Numerical analysis of RTD curves and inclusions removal in a multi-strand asymmetric tundish with different configuration of impact ad

metals Article Numerical Analysis of RTD Curves and Inclusions Removal in a Multi-Strand Asymmetric Tundish with Different Configuration of Impact Pad Markéta Tkadleˇcková1,* , Josef Walek 1, Karel Michalek 1and Tomáš Huczala 2 1Faculty of Materials Science and Technology, VŠB—Technical University of Ostrava, 17. listopadu 2172/15, 70800 Ostrava, Czech Republic; [email protected] (J.W.); [email protected] (K.M.) 2Tˇ RINECKÉŽELEZÁRNY, a.s, Pr˚umyslová1000, StaréMˇesto, 739 61 Tˇrinec, Czech Republic; T[email protected] *Correspondence: [email protected]; Tel.: +420-597-325130 Received: 31 May 2020; Accepted: 24 June 2020; Published: 27 June 2020   Abstract: To effectively remove non-metallic inclusions from the steel during the flowing in a five-strandasymmetrictundish, thenovelconfigurationoftheimpactpadwasdeveloped. For analysis, complex numerical modelling in the programme ANSYS Fluent was used. The Lagrangian Discrete Phase Model of inclusion tracking was applied. The distribution of inclusions, with sizes ranging from 2 µ m to 100 µ m and density from 2500 to 3500 kg · m −3 , was considered only through the shroud tube. The residence time distribution (RTD) curves and inclusion removal efficiency were used for evaluation of steady state steel flow character depending on internal configuration of a tundish with an impact pad in two design modifications (Modification 1—M1, Modification 2—M2). The preliminary results showed that in the case of asymmetric geometry plays a role the computational mesh independency. The assembly method with cut cell approach was satisfactory even when the tundish geometry was changed. The RTD curves with an M1 showed a huge dead volume in the tundish. In the case with an M2, the RTD curves are more or less uniform for all casting strands, and the removal of inclusions to slag increased from about 55% up to 70% in comparison with M1. Keywords: steel; non-metallic inclusion; tundish; impact pad; numerical modelling; RTD; DPM 1. Introduction At present, the world production of continuously cast steel accounts for 96% of the total. In the Czech Republic, approx. 92% of steel is cast by continuous casting [ 1 ]. During the continuous casting of steel, the ladle with steel melt is placed on the rotating casting stand of a casting machine. From the ladle, the steel is cast through the shroud tube into the tundish. Then, the steel is taken through the submerged entry nozzle to the oscillating moulds (in the primary cooling zone), where the “controlled” solidification of steel is ensured. There, under the moulds, is a system of guiding and supportive rollers (the secondary cooling zone), including refrigerating nozzles, which ensure the drawing, transforming, and cooling of the casting strand of steel [2,3]. Tundish is one of the most important technology nodes of a continuous casting machine. It primarily serves as the melt reservoir in the sequential casting during the exchange of ladles and ensures the melt distribution into individual casting strands [ 4 – 8 ]. The tundish also regulates the steel mass flow into moulds, reduces ferrostatic pressure of the liquid steel, and homogenizes the melt temperature [ 9 – 13 ]. Flow in the tundish region during the continuous casting of steel can influence many important phenomena, especially removal of the non-metallic inclusions (e.g., [14,15]). Inclusions are non-metallic particles that can be endogenous or exogenous in nature and, if not removed from the steel melt during its processing, reduce the quality of the finished steel Metals 2020,10, 849; doi:10.3390/met10070849 www.mdpi.com/journal/metals Metals 2020,10, 849 2 of 20 product [ 16 ]. The last point where the amount of non-metallic inclusions in the steel melt can be modified during continuous casting is mainly the tundish. Therefore, a number of studies are devoted to the optimization of the flow in the tundish using different weirs and dams [ 17 – 25 ], impact pads (e.g., [ 26 , 27 ]), ladle shroud [ 28 ], or argon injection [ 29 – 31 ]. To study the steel flow, the authors usually utilize the knowledge of experimental measurements or modelling methods, both physical and numerical (e.g., [ 32 ]). To evaluate the nature of the flow, they use measuring methods of the tracing agent concentration as it passes through the reactor and determine the so-called RTD (residence time distribution) curves. The situation becomes more complicated when performing a check of the reduction of inclusions during the flow of steel melt in the tundish. Because the verification of inclusions rising to the top slag in the tundish by means of operational measurements is unrealistic or very demanding in the case of physical modelling [ 12 , 14 , 33 , 34 ], the authors of the publications use numerical modelling (e.g., [ 35 – 37 ]). However, in the publications dealing with numerical modelling of inclusions removal, there is only a sporadic description of a complex modelling procedure, while the articles are mainly limited to the evaluation of inclusion separation depending on the selected boundary conditions of casting. Nevertheless, the results of numerical modelling depend on the accuracy of the setting