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MHD COMPUTATIONAL MODEL
The design of bus network for high amperage reduction cells has a double fold
task: to optimize the magnetic field within the cell and the electric current distribution both
within the cell and the bus bars itself. The magnetic field should be reduced and optimized
for a stable melt interface and to avoid vigorous velocities within the liquid melt. Since the
magnetohydrodynamic driving force is jxB, the electric current distribution, particularly the
horizontal components, are equally important to the magnetic field optimization.
Historically two different modelling approaches have been used: one for the electric
current distribution for the bus bar network and, often quite different, other mathematical
model for the MHD phenomena within the cell. Very similar data inputs both for the
magnetohydrodynamic simulations and for the electric current modeling in the bus network
are in fact used. Physical and engineering considerations suggest that both problems are
mutually interconnected and should be solved interactively. It means that the computer
program should use the same data input to compute the electric current, voltages,
temperatures in the bus network, and the magnetic field, the current distribution within the
cell with waving metal interface, then finally iterate back to account for the spatially and
temporally variable cell interpolar distance for the current distribution in the supplying bus
network. This affects also the magnetic field, the metal pad waves, velocities, and the
neighbor cells which are interconnected to the particular test cell (4-6).
Electric Current Distribution

The first calculation step needed for an MHD model is the electric current
distribution. This is calculated by coupling the electric current in the fluid zone to the
resistance network representing the elements of individual anodes and cathode collector bars
as well as the whole bus-bar circuit between two adjacent cells. The electric current in the
fluid zones must be computed from the continuous media equations governing the DC
current (which can change in time with the waves and anode burnout process):
(1)
where the fluid flow induced currents in the highly conducting liquid metal are accounted
for. The electric potential in the fluid is governed by the equation:
(2)
and the boundary conditions of zero current at the insulating walls, given current distribution
j
a
at anodes, j
c
at cathode carbon (both supplied from the finite element resistivity network