Numerical Analysis of the Influence of the Modification of the Ladle Shroud on Fluid Flow Behavior in a One-strand Tundish during Continuous Steel Casting

A tundish is a device from which liquid steel is pour into a mold. Therefore tundish hydrodynamic conditions have a significant impact on solidification during continuous steel casting (CSC) process. Modification of ladle shroud workspace, allows for the modification of liquid steel movement in the tundish. In the following work, numerical simulations were performed which allowed the impact of the modification of the ladle shroud workspace on the liquid steel flow structure in a one-strand tundish to be determined. In order to assess the impact of the modification of the ladle shroud on the behavior of the liquid steel in the tundish, simulations were performed, on the basis of which the percentage share of stagnant, ideal mixing and plug flow zones were determined. In addition, the mixing parameters were determined, allowing the estimation of casting duration during sequential casting. The flow fields of liquid steel for each modification of the ladle shroud were performed. The average velocity of liquid steel flowing through the tundish, the Reynolds number and turbulent intensity were also described. The obtained results showed, among others, that the application of three cylinders with a diameter of 0.041 m into the ladle shroud with a diameter of 0.11 m increases the share of active flow in the tundish in relation to the tundish with Conventional Ladle Shroud. At the same time, applying a ladle shroud with a diameter of 0.11 m during casting is the most favorable in relation to the hydrodynamics of the tundish.


INTRODUCTION
A tundish is one of the devices that shapes the hydrodynamics of the liquid steel flowing through a given work space, affecting the chemical homogenization of liquid steel or the content of non-metallic inclusions in continuous slabs, blooms or billets. A tundish should be characterized by flow, which is by definition a share of minimal stagnant flow and maximum plug flow and ideal mixing, enhancing the removal of non-metallic inclusions. Therefore, it is important to test different types of tundish [1][2][3][4][5][6][7][8][9], including those optimized by blowing the liquid steel with an inert gas [10][11][12][13] or heating it in the tundish by means of induction [14][15]. Flow control devices, such as weirs, dams [16][17][18] or turbulence inhibitors [9,19] are most often used to modify the hydrodynamic conditions in a tundish. The use of a ladle shroud (LS) as a device for shaping the hydrodynamics of the flow, without using dams or weirs, seems a promising approach. Selected studies related to the modification of the internal space of the ladle shroud, the depth of its immersion [20] or the introduction of inert gas into it [21,22] are a reference point for the search for new solutions. Trumpet [23], dissipative [24][25][26] or swirling [27][28][29] LS are recognized modifications of the internal space of the ladle shroud. This paper presents the results of numerical simulations concerning the modification of aladle shroud for a one-strand tundish.

CHARACTERISTICS OF THE TEST FACILITY
The tested object was a one-strand tundish with a nominal capacity of 30 t. It had the shape of a wedge widening towards the pouring zone. The tundish was equipped with a low 0.12 m dam, containing two overflow windows with dimensions of 0.14 × 0.05 m, placed in front of the stopper rod system. Detailed information on the tundish has been presented in a previous publication [30]. https://journals.agh.edu.pl/jcme The studies involved a Conventional Ladle Shroud (CLS) (Fig. 1a) and a modified ladle shroud (MLS), where the end of the main pipe was equipped with 3 smaller 0.2 m long cylinders, separating the main liquid steel stream. The MLS cylinder's outlets (no. [1][2][3] are placed in the tundish asymmetrically (Fig. 1b). The internal diameter of the main pipe was 0.07 m for variants 1 and 3, and 0.11 m for variants 2 and 4. The flow rate of liquid steel through the tundish in each variant of the simulation was 35 kg/s. Additional parameters defining the initial conditions of the liquid steel are presented in Table 1. All of the ladle shrouds presented in the study were immersed in liquid steel to a depth of 0.1 m.
The model of the tundish with ladle shrouds was made with Gambit 2.4.6 software. A computational grid consisting of an average of 855,000 tetrahedral elements was prepared using ANSYS Mesher software. Numerical simulations were performed with the help of ANSYS FLUENT 18 software.
In order to determine the hydrodynamics of the flow of liquid steel in the tundish, three planes running along the device were selected, planes A and C are areas 0.25 m away from the central axis of the tundish towards the side longitudinal walls.
On the other hand, the B plane goes along the mentioned axis. Three planes running across the tundish were also created: plane D, running through the center of ladle shroud, plane E was located before the low dam, and plane F was placed in the stopper rod zone (Fig. 1a). Circulation zones occurring on the planes A-C were indicated by rectangles.
In order to assess the impact of the modification of the ladle shroud on the behavior of the liquid steel in the tundish, simulations were performed on the basis of which the percentage share of stagnant, ideal mixing and plug flow zones were determined. Vector flow maps were also obtained. In addition, the transition zone formed during the sequential casting of two steel grades with a different chemical composition was calculated. The characteristics of individual simulation variants is presented in Table 2.

