On the aerodynamic forces on heaving and pitching airfoils at low Reynolds number

The influence that the kinematics of pitching and heaving 2D airfoils have on the aerodynamic forces is investigated using Direct Numerical Simulations and a force decomposition algorithm. Large amplitude motions are considered (of the order of one chord), with moderate Reynolds numbers and reduced frequencies of order 1, varying the mean pitch angle and the phase shift between the pitching and heaving motions. Our results show that the surface vorticity contribution (viscous effects) to the aerodynamic force is negligible compared to the contributions from the body motion (fluid inertia) and the vorticity within the flow (circulation). For the range of parameters considered here, the latter tends to be instantaneously oriented in the direction normal to the chord of the airfoil. Based on the results discussed in the paper, a reduced order model for the instantaneous aerodynamic force is proposed, taking advantage of the force decomposition and the chord-normal orientation of the contribution from vorticity within the flow to the total aerodynamic force. The predictions of the proposed model are compared to those of a similar model from the literature, showing a noticeable improvement on the prediction of the mean thrust, and a smaller improvement on the prediction of mean lift and the instantaneous force coefficients.