Physical experiments and numerical simulations of the influence of turbulence inhibitors and the position of ladle shroud on the steel flow in an asymmetric five-strand tundish

Citation: Walek, J.; Tkadleˇcková, M.; Veliˇcka, M.; Mach˚u, M.; Cupek, J.; Huczala, T.; Cibulka, J.; R˚užiˇcka, J.; Michalek, K. Physical Experiments and Numerical Simulations of the Influence of Turbulence Inhibitors and the Position of Ladle Shroud on the Steel Flow in an Asymmetric Five-Strand Tundish. Metals 2023,13, 1821. https://doi.org/10.3390/ met13111821 Academic Editor: Jiehua Li Received: 5 September 2023 Revised: 27 September 2023 Accepted: 22 October 2023 Published: 29 October 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). metals Article Physical Experiments and Numerical Simulations of the Influence of Turbulence Inhibitors and the Position of Ladle Shroud on the Steel Flow in an Asymmetric Five-Strand Tundish Josef Walek 1,* , Markéta Tkadleˇcková2, Marek Veliˇcka 3, Mario Mach˚u 3, JiˇríCupek 1, Tomáš Huczala 2, JiˇríCibulka 2, Jan R˚užiˇcka 3and Karel Michalek 1 1Department of Metallurgical Technologies, Faculty of Materials Science and Technology, VSB—Technical University of Ostrava, 17. listopadu 2172/15, 70800 Ostrava, Czech Republic; [email protected] (J.C.); [email protected] (K.M.) 2Tˇ RINECKÉŽELEZÁRNY, a.s., Pr˚umyslová1000, StaréMˇesto, 73961 Tˇrinec, Czech Republic; [email protected] (M.T.); [email protected] (T.H.); [email protected] (J.C.) 3 Department of Thermal Engineering, Faculty of Materials Science and Technology, VSB—Technical University of Ostrava, 17. listopadu 2172/15, 70800 Ostrava, Czech Republic; [email protected] (M.V.); [email protected] (M.M.); [email protected] (J.R.) *Correspondence: [email protected]; Tel.: +420-597323534 Abstract: The submitted article deals with the use of physical and numerical modelling to study the process of the steel flow in an asymmetric five-strand tundish that continuously casts steel. For the purposes of physical modelling, a 1:4-scale plexiglass model was used as the operating tundish, and for numerical modelling, the geometry of the operating tundish was created on a 1:1 scale. A model liquid (water) was used in the physical modelling of the melt flow process, while liquid steel was used as the standard flowing medium in the numerical modelling. We assessed the relevant operating parameters influencing the characteristics of the flow of the bath in the tundish—the shape of the turbulence inhibitor, the position of the ladle shroud in relation to the turbulence inhibitor and the distance between the ladle shroud orifice and the bottom of the turbulence inhibitor. The preliminary results show that optimal steel flow characteristic results are achieved by using the TI3-C configuration. The results from both modelling methods achieved the same characteristics, therefore verifying the results of each other and demonstrating that when taken together, the results of physical and numerical modelling can be considered sufficiently informative. Keywords: tundish; turbulence inhibitor; steel flow; retention time; modelling 1. Introduction During the continuous casting of steel, a tundish is placed between the ladle and the mould and is one of the most important technological nodes in the process because it affects the stability of the casting process and the quality of the continuous cast preform. The tundish primarily serves as a reservoir for liquid steel during sequential casting, providing sufficient time for ladle changes without having to prematurely interrupt the flow of liquid steel into the molds [1–3]. The tundish can be used as a flow-through reactor for bath mixing, as, to a certain extent, it is still possible to modify the properties of the cast steel at this point. One of the basic functions of the tundish is to distribute liquid steel between the individual casting strands. The even distribution of steel needs to be ensured so that the physical and chemical properties of the steel are approximately the same in all strands. The steel in the individual casting strands should have the same temperature, the same chemical structure and the same purity in terms of the content of non-metallic inclusions. These individual properties Metals 2023,13, 1821. https://doi.org/10.3390/met13111821 https://www.mdpi.com/journal/metals Metals 2023,13, 1821 2 of 18 are closely related to the characteristics of the steel flow in the tundish. The steel flow is influenced by the internal arrangements of the tundish, and various objects are inserted into the tundish in order to optimize the characteristics of the steel flow in a suitable way. Optimizing the bath flow in the tundish is an important part of the efficient operation of every continuous casting. It is clear from an analysis of the literature that at present, the most common objects inserted into the tundish to improve the characteristics of the flow include turbulence