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vertical intensity of the magnetic field has [5]. In that context, it is very important for an
MHD cell stability analysis code like MHD-Valdis not only to be able to compute rapidly
and accurately the magnetic field [6] and the non-linear bath-metal interface wave
dynamic evolution [7], but also to be able accurately and rapidly compute the metal pad
current density field.

A first step in that direction has been achieved in [8] by demonstrating that MHD-

Valdis 1D mesh busbar representation is able to calculate accurately the busbar network
current distribution. Having done that, the current work concentrates on the main
remaining items affecting the calculation of the metal pad current density field, namely
the metal pad height and the ledge thickness.

FULL CELL 3D ANSYS® BASED MODEL

As stated previously, a non-linear MHD cell stability analysis model like MHD-

Valdis must be able to compute the metal pad current density field rapidly and
accurately. Computation time is important because the magnetic field, the current density
field, the bath and metal flow fields and the bath/metal interface wave evolution must be
recomputed at each time step. Considering that a typical transient cell stability analysis
requires the solution of 4000 time steps, it is clear that practically it is not possible to
spend many CPU hours to solve one time step magnetic field or current density field.

Fortunately, CPU time constraints do not apply to benchmark or comparison

models that can be built in order to verify the accuracy of MHD-Valdis metal pad current
density calculation. Of course, it is always better to validate a mathematical model
solution using measured data, but in the case of the metal pad current density field, it is
unfortunately not an option.

The full 3D ANSYS® based thermo-electric (T/E) model built for the purpose of

weakly coupling T/E and MHD models [1] is one such model that can compute very
accurately the metal pad current density field but does require a lot of CPU time in order
to do it. For example, the metal pad current density field presented in Figure 6 of [1] took
40.6 CPU hours to compute. Of course, it is important to point out that that T/E model
(presented in Figure 4 of [1]) consists of 329,288 elements and is converging the steady-
state ledge shape as part of the solution.

In order to save some CPU time, the inside shell section of that T/E model was

converted into an electric only model (see Figure 1). This simplified model is no longer
able to converge the steady-state ledge shape, therefore it is using a fixed, user defined,
metal pad shape in order to compute the metal pad current density field presented in
Figure 2. The solution was obtained after "only" 1 hour and 39 minutes of CPU time of
computation.