Pré-visualização5 páginas

recirculat- velocities are high and directed upward in a plane locateding flow pattern from the entry plane until, at least, the near the wall (Figure 13(c)) for the BT, and these velocitiesexterior outlet promoting transverse mixing in addition to are considerably lower and slightly directed toward thelongitudinal mixing (Figures 12(a), 12(c), 13(a), and 13(c)). tundish floor (Figure 13(d)) for the tundish with a TI&Meanwhile, using a tundish with the TI&D arrangement, D arrangement.transverse mixing is only observed in the pouring box and, after the dam, the fluid behaves as a plug flow. Velocity fields in horizontal planes are shown in Figures C. Mathematical Model of Mass Transfer12(a) through (d). Figure 12(a) shows the velocity field of water in the upper bath surface in a bare tundish and Figure Dynamics of chemical mixing of the tracer after 30 sec- onds of its injection in the ladle nozzle are shown in Figures12(b) the corresponding field in the tundish with a TI&D arrangement. Figures 12(c) and (d) show the same type of 14(a) and (b) as isoconcentration lines expressed in mass fractions units for longitudinal-vertical planes. Figures 14(a)information for a plane located at half the bath depth. Velocity fields in longitudinal-vertical fields are shown and (b) correspond to the jet entry plane for a BT and a tundish with the TI&D arrangement, respectively. It is seenin Figures 13(a) through (d). Figure 13(a) shows the velocity field at the outlet plane for the bare tundish and Figure 13(b) that, at this short time, the tracer has been dispersed, reaching the interior outlet completely and the exterior one partiallyshows the corresponding field for the tundish with the TI& 1512—VOLUME 31B, DECEMBER 2000 METALLURGICAL AND MATERIALS TRANSACTIONS B (a) (a) (b) (b) (c) (c) (d) (d) Fig. 14—Front view of the isoconcentration lines of tracer at 30 s. After Fig. 15—Upper view of the isoconcentration lines of the tracer at 30 s.the injection: (a) inlet plane in BT arrangement, (b) inlet plane in TI&D After the injection: (a) near the floor plane in BT arrangement, (b) neararrangement, (c) outlet plane in BT arrangement, and (d ) outlet plane in the floor plane in TI&D arrangement, (c) center plane of the bath heightTI&D arrangement. in BT arrangement, and (d ) center plane of the bath height in TI&D arrangement. in the bare tundish. In the tundish with a TI&D arrangement, the tracer remains in a mixing process in the entry zone, and further downstream, it has just passed over the upper side of the dam. Figures 14(c) and (d) show the same type of information for the outlet plane in both kinds of tundishes where the same comments are applicable. Horizontal views of the chemical mixing 30 seconds after injection of the tracer can be seen in Figure 15. Figures 15(a) and (b) show the isoconcentration lines in a plane located near the tundish floor for a bare tundish and the TI& D arrangement, respectively. In the first case, the tracer has already reached the position of the interior outlet and is a little more than halfway from the exterior outlet. In the second case, the tracer is just exiting from the hole in the dam. Figures 15(c) and (d) show the chemical mixing of the tracer, 30 seconds after the injection, in the upper planes of Fig. 16—Mathematically calculated total RTD curves.a bare tundish and the TI&D tundish, respectively. The tracer dispersion has reached the lateral wall of the bare tundish since the momentum transfer and the turbulence are high enough to promote transverse and longitudinal mixing pro- outlets. The tracer is still away from the lateral tundish wall, as can be seen in Figure 15(d). The results of thecesses. In the TI&D arrangement, the tracer is driven toward the top bath surface, but with a lower turbulence, and the mathematical simulations for the total RTD curves at both outlets are shown in Figure 16 for the BT and with a TI&isoconcentration lines are deformed by the presence of the METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 31B, DECEMBER 2000—1513 Table III. Flow Characteristics Results from the 4. Tracer diffusion under turbulent conditions was simulated Calculated Total RTD Curves acceptably well through the mathematical model using the standard k-« model.Arrangement VDead VPlug VMixed tcalc su2 D/UL 5. These results prove that a simple arrangement composed BT 0.1309 0.2112 0.6579 284.0 0.3196 0.1992 of a TI and a pair of dams has a better performance TI&D 0.0785 0.370 0.5515 315.82 0.1596 0.0874 than the complex furniture usually employed in actual tundishes such as weirs, dams, vortex killers, and sophis- ticated impact pads. D arrangement, and the flow quantification parameters are presented in Table III. These values were calculated from ACKNOWLEDGMENTSthe calculated total RTD curves in Figure 16 and following the procedure of Sahai and Emi.[21] The experimental and The authors give thanks to the institutions SNI, CoNaCyT, the simulated results exhibit similar flow characteristics, as COFAA, and IPN for the partial financial support. One of can be seen by comparing Tables II and III. Therefore, us (JdeJB) gives thanks to Instituto Tecnolo´gico de Morelia similar conclusions can be reached from the water model for allowing him a leave of absence at IPN. Thanks are also and the mathematical simulations in a complementary fash- given to FOSECO INC., whose support was determinant to ion. Even the calculated curves (Figure 16) and the experi- perform this study. mental ones (Figure 9) may look physically different. This supports the contention that the mass transfer model LIST OF SYMBOLSdescribes adequately the turbulent chemical mixing of the tracer inside the water model for a BT and a tundish with A cross-sectional area rather complex furniture. C tracer concentration From the analysis of Figures 10 through 15 and the visual Ci tracer concentration at strand i observations of the tracer dispersion during the experimental C1, C2, constants in the turbulence model trials, brief descriptions about the tracer dispersion in the and CD tundish with the TI&D arrangement can be made. E empirical constant in Eq. [16] Just after the injection, the tracer is driven upward to the Ei RTD curve at strand ibath surface without appreciable turbulence. At an interme- Dm molecular tracer diffusivitydiate time after the injection, the tracer strikes the baffle Dt turbulent tracer diffusivity and is re-directed again toward the top bath surface and Deff effective tracer diffusivitydriven along the tundish length. When the front of the tracer G generation term (Eq. [10]) dispersion reaches the level between both outlets, the fluid k turbulent kinetic energy has lost momentum and the tracer descends toward the tun- mi mass of tracer exiting through strand idish floor. Once there, the tracer is diffused toward the M total mass of tracer injected into the vessel outlets obtaining, in this way, a very similar mass of tracer P pressure in both outlets. Moreover, the hole in the dam, located in Q volumetric flow rate the opposite side of the outlets, removes the dead zones very t time efficiently, which would form downstream otherwise. tcalc mean calculated time These fluid flow characteristics are observed neither in VDead dead volume fraction the BT nor in the tundish with a BWIP arrangement; these VPlug plug volume fractiondevices were not as effective as the TI&D arrangement. VMixed mixed volume fraction v+ as defined in Eq. [17] u, v, w velocity vectorsV. CONCLUSIONS y+ as defined in Eq. [18] Water and mathematical modeling techniques have been Greek Symbolsapplied to study the flow of liquid steel in a multiple-strand « dissipation rate of the turbulent kinetic energytundish of a bloom caster and the conclusions derived from m fluid viscositythe results are as follows. meff effective fluid viscosity 1. The employment of an arrangement consisting of a TI mt turbulent fluid viscosity and a pair of dams is more effective to increase the plug r