A fully passive flapping foil turbine was simulated using a two-dimensional Navier–Stokes solver with two-way fluid-structure interaction at a Reynolds number based on freestream flow Re=1100 and 1.1×106 with a NACA 0012 foil. Both pitch angle and angle-of-attack control methodologies were investigated. Efficiencies of up to 30% based on the Betz criterion were found using pitch control, which is commensurate with values reported in the literature for prescribed motion studies. Nonsinusoidal foil pitching motions were found to be superior to sinusoidal motions. Efficiencies exceeding 41% were found using angle-of-attack control, and nonsinusoidal angle-of-attack profiles were found to be superior. The key to improving the efficiency of energy extraction from the flow is to control the timing of the formation and location of the leading-edge vortex at crucial times during the flapping cycle and the interaction of the vortex with the trailing edge. Simulations using Reynolds-averaged Navier–Stokes turbulence modeling suggest that the performance is maintained or only slightly reduced at Re=1.1×106.