inhibitors, which are inserted under the ladle shroud, baffles, dams and weirs, and argon stirring elements [2–6]. Turbulence inhibitors prevent steel spattering when filling an empty tundish. They significantly reduce the turbulence intensity of the input pouring current. They direct the flow of steel, create an area for the steel to flow through the plug flow and assist the flotation of inclusions. Turbulence inhibitors increase and equalize the retention time of the bath in the tundish, increase the proportion of volume with plug flow and eliminate short-circuit flow. The use of the turbulence inhibitors can not only reduce the amount of entrained slag, but also reduce the reoxidation of steel during ladle replacement [7–12]. Baffles fundamentally change the characteristics of the steel flow in the tundish due to their holes. They direct the flow of the bath towards the surface of the steel in the tundish, thereby creating more suitable conditions for some non-metallic inclusions to float, while the adsorption process allows others to adhere to the partition surface. Baffles create thermal homogenization in the tundish. They increase the resistance of the steel flow, thereby increasing the minimum retention time. Baffles eliminate short-circuit flow, increase the proportion of steel volume with plug flow and reduce dead volume [13–17]. Dams and weirs aim to extend and equalize retention times, and eliminate dead volumes and short-circuit flow in the tundish. Dams and weirs can improve the temperature and chemical homogeneity of the steel in the tundish. The use of a weir alone could cause short-circuit flow and the formation of dead volumes. Therefore, it is advisable to combine it with a dam, which should eliminate the short-circuit flow issue. Dams are mainly used to direct the liquid flow towards the metal–slag interface to increase the retention time of the liquid steel in the tundish [18–20]. The argon stirring element in the bottom of the tundish favorably affects the characteristics of the flow. It has a positive effect on the proportion of volume with plug flow and on the reduction of the transition zone. It supports the temperature and chemical homogenization of steel in the tundish. Blown argon acts as a screen that directs the steel flow, thereby greatly promoting the floatation of inclusions and eliminating short-circuit flow. It is important to ensure the appropriate positioning of the argon stirring element and the appropriate flow of argon [21,22]. The optimization of the metallurgical processes of steel flow in the tundish is difficult under operating conditions. Therefore, in laboratory conditions, modelling is used, where the original prototype is replaced by a physical or numerical model. In physical modelling, the real system is replaced by a tangible physical model that is as identical to the behavior of the real system as possible. The purpose of physical modelling is the targeted utilization of the similarities between the processes that take place within the actual device and its model. In this method, both the prototype and the model have the same physical structure and purpose, and these similarities ensure that the results from the model can be applied to the prototype. One of the advantages of physical modelling is the ability to visualize the processes taking place in the real system. The second method of modelling is numerical modelling, which is advantageous for simulating metallurgical processes because, unlike physical modelling, extreme boundary conditions can be simulated. Unlike physical modelling, numerical modelling has a different physical structure to the prototype. The original technological process is replaced by a mathematical model that describes the given event through partial differential equations and continuity equations. This type of modelling is a useful tool, as the results achieved on the model can predict real system behavior during various process changes. Comparing the results of physical and numerical modelling is an effective and optimal variant of model research [2,23–28]. Metals 2023,13, 1821 3 of 18 The aim of the present article is to evaluate the methodology of laboratory experiments and simulations, namely, physical and numeral modelling, regarding the characteristics of steel flow in a tundish. 