Pré-visualização3 páginas

calculation, the defor- mation of the surface is neglected since the effect of the surface deformation on the flow structure in the whole tundish is not big. The normal gradient of all variables is equal to zero except from the normal velocity is zero. (3) At the solid wall: Velocities at the solid wall are zero. To estimate the velocity near a wall, it often uses a Van Driest damping function13,14) modification to reduce the eddy viscosity in the near-wall region: ls\ufffdCsD[1\ufffdexp(\ufffdy\ufffd/26)] ....................(15) Where y\ufffd is the dimensionless distance from the wall, D is a length scale, and A\ufffd is a constant, here A\ufffd\ufffd26. (4) At the exit of the tundish: the velocity gradient is zero. 2.5. Solution Method The magnetic field and the electromagnetic force is firstly calculated using the commercial software of ANSYS 8.0. Electromagnetic force is included in the NS equation. The electromagnetic forces are obtained by interpolation into the momentum equation. A finite volume method has been chosen for this calculation of complicated system, and the computer code in FORTRAN language for solution of flow field is self-developed. The domain is discretized with 200, 68, and 68 points along the long, wide and height axes respectively. It means a 0.92 million node computational grid. The time step (D t) is set to 0.003 s. The filtered non- linear simultaneous equations are solved by using SIM- PLEC algorithm. A combination of Alternating-Direction- semi-Implicit iteration scheme (ADI) and block correction is used to solve the discrete algebraic equations. 3. Numerical Results Numerical simulations are conducted on the flow field in centrifugal flow tundish for the three cases, i.e. (a) electro- magnetic force with the direct nozzle, (b) bending nozzle using height potential energy of molten steel and (c) combi- nation of electromagnetic force and bending nozzle. 3.1. Effect of Electromagnetic Force Figures 3\u20135 show the calculated flow field of centrifugal flow tundish, the electromagnetic force field in Fig. 2 is used as the driven force of swirling flow in rotation cham- ber. Molten steel is poured by using the direct nozzle. It can be observed that flow field of rotation chamber is composed of a toroidal vortex in the central zone and two small vor- tices at the top and bottom respectively as shown in Fig. 3. Figures 4(a)\u20134(c) show the flow patterns in horizontal sec- tion of centrifugal flow tundish at three locations with z\ufffd0.1 m, z\ufffd0.06 m and z\ufffd0.02 m. In Figs. 4(a) and 4(b) show that there is a strong swirling flow in the rotation chamber and a flow crack in the tundish. The crack is a re- sult from bifurcation the upward flow at the upper of the distribution chamber of tundish. Moreover, it can be ob- served in Fig. 4(c) that there is a swirling flow compared with Figs. 4(a) and 4(b), two asymmetrical vortices in the inlet of the distribution chamber and a sink in the outlet of the tundish. The center of swirling flow is accord with geo- metrical center of rotation chamber, as shown in Fig. 5. ISIJ International, Vol. 47 (2007), No. 4 570© 2007 ISIJ Fig. 2. Calculated (a) instantaneous magnetic flux density and (b) averaged electromagnetic force in cylindrical end of tundish. 3.2. Effect of the Bending Nozzle Figures 6\u20138 show the calculated flow field while the bending nozzle is applied in centrifugal flow tundish. Flow pattern in main section as shown in Fig. 6 is significantly different from that of electromagnetic force with the direct nozzle. The vortices pattern in rotation chamber is simple. Figures 7(a)\u20137(c) show the flow patterns in horizontal sec- tion of centrifugal flow tundish at three locations with z\ufffd0.1 m, z\ufffd0.06 m and z\ufffd0.02 m. From Figs. 7(a) and 7(b), ones can see the jet flow discharged from bending nozzle impinges toward the chamber wall, and then the swirling flow can be formed. Figure 7(c) shows the outflow from rotation chamber impinging on the sidewall of tundish at an angle, and vortices are formed near corner and outlet of tundish. The cores of swirling flow at different heights in rotation chamber are not in a line and not accord with the centerline of chamber. This is because the driven force of swirling flow is not uniform in rotation chamber. 