.34 at the cross section of 0.1 m below the SEN inlet. The swirling flow intensity decreased downwards to the SEN outlet, due to the dissipation of the rotational momentum by wall shear stress.

(2) The slag entrainment at the top of tundish was analyzed. The calculated Weber number was only round 0.3, which represents a very small possibility for slag entrainment outside the cylinder away from the tundish inlet region. However, argon protection should be used inside the cylinder instead of top-slag to avoid reoxidation, since a very high steel flow exists at the top surface inside the cylinder.

(3) A high value of shear stress was found on the SEN wall due to the swirling flow in SEN. The values were mostly in the range of 50 Pa to 260 Pa. This high shear stresses are due to the rotational steel flow inside the SEN, besides the axial steel flow.

(4) Different size inclusions were tracked by considering forces acting on them. Number of inclusions touching the tundish top surface increases with an increased inclusion size. This is primarily due to the buoyancy effect. Mainly, inclusions that went into the cylinder came from the left side tangential inlet. Dams may be required to optimize the inclusion motion path.

Acknowledgments

Peiyuan Ni wants to thank the National Natural Science Foundation of China (Grant No. 51704062) for the support.

References

• 1)   Q.  Fang,  H.  Ni,  B.  Wang,  H.  Zhang and  F.  Ye: Metals, 7 (2017), 72, DOI: 10.3390/met7030072.
• 2)   B.  Willers,  M.  Barna,  J.  Reiter and  S.  Eckert: ISIJ Int., 57 (2017), 468.
• 3)   H.  Yu and  M.  Zhu: Ironmaking Steelmaking, 39 (2012), 574.
• 4)   H.  Liu,  M.  Xu,  S.  Qiu and  H.  Zhang: Metall. Mater. Trans. B, 43 (2012), 1657.
• 5)   M.  Barna,  M.  Javurek,  B.  Willers,  S.  Eckert and  J.  Reiter: IOP Conf. Ser.: Mater. Sci. Eng., 143 (2016), 012027, DOI: 10.1088/1757-899X/143/1/012027.
• 6)   S.  Yokoya,  Y.  Asako,  S.  Hara and  J.  Szekely: ISIJ Int., 34 (1994), 883.
• 7)   S.  Yokoya,  R.  Westoff,  Y.  Asako,  S.  Hara and  J.  Szekely: ISIJ Int., 34 (1994), 889.
• 8)   S.  Yokoya,  S.  Takagi,  M.  Iguchi,  Y.  Asako,  R.  Westoff and  S.  Hara: ISIJ Int., 38 (1998), 827.
• 9)   S.  Yokoya,  S.  Takagi,  M.  Iguchi,  K.  Marukawa,  W.  Yasugaira and  S.  Hara: ISIJ Int., 40 (2000), 584.
• 10)   S.  Yokoya,  S.  Takagi,  M.  Iguchi,  K.  Marukawa and  S.  Hara: ISIJ Int., 40 (2000), 578.
• 11)   S.  Yokoya,  S.  Takagi,  M.  Iguchi and  S.  Hara: ISIJ Int., 41 (2001), Supplement, 47.
• 12)   S.  Yokoya,  S.  Takagi,  K.  Tada,  M.  Iguchi,  K.  Marukawa and  S.  Hara: ISIJ Int., 41 (2001), 1201.
• 13)   S.  Yokoya,  S.  Takagi,  M.  Kaneko,  M.  Iguchi,  K.  Marukawa and  S.  Hara: ISIJ Int., 41 (2001), 1215.
• 14)   S.  Yokoya,  S.  Takagi,  S.  Ootani,  M.  Iguchi,  K.  Marukawa and  S.  Hara: ISIJ Int., 41 (2001), 1208.
• 15)   S.  Yokoya,  S.  Takagi,  Y.  Tsukaguchi,  M.  Iguchi,  K.  Marukawa and  S.  Hara: 3rd Int. Conf. on CFD in the Minerals and Process Industries, CSIRO, Melbourne, (2003), 427.
• 16)   S.  Yokoya,  P.  Jönsson,  K.  Sasaki,  K.  Tada,  S.  Takagi and  M.  Iguchi: Scand. J. Metall., 33 (2004), 22.
• 17)   Y.  Tsukaguchi,  S.  Furuhashi and  M.  Kawamoto: ISIJ Int., 44 (2004), 350.
• 18)   Y.  Tsukaguchi,  O.  Nakamura,  P.  Jönsson,  S.  Yokoya,  T.  Tanaka and  S.  Hara: ISIJ Int., 47 (2007), 1436.
• 19)   S.  Kholmatov,  S.  Takagi,  L.  Jonsson,  P.  Jönsson and  S.  Yokoya: ISIJ Int., 47 (2007), 80.