2. Materials and Methods 2.1. Experimental Conditions for Physical Modelling Physical experiments investigating the characteristics of steel flow in a tundish were performed in the Laboratory of Physical and Numerical Modelling at the Department of Metallurgical Technologies, Faculty of Materials Science and Technology, at the VSB—Technical University of Ostrava. The physical model, consisting of a ladle shroud, individual turbulence inhibitors and molds, was made of transparent organic glass (plexiglass) on a geometric scale of 1:4 to the operating tundish. This physical model also included two ladles to ensure the flow of water into the tundish through the ladle shroud. Each casting strand was equipped with a stopper rod, which, if necessary, could regulate the flow from the tundish to the molds. The casting strands were equipped with submerge entry nozzles at the same level as the steel in the molds. Figure 1shows the schema of the ladle, tundish and molds. Figure 2 shows a general overview of the experimental equipment. Metals 2023, 13, x FOR PEER REVIEW 3 of 18 real system behavior during various process changes. Comparing the results of physical and numerical modelling is an effective and optimal variant of model research [2,23–28]. The aim of the present article is to evaluate the methodology of laboratory experiments and simulations, namely, physical and numeral modelling, regarding the characteristics of steel flow in a tundish. 2. Materials and Methods 2.1. Experimental Conditions for Physical Modelling Physical experiments investigating the characteristics of steel flow in a tundish were performed in the Laboratory of Physical and Numerical Modelling at the Department of Metallurgical Technologies, Faculty of Materials Science and Technology, at the VSB— Technical University of Ostrava. The physical model, consisting of a ladle shroud, individual turbulence inhibitors and molds, was made of transparent organic glass (plexiglass) on a geometric scale of 1:4 to the operating tundish. This physical model also included two ladles to ensure the flow of water into the tundish through the ladle shroud. Each casting strand was equipped with a stopper rod, which, if necessary, could regulate the flow from the tundish to the molds. The casting strands were equipped with submerge entry nozzles at the same level as the steel in the molds. Figure 1 shows the schema of the ladle, tundish and molds. Figure 2 shows a general overview of the experimental equipment. The characteristics of the steel flow in the tundish were simulated in the physical model using a model liquid (water). The main advantages of using water are primarily its low cost, good availability and its physical properties, which are similar to liquid steel. The kinematic viscosities of liquid steel and water can be considered to be very similar. Table 1 shows the basic parameters of the prototype and the model. Figure 1. Schema of the ladle, tundish and molds. Figure 1. Schema of the ladle, tundish and molds. Metals 2023,13, 1821 4 of 18 Metals 2023, 13, x FOR PEER REVIEW 4 of 18 Figure 2. Experimental device—the physical model of an asymmetric five-strand tundish. Table 1. Basic parameters of the prototype and the model. Symbol Parameter Prototype Model V Volume of the bath in the tundish [m3] 4.64 37.12 × 10−3 m Weight of the bath in the tundish [kg] 32,480 37.04 Tk Average temperature of the bath [K] 1520 + 273 20 + 273 ρk Average density of the bath [kg·m−3] 7000 998 νk Kinematic viscosity of the bath [m2·s−1] 0.913 × 10−6 1.02 × 10−6 g Gravitational acceleration [m·s−2] 9.81 9.81 pv Pressure above the bath surface [kg·m−1·s−2] 98.06 × 103 98.06 × 103 L1 Internal length of the tundish at the plane of the bottom [m] 6.387 1.597 L2 Distance between SEN [m] 1.5 0.375 D1 Inner diameter of the ladle shroud [m] 0.085 0.021 H1 Bath height appropriate to weight m [m] 0.925 0.231 H2 Distance of the ladle shroud orifice from the bottom of the TI [m] 0.525 0.131 Qm, k Mass flow rate of the bath to the tundish [kg·min−1] 2779 12.39 Qv, k Volumetric flow rate of the bath to the tundish [l·min−1] 397 12.41 Qv, kr Volumetric flow rate on the each SEN [l·min−1] 79.4 2.48 The physical model was equipped with a measuring center, to measure the conductivity and temperature of the model and its regulatory system, as well as volumetric flow Figure 2. Experimental device—the physical model of an asymmetric five-strand tundish. The characteristics of the steel flow in the tundish were simulated in the physical model using a model liquid (water). The main advantages of using water are primarily its low cost, good availability and its physical properties, which are similar to liquid steel. The kinematic viscosities of liquid steel and water can be considered to be very similar. Table 1 shows the basic parameters of the prototype and the model. Metals 2023,13, 1821 5 of 18 Table 1. Basic parameters of the prototype and the model. Symbol Parameter Prototype Model VVolume of the bath in the tundish [m3]4.64 37.12 ×10−3 m Weight of the bath in the tundish [kg] 32,480 37.04 TkAverage temperature of the bath [K] 1520 + 273 20 + 273 ρkAverage density of the bath [kg·m−3]7000 998 νk Kinematic viscosity of the bath [m 2· s −1 ] 0.913 ×10−61.02 ×10−6 gGravitational acceleration [m·s−2]9.81 9.81 pvPressure above the bath surface [kg·m−1·s−2]98.06 ×10398.06 ×103 L1Internal length of the tundish at the plane of the bottom [m] 6.387 1.597 L2Distance between SEN [m] 1.5 0.375 D1Inner diameter of the ladle shroud [m] 0.085 0.021 H1 Bath height appropriate to weight m [m] 0.925 0.231 