Optimum Magnetic Flux Density in Quality Control of Casts with Level DC Magnetic Field in Continuous Casting Mold

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1 , pp Optimum Magnetic Flux Density in Quality Control of Casts with Level DC Magnetic Field in Continuous Casting Mold Hideaki YAMAMURA, Takehiko TOH, Hiroshi HARADA, Eiichi TAKEUCHI 1) and Takanobu ISHII 2) Steel Research Laboratories, Nippon Steel Corporation, Shintomi, Futtsu, Chiba-ken Japan. 1) Steel Research Laboratories, Nippon Steel Corporation, now Hirohata R&D Laboratory, Nippon Steel Corporation, Fuji-cho, Hirohata-ku, Himeji Japan. 2) Nagoya Works, Nippon Steel Corporation, Tokaimachi, Tokai Japan. (Received on February 27, 2001; accepted in final form on May 23, 2001) Application of level DC magnetic field (LMF) in continuous casting mold decreases the mixing length at the ladle change region in sequential casting of different steel grades and improves the inclusion quality of cast slabs. Until now control condition for the mixing of steel compositions which depends on the fluid flow of molten steel has only been clarified. However, control condition for the inclusion whose behavior is not always the same as the behavior of the molten steel flow has not been clarified yet. In this study, continuous casting experiment and numerical analysis were conducted to derive the control index for inclusion and to estimate the optimum condition for improvement of inclusion quality in cast slabs with LMF. The followings are results: Optimum magnetic flux density exists to control the inclusion quality in cast slabs with LMF. Inclusion behavior is explained by the balance between the penetration of inclusion controlled by magnetic field and the floatation of inclusion. This optimum magnetic flux density can be characterized by the interaction parameter, which is expressed by the ratio of inertial force caused by pouring flow to magnetic braking force (Lorentz s force) caused by magnetic field. KEY WORDS: continuous casting; magnetohydrodynamics; electromagnetic brake; inclusion. 1. Introduction In continuous casting of steel in recent years, many attempts have been made to apply various types of electromagnetic forces in the mold 1) as means for intentionally controlling the flow of molten steel in the mold that greatly affects the productivity of continuous casters and the quality of cast steel. Of these efforts, utilization of direct current (DC) magnetic fields started with a localized electromagnetic brake 2) aimed at reducing the velocity of the outlet stream from the submerged entry nozzle (SEN) and is now changing to a full-width electromagnetic brake 3,4) as a nextgeneration electromagnetic brake with superior control capability. Electromagnetic brake by a level DC magnetic field (LMF), a uniform magnetic flux density in the width direction of the mold, was studied for its effect on the flow of molten steel in the mold, and the study results were reported. 4 7) The flow of molten steel in the mold is controlled by changing the downward flow velocity and penetration depth in the mold and the flow velocity and temperature of molten steel in the meniscus through application of the LMF electromagnetic brake. 5) Consequently, the length of intermixed compositions formed during sequence casting of dissimilar grades of steels is shortened, 6) and the number of nonmetallic inclusions in the cast slabs is reduced. 7) In these references control indexes are clarified for the intermixing of different steel compositions that depends only on the flow of molten steel in the mold. However, satisfactory control indexes are not obtained for the inclusions that do not always behave like the molten steel, and optimum electromagnetic brake application conditions are not established either for the inclusions. To derive a control index on the inclusions in the cast slab and optimum control conditions by the LMF electromagnetic brake, the effects of the magnetic flux density and the control index on the inclusions in the slabs cast were investigated by casting experiment and numerical analysis. The findings obtained are reported below. 2. Methods 2.1. Casting Experiment Experimental conditions are shown in Table 1. Mediumcarbon, aluminum-silicon-killed steel was continuously cast on two types of machines. First, 800 mm wide and 170 mm thick slabs were cast at Table 1. Experimental conditions ISIJ

