Three-dimensional numerical calculations on liquid-metal magneto-hydrodynamic flow through circular pipe in magnetic-field inlet-region

Three-dimensional numerical calculations have been performed on liquid-metal magnetohydrodynamic (MHD) flows through a circular pipe in the inlet region of the applied magnetic field, including a sufficient calculation region upstream in the magnetic field section. The continuity equation, the momentum equation including the Lorentz force term, and the induction equation derived from basic equations in the electromagnetism have been solved numerically. Along the flow axis (i.e., the channel axis), the pressure decreases slightly as a normal non-MHD flow, increases once, thereafter, decreases sharply, and finally decreases as a fully-developed MHD flow. The sharp decrease in the pressure, resulting in a large pressure drop in the inlet region is due to the increase in the induced electric current in this region compared with that in the fully-developed region. The velocity distribution changes from a parabolic profile of a laminar non-MHD flow to a profile with peaks near the walls parallel to the magnetic field, and finally to a flat profile of a fully-developed MHD flow.