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 O(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.

No abstract

Numerical simulations of the auto-rotation of a model winged seed are presented. The calculations are performed by solving simultaneously the Navier-Stokes equations for the flow surrounding the seed and the rigid-body equations for the motion of the seed. The Reynolds number based on the descent speed and a characteristic chord length is varied in the range 80-240. Within this range, the seed attains an asymptotic state with finite amplitude auto-rotation, while for smaller values of the Reynolds number no auto-rotation is observed. The motion of the seed is characterized by the coning and pitch angles, the angular velocity and the horizontal translation of the seed. The values obtained for these quantities are qualitatively similar to those reported in the literature in experiments with real winged seeds. When increasing the Reynolds number, the seed tends to rotate at higher speeds, with less inclination with respect to the horizontal plane, and with a larger translation velocity. With respect to the aerodynamic forces, it is observed that, with increasing Reynolds number, the horizontal components decrease in magnitude while the vertical component increases. The force distribution along the wing span is characterized using both global and local characteristic speeds and chord lengths for the non-dimensionalisation of the force coefficients. It is found that the vertical component does not depend on the Reynolds number when using local scaling, while the chordwise component of the force does.

Direct Numerical Simulations of the flow around a pair of flapping wings are presented. The wings are flying in forward flight at a Reynolds number Re = 500, flapping at a reduced frequency k = 1. Several values of the radius of flapping motion are considered, resulting in a database that shows a smooth transition from the wing rotating with respect to its inboard wingtip (flapping), to a vertical oscillation of the wing (heaving). In this transition from flapping to heaving, the spanwise-averaged effective angle of attack of the wing increases while the effect of the Coriolis and centripetal accelerations becomes weaker. The present database is analyzed in terms of the value and surface distribution of the aerodynamic forces, and in terms of 2D and 3D flow visualizations. While the former allows a decomposition of the force in pressure (i.e., the component of the force normal to the surface of the wing) and skin friction (i.e., tangential to the surface of the wing), the latter allows the identification of specific flow structures with the corresponding forces on the wing. It is found that the aerodynamic forces in the vertical direction (lift) tend to increase for wings moving with larger radius of flapping motion, becoming maximum for the heaving configuration. This is mostly due to the increase of the spanwise-averaged effective angle of attack of the wing with the radius of the flapping motion. Also, the local changes in the effective angle of attack have a strong effect on the structure of the leading edge vortex, resulting in changes in the distribution of suction along the span near the leading edge of the wing. The effect of the apparent accelerations is mostly felt on the spanwise position where the separation of the LEV occurs. On the other hand, the differences in the force in the streamwise direction (thrust/drag) between the configurations with different radius of flapping motion seems to be linked to the position of the stagnation point dividing the suction and pressure side boundary layers, which seems to be controlled by the local effective angle of attack. Finally, the results of the DNS are used to evaluate the performance of an unsteady panel method, and to explain its deficiencies.

No abstract