  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.