of the model. In published papers, the mathematical formulations of solving equations are obviously discussed. In this case, the [38–40] presented only short information about the study of mesh independence. Because numerical modelling is a very valuable tool in metallurgy, especially in cases where a physical model of the equipment is not available, the submitted paper aims to present a complete procedure of numerical solution. Because most authors used the package CFD ANSYS Workbench (CFD—Computational Fluid Dynamics) with software ANSYS Fluent, we also carried out our analysis using this software. The numerical solution of inclusions removal using Lagrangian approach is demonstrated in the development of the configuration change design of the impact pad for an asymmetric five-strand tundish. The presented solution lies in a specific complexity of the geometry of the tundish model, which is, in addition to the asymmetrical shape of the tundish, also complicated by the presence of impact pad and stoppers. Therefore, in addition to the description of the modelling procedure and the selection of appropriate physical models, attention is paid in the discussion to the preparation of an independent computational mesh. An independent computational mesh is important in case of the complex geometry of the modelled area, or in case of change of geometry of the modelled area, and if we do not have other methods of process verification available, and based on the result of numerical modelling, we give recommendations for operation. The flow character of the steel melt in the tundish is studied using velocity vectors, temperature fields profile, RTD curves, retention times and volumes in the tundish (mixed, dead and plug). A removal efficiency of inclusions was evaluated depending on steady state steel flow character and internal configuration of tundish with an impact pad in two design modifications (Modification 1—M1, Modification 2—M2). 2. Numerical Model Description In order to obtain the RTD curves and apply a Lagrangian approach for the analysis of the inclusions and their removal, it was first necessary to calculate the steady velocity and temperature field of the flowing steel in the tundish. Subsequently, the RTD curves, the trajectories of the inclusions and their separation were calculated for a steady flow pattern. The following assumptions were considered: blacksquareThe flow was considered to be incompressible, viscous, and turbulent. The flow represented steady state with constant casting temperature. The calculation of steel flow included the effect of the natural convection. The transfer and conduction of heat were assumed through convection as well as conduction.  The heat losses were considered to be through the walls of the tundish and through the melt surface. The inclusions were spherical in shape and are let into the domain through a shroud tube. Metals 2020,10, 849 3 of 20 There is no exchange of mass, heat or chemical reactions between the melt and the inclusion. The inclusion is small enough, and its presence does not affect the velocity field of the melt.  There is no coagulation or coalescence of inclusions. If the inclusion hits a wall, it is reflected. If the inclusion touches the top surface of melt, it is absorbed (as into slag) and escapes the domain. When taking into account the forces acting on the inclusion particle, the following were included: Gravity force Aerodynamic drag force Influence of pressure gradient Virtual mass force The influence of the pressure gradient and the virtual mass force should be considered if the density of the continuum (melt) is greater than the density of the particle (inclusion). The virtual mass force accelerates the surrounding continuous phase in the immediate vicinity of the particles. On the other hand, it can be considered that the sizes of the particles are very small and their response times to the flow are minor. More details about virtual mass force can be found e.g., in [41]. Numerical modelling of steel flow and inclusion removal in a 5-strand asymmetric tundish was therefore modelled in three steps according to the above prerequisites: 1. Basic calculation of steady flow, obtaining a steady velocity and temperature field 2. Calculation of RTD curves 3. Calculation of inclusion removal The result of the calculation are velocity and temperature fields, RTD curves, the removal efficiency of inclusions escaped into the melt surface and percentage of inclusions torn down into the submerge entry nozzles of the casting strands. To be able calculate the steel flow, the Navier-Stokes equations together with the model of turbulence must be applied. In RTD curves calculation, the Species Model is good to use because the model enables calculation of the species transport, respectively concentration change monitoring without reaction. To simulate a behaviour of discrete second phase (inclusions) in continuous phase (steel melt), the ANSYS Fluent allows use of the Discrete Phase Model with the Lagrangien approach. This approach is very comfortable, and the calculation is very fast [42]. 2.1. Governing Equations The equations for mass, momentum and energy were solved. For the flow involving species mixing, a species conservation equation was used. For inclusion trajectory calculations the Lagrangian approach was applied. 