2 Fig. 1. Schematic view of LMF electromagnetic brake installed in the mold. a speed of 0.7 m/min on a vertical continuous caster with a machine length of 8 m. In the mold an LMF electromagnetic brake was installed in such a way that the electromagnet core was located at 460 to 710 mm from the meniscus. The magnetic flux density was changed from 0 to 0.5 Tesla (T). Two types of SEN, one with an outlet angle of 0 and the other with an outlet angle of 45, were used for pouring the molten steel from the tundish into the mold. Next, a vertical-bend continuous caster with a vertical section length of 2.5 m and a bending curvature of 10.5 m was used to cast slabs with a width of to mm and thickness of 245 mm at a speed of 0.7 to 2.0 m/min. The mold was equipped with an LMF electromagnetic brake so that the electromagnet core was located at 350 to 550 mm from the meniscus. The magnetic flux density was changed from 0 to 0.5 T. The mold with the LMF electromagnetic brake is schematically illustrated in Fig. 1. Samples were taken at a pitch of 10 mm from the quarter width of each slab cast. Nonmetallic inclusions were extracted from the samples by the slime electrolytic extraction method. Inclusions 37 mm or larger in size were counted, and the distribution of the inclusions in the thickness direction was determined. Samples were also taken from the midthickness of the narrow face of each slab cast and in parallel with the broad face. These samples were etched on the surface to reveal dendrites, and the tilt angle of dendrites was measured at a pitch of 5 mm from the surface of the narrow face. The downward velocity of molten steel along the narrow face was calculated from the measured tilt angle of dendrites by the equation of Okano et al. 8) 2.2. Numerical Analysis The motion of liquid metal is described by the continuity equation and the Navier Stokes equation. div u 0...(1) u ( u grad) u 1 grad P div( ν grad u) g 1 F X t ρ ρ...(2) The electromagnetic field is expressed by Maxwell s equations under magnethydro-dynamics approximations and Ohm s low. B rot E...(3) t rot B mj...(4) div B 0...(5) J s(e u B)...(6) The numerical analysis used the general-purpose software FLUENT. Analysis by the finite difference method with the k e model of the continuity equation and the Navier Stokes equation and analysis by the finite difference method with the electromagnetic induction equations were coupled by using the electric potential equation or Eq. (7), in order to analyze the electromagnetic fluid. The magnetic field analysis allows for the electric conductivity of the solidifying shell. grad f div s(u B)...(7) The behavior of inclusions was analyzed by the particle tracking method. Under the flow of molten steel obtained by the electromagnetic fluid analysis, particles are given from the outlet holes of the SEN, and their trajectories were tracked by time integrating the equation of motion or the BBOT equation with the hysteresis term omitted as expressed by Eq. (8). The three terms on the right side of Eq. (8) are the drag force, gravity force and external electromagnetic force, respectively. dup g( ρp ρ) FD ( u up ) FE...(8) dt ρp CD FD 18η Re...(9) ρpdp ρ du ( up ) ρ u FE up...(10) 2 ρp dt ρp x Particles in contact with the meniscus surface are assumed to be absorbed and removed, and particles in contact with the solidifying shell are assumed to be entrapped by the solidifying shell when the molten steel flow velocity is 10 cm/s or less at the front of the solidifying shell. The diameter of inclusions is put at 100 mm. The analysis was performed on 800 mm wide by 190 mm thick slabs cast on the vertical machine at a speed of 0.8 m/min and with an SEN outlet angle of 45. The magnetic field was applied uniformly in the width direction at 460 to 710 mm from the meniscus, and the magnetic flux density was changed from 0 to 0.5 T. 3. Results 3.1. Casting Experiment Figure 2 shows the distribution of the number of inclusions in the thickness direction of slabs cast on the vertical machine with the SEN outlet angle of 45 and by changing the magnetic flux density from 0 to 0.25 to 0.5 T. The vertical continuous caster is free from the zone of inclusion concentration observed in the upper side of slabs produced on curved continuous casters. When the magnetic flux density was 0 T, the number of inclusions slightly increased at 10 to 20 mm below the slab surface, but then decreased with increasing depth below the slab surface. When the magnetic flux density was 0.25 T, the number of inclusions did not increase at 10 to 20 mm below the slab surface and was ex ISIJ 1230

