From flapping to heaving: A numerical study of wings in forward flight

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.