H2 Distance of the ladle shroud orifice from the bottom of the TI [m] 0.525 0.131 Qm, k Mass flow rate of the bath to the tundish [kg·min−1]2779 12.39 Qv, k Volumetric flow rate of the bath to the tundish [l·min−1]397 12.41 Qv, kr Volumetric flow rate on the each SEN [l·min−1]79.4 2.48 The physical model was equipped with a measuring center, to measure the conductivity and temperature of the model and its regulatory system, as well as volumetric flow meters, and conductivity and temperature probes, which were placed in the ladle shroud and in each submerge entry nozzle. The conductivity probes measured conductivity continuously using two opposite platinum electrodes, and the temperature probes measured in the range 0–60 ◦C using a temperature Ni resistance sensor. Laboratory experiments were conducted in accordance with the theory of similarity between the prototype and the model, based on the identity of Froude’s criterion. It was necessary to ensure, in particular, geometrical similarity between the prototype and its model, and the dynamic similarity of fluid flow through each. Before each experiment, the relevant internal arrangement of the tundish was set up, i.e., inserting the relevant turbulence inhibitor into the tundish and setting the position and height of the ladle shroud relative to the turbulence inhibitor, until a steady state of casting was reached. Subsequently, the experiment itself was started and an impulse of 50 mL of aqueous KCl solution was injected into the ladle shroud. The response to the impulse was monitored by the submerge entry nozzles, particularly the change in conductivity and temperature. As the results of each experiment were affected by minor flow fluctuations in the tundish, each experiment was repeated three times to ensure the reproducibility of the results. If a discrepancy was noted between the results, further experiments were performed until three matching results were attained. For further evaluation, the mean of all three correct measurements was calculated. The main aim of physical modelling was to achieve insight into the influence of relevant parameters on the characteristics of steel flow in the tundish, in particular: •The shape of the turbulence inhibitor; •The position of the ladle shroud in relation to the turbulence inhibitor. Three variants of turbulence inhibitor were used for modelling, referred to as TI1 (i.e., turbulence inhibitor 1), TI2 and TI3 (see Figure 3). TI1 was a basic square variant, located at the back wall of the tundish; TI2 was a rectangular variant and extended over the entire width of the tundish; and TI3 was a variant TI2 with a convex bottom. Metals 2023,13, 1821 6 of 18 Metals 2023, 13, x FOR PEER REVIEW 5 of 18 meters, and conductivity and temperature probes, which were placed in the ladle shroud and in each submerge entry nozzle. The conductivity probes measured conductivity continuously using two opposite platinum electrodes, and the temperature probes measured in the range 0–60 °C using a temperature Ni resistance sensor. Laboratory experiments were conducted in accordance with the theory of similarity between the prototype and the model, based on the identity of Froude’s criterion. It was necessary to ensure, in particular, geometrical similarity between the prototype and its model, and the dynamic similarity of fluid flow through each. Before each experiment, the relevant internal arrangement of the tundish was set up, i.e., inserting the relevant turbulence inhibitor into the tundish and setting the position and height of the ladle shroud relative to the turbulence inhibitor, until a steady state of casting was reached. Subsequently, the experiment itself was started and an impulse of 50 mL of aqueous KCl solution was injected into the ladle shroud. The response to the impulse was monitored by the submerge entry nozzles, particularly the change in conductivity and temperature. As the results of each experiment were affected by minor flow fluctuations in the tundish, each experiment was repeated three times to ensure the reproducibility of the results. If a discrepancy was noted between the results, further experiments were performed until three matching results were attained. For further evaluation, the mean of all three correct measurements was calculated. The main aim of physical modelling was to achieve insight into the influence of relevant parameters on the characteristics of steel flow in the tundish, in particular: • The shape of the turbulence inhibitor; • The position of the ladle shroud in relation to the turbulence inhibitor. Three variants of turbulence inhibitor were used for modelling, referred to as TI1 (i.e., turbulence inhibitor 1), TI2 and TI3 (see Figure 3). TI1 was a basic square variant, located at the back wall of the tundish; TI2 was a rectangular variant and extended over the entire width of the tundish; and TI3 was a variant TI2 with a convex bottom. (a) (b) (c) Figure 