The article presents the results of liquid steel flow and mixing in tundish when applying turbulence inhibitor to modernize the tundish working zone. The flow of six-strand continuous casting tundish of a trough-type was investigated with numerical modeling. For turbulence modeling, the Reynolds-Averaged Navier-Stokes (RANS) equation and the Large Eddy Simulation (LES) methods have been used. Numerical simulations are carried out with the finitevolume commercial code AnsysFluent

M. Warzecha

P. Warzecha

T. Merder

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Analysis of liquid steel flow in a multi-strand tundish using numerical methods

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462  METALURGIJA 54 (2015) 3, 462-464P.  WARZECHA, M. WARZECHA, T. MERDER ANALYSIS OF LIQUID STEEL FLOW IN A MULTI-STRAND TUNDISH USING NUMERICAL METHODSReceived – Prispjelo: 2014-02-21Accepted – Prihvaćeno: 2014-11-20Original Scientific Paper – Izvorni znanstveni radISSN 0543-5846METABK 54(3) 462-464 (2015)UDC – UDK 669.18:669.13:518.1:531.39=111P. Warzecha, M. Warzecha: Department of Metals Extraction and Re-circulation, Czestochowa University of Technology, Czestochowa, Po-landT. Merder: Silesian University of Technology, Department of Metal-lurgy, Katowice, Poland The article presents the results of liquid steel flow and mixing in tundish when applying turbulence inhibitor to modernize the tundish working zone. The flow of six-strand continuous casting tundish of a trough-type was inves-tigated with numerical modeling. For turbulence modeling, the Reynolds-Averaged Navier-Stokes (RANS) equation and the Large Eddy Simulation (LES) methods have been used. Numerical simulations are carried out with the finite-volume commercial code AnsysFluent.Key words: steel, continuous casting, tundish, numerical modelingINTRODUCTIONThe requirements and regulations regarding the pu-rity of steel produced are constantly increasing; there-fore modern tundishes start to play an important role of refining treatments by improving the quality and purity of cast steel [1]. One of the important factors affecting the purity of steel is the content of non-metallic inclu-sions in the steel product, including their size, quantity, distribution, chemical composition and mineralogy. As the inclusions follow the movement of liquid steel, it is therefore necessary to analyze in detail its structure, which influences the transport and separation of non-metallic inclusions [2-3]. Significant impact on the flow field has also the building of the tundish workspace [4]. Analysis of the liquid steel flow structure inside the tundish is difficult to perform, mainly due to high temperatures of the pro-cess occurring in the tundish and visual opacity of the liquid steel. These limitations impacted the fact that ex-perimental studies are strongly supported by numerical modeling [2, 4].The present state of the Computational Fluid Dy-namics (CFD) techniques allows calculating the fluid flow in tundish with a satisfying accuracy. This is con-firmed by a good agreement between flow fields pre-dicted mathematically and measured with laser-optical method done in water models [5].For modeling turbulent flow based on the Reynolds-Averaged Navier-Stokes equation (RANS) equation, standard [6-8] or realizable [9] k-ε models are mostly used. Numerical simulations are carried out with the fi-nite-volume commercial code AnsysFluent, using a nu-merical method based on the Navier-Stokes equations. Today, it is wide used in comprehensive analysis of commercial plants. In numerical modeling, the choice of proper turbulence model is crucial, as it has a great impact on the flow structure of the fluid. In the analysis of the turbulent flow using RANS method one get the averaged values. In the case of the Large Eddy Simula-tion (LES) method, which was used to carry out present numerical simulations, all large turbulent scales are solved directly and only a small scales, smaller than the filter size are being modeled. From those simulations one gets also the information about the instantaneous velocity field inside the tundish.INVESTIGATED TUNDISH DESRIPTIONThe subject of this study is a CSC tundish operating at a steel plant in Poland. This is a trough-type tundish with six nozzles and nominal capacity of 22 Mg. It is used for casting ingots