A novel passive flow control concept for subsonic and transonic flows over 2D airfoils is proposed and examined via CFD. The control concept is based on the local modification of the airfoil geometry via a newly proposed Surface-based Trapped Vortex Generator (STVG) concept. For transonic flows, the upper surface modifications demonstrated the ability to reduce the strength of the shockwave on the upper surface of the airfoil with only a small penalty in lift, yet, with increased lift-to-drag ratio. Lower surface modifications could significantly increase the lift-to-drag ratio for the full range of the investigated angles of attack. For helicopter main rotor flows, three major contributions were made. First, the STVG control was applied to dynamic stall conditions at constant freestream. Here the aim was to mitigate the negative effects of dynamic stall, i.e. for the reduction of peak negative pitching moment while not deteriorating significantly the original lift and drag characteristics. In case of the upper surface modifications, the best geometries could reduce the peak negative pitching moment by as much as 37-63%, while sacrificing only 2-10% of peak lift and reducing drag by 14-38%. On the other hand, the lower surface modifications demonstrated the ability to increase lift by 4-16% with only minor penalty in pitching moment and drag. Second, a comprehensive methodology for simulating 2D (shock-induced) dynamic stall at fluctuating freestream was proposed in this work. The conditions were representative of the flow experienced by a helicopter rotor blade section of the UH-60A helicopter in forward flight. The results suggest that the fluctuating freestream alters the dynamic stall mechanism documented for constant freestream in a major way. Finally, the novel STVG passive flow control concept was investigated for controlling the flow in 2D shock-induced dynamic stall at fluctuating freestream. Results showed that the best geometries could reduce the peak negative pitching moment by as much as 9-23% during the transonic phase of a cycle and by as much as 19-71% during the dynamic stall phase. Also, they are able to reduce peak drag by 8-20% for the transonic phase and by 15-44% in the dynamic stall phase.