3. Variants of turbulence inhibitors used for physical modelling: (a) TI1; (b) TI2; (c) TI3. The individual turbulence inhibitors were located in the tundish between the third and fourth casting strands (see Figure 4). The other monitored parameter, based on Figure 3. Variants of turbulence inhibitors used for physical modelling: (a) TI1; (b) TI2; (c) TI3. The individual turbulence inhibitors were located in the tundish between the third and fourth casting strands (see Figure 4). The other monitored parameter, based on operational cases, was the position of the ladle shroud in relation to the turbulence inhibitor (see Figure 4).which were based on operational cases Metals 2023, 13, x FOR PEER REVIEW 6 of 18 operational cases, was the position of the ladle shroud in relation to the turbulence inhibitor (see Figure 4).which were based on operational cases The positions of the ladle shroud in relation to the turbulence inhibitor in the model were as follows: • Rear position 1 (R1)—identical for all variants; • Rear position 2 (R2)—identical for all variants; • Center position (C)—for TI1; Rear position 3 (R3) for TI2 and TI3; • Front position 1 (F1)—for TI1; identical to Center position (C) for the TI2 and TI3. (a) (b) (c) Figure 4. Internal arrangement of the tundish model including the individual positions of the ladle shroud for the individual turbulence inhibitors: (a) TI1-R1, R2, C, F1; (b) TI2-R1, R2, R3, C; (c) TI3R1, R2, R3, C. 2.2. Experimental Conditions for Numerical Modelling As part of numerical modelling, parallel numerical simulations were performed in the CFD (Computational Fluid Dynamics) environment of the ANSYS Fluent program, version 19.2, which is part of the ANSYS Workbench software package. Numerical simulations aimed to verify the results of the physical modelling for selected variants. Variants with all types of the turbulence inhibitors, TI1, TI2 and TI3, were chosen for verification. The ladle shroud was in its central position, i.e., always above the geometric center of the respective turbulence inhibitor (position C). Figure 5 shows the 3D geometry of the tundish using TI3. For the numerical simulations, a tundish model was created at a scale of 1:1. The components of the tundish model were the appropriate turbulence inhibitor, ladle shroud, stopper rods and outlet nodes, including the submerge entry nozzles. Figure 5. 3D geometry of the modelled area using TI3. Figure 4. Internal arrangement of the tundish model including the individual positions of the ladle shroud for the individual turbulence inhibitors: ( a ) TI1-R1, R2, C, F1; ( b ) TI2-R1, R2, R3, C; ( c ) TI3-R1, R2, R3, C. The positions of the ladle shroud in relation to the turbulence inhibitor in the model were as follows: •Rear position 1 (R1)—identical for all variants; •Rear position 2 (R2)—identical for all variants; •Center position (C)—for TI1; Rear position 3 (R3) for TI2 and TI3; •Front position 1 (F1)—for TI1; identical to Center position (C) for the TI2 and TI3. Metals 2023,13, 1821 7 of 18 2.2. Experimental Conditions for Numerical Modelling As part of numerical modelling, parallel numerical simulations were performed in the CFD (Computational Fluid Dynamics) environment of the ANSYS Fluent program, version 19.2, which is part of the ANSYS Workbench software package. Numerical simulations aimed to verify the results of the physical modelling for selected variants. Variants with all types of the turbulence inhibitors, TI1, TI2 and TI3, were chosen for verification. The ladle shroud was in its central position, i.e., always above the geometric center of the respective turbulence inhibitor (position C). Figure 5shows the 3D geometry of the tundish using TI3. For the numerical simulations, a tundish model was created at a scale of 1:1. The components of the tundish model were the appropriate turbulence inhibitor, ladle shroud, stopper rods and outlet nodes, including the submerge entry nozzles. Metals 2023, 13, x FOR PEER REVIEW 6 of 18 operational cases, was the position of the ladle shroud in relation to the turbulence inhibitor (see Figure 4).which were based on operational cases The positions of the ladle shroud in relation to the turbulence inhibitor in the model were as follows: • Rear position 1 (R1)—identical for all variants; • Rear position 2 (R2)—identical for all variants; • Center position (C)—for TI1; Rear position 3 (R3) for TI2 and TI3; • Front position 1 (F1)—for TI1; identical to Center position (C) for the TI2 and TI3. (a) (b) (c) Figure 4. Internal arrangement of the tundish model including the individual positions of the ladle shroud for the individual turbulence inhibitors: (a) TI1-R1, R2, C, F1; (b) TI2-R1, R2, R3, C; (c) TI3R1, R2, R3, C. 2.2. Experimental Conditions for Numerical Modelling As part of numerical modelling, parallel numerical simulations were performed in the CFD (Computational Fluid Dynamics) environment of the ANSYS Fluent program, version 19.2, which is part of the ANSYS Workbench software package. Numerical simulations aimed to verify the results of the physical modelling for selected variants. Variants with all types of the turbulence inhibitors, TI1, TI2 and TI3, were chosen for verification. The ladle shroud was in its central position, i.e., always above the geometric center of the respective turbulence inhibitor (position C). Figure 5 shows the 3D geometry of the tundish using TI3. For the numerical simulations, a tundish model was created at a scale of 1:1. The components of the tundish model were the appropriate turbulence inhibitor, ladle shroud, stopper rods and outlet nodes, including the submerge entry nozzles. Figure 5. 