2.1.1. Steel Flow Equations The three-dimension steel turbulent flow was described by the Navier-Stokes equation together with the continuity equation and a standard kε turbulent model. In the case of non-stationary incompressible isothermal flow, they have the following form [43,44]: Continuity equation ∂u ∂x+∂v ∂y+∂w ∂z=0 (1) Navier–Stokes equations ∂u ∂t+∂(uu) ∂x+∂(uv) ∂v+∂(uw) ∂z=−1 ρ ∂p ∂x+v ∂2u ∂x2+∂2u ∂y2+∂2u ∂z2!+fx(2) ∂v ∂t+∂(vu) ∂x+∂(vv) ∂v+∂(vw) ∂z=−1 ρ ∂p ∂y+v ∂2v ∂x2+∂2v ∂y2+∂2v ∂z2!+fy(3) Metals 2020,10, 849 4 of 20 ∂w ∂t+∂(wu) ∂x+∂(wv) ∂v+∂(ww) ∂z=−1 ρ ∂p ∂z+v ∂2w ∂x2+∂2w ∂y2+∂2w ∂z2!+fz(4) where x,y, and zare coordinates, u,v,ware velocity components, pis pressure, and fis components of outer volume force. The turbulence kinetic energy kand its rate of dissipation ε are obtained from the following transport equations [42]: ∂ ∂t(ρk)+∂ ∂xi (ρkui)=∂ ∂xj" µ+µt σk!∂k ∂xj#+Gk+Gb−ρε −YM+Sk(5) ∂ ∂t(ρε)+∂ ∂xi (ρεui)=∂ ∂xj"µ+µt σε∂ε ∂xj#+C1ε ε k(Gk+C3εGb)−C2ερε2 k+Sε(6) where G k represents the generation of turbulence kinetic energy due to the mean velocity gradients, G b is the generation of turbulence kinetic energy due to buoyancy, Y M is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. C 1ε ,C 2ε , and C 3ε are constants. σk and σε are the turbulent Prandtl numbers for kand ε , or more precisely S k and S ε are user-defined source terms. The turbulent viscosity µtis computed by combining kand εas follows: µt=ρCµk2 ε(7) where C µ is a constant. The model constant was used with the following default values C 1ε =1.44, C2ε=1.92, Cµ=0.09, σk=1.0, and σε=1.3 [42]. 2.1.2. Species Transport Species model was used in the case of dimensionless concentration monitoring during a steady steel flow in the tundish and determination of residence time distribution curves (RTD curves). The local mass fraction of each species Y i through the solution of a convection-diffusion equation for the ith species was predicted in the following general form [42]: ∂ ∂t(ρYi)+∇·ρ→ vYi=−∇· → Ji+Ri+Si(8) where R i is the net rate of production of species iand S i is the rate of creation by addition from the dispersed phase. 2.1.3. Lagrangian Discrete Phase Model The Lagrangian discrete phase model performs trajectory calculations for dispersed phases (particles), including coupling with the continuous phase by integrating the force balance on the particle. This force balance can be written as [42]: d→ up dt = → u−→ up τr + → gρp−ρ ρp + → F(9) where → F is an additional acceleration (force/unit particle mass) term, → u−→ up τr is the drag force per unit particle mass and τr=ρpd2 p 18µ 24 CdRe (10) where τr is the droplet or particle relaxation time, uis the fluid phase velocity, u p is the particle velocity, µ is the molecular viscosity of the fluid, ρ is the fluid density, ρp is the density of the particle, and d p is the particle diameter. Cdis drag force coefficient. Re is the relative Reynolds number. Metals 2020,10, 849 5 of 20 2.2. Model Setting The basic 3D geometry of the 5-strand asymmetric tundish represents the internal volume of the modelled area (see Figure 1). The volume of the tundish is affected by a shroud tube, which is 650 mm away from the bottom. Below the shroud tube there is an impact pad, which has been designed in two design modifications M1 and M2 for the purpose of optimizing the separation of inclusions, as can be seen in Figure 1a,b. The height of the steel level in the tundish corresponds to a working volume of 32 ton and is 925 mm. The inner volume of the tundish is also reduced by the presence of stoppers. The modelled geometry includes submerged entry nozzles referred to as CS1 to CS5 (Casting Strand 1—Casting Strand 5). The distance between individual submerge entry nozzles was 1500 mm. The total length of the tundish was 6387 mm. Metals 2020, 10, x FOR PEER REVIEW 6 of 20 (a) (b) (c) Figure 1. 3D geometry of the modelled area, where (a) represents the floor plan of the tundish with the impact pad design M1 (b) represents the floor plan of the tundish bottom with the impact pad design M2 (c) front view of the tundish with elevated position of the impact pad, which is identical for both designs (i.e., M1 and M2). CS1–CS5 are Casting Strands. Table 1. Boundary conditions of model setting. Parameter Value Parameter Value Casting speed-velocity inlet/m·s −1 1.04 Working capacity of tundish/t 32.4 Mass flow rate in velocity inlet/t·min −1 2.4 Wall Roughness/m 0.005 Casting temperature/K 1773 Steel level in tundish/mm 925 Operating temperature/K 1773 Turbulent intensity/% 10 Operating pressure/Pa 101,325 Hydraulic Diameter/m 0.085 Gravity/m·s −2 −9.81 Heat flux of free surface/W·m −2 15,000 Thermo-physical properties f = T Heat flux of tundish walls/W·m −2 2500 Table 2. Thermo-physical properties of steel defined as a function of temperature. Temperature °C Density kg·m −3 Specific Heat J·kg −1 ·K −1 Thermal Conductivity W·m −1 ·K −1 Viscosity kg·m −1 ·s −1 1520 6970 821 35 0.0055 1510 6978 817 35 0.0056 1500 6985 813 35 0.0057 1490 6993 809 35 0.0058 1480 7001 805 35 0.0059 Figure 1. 