3 Fig. 2. Effect of magnetic flux density on inclusion distribution in slab cast by vertical CC with SEN outlet angle of 45. Fig. 4. Relation between magnetic flux density and inclusion number under the magnetic field. Fig. 3. Effect of magnetic flux density on velocity distribution of molten steel flow at the narrow face of slab cast by vertical CC with SEN angle of 45. Fig. 5. Relation between magnetic flux density and downward flow velocity under the magnetic field. Fig. 6. Relation between maximum downward flow velocity and inclusion number at the peak point of distribution. tremely small through the slab thickness. When the magnetic flux density was 0.5 T, the number of inclusions was larger than when the magnetic flux density was 0 T. Especially, a large peak was observed at 20 to 30 mm below the slab surface. When converted to the distance from the meniscus, this position was just below the magnetic field application zone. Figure 3 shows the distribution of the downward flow velocity in the depth direction of the narrow face of the strand as determined from the tilt angle of dendrites in the strand. The molten steel flows downward inside of the point where it impinges on the narrow face of the mold as it is discharged from the SEN. The downward flow velocity decreases with increasing magnetic flux density. When the magnetic flux density was 0.25 T, the downward flow velocity decreased to a level approximately equal to the casting speed as the molten steel passed the magnetic field applied. Above the position where the outlet stream impinged on the narrow face of the mold, some of the outlet stream inverted and formed an upward flow. The upward flow velocity tended to increase with increasing magnetic flux density. The application of a magnetic field was recognized to markedly change the number of inclusions just below the magnetic field application zone. Figure 4 shows the effect of the magnetic flux density on the number of inclusions just below the magnetic field application zone. The number of inclusions decreased when the magnetic field was applied, but increased when the magnetic flux density was raised to 0.5 T. Figure 5 shows the effect of the magnetic flux density on the downward flow velocity just below the magnetic field application zone. Unlike the number of inclusions, the downward flow velocity just below the magnetic field application zone decreased with increasing magnetic flux density. Figure 6 shows the relationship between the maximum downward flow velocity and the number of inclusions just below the magnetic field application zone when the SEN outlet angle was 0 and 45. As the maximum downward velocity increased, the number of inclusions just below the magnetic field application zone tended to decrease. Figure 7 shows the distribution of the number of inclusions in the thickness direction of slabs cast on the verticalbend machine with a magnetic flux density of 0.32 T and by changing the casting speed from 0.7 to 1.0 to 1.6 m/min. Each position in the depth direction of the slab is converted by the square root law to the corresponding distance from the meniscus. When the casting speed was 1.6 m/min, the number of inclusions increased in positions deeper than the strand surface layer and the strand bending point. When the ISIJ

4 Fig. 7. Effect of casting speed on inclusion distribution in slab cast by vertical-bend CC for B 0.32 T. casting speed was decreased to 1.0 m/min, the number of inclusions decreased in both positions. When the casting speed was decreased further to 0.7 m/min, the number of inclusions increased in the position deeper than the position just below the magnetic field application zone. Figure 8 shows the distribution of the downward flow velocity on the narrow face of the strand as obtained from the tilt angles of dendrites in the strand by converting each position in the depth direction of the strand to a corresponding distance from the meniscus. When the casting speed was high at 1.0 or 1.6 m/min, the outlet stream impinged on the upper narrow face of the mold and formed an upward flow. The velocity of the inverted upward flow decreased with decreasing casting speed. When the casting speed was decreased to 0.7 m/min, the outlet stream formed no upward flow on the narrow face of the mold, but entirely flowed downward. The downward flow velocity in the mold was maximum just below the position where the outlet stream impinged on the narrow face. It then decreased to a great extent as the molten steel flowed past the magnetic field application zone. The maximum downward flow velocity increased with increasing casting speed. The effect of the casting speed on the number of inclusions just below the magnetic field application zone is shown in Fig. 9. The number of inclusions decreased as the casting speed was decreased to 1.0 m/min, but increased as the casting speed was decreased to below 1.0 m/min Numerical Analysis Figure 10 shows the distribution of molten steel flow velocity vectors calculated by changing the magnetic flux density. When the magnetic flux density is 0 T, the outlet stream from the SEN impinges on the narrow face, flows down the narrow face, and decreases in velocity as it reaches deeper positions. At the midwidth, an upward flow forms as if to compensate for the downward flow. As the magnetic flux density increases, the downward flow velocity near the narrow face decreases. Accordingly, the upward flow at the midwidth decreases in velocity and approaches a plug Fig. 8. Effect of casting speed on velocity distribution of molten steel flow at the narrow face of slab cast by vertical-bend CC for B 0.32 T. Fig. 9. Relation between casting speed and inclusion number under the magnetic field in slab cast by vertical-bend CC. Fig. 10. Change in calculated flow vector distribution with magnetic flux density ISIJ 1232