intended for production of small cross-section rolled products. It is symmetrical with re-spect to its central cross-section. The basic refractory lining is produced of andalusite tiles, and the working layer is made up of a high-magnesite gunite mix. The tundish is equipped with a turbulence inhibitor. The tundish is used for sequence casting (more than ten heats). Technological conditions of tundish operation, as used in numerical simulations, are given in Table 1. These relate to the actual casting square ingots with di-mension of 160 x 160.NUMERICAL MODELOne of the problems encountered with the modeling of the flow through the tundish is to describe the structure of turbulence. Turbulent flows are characterized by the 463P. WARZECHA et al.: ANALISYS OF LIQUID STEEL FLOW IN A MULTI-STRAND TUNDISH USING NUMERICAL...METALURGIJA 54 (2015) 3, 462-464vortex structures with a wide range of spatial and time scales. The largest eddies are comparable with the char-acteristic length scale of the average flow. The smallest scale eddies are responsible for dissipation of kinetic en-ergy. Using the Favre averaging [10] method for the Na-vier-Stokes equation, one gets the well-known continuity and momentum equations for the RANS method [11]:  (1)  (2)The vectors ui and xi are velocity and position, t is time, p is pressure, ρ is density, μ is molecular viscosity and Sji is the strain-rate tensor defined by:  (3)The last term in the equation (2) that contains the fluctuating velocities u’ represents the effect of turbu-lence, which requires modeling. One of the most com-monly used methods is the Boussinesq’s hypothesis [12] that relates the Reynolds stresses to the average speed gradients.The LES method uses a spatial filtering operation to filter out all scales smaller than the filter size. Structures that are smaller than the filter size are considered to be unknown and must be modeled. As a result of spatial fil-tering and the Favre averaging procedure applied to con-tinuity and momentum equations, a system of differential Navier-Stokes equations for LES method can be obtained [11]. One of the most commonly used subgrid-scale mod-el for the LES method is the Smagorinsky model [13].For the purpose of solving the differential equation system, it is necessary to assume suitable initial and boundary conditions, which correspond to the condi-tions used in industrial process. In order to correspond in the investigated process to real casting conditions, the boundary conditions for steel flowing through the shroud was adopted having the velocity of 0,985 m/s and turbulence intensity of 5 %. The scheme of the tundish and boundary conditions used in computations are shown in Figure 1. Figure 2 shows cross sections of the tundish through the inlet and outlet zones. Results presented further in this paper are shown for these cross-sections.Detailed boundary and operating conditions which correspond to the conditions of the industrial process can be found in Table 2.Table 2  Technology-specific operating conditions of tundishes used in simulationsParameter ValueInlet velocity / m∙s-1 0,985Inlet turbulence intensity / % 5Inlet temperature / K 1 781Density of molten steel / kg m-3 7 010Viscosity of molten steel / kg m-1 s-1 7,0∙10-3Specifi c heat / J kg-1 K-1 821Thermal conductivity / W m-1K-1 30,5The computational domain discretization has been developed by applying the computational mesh consist-ing of over 0,6 million control volumes for the RANS test case and 2,3 million for the LES test case. First computations were carried out under steady state (stable production) casting conditions. For the computation of the liquid steel flow through the tundish, the boundary condition of “no-slip” type was adapted for all walls, using the so called “wall function” [11]. During compu-tations, the steel free surface was assumed as a flat sur-face – a wall with zero shear stresses.RESULTSThe objective of the performed studies was to analyze the flow field structure inside the six-strand tundish with the use of RANS and LES methods. Figures 3 and 4 show contour plots of the velocity and temperature field.The numerical results are shown in two cross-sec-tions through the inlet and outlet zones of the investi-gated tundish. In both methods, by comparing the ve-locity distribution of liquid steel inside the