3D geometry of the modelled area, where ( a ) represents the floor plan of the tundish with the impact pad design M1 ( b ) represents the floor plan of the tundish bottom with the impact pad design M2 ( c ) front view of the tundish with elevated position of the impact pad, which is identical for both designs (i.e., M1 and M2). CS1–CS5 are Casting Strands. The design of the impact pad, referred to as M1 (Figure 1a), is a raised hollow square construction block bounded by walls so that the flowing steel stream from a shroud tube is directed to the surface of steel melt in the tundish. Another design of the impact pad, referred to as M2 (Figure 1b), is represented by a hollow rectangular construction block extended to the entire width of the central part of the bottom of the tundish. In both cases, i.e., M1 and M2, this is an eccentric position of the impact point between the CS3 and CS4. In addition to adjusting the impact pad’s shape, we also changed the position of the shroud tube so that it would always point to the centre of the bottom of impact pads. The inner diameter of the shroud tube corresponds to a hydraulic diameter used on the inlet (see Table 1). Some curvatures of the geometry, especially between the transition of vertical outer walls of the tundish and the bottom, were neglected due to the subsequent preparation of the computational mesh. The details in the area of stoppers and outlet nodes, or more precisely the details of the impact pads have been maintained. A velocity-inlet boundary condition was defined at the mouth of the shroud tube with a constant inlet velocity of 1.04 m · s −1 (corresponding to a mass flow of 2 t · min −1 ) and a constant casting temperature of 1773 K. Turbulence was defined by a hydraulic diameter of 0.085 m and an intensity Metals 2020,10, 849 6 of 20 of 10%. The outflow boundary condition was considered on the outlets. Zero shear stress was defined on the melt surface. Table 1. Boundary conditions of model setting. Parameter Value Parameter Value Casting speed-velocity inlet/m·s−11.04 Working capacity of tundish/t 32.4 Mass flow rate in velocity inlet/t·min−12.4 Wall Roughness/m 0.005 Casting temperature/K 1773 Steel level in tundish/mm 925 Operating temperature/K 1773 Turbulent intensity/% 10 Operating pressure/Pa 101,325 Hydraulic Diameter/m 0.085 Gravity/m·s−2−9.81 Heat flux of free surface/W·m−215,000 Thermo-physical properties f =THeat flux of tundish walls/W·m−22500 The steady state flow calculation included the effect of natural convection. The transfer and conduction of heat were assumed by through convection as well as conduction. The heat losses were considered to be through the walls of the tundish and through the melt free surface. The value of the heat losses through the bottom and walls of the tundish was 2500 W · m −2 . Values of heat losses through the walls of the tundish used in the numerical simulation were set based on the literature [ 18 , 45 – 47 ]. In the case of heat flux on the free surface of steel melt, a slag thickness of 30 mm was considered. The heat fluxes on the wall were averaged and take into account the insulating effects of the brickwork lining. Thermo-physical properties of steel were defined as a function of temperature. To simulate the concentration change, it was necessary to define two components: the old and the new melt as a mixture (no reaction was considered, the thermo-physical properties are the same). The change in the concentration was performed using the species mass fraction function from value 0 (old melt) up to value 1 (new melt). All parameters of model setting are summarizing in Figure 1and in Tables 1–3. Distribution sizes and densities of inclusions are listed in Tables 4and 5. Table 2. Thermo-physical properties of steel defined as a function of temperature. Temperature ◦C Density kg·m−3 Specific Heat J·kg−1·K−1 Thermal Conductivity W·m−1·K−1 Viscosity kg·m−1·s−1 1520 6970 821 35 0.0055 1510 6978 817 35 0.0056 1500 6985 813 35 0.0057 1490 6993 809 35 0.0058 1480 7001 805 35 0.0059 Table 3. Calculation parameters. Type of Calculation Type of Results Turbulent Model Thermo-Physical Properties (f =T) Free Surface Steady Velocity/Temperature Standard k-ε/Standard Wall Function Piecewise-linear Specified Shear =0 Transient RTD/Inclusions Standard k-ε/Standard Wall Function Piecewise-linear Specified Shear =0 Metals 2020,10, 849 7 of 20 Table 4. Diameters of simulated inclusions and their distribution in the total volume of inclusions. Diameter of Inclusions/µm Distribution/% 2 35 5 25 10 20 20 10 50 5 100 5 Table 5. Densities of simulated inclusions and their distribution in the total volume of inclusions. Density of Inclusions/kg·m−3Distribution/% 2500 20 3000 60 3500 20 3. Results and Discussion The results of numerical modelling predict velocity, temperature, and concentration profiles under steady steel flow in the tundish. The size of the plug, mixed and dead volume are assessed using RTD curves. The distribution and tracing of inclusions are assessed both by residence times and distribution profiles of inclusions as well as by the removal efficiency of inclusions obtained from the data statements of the calculation. An analysis of the independence of the computational mesh was performed before the evaluation of the results of numerical simulation was initiated. 