• 20)   S.  Kholmatov,  S.  Takagi,  P.  Jönsson,  L.  Jonsson and  S.  Yokoya: Steel Res. Int., 79 (2008), 698.
• 21)   S.  Kholmatov,  S.  Takagi,  L.  Jonsson,  P.  Jönsson and  S.  Yokoya: Steel Res. Int., 79 (2008), 31.
• 22)   L.  Hallgren,  A.  Tilliander,  S.  Yokoya,  P.  Jönsson and  S.  Hagman: ISIJ Int., 50 (2010), 1763.
• 23)   Y.  Tsukaguchi,  H.  Hayashi,  H.  Kurimoto,  S.  Yokoya,  K.  Marukawa and  T.  Tanaka: ISIJ Int., 50 (2010), 721.
• 24)   H.  Sun and  J.  Zhang: ISIJ Int., 51 (2011), 1657.
• 25)   D.  Geng,  H.  Lei,  J.  He and  H.  Liu: Acta Metall. Sin. (Engl. Lett.), 25 (2012), 347.
• 26)   T.  Wondrak,  S.  Eckert,  V.  Galindo,  G.  Gerbeth,  F.  Stefani,  K.  Timmel,  A. J.  Peyton,  W.  Yin and  S.  Riaz: Ironmaking Steelmaking, 39 (2012), 1.
• 27)   Z.  Tan,  M.  Ersson and  P.  Jönsson: ISIJ Int., 52 (2012), 1066.
• 28)   Y.  Yang,  P.  Jönsson,  Z.  Su,  J.  He and  K.  Nakajima: Steel Res. Int., 86 (2015), 361.
• 29)   D.  Li,  Z.  Su,  J.  Chen,  Q.  Wang,  Y.  Yang,  K.  Nakajima,  K.  Marukawa and  J.  He: ISIJ Int., 53 (2013), 1187.
• 30)   H.  Sun and  J.  Zhang: Metall. Mater. Trans. B, 45 (2014), 936.
• 31)   D.  Li,  Z.  Su,  K.  Marukawa and  J.  He: J. Iron Steel Res. Int., 21 (2014), 159.
• 32)   H.  Bai,  M.  Ersson and  P.  Jönsson: Metall. Mater. Trans. B, 46 (2015), 2652.
• 33)   Y.  Yang,  P.  Jönsson,  M.  Ersson,  Z.  Su,  J.  He and  K.  Nakajima: Steel Res. Int., 86 (2015), 1312.
• 34)   Z.  Tan,  M.  Ersson and  P.  Jönsson: Math. Probl. Eng., 2015 (2015), Article ID 805734.
• 35)   H.  Bai,  M.  Ersson and  P.  Jönsson: Steel Res. Int., 88 (2017), Article No. 1600339, DOI: 10.1002/srin.201600339.
• 36)   H.  Bai,  M.  Ersson and  P.  Jönsson: ISIJ Int., 56 (2016), 1404.
• 37)   P.  Ni,  L.  Jonsson,  M.  Ersson and  P.  Jönsson: Steel Res. Int., 87 (2016), 1356.
• 38)   P.  Ni,  L.  Jonsson,  M.  Ersson and  P.  Jönsson: Steel Res. Int., 88 (2017), 1600155.
• 39)   S. V.  Patankar: Numerical Heat Transfer and Fluid Flow, Hemispere Publishing Corp., New York, (1980), 15.
• 40)   T.-H.  Shih,  W. W.  Liou,  A.  Shabbir,  Z.  Yang and  J.  Zhu: Comput. Fluids, 24 (1995), 227.
• 41)   ANSYS  Fluent Theory Guide, Release 17.0, ANSYS Inc., Canonsburg, (2016), 85.
• 42)   H. K.  Versteeg and  W.  Malalasekera: An Introduction to Computational Fluid Dynamics, The Finite Volume Method, 2nd ed., Pearson Education Limited, Essex, UK, (2007), 80.
• 43)   B. E.  Launder,  G. J.  Reece and  W.  Rodi: J. Fluid Mech., 68 (1975), 537.
• 44)   F. S.  Lien and  M. A.  Leschziner: Comput. Fluids, 23 (1994), 983.
• 45)   D. C.  Wilcox: Turbulence Modeling for CFD, DCW Industries, Inc., La Canada, California, (1998), 84.
• 46)   G. V.  Samsonov,  C. N.  Turton and  T. I.  Turton: The Oxide Handbook, IFI/Plenum, New York, (1973), 34.
• 47)   A.  Li and  G.  Ahmadi: Aerosol Sci. Technol., 16 (1992), 209.
• 48)   P. G.  Saffman: J. Fluid Mech., 22 (1965), 385.
• 49)   S. A.  Morsi and  A. J.  Alexander: J. Fluid Mech., 55 (1972), 193.
• 50)   A. D.  Gosman and  E.  Ioannides: J. Energy, 7 (1983), 482.
• 51)   D. I.  Graham: Int. J. Multiph. Flow, 24 (1998), 335.
• 52)   R.  Hreiz,  C.  Gentric and  N.  Midoux: Chem. Eng. Res. Des., 89 (2011), 2521.
• 53)   L.  Jonsson and  P.  Jönsson: ISIJ Int., 36 (1996), 1127.
• 54)   Z.  Xiao,  Y.  Peng and  C.  Liu: Chin. J. Mater. Sci. Technol., 3 (1987), 197.
• 55)   G. N.  Shannon and  S.  Sridhar: High Temp. Mater. Process., 24 (2005), 111.
• 56)   R.  Sambasivam: Ironmaking Steelmaking, 33 (2006), 439.