We numerically assess the influence of non-uniform magnetic flux density and connected load resistance on turbulent duct flows in a liquid metal magnetohydrodynamic (MHD) electrical power generator. When increasing the magnetic flux density (or Hartmann number), an M-shaped velocity profile develops in the plane perpendicular to the magnetic field; the maximum velocity in the sidewall layer of the M-shaped profile increases to maintain the flow rate. Under the conditions of a relaminarized flow, the turbulence structures align along the magnetic field and flow repeatedly like a von Kármán vortex sheet. At higher Hartmann numbers, the wall-shear stress in the sidewall layer increases and the sidewall jets transit to turbulence. The sidewall jets in the MHD turbulent duct flows have profiles similar to the non-MHD wall jets, i.e. a mean velocity profile with outer scaling, Reynolds shear stress with the opposite sign in a sidewall jet, and two maxima for the turbulent intensities in a sidewall jet. The Lorentz force suppresses the vortices of the secondary mean flow near the Hartmann layer for low Hartmann numbers, whereas the secondary vortices remain near the Hartmann layer for high Hartmann numbers. An optimal load resistance (or load factor) to obtain a maximum electrical efficiency exists, because the strong Lorentz force for a low load factor and unextracted eddy currents for a high load factor reduce efficiency. When the value of the load factor is changed, the profiles of mean velocity and r.m.s. for the optimal load factor produce almost the same profiles as the high load factor near the open-circuit condition.
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