3D geometry of the modelled area using TI3. Figure 5. 3D geometry of the modelled area using TI3. This created and defined geometry was subsequently imported into the meshing preprocessor environment, where a regular structured mesh was generated using the cut cell method. After creating the geometry and generating the computational mesh, the model was defined in Fluent. The standard k-epsilon turbulence model was chosen for the calculation of the steady flow field, taking into account the characteristics of the steel flow in the tundish. A standard wall function was defined on the walls of the tundish. Subsequently, the material properties of the following mediums were defined. To verify the results from the physical experiments, steel was simulated as a material in the numerical simulations. The thermophysical properties of steel were defined as a function of temperature for three values using a linear function. The defined thermophysical properties of steel are shown in the Table 2. Table 2. Thermophysical properties of steel for numerical simulations. Temperature (K) Density (kg·m−3) Specific Heat (J·kg−1·K−1) Thermal Conductivity (W·m−1·K−1) Viscosity (kg·m−1·s−1) 1793 6970 821 35 0.0055 1773 6985 813 35 0.0057 1753 7001 805 35 0.0059 In the next step, the boundary conditions were set. The operating conditions of the numerical simulations were also set within the boundary conditions. Values for heat loss through the walls of the tundish were set based on the literature [ 29 , 30 ]. The defined boundary conditions are listed in the Table 3. Calculations for the characteristics of the flow in the tundish basin took place in SW ANSYS Fluent and were solved by the numerical finite volume method. In order to achieve a convergent calculation solution, which is the goal in numerical simulations, it was necessary to determine the sizes of the residuals and the number of iterations. For the transient calculation, it was also necessary to determine the time step size, the number of time steps and the maximum number of iterations per time step. Metals 2023,13, 1821 8 of 18 Table 3. Model setup boundary conditions for numerical simulations. Parameter Value Mass flow rate of the steel through the ladle shroud [kg · s −1 ] 46.32 Casting temperature [K] 1773 Turbulence intensity [%] 10 Hydraulic diameter [m] 0.085 Heat flux of the free surface [W·m−2]15,000 Heat flux through the walls of the tundish [W·m−2]2500 Gravity [m·s−2]−9.81 Operating pressure [Pa] 101,325 Operating temperature [K] 1773 3. Results and Discussion The evaluation of the physical experiments was carried out in three phases. In the first phase, retention time results were compared; in the second phase, the results were compared on the basis of the distribution of individual volumes in the tundish; and in the last evaluation phase, visualization photos were taken, with injected dye showing the characteristics of the bath flow in the tundish. As the results of each trial were affected by minor flow fluctuations in the tundish, each trial was repeated three times to ensure the reproducibility of the results. For further assessment, the mean of all three correct measurements was calculated. The characteristics of steel flow in the tundish were studied as part of numerical simulations. A basic calculation of steady flow was performed in order to obtain a stationary flow field of the steel in the tundish. With this steady flow field, a transient calculation of RTD curves was subsequently performed using the species model. 