3.1. Independence of Computational Mesh During the optimization of steel flow in the tundish, numerous types of results can be observed. And if we want to ensure a timely response to the technical problems connected with final quality of steel billets influenced by the tundish metallurgy, we need the optimal, quickly prepared and universal method of numerical approach. The importance of computational mesh independence is especially important if we do not have verification methods other than numerical simulations available for the first process optimization designs. For this reason, we validated the approaches of computational mesh generation for the case of optimization of internal configuration of tundish construction, which affects the steel flow, or removal of non-metallic inclusions. For generation of mesh, the ANSYS Meshing was applied. The computational mesh is necessary for the discretization of equations of flow and heat-transfer or substance redistribution, etc., which are solved using the numerical methods. On the other hand, we need the mesh to be as coarse as possible, but at the same time, it must be able to capture the potential of the task and all variables. Also, it is good to take into account the mesh requirements for the computing performance (CPU and memory requirements). Bad quality of the computational mesh can lead to convergence difficulties, bad physics description, and diffuse solution. Therefore, at first, the mesh quality can be controlled by mesh metric tools, such as Element Quality, Aspect Ratio, Jacobian Ratio, Warping Factor, Parallel Deviation, Maximum Corner Angle, Skewness and Orthogonal Quality. Especially in the case of CFD simulation, it is good to control the skewness and orthogonal quality when the values are between 0 to 1. The value of metrics with an evaluation of quality mesh is defined in Table 6[42]. Table 6. Metrics spectrum for skewness and orthogonal quality of computational mesh [42]. Metric Unacceptable Bad Acceptable Good Very Good Excellent Skewness 0.98–1.00 0.95–0.97 0.80–0.94 0.50–0.80 0.25–0.50 0–0.25 Orthogonality 0–0.001 0.001–0.14 0.15–0.20 0.20–0.69 0.70–0.95 0.95–1.00 Metals 2020,10, 849 8 of 20 After the tundish meshing, it is necessary to realize the primary simulations with control not only of the character of convergence solution by residuals but also to monitor the velocity and temperature at the point or through the surface at the inlet and outlet area to achieve constant values of variables. To prepare the computational mesh for an asymmetric five-strand tundish with an impact pad and stoppers, in our case during the mesh tuning we compared the solution using the mesh with tetrahedral and hexahedral elements. In all verified cases, at/on the inlet and outlets, we monitored the velocity and temperatures using the velocity surface monitor and temperature point monitor. For generation of the mesh, we used initially the hexahedral method with patch conforming algorithm of mesh generation, and then the same method with patch independent algorithm as well as the multizone method. The direct utilization of Hexa dominant method was not possible. To use the multizone method, there was a need to slice the geometry and to define the interfaces between the individual slice surfaces of geometry in ANSYS fluent. This method was very time-consuming and difficult. Therefore, for the next validation of approaches, it was evaluated as not suitable. In the case of patch conforming algorithm, the size of elements was not sufficiently small, which was manifested even during the unstable convergence of the calculation and also by the large distortion of the calculated velocity at the nozzle, or in the velocity differences between nozzles (Figure 2). Therefore, the patch independent method was used, which neglected some small edges. At the same time, to achieve good mesh quality, it was necessary to reduce the size of the elements, which led to an increase in the number of elements up to 5 million and an increase in computing time. Metals 2020, 10, x FOR PEER REVIEW 9 of 20 Figure 2. Graphical comparison of the evolution of calculation of Mass-Weighted Average Velocity Magnitude through the selected nozzle of a 5-strand asymmetric tundish during validation of a computational mesh type. Figure 3. Final computational meshes prepared by Assembly Method with Cut Cell. 3.2. Flow and Temperature Fields As can be inferred from the longitudinal and transverse sections of the velocity vectors for the M1 configuration in Figures 4–6, the impacting casting stream from a shroud tube bounces from the bottom of the impact pad. The bounded impact space of the square impact pad M1 directs the impacting stream back concentratedly towards the surface. From the surface, the stream is directed to the front and rear walls of the tundish. As Figures 5 and 6 indicate, in the tundish with M1 impact pad, the circulation field was predicted between the front wall of the tundish and the impact pad. After the stream reflects against the front wall of the tundish, it continues towards the rear wall of the tundish, where it meets the strand near the rear wall of the tundish. At the same time, when the front space of the tundish is filled, steel begins to flow into the nozzles of CS3 and CS4. The higher flow velocity at the rear wall directs the steel flow along the wall toward the nozzle of CS5. The stream headed toward the right behaves similarly (from the front view of the tundish), i.e., to nozzles of CS2 