Li, J., Chua, K. T. E., Nguyen, V.-T., Wise, D. J., & Chan, W. H. R. (2025). Permeability of magnetohydrodynamical flows through porous structures under various external magnetic fields and forces. Fusion Engineering and Design, 219, 115294. https://doi.org/10.1016/j.fusengdes.2025.115294
Abstract:
Unlike in low-speed hydrodynamical flows where permeability is constant for a given porous structure,
magnetohydrodynamical (MHD) flows are subject to the induced Lorentz force in the presence of an external
magnetic field that significantly changes flow patterns and speeds. We conducted pore-scale MHD simulations
using the lattice Boltzmann method to investigate permeability under a broad range of magnetic fields and
driving forces. A simple cross-channel structure is first simulated for a systematic parametric study. At low
Reynolds numbers, MHD flows continue to exhibit Darcy-law characteristics of conventional hydrodynamical
flows where permeability is independent of driving forces for a given magnetic field. As the magnetic field
strength increases, we verified that the obtained permeability reduces significantly when the magnetic field is
imposed transversely and less so when in the flow-aligned direction. For low Hartmann numbers and arbitrary
magnetic field orientations, we developed a superposition model for the permeability as if the magnetic field
components were imposed independently. The superposition model is verified in simulations of a complicated
Sierpinski carpet structure at low Hartmann numbers, demonstrating its practical applicability. Additionally,
permeability reductions of the Sierpinski carpet in different directions were found to be almost identical for
a given external magnetic field, unlike the situation in the simple cross-channel geometry. This is due to the
flow passage becoming tortuous, with resisting Lorentz forces always induced in many locations where the
local flow is bent by the carpet structure. This occurs even if the overall bulk flow direction is aligned with
the imposed magnetic field orientation.
License type:
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Funding Info:
This research is supported by core funding from: Institute of High Performance Computing (A*STAR IHPC)
Grant Reference no. : NA