5 Fig. 11. Change in calculated flow vector distribution with magnetic flux density; enlarged views of the meniscus. Fig. 12. Change in calculated particle trajectory with magnetic flux density; particle diameter 100 mm. flow. Figure 11 shows enlarged views of the meniscus. Application of a magnetic field decreases the velocity of the outlet stream and causes the outlet stream to impinge on the upper narrow face of the mold. The inverted upward flow increases in velocity at the magnetic flux density of 0.25 T and decreases in velocity at the magnetic flux density of 0.5 T. The calculated trajectories of 100 mm inclusions are shown in Fig. 12. When the magnetic flux density is 0 T, some inclusions ride on the downward flow near the narrow face of the mold, penetrate into the strand, and are entrapped there. Some inclusions float together with the upward flow at the midwidth of the mold to the free surface and are removed from the meniscus to the outside of the system. When a magnetic field is applied, the penetration depth of inclusions decreases. When the magnetic flux density is 0.25 T, the amount of inclusions floated by the inverted upward flow increases. When the magnetic flux density increases to 0.5 T, the penetration depth of inclusions decreases further, but no upward flow is formed near the midwidth, and the molten steel flows in a pattern close to that of plug flow. Near the magnetic field application position, the inclusions remain still and are entrapped by the solidifying shell. As a result, the number of inclusions increases in the strand just below the magnetic field application zone when the magnetic flux density increases to 0.5 T. 4. Discussion The experimental results and the analytical results both show that the inclusion content of slabs is governed by the flow of molten steel in the mold or the balance between the penetration of inclusions by the downward flow and the flotation of inclusions by the upward flow. When an electromagnetic brake is applied, the flow of the molten steel in the mold depends on the relationship between the downward flow formed by the SEN outlet stream and the electromagnetic braking force acting on the downward flow. The behavior of inclusions that do not always flow in the same way as the molten steel is considered to be capable of being arranged by the interaction parameter N given by Eq. (11) as ratio of the electromagnetic braking force expressed by ISIJ

6 Fig. 13. Relation between interaction parameter and inclusion number. Fig. 15. Schematic explanation of relation between interaction parameter and inclusion number. Fig. 14. Relation between inclusion diameter and floating velocity of inclusion. the Lorentz s force to the inertia force due to the pouring stream of the molten steel into the mold. 2 Lorentz s force σbl N...(11) Inertia force ρu The value of flow velocity u of the molten steel at the top of the magnetic field is obtained by incorporating casting conditions into molten steel flow velocity equations derived by a hydrodynamic study. 9) The relationship between the interaction parameter and the number of inclusions just below the magnetic field application zone is shown in Fig. 13. It is evident that the number of inclusions can be arranged by the interaction parameter, regardless of the casting conditions, and that there is the value of the interaction parameter at which the number of inclusions is minimum. However, this optimum value is obtained under the given conditions such as the experimental conditions shown in Table 1. If the flow pattern in mold changes by change in the casting conditions such as the flow rate of Ar gas from nozzle or application of the electro-magnetic stirrer, the optimum value shifts. Figure 14 shows the relationship between the size and floating velocity of inclusions as calculated by using Stokes law. If the flow of the molten steel is the plug flow type when the molten steel is cast at the speed of 0.7 m/min, the downward flow velocity is about 1 cm/s and approximately corresponds to the floating velocity of inclusions 100 to 200 mm in size. If the magnetic flux density is made high enough for the flow of the molten steel in the mold to become a plug flow, the inclusions are considered not to flow up or down, but to remain still to be entrapped by the solidifying shell, increasing the inclusion content of slabs thus cast. The relationship between the interaction