and CS1. However, the longer flow path of the steel along the rear wall of the tundish results in slowing down of the steel flow velocity and, as a result of the presence of stoppers, also in demarcation of the steel flow, in particular along the rear wall. Behind the stopper of CS1 and at the bottom behind the mouth of CS2, a stagnant steel area with a very low flow velocity is visible. In order to avoid adverse flow phenomena in the M1 configuration, a modification of the impact area, referred to as M2, was proposed. As already noted in the introduction to the description of the calculation conditions, the modification of the impact area configuration involved the Figure 2. Graphical comparison of the evolution of calculation of Mass-Weighted Average Velocity Magnitude through the selected nozzle of a 5-strand asymmetric tundish during validation of a computational mesh type. Eventually, the assembly method with a cut cell approach, which could be used only for CFD calculation, was tested. The size of 5.3 mm was achieved as an independent size of the element and at the same time a high-quality mesh was obtained. Just couple of cells achieved substandard metrics, such as skewness and orthogonality. At the same time, by using this method we achieved a very fast stabilization of the expected velocity (depending on the flow rate on the inlet) at the outputs that were equal and constant through of all outlets. The approach chosen was satisfactory even when the tundish geometry was changed. The statistics of individual meshes are given in Table 7. Comparison of final meshes is shown in Figure 3. The total number of elements was 670,008 for the configuration with an M1 impact pad, respectively 708,778 for M2 impact pad, using the assembly method with cut cell. The computational time of flowing under steady state condition on PC with 6 cores took about 4 h. Metals 2020,10, 849 9 of 20 Table 7. The statistics of used mesh during setting validation of the numerical model. Method Type of Elements No. of Elements Element Size mm CPU (6 Processors) FL +TH Eq Skewness Min./Max. Orthogonality Min./Max. Patch Conforming Tetra 1,107,862 3.4 6 h 0.22 0.85 Patch Independent Tetra 5,739,912 1.7 10 h 0.0006/0.61 0.43/0.99 Assembly method Hexa 670,008 (M1) 708,778 (M2) 5.3 4 h 1.3 · 10–10/0.55 0.55/1.00 Metals 2020, 10, x FOR PEER REVIEW 9 of 20 Figure 2. Graphical comparison of the evolution of calculation of Mass-Weighted Average Velocity Magnitude through the selected nozzle of a 5-strand asymmetric tundish during validation of a computational mesh type. Figure 3. Final computational meshes prepared by Assembly Method with Cut Cell. 3.2. Flow and Temperature Fields As can be inferred from the longitudinal and transverse sections of the velocity vectors for the M1 configuration in Figures 4–6, the impacting casting stream from a shroud tube bounces from the bottom of the impact pad. The bounded impact space of the square impact pad M1 directs the impacting stream back concentratedly towards the surface. From the surface, the stream is directed to the front and rear walls of the tundish. As Figures 5 and 6 indicate, in the tundish with M1 impact pad, the circulation field was predicted between the front wall of the tundish and the impact pad. After the stream reflects against the front wall of the tundish, it continues towards the rear wall of the tundish, where it meets the strand near the rear wall of the tundish. At the same time, when the front space of the tundish is filled, steel begins to flow into the nozzles of CS3 and CS4. The higher flow velocity at the rear wall directs the steel flow along the wall toward the nozzle of CS5. The stream headed toward the right behaves similarly (from the front view of the tundish), i.e., to nozzles of CS2 and CS1. However, the longer flow path of the steel along the rear wall of the tundish results in slowing down of the steel flow velocity and, as a result of the presence of stoppers, also in demarcation of the steel flow, in particular along the rear wall. Behind the stopper of CS1 and at the bottom behind the mouth of CS2, a stagnant steel area with a very low flow velocity is visible. In order to avoid adverse flow phenomena in the M1 configuration, a modification of the impact area, referred to as M2, was proposed. As already noted in the introduction to the description of the calculation conditions, the modification of the impact area configuration involved the Figure 3. Final computational meshes prepared by Assembly Method with Cut Cell. 3.2. Flow and Temperature Fields As can be inferred from the longitudinal and transverse sections of the velocity vectors for the M1 configuration in Figures 4–6, the impacting casting stream from a shroud tube bounces from the bottom of the impact pad. The bounded impact space of the square impact pad M1 directs the impacting stream back concentratedly towards the surface. From the surface, the stream is directed to the front and rear walls of the tundish. As Figures 5and 6indicate, in the tundish with M1 impact pad, the circulation field was predicted between the front wall of the tundish and the impact pad. After the stream reflects against the front wall of the tundish, it continues towards the rear wall of the tundish, where it meets the strand near the rear wall of the