Dev. Chem. Eng. Mineral Process. 14(3/4), pp. 363-374, 2006. Heat Transfer and Inclusion Behavior in Continuous Casting Tundishes Miao-Yong Zhu'*, Yong-Lai Wul, Shu-Guo Zheng', Ya-Xian Chen2 and Zong-Ze Huang2 I School of Materials and Metallurgy, Northeastern University, Shenyang 110004, I? R. China Baoshan Iron & Steel Co. Ltd, Shanghai 201900, P. R. China In this study, a mathematical model describing the three-dimensional turbulent flow, heat transfir and inclusion behavior in continuous casting tundishes was developed. Numerical calculations were performed to study the characteristics of flow, heat transfer and inclusion behavior in a one-strand tundish withlwithoutflow control. The results show that it is necessary to employ flow control devices in order to improve the efectiveness of removal of nonmetallic inclusions in the tundish. Without flow control, the hot melt ascends and cooled melt descends and then recirculates back to the inlet along the bottom of the tundish. However, the phenomenon of temperature stratiJcation occurs after the steel flow passes through the dam in the tundish. Inclusions with diameter greater than 30 pm can be removed in the tundish, and reasonableflow control devices will assist the removal of inclusions of size 20-25 pm. Introduction Continuous casting of molten steel has become a widely used process and an increasingly important step in steel production in the past decades. In the continuous casting machine, molten steel is poured from a tundish into a mold and solidification of the molten steel takes place in the mold with water cooling, continuously yielding steel products. The primary role of a tundish is to act as a distributor of molten steel between the ladle and the molds. In addition, it has been increasingly recognized that tundishes provide the significant opportunity for removal of nonmetallic inclusions from molten steel. Being lighter than molten steel, nonmetallic inclusions in steel can be removed after floating to the top slag, also the turbulence of the incoming stream helps the agglomeration of the smaller sized nonmetallic inclusions to form a larger inclusion and subsequently promoting floating. In order to optimize nonmetallic inclusion flotation and improve the steel cleanliness, an in-depth understanding of the fluid flow and heat transfer of the molten steel encountered in tundishes is needed. Direct information concerning fluid flow and temperature fields in an actual tundish is * Authorfor correspondence (myzhu@mail.neu.edu.cn). 363 Miao-Yong Zhu, Yong-Lai Wu, Shu-Guo Zheng, Yo-Xian Chen and Zong-Ze Huang very difficult to obtain. Therefore, several recent studies [l-151 have used both physical modeling and mathematical modeling of the fluid flow, heat transfer and the inclusion separation behavior. Lai et al. [I] performed the calculations of three-dimensional flow in a symmetrical twin-strand tundish by using the k - E turbulence model. Velocity and turbulence were measured in a one-sixth scale water model by using laser doppler velometer. Szekely and El-Kaddah [2] numerically calculated 3-D fluid flow and residence time distribution (RTD) curves in a tundish with and without flow control devices. He and Sahai [3] developed a 3-D mathematical model to predict the flow field in tundishes with inclined sidewalls, and the predictions were validated by a onethird scale water model. By comparison with the vertical walls, in terms of flow patterns and RTD curves, they suggested that the tundish with inclined walls provides greater opportunity for the floatation of inclusions within the molten steel. Tacke and Ludwing [4] solved a transport equation for particles by consideration of their buoyancy, convection and turbulent dispersion by using PHOENICS code. The particle concentration field and the percentage of removal were predicted. Lee et al. [5] predicted 3-D fluid flow, turbulence and tracer dispersion in a one-strand tundish with and without a dam and weir also by using PHOENICS code, and predicted results were tested by water modeling experiments. Sinha and Sahai [6] developed a model that addresses the inclusion transport and removal phenomena from the molten steel, and investigated the effect of various flow control devices on inclusion reduction. They proposed that the mechanism of inclusion removal by sticking to the wall played a major role in the total inclusion removal. Joo et al. [7] studied the fluid flow and heat transfer and inclusion flotation by mathematical modeling. Their results showed that the use of flow modification was reasonably effective in further reducing inclusion, and small inclusions were not readily removed with or without flow control. Recently Zhang et al. [8] also studied fluid flow and inclusion removal in a tundish, and determined the percentages of inclusion removal by flotation and adhesion. These