3.1. Evaluation Methodology of the Physical Experiments In the case of tundish metallurgy, it is important to know the amount of time a certain element of the melt spends in the tundish. The aim is to achieve characteristics that allow each element of the melt to stay in the tundish for as long as possible. The period of time that a certain part of the steel stays in the tundish is referred to as the retention time. The distribution of retention times is referred to as the RTD (residence time distribution). Retention times were determined by the conductivity method, which uses the differences in the conductivity of liquids. An aqueous solution of KCl, which is characterized by ionic conductivity, was used as an indicator medium in the individual experiments. The conductivity was measured with a conductivity probe at the input and output points of the tundish. The calculated results formed RTD C-curves [2]. The evaluation of the experiments was based on the measured data from the RTD curves. The minimum (c min ) and maximum (c max ) concentrations were determined from the measured course of the concentration change. From this, the dimensionless concentrations were calculated [2]. − c=(c−cmin)/(cmax −cmin)(1) The theoretical average retention time was calculated using the liquid volume in the tundish and the volumetric liquid flow rate through the tundish [2]. − τ=V/QV(2) The theoretical retention time considers a steady state when the volumetric liquid flow rate input into the tundish is the same as the volumetric liquid flow rate output. Since the steel flow in a multi-strand asymmetric tundish is associated with a dispersion of retention times, it was necessary to calculate the real retention time in order to evaluate the bath flow in the tundish [2]. − τreal =Zc·τ·dτ/Zc·dτ(3) Metals 2023,13, 1821 9 of 18 Furthermore, the minimum retention time ( τmin ) was determined from the measured course of the concentration change, which was defined as the time of the first appearance of the marker at the output, and the maximum retention time ( τmax ), which was the time it took to reach maximum concentration at the output of the tundish. The coefficient of variation (v) was determined from the retention times, which indicates the variability of the retention times in the individual casting strands. The coefficient of variation is expressed as the quotient of the standard deviation and the mean [2]. v=s/− x·100(4) The tundish was assessed as a whole and the non-uniformity of the flow was evaluated according to the values of the individual minimum retention times and the appropriate coefficients of variation. The higher the coefficient of variation, the less equal the minimum retention times were, resulting in large differences. This condition is not optimal. The aim is to achieve the highest possible minimum retention times and, at the same time, low coefficients of variation. The obtained retention times can be used to calculate parameters that further refine the characteristics of the flow in the tundish. The total volume of the tundish basin was separated into three parts: mixed volume (V m ), volume with plug flow (V p ) and dead volume (V d ), all of which have different flow characteristics [ 2 ]. In the mixed volume area, there was an intensive mixing of steel, which was caused by the kinetic energy of the input casting current. The proportion of the mixed volume in the tundish was always ensured. Only during the replacement of casting ladles during sequential casting, when the supply of steel to the tundish is interrupted, does the mixed volume drop to zero. The proportion of mixed volume in the tundish was determined as an addition to the total volume [2]. (Vm/V) + (Vp/V) + (Vd/V) = 1 (5) This mixed volume area was followed by the area with plug flow, which was uniform with the bath flow, where no element of the melt overtakes another element. In this volume, the steel flow already had a laminar characteristic, and therefore more favorable conditions were created for the floating of inclusions [2]. Vp/V=τmin/− τ(6) The third volume area of the tundish was the so-called dead volume. In this area, the steel flows very slowly and the melt has twice the average retention time. The dead volume reduces the active volume of the tundish, thus shortening the retention time of the steel flow. Local solidification of steel can occur in this area [2]. (Vd/V)=1−(− τreal/− τ(7) 3.2. Evaluation of the Flow Characteristics from the Physical Modelling Since the input to the tundish is positioned between casting strands 3 and 4, it is important that the highest possible minimum retention times for these strands are achieved, in order to eliminate short-circuit flow. The measured characteristics RTD C-curves show the dependence of the impulse change of concentration on time, the ladle shroud and all five casting strands for the selected variants, as can be seen in Figure 6. All measured and calculated flow characteristics are summarized in the Table 4. For better clarity, the flow characteristics are graphically displayed in Figures 7and 8. Metals 2023,13, 1821 16 of 18 Table 5. Minimum retention times and their coefficients of variation for variants in the numerical simulations. Variant CS1 τmin (s) CS2 τmin (s) CS3 τmin (s) CS4 τmin (s) CS5 τmin (s) Ø τmin (s) v (%) TI1-C 135 79 45 44 85 78 48 TI2-C 120 54 44 45 59 64 49 TI3-C 155 60 49 46 55 73 63 3.5. Comparison of the Results of the Physical Experiments and Numerical Simulations Table 6shows the minimum retention times from the results of the physical experiments for the selected variants, their conversion to the conditions of the prototype (time scale M τ = 