tundish. At the same time, when the front space of the tundish is filled, steel begins to flow into the nozzles of CS3 and CS4. The higher flow velocity at the rear wall directs the steel flow along the wall toward the nozzle of CS5. The stream headed toward the right behaves similarly (from the front view of the tundish), i.e., to nozzles of CS2 and CS1. However, the longer flow path of the steel along the rear wall of the tundish results in slowing down of the steel flow velocity and, as a result of the presence of stoppers, also in demarcation of the steel flow, in particular along the rear wall. Behind the stopper of CS1 and at the bottom behind the mouth of CS2, a stagnant steel area with a very low flow velocity is visible. In order to avoid adverse flow phenomena in the M1 configuration, a modification of the impact area, referred to as M2, was proposed. As already noted in the introduction to the description of the calculation conditions, the modification of the impact area configuration involved the extension of the impact area of the pad in a cross-section view toward the front and rear walls of the tundish (and creation of a rectangular bounded impact area) and shifting the shroud tube position so that it is directed toward the centre of impact area (similar to M1). While in the M1 configuration the inlet flow between the front and rear part of the tundish is unevenly distributed following the impact of the melt stream, in the M2 configuration the impacting stream is directed evenly toward both the front and rear tundish walls and then upwards toward the surface. Near the surface, the stream again flows evenly both to the right and to the left of the shroud tube, as indicated by the arrows for M2 in Figure 6. The higher flow velocity at the surface and closer to the rear tundish wall directs the flow from the back of the tundish to the front area. Therefore, the nozzles of CS3 and CS4 are not affected first, was the case with M1, but rather the nozzles of CS5 and CS4. Immediately after reaching the nozzles Metals 2020,10, 849 16 of 20 size of 50 to 100 µ m are removed from 80% in average through the surface in all modelled versions. The M1 variant for inclusions with a density of 3000 kg · m −3 and a diameter of 10 µ m shows a minimum removal efficiency of inclusions through the surface, at only 52%. In the M2 version, approximately 70% of the inclusions are removed through the surface and the distribution of inclusions in nozzles of the casting strands is on average approximately 5%. However, what is taken into account is that the proportion of these large inclusions is only 5% of the total amount of inclusions in the melt volume flowing through the tundish. As the diameter of the inclusions increases, the conditions for capturing the inclusions by the slag improve which is consistent with results of the other authors, e.g., [ 30 ] or [ 34 ]. This trend is explained by the change of the forces affecting the particles according to their size, where the particles up to 40 µ m are carried away by inertial forces, while the flotation principle starts to be applied in larger inclusions. If we compare the achieved results with the results of the authors in more detail [ 34 , 38 ], it should be noted that the efficiency of inclusions removal will be significantly affected by their density and the amount of steel melt in the tundish. This will be the subject of further research. Metals 2020, 10, x FOR PEER REVIEW 16 of 20 modelled versions. The M1 variant for inclusions with a density of 3000 kg⋅m −3 and a diameter of 10 µm shows a minimum removal efficiency of inclusions through the surface, at only 52%. In the M2 version, approximately 70% of the inclusions are removed through the surface and the distribution of inclusions in nozzles of the casting strands is on average approximately 5%. However, what is taken into account is that the proportion of these large inclusions is only 5% of the total amount of inclusions in the melt volume flowing through the tundish. As the diameter of the inclusions increases, the conditions for capturing the inclusions by the slag improve which is consistent with results of the other authors, e.g., [30] or [34]. This trend is explained by the change of the forces affecting the particles according to their size, where the particles up to 40 µm are carried away by inertial forces, while the flotation principle starts to be applied in larger inclusions. If we compare the achieved results with the results of the authors in more detail [34,38], it should be noted that the efficiency of inclusions removal will be significantly affected by their density and the amount of steel melt in the tundish. This will be the subject of further research. When all inclusions distributed in the calculation of removal of inclusions at once by the steel stream from a shroud tube are represented, the efficiency of inclusion removal through the surface in the variant with M1 after rounding is 57%, and in the variant with M2, 72%. Therefore, it can be concluded that the modification of an impact pad in the M2 configuration significantly contributed to the directed steel flow in the tundish and to the increase of the removal efficiency of inclusion through the surface. Metals 2020, 10, x FOR PEER REVIEW 17 of 20 Figure 11. Comparison