studies using physical and mathematical modeling provide important information for better understanding the characteristics of flow, and thus improving the efficiency of inclusion flotation and removal. However, the simulation of inclusion behavior still requires further study. In our work, the fluid flow, heat transfer and the inclusion behavior in an actual tundish, with and without flow control, were studied numerically and the functions of the flow control devices are discussed. Table 1. Important physical parameters for modelingfluid flow in a tundish. Tundish length (top/bottom) Tundish width (top/bottom) Tundish depth Weir distance @om inlet Weir depth below free surface Dam distance from inlet Dam depth Inlet flowrate 3 64 4.05 13.70 0.812 / 1.373 m 1.335 m 0.550 0.85 0.700 0.280 3 .o rn m m m m todmin Heat Transfer and Inclusion Behavior in Continuous Casting Tundishes Mathematical Formulation The system selected for the present study was a one-strand slab caster tundish with a capacity of 26 ton. The submerged depth of the long nozzle was 300 mm, and the important physical parameters are given in Table 1. The following assumptions were made in the establishment of a mathematical model for flow and inclusion behavior in the tundish. 1. The flow in the tundish is steady, incompressible and turbulent. 2. The top surface is flat, and no tangential stresses are present. 3. The inclusions were assumed to be spherical. Collision of inclusions was considered to take place instantly and to be strong enough to combine together. Any inclusion reaching the top surface was assumed not to revert back into the system at a later time. 0) Fluidflow and heat transfer The turbulent flow and heat transfer in the tundish can be described by the continuity equation, the Navier-Strokes equation, turbulence model and energy conservation equation, and can be written as: Continuity equation: Navier-Stokes equation: ...(2) where pc8 is the effective viscosity, which can be determined by the k - E turbulence model [ 161. Energy conservation equation: ...(3) and refis the effective diffusivity, which is defined as: ...(4) and o , , ~ are laminar and turbulent Prandtl numbers, respectively. In the where present study, both of them were taken to be unity. 3 65 Miao-Yong Zhu, Yong-Lai Wu, Shu-Guo Zheng, Ya-Xian Chen and Zong-Ze ffuang Consider the boundary conditions. At the fiee surface, which was assumed to be flat, the normal velocity components and the normal gradients of all other variables were set to be zero. On the solid walls, no-slip boundary conditions were imposed. Near the tundish walls, the velocities parallel to the walls and the turbulence quantities were predicted by using the wall function [16]. At the jet entry, a flat ,and the turbulent kinetic energy and turbulent energy velocity was assumed, u = u,"~~, dissipation were determined fiom the expressions: k = 0.01~:,, , = kls /(d,,,, 21, where ulnlefis inlet velocity and drnlefis inner diameter of inlet. At the outlet, the normal gradients of all variables (momentum and scalar properties) were set to be zero, and the velocities were obtained by the final convergence of the calculation rather than directly fixed by the mass balance of the inlet and outlet. For modeling of the heat transfer process of molten steel in the tundish, the incoming steel jet was considered to be at a constant temperature of 1836 K. The heat loses through the walls and overlaying slag, and flow in tundish during casting, were all assumed to be steady state. The heat fluxes through the walls and the top slag, as employed here, were based on the recommendation of Charkrabortyand Sahai [I41 as given in Table 2. Table 2. Heat losses through sidewall and base of tundish and top slag (kW/m2). Top slag 15 1 Longitudinal wall I 3.2 1 I Transverse wall 3.8 I Base I 1.4 (ii) Inclusion behavior According to Linder's study [ 171, the relation between the radius of inclusion R, (m) and the number density ni (defined as the number of inclusions with radius R, in unit volume of molten steel) can be expressed as: where A and B are constants which are related to the time and position in the tundish, but have no relation to the size of inclusion. Upon integration of Equation ( 5 ) , the total number density of inclusions nrorand concentration of inclusions (volume of inclusion / volume of molten steel) can be expressed as: ,..(6) The relation between C and nfo,can be established with an equivalent radius, R,, as: ,..