By using a Navier–Stokes model, we examine a novel flow energy harvesting device consisting of a flapping foil mounted on a damper (representing the power generator) and a rotational spring. Self-induced and self-sustained flapping motions, including a heaving motion h(t) and a pitching motion α(t), are excited by an incoming flow and power extraction is achieved from the heaving response. Depending upon the configuration of the system and the mechanical parameters (e.g., the location of the pitching axis and the stiffness of the rotational spring), four different responses are recorded: (i) the foil remains stable in its initial position (α=0 and h=0); (ii) periodic pitching (around α=0) and heaving motions are excited; (iii) the foil undergoes irregular motions characterized by switching between oscillations around two pitching angles; and (iv) the foil rotates to a position with an angle to the incoming flow and oscillates around it. The existence of response (ii) suggests the feasibility of controllable and stable flow energy extraction by this device. Through numerical simulations with a Navier–Stokes model we have determined combinations of geometric and mechanical parameters to achieve this response. The corresponding energy harvesting capacity and efficiency are predicted.