Three dimensional numerical simulations were made on supersonic compressible flows in disk channels in order to obtain knowledge which is important for designing a disk MHD channel. Effects of the cross sectional area ratio and of channel height on both flow field and total pressure loss were investigated. For small area ratios, the flow Mach number decreased along the radial direction and total pressure loss was induced mainly by pseudo-shock wave and boundary layer separations. It was clarified that an optimal area ratio which makes the total pressure loss minimum, exits and that the total pressure loss decreases with an increase in the channel height. Furthermore, new thin swirl vanes with a simple shape were proposed in order to improve the disk MHD generator performance. The numerical simulations on the flow in which swirl vanes with different shapes are installed, have suggested that although the elliptic shape can provide a larger swirl compared with the circular shape, the total pressure loss in the downstream becomes larger owing to a larger viscous dissipation in the wake.