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Using ANSYS and CFX to Model Aluminum Reduction Cell since 1984 and Beyond

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Rigorously, the change of the bath-metal interface and of the anodes shape also affected the current density
field in the metal pad, which in turn affected the magnetic field so both need to be updated. Then the CFD
problem needs to be solved again with the new anode shape and the updated MHD Lorentz body force.
Hopefully after a few iterations between the CFD solution and the anode geometry and MHD Lorentz body
force update, the global solution will nicely converge!

Clearly, there are a lot of challenges associated with the successful development of this step:

1) The CFD code must be able to converge efficiently this closed domain, multi-phases, body force

driven problem, CFX can;

2) The interfacing of ANSYS with CFX CFD solver must be smooth and efficient (in 1993, the author

successfully coupled ANSYS and FIDAP in order to solve a MHD flow in a simple test problem);

3) Updating the magnetic field must be performed at a minimum computing cost (Biot-Savard subtraction

of old source terms and addition of the new ones, then restarting of the non-linear convergence from
the previous solution);

4) Restarting the CFD convergence after an update of the anode geometry and MHD Lorentz force must

be equally efficient.

Finally, even with the most efficient numerical scheme, solving this problem will require tremendous
computing resources. Solving this type of problem may not become affordable before two or even three
computer generations from now!

As proof of this, steps 1 and 2 have been already been developed and published (Reference 32) but as
expected, solving that model required far too much computing resources. For that reason, that impressive
model cannot be used for design work. For that, the author continues to recommend using a separate
specialized MHD solver called MHD-Valdis (Reference 33).

Step 3, 3D thermo-electro-magneto-hydro-dynamic full cell and
external busbars model:

After having solved a fully coupled electro-magneto-hydro-dynamic model using a fixed ledge geometry, it
is time to consider yet another coupling: the impact of the flow solution on the liquid/ledge heat transfer
coefficient and hence on the shape of the ledge thickness.

Practically, this means that after having solved the initial flow solution, the local heat transfer coefficient
on the liquid/ledge interface must be reevaluated and the thermo-electric ledge convergence loop must be
repeated in addition to the anode geometry adjustment. The rest of the numerical scheme remains the same
of course, the current density will be updated as part of the thermo-electric ledge convergence process so
the magnetic field needs to be updated. Yet this time in addition to the Biot-Savard source term changes,
the ferro-magnetic shielding property of the potshell needs to be updated as well as the potshell temperature
changed as part of the thermo-electric ledge convergence process.

Implementing step 3 on top of step 2 is quite straightforward, yet obviously the required computer
resources are getting even bigger with each additional interaction added to the numerical scheme. An effort
in that direction has already been published (Reference 34). Unfortunately surely because the required
computing resources would have been excessive, the coupling loop between the solution of the MHD flow
with a given ledge geometry and the solution of the ledge geometry with a given distribution of heat
transfer coefficients was not performed.

Step 4, 3D thermo-electro-mechanical-magneto-hydro-dynamic full
cell and external busbars model:

Now that we have a converged ledge profile compatible with the MHD flow on an assumed rigid potshell
geometry, we can solve the "simple" cathode potshell plastic deformation and lining swelling mechanical
model to obtain the deformed shape of the potshell and the corresponding deformed shape of the cell
cavity.