3.3. Effect of the Bending Nozzle and Electromagnetic Force Figures 9 and 10 show the calculated flow field in case that the bending nozzle and electromagnetic force are used ISIJ International, Vol. 47 (2007), No. 4 571 © 2007 ISIJ Fig. 3. Flow patterns in main section of centrifugal flow tundish using the electromagnetic force. Fig. 4. Flow patterns in horizontal section of centrifugal flow tundish (a) through the upper plane (z\ufffd0.1 m), (b) through the center plane of rotation chamber (z\ufffd0.06 m) and (c) through outlet of rotation chamber (z\ufffd0.02 m). Fig. 5. Instantaneous velocity field near the bottom of tundish through outlet of rotation chamber (z\ufffd0.02 m). Fig. 6. Flow patterns in main section of centrifugal flow tundish using the bending nozzle. Fig. 7. Flow patterns in horizontal section using the bending nozzle (a) through bending nozzle (z\ufffd0.1 m), (b) through the center plane of rotation chamber (z\ufffd0.06m) and (c) through outlet of rotation chamber (z\ufffd0.02 m). Fig. 8. Instantaneous velocity field in horizontal section using the bending nozzle through outlet of rotation chamber (z\ufffd0.02 m). together. The flow patterns are complex compared with those of above. The values of velocity component at hori- zontal and vertical direction are in same order in rotation chamber. There are two vortices in main section of the rota- tion chamber and two big vortices in the distribution cham- ber, which can be observed in Fig. 9. Figures 10(a)\u201310(c) show the flow patterns in horizontal section of centrifugal flow tundish at three locations with z\ufffd0.1 m, z\ufffd0.06 m and z\ufffd0.02 m. Figures 10(a)\u201310(c) illustrate that a strong swirling flow is formed in rotation chamber and the com- plex vortices patterns in the distribution chamber. The in- tensity of swirling flow in rotation chamber is remarkably strengthened. Figure 11 shows the transient fluctuation of the averaged velocities at three heights with x\ufffd0.0315 m, y\ufffd0.0282 m, the vertical distances, z\ufffd0.1 m, z\ufffd0.06 m and z\ufffd0.02 m, respectively. It can be concluded that when the time is more than 250 s, transient velocities at three locations are not variational with time, which indicated that the fluctuation of the velocity is steady. If the bending nozzle is applied, in- crement of maximum velocity which is only produced by magnetic field exceeds 0.2 m/s or 17% of the original ve- locity observed in Fig. 12. The effectiveness of the bending nozzle, which is an innovative technique, has been con- firmed in the present study. 4. Conclusions Three-dimensional turbulent flow fields in centrifugal flow tundish have been studied using LES method. It is concluded that: (1) When the rotating magnetic field with the direct nozzle is applied, the flow field of rotation chamber in- cludes two strong recirculation flows and two small vortices in vertical section. When the bending nozzle is only ap- plied, the swirling flow in horizontal section is strong, but small in vertical section. If the rotating magnetic field and the bending nozzle are applied together, the swirling flow in horizontal section is significantly enhanced, and flow struc- ture become complex. (2) Transient velocities in flow field are steady while the operation time is more than 250 s. (3) When the bending nozzle is applied, increment of maximum swirling velocity exceeds 17% of the original velocity, which is produced by rotating magnetic field with the direct nozzle. ISIJ International, Vol. 47 (2007), No. 4 572© 2007 ISIJ Fig. 9. Flow patterns in main section of centrifugal flow tundish using the electromagnetic force and the bending nozzle. Fig. 10. Flow patterns in horizontal section using the electro- magnetic force and the bending nozzle (a) through bending nozzle (z\ufffd0.1 m), (b) through the center