Electric current redistribution and Lorentz force localization in magnetohydrodynamic flow through a sudden expansion

Abstract

In this study, we performed three-dimensional numerical simulations using the robust magnetohydrodynamic (MHD) solver AnuPravaha to investigate electric current redistribution in MHD flow through a suddenly expanded channel. The code performance was rigorously validated against standard benchmark cases, including Shercliff and Hunt's cases. The simulations were conducted for Hartmann number ranging from 10 to 50 under the presence of a transverse magnetic field, considering both electrically insulating and electrically conducting wall conditions. The results indicate that the sudden expansion significantly alters the electric potential field and leads to the formation of concentrated high current density zones near the expansion edges and corner regions. At low magnetic interaction, the current distribution remains relatively uniform, whereas at higher Hartmann number the current closure paths are strongly distorted, resulting in pronounced current redistribution across the expanded section and the formation of a highly localized Lorentz-force-driven electromagnetic braking region downstream of the expansion. A quantitative parameter named the Current Concentration Index (CCI) is introduced to measure current intensification within the expansion region relative to the inlet section, and CCI increases from 1.2997 to 1.5582 for insulating walls and from 1.3050 to 1.5729 for conducting walls as Hartmann number increases from 10 to 50. Similarly, the Lorentz Force Localization Ratio rises from 9.5131 to 16.4236 for insulating walls and from 4.0799 to 8.1194 for conducting walls, indicating stronger confinement of electromagnetic braking near the expansion plane.