(7) 366 Heat Tranqer and Inclusion Behavior in Continuous Casting Tundishes The behavior of inclusions in the tundish can be represented by: where (P stands for C and n,,,, respectively, Sc ((P = C) is the source term for the transport equation of C, and S, (@ = n,J is the source term for the transport equation of n,,,, by which the mechanism of inclusion collision can be expressed, s is the Stokes floating velocity of inclusions. Brownian motion, laminar shear, turbulent collision and differences in velocity cause inclusion collisions. The main collision for inclusions in the tundish is the turbulent collision which can be expressed by the equation of Saffman and Turner [ 181 as: t) 112 C, = 1.30( where E is turbulence dissipation rate, and v is kinematic viscosity of molten steel. The boundary conditions for the equations of C and nrorat the interface of the top slag and metal can be expressed by: ...(10) F, = vi . nlo,,s”r/oce ...(11) where CSllflace and nror,sl,~acce are the values at the slag-metal interface for C and n,,,, respectively. Collision of inclusions at the wall of tundish can be considered as mass transfer through a boundary layer near a solid surface, and the total diffusive flux of mass and diffusive flux of number density can be given as: ..#.(12) ..,.(13) C, = 0.01. ro/ ( p v ) where the shear stress in C2 can be determined from the k - - ~model and the wall function. 367 Miao- Yong Zhu, Yong-Lai Wu,Shu-Guo Zheng, Ya-Xian Chen and Zong-Ze Huang (iii) Numerical solution procedure The differential equations have been discretized by using a control-volume method. The SIMPLE algorithm (Semi-Implicit Method for solving Pressure-Linked Equations) was adopted to predict the fluid flow in the tundish [19], and the computation domain corresponding to the whole tundish was divided into a nonuniform grid of 60(longitudinal)x20(transverse)x 20(vertical). The program employed in our work was developed by the present authors and the computation was performed on a personal computer. About 2000 iterations were required in order to obtain fully converged results. Results and Discussion (0 Flow and heat transfer in the tundish Figure I shows the predicted flow patterns at the middle and near-wall longitudinal vertical planes, and the inlet and outlet transverse vertical planes of the tundish without flow control. It can be seen that the stream jet coming from the ladle reaches the bottom of the tundish at high velocities and then spreads in all directions, although it mainly flows along the tundish side wall. However, one recirculation jet was formed near the bottom of the tundish which confined the upward flow developing in the main part of the tundish. This type of flow did not favor nonmetallic inclusions flotation, which had also been confirmed indirectly by the predictions of the RTD curve and water modeling. For the flow pattern, the present tundish without flow control was not useful for the flotation of inclusions. Figure 2 provides the corresponding temperature isotherms for the two longitudinal vertical planes as shown in Figurel. The temperature of molten steel dropped from the top free surface to the bottom, although the drop was not significant with the stream entering at 1563°C and exiting at 1557"C, and the tundish was considered to provide good protection from heat loss during the casting. The distribution of temperature in the tundish shows that, without flow control, hot melt ascends and cooled melt descends and then recirculates back to the inlet along the bottom of the tundish. Figure I. Predictedjlow patterns at the middle (a) and near-wall (b) longitudinal vertical planes, and inlet (c) and outlet (4 transverse vertical planes of tundish withoutjlow control. 368 Heat Transfer and Inclusion Behavior in Continuous Casting Tundishes (c) Figure I continued 1558.1 Figure 2. Predicted temperaturefields (“C) at the middle (a) and near-wall (6) planes in the tundish withoutflow control. 369 Miao-Yong Zhu, Yong-Lai Wu,Shu-Guo Zheng, Ya-Xian Chen and Zong-Ze Huang Figure 3. Predictedflow patterns at middle (a) and near-wall (6) longitudinal vertical planes of tundish withflow control. Figure 4. Predicted temperaturefields (“C) at the middle (a) and near-wall (b) planes in the tundish withflow control. 3 70 Heat Transfer and Inclusion Behavior in Continuous Casting Tundishes Figure 3 shows the predicted flow patterns in the same two longitudinal vertical planes of the tundish with one weir and one dam. Compared with the flow in the tundish without flow control, the dam and weir have a significant effect on the flow pattern in the tundish, thus affecting the inclusion behavior. In this case, strong turbulence was confined within the region near the inlet which helped the collision and coalescence of inclusions, and the stream from the ladle flowed mainly along the free surface of the tundish after it passed through the dam and weir. Therefore, this flow pattern may benefit the floatation of nonmetallic inclusions. Figure 4 shows the corresponding temperature isotherms at two longitudinal vertical planes of the tundish with one weir and one dam. It can be seen that the temperature difference of molten steel was small within the region where strong turbulence was