A weakly conducting fluid containing a positive electric charge is entering a pipe with conducting solid walls. The pipe is assumed to be grounded on its outside surface (to insure this, a separate solid was wrapped around the outside and defined to be a perfect conductor at zero potential). This problem was originally investigated by a FLOW-3D user, Harold Walmsly, who raised questions about simulation results when the solid/fluid boundary is, or is not, coincident with a mesh/grid line. When coincident, grid elements contain either pure fluid or pure solid. Alternatively, the boundary could be within a grid element creating a “mixed” cell containing both fluid and solid. The question raised was why there are differences in the computational results and is this some problem associated with the FAVOR™ method? This note addresses these questions and describes a code change to improve the electrical treatment of mixed cells.
Two basic options are available for simulating this arrangement. Either the solid can be considered a perfect conductor having a specified potential (an “electrode”) or it can have a finite conductivity in which case the simulation will compute potentials and charge densities in the solid.
Thus, having a mixed cell boundary, or not, and allowing for currents in the solid pipe, or not, constitutes a set of four possible arrangements whose results can be compared.