MATHEMATICAL MODEL
The general mathematical model included the equations of continuity and momentum [30]: where: t -time, s, ρ -density, kg•m −3 , u -velocity of the steel flow, m• s −1 , g -gravitational acceleration, m•s −2 , p -pressure, Pa, τ -stress tensor, Pa, μ -viscosity, kg•m −1 •s −1 , I -unit tensor. https://journals.agh.edu.pl/jcme The effect of the temperature gradient in the liquid steel was calculated on the basis of the energy equations [30]: where: Species transport equation was used to calculate tracer motion in the liquid steel within time [30]: Under non-isothermal conditions, a polynomial density model was applied [31]: where: To describe the turbulent movement of liquid steel, the realizable k -ε model was adopted, which uses the following constant values: C 2 = 1.9, σ k =1.0, σ ε = 1.2.
In the conducted numerical simulations, the medium flowing through the tundish was liquid steel of the following parameters: viscosity -0.007 kg/(m•s), thermal conductivity of steel -41 W/(m•K), heat capacity of steel -750 J/(kg•K). The simulation of non-isothermal conditions of the CSC process was performed, assuming thermal losses, in the form of: −2600 W/m 2 for the walls and bottom of the tundish; −15000 W/m 2 for the free surface of liquid steel and −1750 W/m 2 for the walls of elements immersed in a liquid, i.e. a stopper rod, a dam or a ladle shroud wall [30]. Natural convection was also considered. The top wall of the tundish with assumed zero tangential stresses was assumed as a free surface. Other walls were assumed as a standard wall function. The SIMPLEC (Semi-Implicit Method for Pressure-Linked Equations-Consistent) algorithm was used to describe the coupling of the pressure and velocity fields in the model. The UDS (User Defined Scalars) function was used to simulate the marker. The numerical model presented has been validated by industrial and physical trials in the co-authors previous work [31,32]. The registration of the marker concentration change as a function of time was the basis for the determination of RTD (Residence Time Distribution) curves. Based on previous papers [30,33], the duration of the transition zone was determined on the basis of the F-curve in the range of dimensionless concentration within the range of 0.2-0.8. The simulations were performed with two simplifications during ladle change over: steady level of liquid steel in the tundish and steady casting speed. The intensity of turbulence in the pouring zone of the tundish on the B plane was also analyzed, and the average flow rate of the liquid steel through the tundish was determined. The Reynolds number was also calculated (8): where: ρ -density of liquid steel, kg/m 3 , L -liquid steel depth in the tundish, m, v av -average velocity of liquid steel in the tundish, m/s, η -viscosity of liquid steel, kg/(m•s).
Turbulence intensity was described by means of the following Equation (9): where: k -kinetic energy, m 2 /s 2 , u -liqvelocity of the steel flow, m• s −1 .