confined by weir and dam. However, the phenomenon of temperature stratification occurred after the steel flow passed through the dam, and the temperature of molten steel at the upper part of the tundish was higher than that of the lower part of the tundish. (ii) Inclusion behavior in the tundish The fluid flow in the tundish provides the basic information for explaining and understanding the inclusion behavior. In order to have an in-depth understanding of the effect of flow control on inclusion removal in the tundish, it is necessary to describe the inclusion behavior quantitatively. Figure 5 provides the concentration distribution of inclusion in the tundish without and with flow control after 10 minutes casting. The inclusion concentration of molten steel before casting was 1 2 8 ~ 1 0 -Figure ~. 5 clearly shows that the inclusion removal in the tundish with flow control is much better than that of without flow control, and the inclusion concentration near the surface of the tundish with flow control is lower than in the other region, which is the opposite observation for the tundish without flow control. Figure 6 shows the variation of average concentration and number density with time in the tundish, and demonstrates more clearly the effectiveness of inclusion removal in the tundish with flow control devices. Figure 5. Variation of inclusion concentration (ppm) in the tundish after 10 minutes casting: (a) withoutflow control; (b) with flow control. 371 Miao-Yong Zhu, Yong-Lai Wu,Shu-Guo Zheng, Ya-Xian Chen and Zong-Ze Huang 140 ---with 20 0 200 400 flow control without flow control 600 800 11 00 Casting time (sec) Figure 6. The variation of inclusion concentration in the tundish during casting. Table 3. Number density of inclusion (number/cm:’) in 10 minutes or 15 minutes casting in the tundish withoutflow control. Time (min.) 10 15 10-15 pm 2493 1788 20-25 pm 36.74 27.40 30-35 pm 0.54 0.42 40-45 pm 0.008 0.006 Table 4. Number density of inclusion (number/cm3) in I0 minutes or I5 minutes casting in the tundish with jlow control. Time (min.) 10 15 10-15 pm 1373 816 20-25 pm 16.97 10.03 30-35 pm 40-45 pm 0.2 1 0.12 0.003 0.002 After 10 or 15 minutes casting, the number densities for inclusions with different sizes in the tundish without and with flow control are given in Table 3 and Table 4. It can be seen that the inclusions with diameter above 30 pm were removed, and reasonable flow control devices will be helpful for the removal of inclusions with a size range of 20 to 25 pm. 3 72 Heat Transfer and Inclusion Behavior in Continuous Casting Tundishes Conclusions A mathematical model was developed in order to predict the fluid flow, heat transfer and the inclusion behavior in tundishes for continuous casting. The fluid flow, heat transfer and inclusion behavior in an one-strand tundish, with and without flow control, were studied numerically. The following conclusions can be made. 1. In order to improve the effectiveness of removal of nonmetallic inclusions in the tundish, it is necessary to employ flow control devices because they influence the flow pattern and turbulence for improved inclusions floatation. 2. The distribution of temperature in the tundish shows that hot melt ascends and cooled melt descends and then recirculates back to the inlet along the bottom of the tundish without flow control. However, the phenomenon of temperature stratification occurs after the steel flow passes through the dam. The temperature of molten steel at the upper part of the tundish is higher than that of the lower part of the tundish with one dam and one weir. 3. The inclusions with diameter greater than 30 pm can be removed in the tundish, and reasonable flow control devices will be helpful for the removal of inclusions with the size range of 20 to 25 pm. Acknowledgements The National Science Foundation of China and Baoshan Iron and Steel Co. (Grant No. 50274022), and the Program for New Century Excellent Talents in University (NCET-04-0285) are gratefully acknowledged for supporting this work. References Lai, K.Y.M., Salcudean, M., and Tanaka, S. 1986. Mathematical modeling of flows in large tundish systems in steelmaking. Met. Trans. B., 17B(5), 449-459. 2. Szekely, J., and El-Kaddah, N. 1986. The mathematical modelling of three-dimensional heat flow, fluid flow and turbulence phenomena in tundishes. Steelmaking Conference Proceedings, ISS-AIME, Warrendale, Pennsylvania, USA, 69,761-776. 3 . He, Y., and Sahai, Y. 1986. Fluid dynamics of continuous casting tundishes - mathematical modeling. Steelmaking Conference Proceedings, ISS-AIME, Warrendale, Pennsylvania, USA, 69,745-754. 4. Tacke, K.H., and Ludwig, J. 1987. Steel flow and inclusion separation in continuous casting tundishes. Steel Res., 58(6), 262-270. 5. Lee, S.M., Koo, Y.S., Kang, T., et al. 1990. 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