tundish, sig-nificant differences can be observed. In the case of the LES method, the turbulent natural convection flow with distinct vortex structures is present, while in the RANS method the smooth flow field is seen.Similar differences are obtained for the temperature field distribution. Although the temperature range is sim-Table 1 Parameters used in the investigated tundishParameter ValueNominal capacity / Mg 22Molten steel level / m 0,78Shroud diameter / m 0,05Number of tundish nozzles 6Outlet diameter / m 0,017Casting speed / m∙min-1 1,9Figure 1  Scheme of the tundish with boundary conditions adapted in numerical calculationsFigure 2  Location of the cross-sections of the tundish to visualize the results464P. WARZECHA et al.: ANALISYS OF LIQUID STEEL FLOW IN A MULTI-STRAND TUNDISH USING NUMERICAL... METALURGIJA 54 (2015) 3, 462-464ilar for both methods, the temperature distribution inside the tundish determined by both methods varies notably.The numerical model allows analyzing working conditions and it provides a source of good knowledge about steel casting conditions.CONCLUSIONSIn the present paper the results of liquid steel flow inside the tundish have been investigated with the RANS and the LES methods for turbulent flow. Com-parisons of the results obtained from the two methods show differences in both velocity and temperature field distribution. In the case of the LES method, the turbu-lent natural convection flow with distinct vortex struc-tures is present. This can be very important, especially, when investigations refer to the distribution of non-me-tallic inclusions in the tundish and their separation pro-cess from liquid steel.Acknowledgements To the National Science Centre: project No 2013/09/B/ST8/00143. This research was also support-ed in part by PL-Grid Infrastructure.References[1] H. Tozawa, Y. Kato, K. Sorimachi, T. Nakanishi, Agglo-meration and flotation of alumina clusters in molten steel, ISIJ Int. 39 (1999) 5, 426-434.[2] M. Warzecha, T. Merder, Numerical analysis of the non-metallic inclusions distribution and separation in a two-strand tundish, Metalurgija 52 (2013) 2, 153-156.[3] G. Luo-fang, L. Hong, L. Hai-tao, W. Yao, S. Wen-chen, Numerical simulation of fractal agglomerating-growth of Al2O3 inclusions in tundish, J. of Iron and Steel Research Int. 20 (2013) 11, 7-12.[4] M. Warzecha, T. Merder, P. Warzecha, Effect of the struc-tural parameters changes in the multi-strand tundish on the non-metallic inclusions distribution and separation, Meta-lurgija 53 (2014) 4, 439-442.[5] N. Alkishriwi, M. Meinke, W. Schröder, A. Braun, H. Pfei-fer, Large-Eddy Simulations and particle-image velocime-try measurements of tundish flow, Steel Res. Int. 77 (2006) 8, 565-575.[6] L. Zhong, B. Li, Y. Zhu, R. Wang, W. Wang, X. Zhang, Flu-id flow in a four-strand bloom continuous casting tundish with different flow modifiers, ISIJ Int. 47 (2007) 1, 88-94.[7] A. Kumar, S. Chakraborty, N. Chakraborti, Fluid flow in a tundish optimized through genetic algorithms, Steel Res. Int. 78 (2007) 7, 517-521.[8] K. Raghavendra, S. Sarkar, S.K. Ajmani, M.B. Denys, M.K. Singh, Mathematical modelling of single and multi-strand tundish for inclusion analysis, Applied Mathemati-cal Modelling 37 (2013) 9, 6284-6300.[9] L. Chaoxiang, L. Biao, Z Shengyu, Numerical smulation on the fow sate of doss layer in tndish, AASRI Procedia 3 (2012), 313-318.[10] J. O. Hinze, Turbulence, Published by McGraw-Hill Publi-shing Co., New York. (1975), 1-82.[11] ANSYS Fluent Theory Guide, Turbulence, Published by SAS IP, Inc. (2012), 39-122.[12] D. C. Wilcox, Turbulence modeling for CFD, Published by DCW Industries, Inc., La Canada, California (1993), 73-170.[13] J. Smagorinsky, General circulation experiments with the primitive equations. I The basic experiment, Monthly We-ather Review, 91 (1963) 3, 99-164. Note:  The responsible translator for English language is Beata M. Wolna, M.A.- proofreader, PolandFigure 3  Instantaneous velocity field distribution, given in m/s, in cross-sections 1 and 2 using a) the RANS and b) the LES methodsFigure 4  Instantaneous temperature field distribution, given in Kelvin, presented in cross-sections 1 and 2 for a) the RANS and b) the LES methods

Analysis of liquid steel flow in a multi-strand tundish using numerical methods

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