Thrust generation in heaving and flapping wings in forward flight

Abstract

In this paper, we consider the effect of different flapping kinematics on the generation of aerodynamic forces in a pair of wings in forward flight. To this end, we use an unsteady panel method solver to perform a parametric study of three different parameters: the flapping radius, the reduced frequency, and the aspect ratio. Varying the flapping radius the motion of the wings smoothly changes from pure flapping (R = 0, rotation around the wing root) to heaving (R = ∞, vertical oscillation of the wings). The results indicate that the thrust generated increases with the flapping radius and the reduced frequency. However, the propulsive efficiency changes little with the radius of flapping (less than 2%), and remains roughly constant for R 2c. Only for small aspect ratios (AR = 1) the results show a slightly better propulsive efficiency for flapping with R ≈ 3c over heaving.

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

“…Only during the stroke reversals, when the velocity of the wing due to the flapping motion is close to zero, both DNS and UPMs provide similar values for the drag coefficient. At that time instant, the UPM sheds a strong vortex into the wake [62], resulting in a vortical structure qualitatively similar to that observed in Figure 6, which seems to be correlated with the similarities observed in C n z between the UPM and the DNS. The fact that C n z is well predicted by the UPM, but C n x is not, hints that the distribution of c n in the DNS and UPMs are different.…”

“…Despite these strict assumptions, UPMs have been used by several authors to study flapping flight of birds and insects [57,58,59,60], and some of the limitations of UPMs for the modeling of Micro Air Vehicles have been already discussed in the literature [61]. In this section, we report the aerodynamic forces obtained for the present configuration using the UPM of Arranz & Flores [62]. The results of the UPM are compared to the DNS results presented in the previous section, to evaluate the appropriateness of a UPM to model the aerodynamic forces in the present case.…”

“…The UPM of Arranz & Flores [62] uses an indirect formulation, discretizing the 3D surface of the wing with trapezoidal panels with uniform distributions of sources and doublets. The wake is allowed to move with the flow, adjusting the doublets in the panels shed into the wake at each timestep imposing the Kutta condition at the wing TE.…”

“…After being shed, the intensity of the doublets in the wake panels remains constant. The interested reader can find further details in [62]. It should be noted that the present implementation of the UPM only considers a vortex sheet shed at the trailing edge, while other methods also consider a vortex sheet shed at the leading edge [60].…”

“…For the present calculations, the resolution is the same as in [62], discretizing the wings with M x × M y = 24 × 32 panels in each wing, and truncating the wake 12c downstream of the trailing edge. All configurations in Table 1 have been simulated, but for brevity only the cases 2W-R000, 2W-R020 and 2W-Rinf are discussed below.…”