  The friction drag reduction in a turbulent channel flow generated by
surface-mounted rotating disc actuators is investigated numerically. The wall
arrangement of the discs has a complex and unexpected effect on the flow. For
low disc-tip velocities, the drag reduction scales linearly with the percentage
of the actuated area, whereas for higher disc-tip velocity the drag reduction
can be larger than the prediction found through the linear scaling with
actuated area. For medium disc-tip velocities, all the cases which display this
additional drag reduction exhibit stationary-wall regions between discs along
the streamwise direction. This effect is caused by the viscous boundary layer
which develops over the portions of stationary wall due to the radial flow
produced by the discs. For the highest disc-tip velocity, the drag reduction
even increases by halving the number of discs. The power spent to activate the
discs is instead independent of the disc arrangement and scales linearly with
the actuated area for all disc-tip velocities. The Fukagata-Iwamoto-Kasagi
identity and flow visualizations are employed to provide further insight into
the dynamics of the streamwise-elongated structures appearing between discs.
Sufficient interaction between adjacent discs along the spanwise direction must
occur for the structures to be created at the disc side where the wall velocity
is directed in the opposite direction to the streamwise mean flow. Novel
half-disc and annular actuators are investigated to improve the disc-flow
performance, resulting in a maximum of 26\% drag reduction.