of the proportions of inclusions removed into the slag and torn down into casting strands for the fractions represented in the steel stream through a shroud tube by a 100% share. Table 8. Comparison of residence times of inclusions and efficiency of their removal through the melt surface for individual fractions represented in the steel casting strand through a shroud tube by a 100% share. Inclusion Diameter (µm) Inclusion Density (kg·m −3 ) Min. Residence Time (s) Max. Residence Time (s) Avg. Residence Time (s) Inclusion Removal Efficiency (%) M1 M2 M1 M2 M1 M2 M1 M2 2 2500 7.6 6.5 3220.0 2874.0 233.2 217.8 54.5 68.6 2 3000 7.6 6.8 3726.0 3232.0 246.6 228.3 54.2 69.1 2 3500 8.0 6.8 2927.0 2386.0 234.2 228.4 55.9 68.9 5 2500 7.6 6.5 3012.0 2723.0 223.7 237.1 53.4 70.1 5 3000 7.6 7.0 3090.0 2940.0 238.7 209.8 55.1 68.6 5 3500 8.0 6.9 2701.0 1925.0 215.3 201.0 54.9 67.1 10 2500 7.6 7.1 2745.0 4398.0 234.2 209.6 54.5 69.6 10 3000 7.6 6.4 3494.0 2882.0 222.7 208.8 52.8 69.4 10 3500 8.0 6.5 3494.0 2641.0 229.3 222.4 54.2 69.8 20 2500 7.6 6.4 3465.0 2537.0 230.5 222.2 57.6 72.8 20 3000 7.6 7.4 3912.0 2301.0 234.5 212.4 56.9 71.1 20 3500 8.0 6.7 4332.0 2212.0 246.8 216.3 57.2 70.9 50 2500 7.5 6.4 2224.0 1961.0 198.1 173.1 73.6 83.9 50 3000 7.4 7.1 2059.0 2371.0 199.3 167.9 70.9 80.2 50 3500 8.0 6.6 2348.0 2547.0 221.9 186.3 68.8 81.1 100 2500 6.9 6.6 1024.0 1498.0 78.4 71.7 95.0 96.7 100 3000 7.1 5.5 978.3 1303.0 87.8 83.6 94.6 96.7 100 3500 7.0 6.6 1423.0 1458.0 102.6 88.4 92.0 95.6 Table 9. Comparison of percentage proportions of inclusions removed through the surface and torn down into individual nozzles of casting strands for the variants with M1 and M2 and considering the distribution of inclusions of all sizes and densities as shown in Table 4 and Table 5. CS1 CS2 CS3 CS4 CS5 Removal Efficiency of Inclusions trough the Surface M1 7.46 7.48 10.70 8.35 9.20 56.80 M2 3.98 5.11 7.62 6.31 5.32 71.66 4. Conclusions Figure 11. Comparison of the proportions of inclusions removed into the slag and torn down into casting strands for the fractions represented in the steel stream through a shroud tube by a 100% share. Metals 2020,10, 849 17 of 20 Table 9. Comparison of percentage proportions of inclusions removed through the surface and torn down into individual nozzles of casting strands for the variants with M1 and M2 and considering the distribution of inclusions of all sizes and densities as shown in Tables 4and 5. CS1 CS2 CS3 CS4 CS5 Removal Efficiency of Inclusions trough the Surface M1 7.46 7.48 10.70 8.35 9.20 56.80 M2 3.98 5.11 7.62 6.31 5.32 71.66 When all inclusions distributed in the calculation of removal of inclusions at once by the steel stream from a shroud tube are represented, the efficiency of inclusion removal through the surface in the variant with M1 after rounding is 57%, and in the variant with M2, 72%. Therefore, it can be concluded that the modification of an impact pad in the M2 configuration significantly contributed to the directed steel flow in the tundish and to the increase of the removal efficiency of inclusion through the surface. 4. Conclusions The paper deals with the control of a non-metallic inclusion removal during steel flow in a five-strand asymmetric tundish of a continuous casting machine, while using two types of impact pads referred to as M1 and M2. Numerical modelling was used to study steel flow in the tundish and removal efficiency of inclusions. The following findings were achieved from the research and development of the authors: 1. The prerequisite for the use of numerical modelling is achieving stability of the calculation and convergence of the task, which is largely dependent on the quality of the computational mesh. The authors of the paper verified several methods of creation of computational mesh, namely patch conforming, patch independent, multizone and assembly method. The assembly method with the prevalence of Hexa elements seemed to be the most suitable, which proved competent thanks to its speed, simplicity, and accuracy, especially in the case of geometry modification of the modelled area. 2. The removal efficiency of inclusions was numerically analysed for the two proposed impact area configurations designated M1 and M2. Prior to the analysis of the inclusion removal, the steady steel flow in the tundish, including the heat conduction through the tundish walls and surface, was calculated. The flow character was evaluated using RTD F curves. 3. The configuration of the tundish equipped with an impact pad designated as M2 resulted in a higher proportion of steel plug flow and better inclusion removal efficiency by as much as 15% compared to the application with an M1 impact pad. Author Contributions: Methodology, M.T., K.M., and J.W.; data resources, T.H.; numerical modelling, M.T.; writing—original draft, M.T.; writing—review and editing, M.T., K.M., J.W., and T.H. All authors have read and agreed to the published version of the manuscript. Funding: This paper was created in the project No. CZ.1.05/2.1.00/19.0387 “Development of research and development basis of RMSTC” within the frame of the operation programme Research and Development for Innovations financed by the Structural Funds and from the state budget of the Czech Republic. 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