Evaluating approaches to accurately compute electro-vortex flows in liquid metal electrodes

Abstract

We quantitatively evaluate three approaches commonly used in the literature to simulate electro-vortex flow (EVF) in the finite volume framework of OpenFOAM. These approaches differ in the method of computing magnetic field (B0) due to an applied current density (J0). The first approach involves the use of Biot–Savart law whereas the latter two approaches involve the magnetic vector potential, A0, with and without the Green’s identity that relates A0 to J0. Contrary to our expectation, the EVF resulting from the three approaches significantly differs in magnitude. The use of vector potential leads to a higher B0 that enhances the velocity magnitude thus requiring finer mesh and lower time steps. These differences likely arise from the boundedness of the domain and the assumption of the Coulomb gauge for A0. We conclude that the Biot–Savart law approach is suitable to simulate EVF in bounded fluid domains, not only for its accuracy, but also in terms of computational cost. We find that J0, B0 and A0 are not solenoidal in the numerics, particularly near the current collector (CC) where the current diverges. To reduce the continuity errors, we propose adding corrector loops for these quantities and the use of fictitious pressure for A0. We also find that Neumann boundary condition on electric potential at the CC leads to reduction in continuity errors in J0. Our study has implications on the codes and softwares those use magnetic vector potential to compute current-driven MHD flows.