0.5) and the minimum retention times determined from the results of the numerical simulations. These results also show the permanent change in concentration of the impulse and the transformation of the obtained F-curves into C-curves. When using TI2 and TI3, the converted minimum retention times of the prototype were always higher than the minimum retention times found in the numerical simulations. When using TI1, the converted minimum retention times of the prototype were also higher, with the exception of casting strands closest to the ladle shroud, CS3 and CS4, where the higher minimum retention times were equal to those from numerical simulations. Table 6. Comparison of minimum retention times from the physical experiments and numerical simulations. Variant Conditions CS1 τmin (s) CS2 τmin (s) CS3 τmin (s) CS4 τmin (s) CS5 τmin (s) Ø τmin (s) TI1-C Model 87 48 19 19 47 44 Prototype 174 96 38 38 94 88 NS 135 79 45 44 85 78 TI2-C Model 108 52 23 23 48 51 Prototype 216 104 46 46 96 102 NS 120 54 44 45 59 64 TI3-C Model 93 43 25 25 57 49 Prototype 186 86 50 50 114 98 NS 155 60 49 46 55 73 Deviations in the values of the minimum retention times in the physical and numerical model can be explained by different influences, such as using two different methods to determine retention times. This is the reason for implementing an instantaneous impulse (Dirac impulse—C-curve) in the physical experiments, in contrast to permanent change of marker concentration (Heaviside unit step—F-curve) in the numerical simulations. In the numerical simulations, the selected turbulence model (e.g., k-epsilon, k-omega), in some cases, affected the resulting retention time values. Numerical modelling confirmed the results from the physical modelling, and with regard to determining the minimum retention times on individual casting strands, the verification of the results can be considered sufficiently determining. Within all modelled variants, the minimum retention times were detected first on CS3 and CS4, then on CS2 and CS5, and lastly on the furthest, CS1. 4. Conclusions In the case of this asymmetric tundish, it is important to increase the values of the minimum retention times for casting strands 2, 3, 4 and 5, and, at the same time, reduce the minimum retention time for casting strand 1. This was partially achieved in regard to the the coefficients of variation by using TI3. The V p /V d ratio has proven to be a Metals 2023,13, 1821 17 of 18 determining factor for the characteristics of the flow of the bath in the tundish. In regard to the removal of non-metallic inclusions and other possible impurities, it is advantageous for the value of the ratio to be as large as possible. In accordance with the literature, the shape of the turbulence inhibitor and the position of the ladle shroud in relation to the turbulence inhibitor appeared to be crucial parameters influencing the characteristics of the steel flow in the tundish. It is important that the entire volume of the flow falls inside the turbulence inhibitor and to avoid positions where the flow falls mainly on the front edge of the turbulence inhibitor. As part of the model research solution, geometric modifications to existing turbulence inhibitors and other technological parameters used in the operating conditions were proposed and verified, in order to optimize steel flow in the tundish. The optimization of the steel flow in the tundish using TI3 has been proven through physical and numerical modelling. The comparison of the results of physical and numerical modelling is an effective and optimal variant of model research, providing a modern approach to solving practical industrial problems. Author Contributions: Conceptualization and methodology, characterization, visualization and writing—original draft, J.W.; methodology, characterization and writing—review and editing, M.T.; writing—review and editing, M.V., M.M., J.C. (JiˇríCupekand), T.H., J.C. (JiˇríCibulka) and J.R.; methodology, characterization and writing—review and editing, K.M. All authors have read and agreed to the published version of the manuscript. Funding: This study was conducted with the support of a student grant competition run by the VSB—Technical University of Ostrava, project number SP2023/034—Research and Development of Composite Multifunctional Materials for Sustainable Progress. Data Availability Statement: Not applicable. Acknowledgments: This research was undertaken thanks to project No. CZ.02.1.01/0.0/0.0/17_049/ 0008399 of the EU, and CR financial funds provided by the Operational Programme Research, Development and Education, Call 02_17_049 Long-Term Intersectoral Cooperation for ITI, Managing Authority: Czech Republic—Ministry of Education. Conflicts of Interest: Markéta Tkadleˇcková; Tomáš Huczala and JiˇríCibulka were employed by the company Tˇ RINECKÉŽELEZÁRNY, a.s. The authors declare no conflict of interest. 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