Understanding magnetohydrodynamic (MHD) phenomena associated with complex duct geometries and buoyancy effects is required to effectively design liquid metal (LM) blankets for fusion reactors. These topics are investigated in the present work by numerically simulating 3D LM MHD flow using HIMAG (HyPerComp Incompressible MHD solver for Arbitrary Geometry), a code developed by HyPerComp with support from UCLA. In Part I of this dissertation, the simulated geometry is a manifold consisting of a rectangular feeding duct which abruptly expands along the applied magnetic field direction to distribute LM into several parallel channels. As a first step in qualifying the flow, a magnitude of the curl of the induced Lorentz force is used to distinguish between inviscid, irrotational core flows and boundary and internal shear layers where inertia and/or viscous forces are important. Scaling laws are obtained which characterize the 3D MHD pressure drop and flow balancing as a function of the flow parameters and the manifold geometry. Associated Hartmann (Ha) and Reynolds (Re) numbers in the computations are ~10^3 and ~10^1-10^3 respectively while the expansion ratio is varied from 4 to 12. An accurate model for the pressure drop is developed for the first time for inertial-electromagnetic and viscous-electromagnetic regimes based on 96 computed cases. Analysis shows that increasing the distance between the manifold inlet and the entrances of the parallel channels can improve flow balance by utilizing the effect of flow transitioning to a quasi-two-dimensional state in the expansion region of the manifold. Lastly, a Resistor Network Model is developed to describe the effect of the length of the poloidal channels on flow balancing in LM manifold. As the poloidal channels lengthen, the flow balance improves.

The simulated geometry in Part II consists of a straight, vertical duct which runs perpendicular to a strong, fringing applied magnetic field. There is also a region of applied heating as the primary goal of Part II is to explore buoyancy effects in MHD duct flows. The unsteady 3D MHD equations are solved using HIMAG. Results are presented for both upwards and downwards flows in electrically conducting (wall conductance ratio cw=0.12) and nonconducting ducts for a range of Ha~10^2, Re~10^3-10^4, and Grashof (Gr) numbers~10^7-10^8. While increasing Gr or decreasing Re increases buoyancy effects, increasing Ha was shown to increase maximum temperature by enhancing flow stability. The extent to which the flow is quasi-2D is analyzed and buoyant effects, in competition with Joule dissipation, are shown to bring about 3D flow features and newly discovered MHD mixed convection phenomena. Steeply diminishing volumetric heating, which approximates nuclear heating, is applied to the vertical MHD flows for comparison to flows with surface heating only. Surface heating generates stronger buoyancy effects than volumetric heating of the same total power; however, many of the same phenomena occur. Therefore, surface heating, the only option for lab experiments, can be useful in exploring the effects of volumetric heating in MHD flows. Lastly, the results of a surface heating case are presented for the purpose of comparison with other codes and experiments, especially the MaPLE-U experiment that is currently is underway at UCLA.