Operating low-pressure turbines (LPT) at off-design conditions or considering more aggressive designs can lead to laminar separation on the suction side of the LPT blades resulting in significant turbine and overall engine performance losses. In these instances, performance improvements may be achieved with active flow control (AFC). In an extensive experimental research program at the Air Force Research Laboratory (AFRL) at Wright-Patterson AFB, Dr. R.B. Rivir and co-workers systematically investigated the benefits of AFC with steady and pulsed vortex generator jets (VGJs) for a linear PakB LPT cascade. Pulsed VGJs were found to be very effective in mitigating separation. We are employing two in-house computational fluid dynamics (CFD) research codes for investigating the physical mechanisms associated with AFC for LPT geometries. For simulations of the entire LPT blade, a high-order-accurate finite volume code based on the compressible Navier-Stokes equations is used. Data from direct numerical simulations (DNS) with up to 19.4 million grid points of a PakB blade at Re=25,000 are compared with experimental data. For our fully resolved DNS that focus exclusively on the separated flow region, we are employing a high-order-accurate compact finite difference code based on the incompressible Navier-Stokes equations in vorticity-velocity formulation. Here, we study a separation bubble on a flat plate and on a curved wall model-geometry under LPT conditions. These simulations enable us to identify the intricate physical mechanisms associated with unsteady separation, transition, flow instabilities, and active control using VGJs. In particular, our simulation results provide an explanation for the stunning effectiveness of pulsed VGJs for separation control.