Keywords: MHD flows, slag, electrode, three-dimensional, electric furnace.

In slag cleaning furnaces, electrodes are immersed into the slag bath. In such a device the electric current not only generates heat in the slag but also a magnetic field. The current interacts with this self-induced field to produce body forces within the bath and the energy released by the electrodes leads to a temperature difference in the slag which will lead to thermal buoyancy forces in the vertical direction that resist the electromagnetic effects, although the latter is relatively small for large-scale furnaces. Recently, attention has been increasingly paid to understand magnetohydraudynamic (MHD) flows in metallurgical processes [1,2,3].

In the present paper, a three-dimensional mathematical model has been developed to simulate the flow and heat transfer in a slag cleaning furnace. The MHD model has been implemented into the CFX4 code [4] using user subroutines. Turbulence in the slag is modeled by the standard turbulence model [5] while the buoyancy effect is included in the transport equation. Results are given in the form of velocity vector plots, distributions of slag temperature, electric potential, heat generation and turbulent kinetic energy, and the change of the slag temperature with the electric potential. The predicted slag temperature is compared with the plant data.

The physical model considered is an industrial-scale slag cleaning furnace. The furnace is equipped with three electrodes that are located symmetrically and are immersed half way into the slag. The furnace is of cylinder with inside diameter of m. The height of slag layer is m. The electrode diameter is m. The center of the electrode is located at m. The computational domain is taken as one third of the furnace .

Boundary conditions are as follows: at walls the no-slip boundary conditions are imposed for the momentum transfer and the standard logarithmic wall treatment is used. The typical temperature of the sidewall is set at a constant K. This sidewall temperature is deduced from the cooling heat loss rate on the outside surface of the furnace wall. The slag-matte interface is treated as motionless and no-slip wall, and its temperature is set at K. At the slag surface, both convection and radiation heat losses are taken into account:

Here is convective heat transfer coefficient, is the Stefan-Boltzmann constant ( W/mK). is the roof temperature and is set to K. is the emissivity of the slag surface and is set to be . Here we introduce a factor, , considering the radiation heat transfer within a confined enclosure and the effect of the coke layer above the slag surface, and define as a modified factor [3].

The boundary conditions for the electric potential are as follows: the furnace wall is assumed insulated. At the bottom slag-matte interface the electric potential is set a value close to zero. The normal gradient of the electric potential is assumed to be zero at the free surface of slag. The electric potential on all surfaces of the electrode is presumed to be uniform.

The CFX4.3 [4] was utilized to solve the governing equations. A non-uniform mesh ( ) in axial, radial and azimuthal directions was used for all computations.

With the MHD model implemented into the CFX4 code [4], we simulated three-dimensional flow and heat transfer in a slag cleaning furnace. The main conclusions can be drawn from the present investigation:

The flow of the slag is quite complex and three-dimensional. The strongest flow appears near the electrode surface. In the bulk region the change of the slag temperature with the azimuth and radius is not great, and the highest slag temperature is around the electrode surface.

The electric potential drops sharply near the electrode. About 40% of the electric potential drops within a region of about m from the electrode surface for the furnace considered.

Most of heat released by the electrode is around the electrode surface, and the heat generation decreases rapidly away from the electrode. The highest heat generation is at the corner of the electrode tip.

The slag temperature increases with increasing the electric potential. Predicted slag temperature is well agreed with the plant data measured in an actual operating furnace. For the cases considered, the most appropriate range of the electric potential is between V and V.

1

Sheng, Y.Y., Irons, G.A., Tisdale, D.G., "Transport phenomena in electric smelting of nickel matte: part II Mathematical modeling", Metall. Materials Trans. B, 29B, 85-94, 1998. doi:10.1007/s11663-998-0010-5

2

Robertson, D.G.C., Kang, S., "Model studies of heat transfer and flow in slag- cleaning furnaces", Fluid Flow Phenomena in Metals Processing, Ed. By N. EI-Kaddah, D.G.C. Robertson, S.T. Johansen, and V.R. Voller, 157-168, 1999.

3

Xia, J.L., Ahokainen, T., "Three-Dimensional Flow and Heat Transfer in slag", Int. Comm. of Heat Mass Transfer (in press), 2002. doi:10.1016/S0735-1933(02)00329-9

4

AEA Technology, CFX-4.3, "Solver Manual", Harwell, 1997.

5

Launder, B.E., Spalding, D.B., "The numerical computation of turbulent flow", Computer Methods in Applied Mech. and Eng., 3, 269-289, 1974. doi:10.1016/0045-7825(74)90029-2

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