Numerical Computation for the Melt Convection of the Model System of Continuous Steel Casting with Various Magnetic Fields

Abstract

Melt flow in the model system of continuous steel casting process was numerically computed with an application of various magnetic fields. The model geometry is 1ϫ1ϫ2 which is not in accordance with the current shape employed in a practical industry. Electric coil to produce a magnetic field was either vertical, horizontal and parallel, or perpendicular to the nozzle jet from the tandish. Detailed melt flow in the mold is graphically presented. The axial magnetic field appears to suppress the jet flow most effectively.KEY WORDS: continuous steel casting; magnetic field; numerical calculation.In the X-or Y-directional magnetic fields, two electric coils were located at the outside of the vertical walls with the electric current in the same direction. The dimensional equivalent size is as follows. The width of the rectangular mold is lϭ0.064 m and the diameter of an electric coil is 0.1 m. The molten steel is presumed to come down from the tandish through a rectangular pipe of 0.1lϫ0.1l and flows out in the oblique direction into the mold. The molten steel is at higher temperature. Four surrounding boundaries of mold is kept at cold temperature with top and bottom boundaries presumed to be thermally adiabatic. From the bottom boundaries, the molten steel was assumed to flow out with uniform equivalent volume flow rate as that from the top inlet.The three-dimensional model equations consist of the equation of continuity, momentum equations, energy equation, Ohm's law, continuity equation of electric current. The magnetic induction was computed from Biot-Savart law as follows. The dimensionless equations are as follows. The initial and boundary conditions for computation are as follows.At the top inlet, Wϭ1, Tϭ0.5, At the top surface, U ᠬ ϭ0, ∂T/∂Zϭ0, J ᠬ ϭ0 At the bottom boundary, Wϭ1/100, ∂T/∂Zϭ0, ∂J z /∂Zϭ0The dimensionless variables are defined in the nomenclature. The characteristic dimensionless values are defined as follows.w in is a velocity through the top nozzle and l in ϭl/10. Re in represents the inlet condition correctly. Actual Reynolds number at the bottom exit should be 1/100 of Re above.The above dimensionless equations were approximated with finite difference equations. The pressure was computed by the HSMAC method. The inertial terms were approximated with the third-order upwind scheme. The dimensionless time increment is 2ϫ10 Ϫ4 . The rectangular enclosure was divided into 50 3 grids with non-uniform staggered mesh. The detailed view of the nozzle is shown in Fig. 2. The inside of the nozzle was assumed to be stair-steps for the sake of simplicity with 0.01 dimensionless length. Computed ResultsThe computational conditions are as follows. Reϭ10 directional velocity component U max in the X-directional magnetic field at Haϭ0, 100, 200 and 500. At t=5, magnetic field was impressed. The convergence is smooth to suggest the stable numerical computation. (f) suggests the Z-directional magnetic field appears to provide very large magnetic suppression in comparison to those in the X-or Y-directional on...

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