  We numerically investigate the effect of a periodic array of asymmetric
obstacles in a two-dimensional active nematic. We find that activity in
conjunction with the asymmetry leads to a ratchet effect or unidirectional flow
of the fluid along the asymmetry direction. The directional flow is still
present even in the active turbulent phase when the gap between obstacles is
sufficiently small. We demonstrate that the dynamics of the topological defects
transition from flow-mirroring to smectic-like as the gap between obstacles is
made smaller, and explain this transition in terms of the pinning of negative
winding number defects between obstacles. This also leads to a non-monotonic
ratchet effect magnitude as a function of obstacle size, so that there is an
optimal obstacle size for ratcheting at fixed activity.