parameter and the number of inclusions in the slab is discussed here according to the above results. When the interaction parameter is small in value as schematically illustrated in Fig. 15 or when the effect of the inertia force due to the flow of the molten steel is greater than that of the electromagnetic braking force, the inclusions are less likely to remain still to be entrapped by the solidifying shell, but since more inclusions penetrate into the mold, the number of inclusions increases. When the interaction parameter increases in value, the effect of the electromagnetic braking force increases, and the number of inclusions entering the mold decreases, but the probability of inclusions remaining still to be entrapped by the solidifying shell increases to increase the number of inclusions. Increase in the electromagnetic braking force causes decrease in velocity of flow. With decreasing the velocity of flow on the solidification front, velocity gradient and thickness of the velocity boundary layer are decreased, then the washing force should be decreased. 10,11) As a result, the number of inclusions is minimum in the region where the electromagnetic braking force balances the inertia force due to the flow of the molten steel, and there is an optimum value for the interaction parameter. To reduce the inclusion content of slabs cast under a given set of conditions, it is considered necessary to select an optimum magnetic flux density for those casting conditions. 5. Conclusions For the purpose of deriving a control index and optimum control conditions for inclusions in slabs cast by applying an electromagnetic brake with an LMF in the mold, the relationship among the magnetic flux density, control index and inclusions in slabs was studied by casting experiment and numerical analysis. The following findings were obtained: (1) To reduce the number of inclusions in the slab by the LMF electromagnetic brake, there exists an optimum magnetic flux density for specific casting conditions. (2) Increasing the magnetic flux density decreases the downward flow velocity near the narrow face of the mold due to the outlet stream from the SEN and prevents the inclusions from penetrating into the strand in the mold. At the same time, the upward flow formed at the midwidth of the 2001 ISIJ 1234

7 mold is also reduced in velocity to retard the flotation of the inclusions. (3) The optimum magnetic flux density can be represented by the interaction parameter that is a ratio of the braking force due to the magnetic field to the inertia force due to the flow of the molten steel. To reduce the number of inclusions in slabs cast, it is necessary to control the magnetic flux density of the electromagnetic brake by using the interaction parameter. (4) The presence of the minimum number of inclusions can be explained by the balance between the penetration of inclusions due to the downward flow velocity braked by the magnetic field and the flotation of inclusions by the upward flow of the molten steel. Nomenclature B : Magnetic flux density (T) C D : Drag coefficient ( ) D P : Diameter of particle (m) E : Electric field density (V/m) F X : External body force (N/m 3 ) g : Gravitational acceleration (m/s 2 ) J : Induced electric current density (A/m 2 ) L : Length (Slab thickness) (m) P : Pressure (Pa) Re : Reynolds number ( ) t : Time (s) u : Velocity of molten steel (m/s) u P : Velocity of particles (m/s) x : Distance in casting direction (m) h : Viscosity of molten steel (Pa s) m : Magnetic permeability (H/m) n : Kinematic viscosity of molten steel (m 2 /s) r : Density of molten steel (kg/m 3 ) r P : Density of particle (kg/m 3 ) s : Electric conductivity (S/m) f : Electric potential (V) REFERENCES 1) E. Takeuchi, M. Zeze, T. Toh and S. Mizoguchi: Magnetohydrodynamics in Process Metallurgy, TMS, Warrendale, PA, (1991), ) J. Nagai, K. Suzuki, S. Kojima and S. Kollberg: Iron Steel Eng., 61 (1984), 41. 3) M. Sugisawa, S. Moriwaki, M. Sakurai, Y. Tomiyama, S. Idogawa and S. Takeuchi: CAMP-ISIJ, 4 (1991), ) H. Harada, T. Toh, E. Takeuchi, M. Zeze and T. Ishii: New Advancement in Electromagnetic Processing of Materials, ISIJ, Tokyo, (1999), ) M. Zeze, H. Harada, E. Takeuchi and T. Ishii: Iron Steelmaker, 20 (1993), 53. 6) H. Harada, E. Takeuchi, M. Zeze and T. Ishii: Tetsu-to-Hagané, 86 (2000), ) T. Ishii, N. Konno, T. Okazaki, A. Uehara, E. Takeuchi, H. Harada, T. Kikuchi and K. Watanabe: CAMP-ISIJ, 9 (1996), ) S. Okano, T. Nishimura, H. Ooi and T. Chino: Tetsu-to-Hagané, 61 (1975), ) A. Imamura, A. Kusano and N. Moritama: Tetsu-to-Hagané, 78 (1992), ) K. Okazawa, A. Kiyose, I. Sawada, T. Toh and W. Takeuchi: Tetsuto-Hagané, 82 (1996), ) J. Fukuda, Y. Ohtani, A. Kiyose, T. Kawase and K. Tsutsumi: Proc. of 3rd European Conf. on Continuous Casting, UNESID, Madrid, (1998), ISIJ