RESULTS AND DISCUSSION
While analyzing the flow of liquid steel on plane A, a circulation zone was found in each variant in the area of the tundish stopper rod system (rectangle 1 at Fig. 2a-d). The circulation is the largest in variants 3 and 4. In each of the variants, there is also a recirculation located at the ladle shroud, under the free surface of the liquid steel, which differs in shape and size depending on the ladle shroud variant (Plane A, rectangle 4 at Fig. 2a, Fig. 2c, Fig. 2d and Plane A, rectangle 3 at Fig. 2b). A characteristic circulation (not appearing in variant 2) is the circulation located under the free surface of the metal, between the pouring zone and the low overflow dam (Plane A, rectangle 2 at Fig. 2a, Fig. 2c and Fig. 2d). The C plane shows a similar flow to the symmetrical A plane. Circulations are formed in similar places, they differ only in shape or size. The biggest difference can be observed in the case of variant 4 (Fig. 2d). The recirculation zone in the area of the tundish stopper rod system takes an angle to a little horizontal (it occurs similarly in variant 3) (Plane C, rectangle 1 at Fig. 2c and Fig. 2d). The sizes of the circulation areas located at the ladle shroud under the free surface of the liquid steel also change. In variants 2 and 4 (rectangle 3 at Fig. 2b and rectangle 4 at Fig. 2d), where the circulation at the ladle shroud on the A plane was smaller, it is characterized by a larger size on the C plane, unlike in variants 1 and 3 (rectangle 4 at Fig. 2a and Fig. 2c), where the recirculation has a larger surface on the A plane and occupies a smaller area on the C plane. The B plane indicates a similar liquid steel flow through the tundish between the variants. Two circulation zones come to the fore. One is located between the pouring stream and the closer short wall of the device (rectangle 1 at Fig. 3a-d), while the other is shaped in the middle of the tundish bottom, between the above-mentioned short wall and the overflow dam (rectangle 2 at Fig. 3a-d). Analysis of velocity paths on the plane D shows circulation areas at both sides of the pouring stream, and whose sizes are very similar to each other (Plane D, Fig. 4). As the liquid steel flows through the stopper rod, circulations decrease (Plane E, Fig. 4) until they reach the stopper rod zone where they are mostly very small (the exception is variant no. 3) (Plane F, Fig. 4).
In all variants on plane E they are circulations under the free surface of a metal bath. In variants no. 1, 3 and 4 (Plane E, Fig.4a, Fig. 4c and Fig. 4d), very small vortices are creating at the bottom of the tundish. On plane F, fluid flow is asymmetrical in all variants. The most similar flow field at plane E occurs in variant no. 3. https://journals.agh.edu.pl/jcme While analyzing the percentage share of the volume of individual flows, it was observed that the highest share of active flow was found in two variants: 2 and 4, and its value was approx. 71.4%. The mentioned variants differ in the share of the ideal mixing flow and the plug flow. The share of ideal mixing flow for variant 4 is 62.52%, while for variant 2 it is 58.13%. Variant 3 is marked by the same share of the ideal mixing flow exceeding 57% as in the case of variant 2. At the same time, the share of the plug flow in the variant with a modified ladle shroud with a main pipe 0.07 m in diameter is slightly over 5%. The mentioned variant unfavorably affects the results due to the high share of stagnant flow, which is over 36%. Variant 1 has almost the same plug flow share as variant 4, while the ideal mixing flow share is 59.6% (Fig. 5a and Fig. 5c). Additionally, as part of the analysis of the effect of the ladle shroud on the hydrodynamics of liquid steel flow through the tundish, the transition zone was determined. Based on the range of transition zone, casting speed, steel density and the dimensions of the slab, it was possible to calculate the approximate weight of the mixed steel grade. The lowest weight of the steel in the intermixing zone was obtained for variant 2 -24146 kg, and the highest for variant 3 -28475 kg. Comparing the obtained results with the basic ladle shroud defined as variant 1, variant 4 also has a favorable effect, since the weight of the mixed grade obtained as a result of applying this modification is 979 kg lower ( Fig. 5b and Fig. 5d). The highest weight of the steel in the intermixing zone in variant 3 occurs due to the highest share of stagnant flow of all variants. The lowest weight of steel in the intermixing zone in variant 2 is due to a small share of stagnant flow and the highest share of plug flow.
While analyzing the diagram showing the velocities of liquid steel for the lines passing through the individual internal cylinders of the ladle shroud (Fig. 6) in variants 3 and 4, a significant increase in the liquid steel velocity was observed at the height of approx. 0.75-1.15 m, which corresponds to the modification located here. Liquid steel velocity expansion is a result of decreasing area of ladle shroud outflow by using cylinders. The highest liquid steel velocity was recorded for variant 3 (smaller diameter of cylinders). The diagram also presents the differences in the velocities of the liquid steel between lines 1, 2 and 3 in the vicinity of the tundish bottom. The biggest differences appear in variant 3. The intensity of turbulence in the pouring zone on the B plane was also analyzed (Fig. 8). In variants 1 and 4, turbulences arise in the area of the flood stream and at the bottom of the tundish as a result of the contact of the liquid steel flowing into the tundish with its bottom. In variant 4, they are slightly more intense at the ladle shroud than in variant 1. The largest area of turbulence with increased intensity occurs in variant 3, and the intensity of turbulence with the maximum value is located under the ladle shroud. In variant 2, the intensity of turbulence in the analyzed range is characterized by the smallest fluctuations.

CONCLUSION
Based on the performed numerical simulations, it was found that: • The use of the tested variants of the ladle shroud does not significantly affect the shape of the directions of liquid steel flow, but it does affect the intensity of turbulence in the pouring zone. • Reduction in the diameter of the main pipe and reduction in the diameter of the cylinders modifying the internal space of ladle shroud increases the flow rate of liquid steel within the modification, which may intensify the erosion of the ladle shroud.