The sweeping jet can be a promising candidate in film cooling applications since it has a large lateral jet spreading which can be considered an advantage when compared to the regular steady jet film cooling. Fluidic oscillators can generate a sweeping jet without the need for any moving parts. In addition, they can be more conveniently manufactured by additive manufacturing techniques. This two-part paper presents a numerical study to investigate the application of using air/mist sweeping jets in film cooling for protecting turbine airfoils. Part I focuses on validating the computational mode by comparing the thermal-flow and heat transfer behavior between steady and sweeping air-only jets to ensure they are consistent with published information. Part II focuses on the mist behavior and its effect on heat transfer enhancement in the sweeping jet film cooling by adding micro-liquid droplets. An unsteady Reynolds-averaged Navier–Stokes (URANS) simulation accompanied by the k–ω shear stress transport (SST) turbulence model was used in this study. A comparison is made between steady and sweeping jets at two blowing ratios (BR = 1 and 2). The results show that the steady jet provided better film cooling performance along the centerline compared to that of the sweeping jet for both blowing ratios. However, the sweeping jet provided better and more uniform film cooling performance in the spanwise direction. Both jets experienced a significant jet-liftoff when the blowing ratio was 2. The entrainment was significant in the sweeping jet case for both blowing ratios. The sweeping jet caused an increase of 9.5% in total pressure losses compared to the steady jet. It was found that for the sweeping jet, a pair of counter-rotating vortices is inward-rushing toward the wall in the center rather than outward-rushing as in a typical steady jet film cooling flow field. A detailed analysis is presented to understand the instantaneous vortex dynamics of the sweeping jet that leads to the inward rotating counter-rotating vortex pair (CRVP) (i.e., reversed CRVP). The result shows that the pair of counter-rotating vortices is just a time-averaged image of a single vortex sweeping back and forth in the domain; it does not actually exist in real time.