Three-dimensional vortex wake structure of a flapping-wing micro aerial vehicle in forward flight configuration

Abstract

This paper investigates the formation and evolution of the unsteady three-dimensional wake structures generated by the flapping wings of the DelFly II micro aerial vehicle in forward flight configuration. Time-resolved stereoscopic particle image velocimetry (Stereo-PIV) measurements were carried out at several spanwise-aligned planes in the wake, so as to allow a reconstruction of the temporal development of the wake of the flapping wings throughout the complete flapping cycle. Simultaneous thrust-force measurements were performed to explore the relation between the wake formation and the aerodynamic force generation mechanisms. The three-dimensional wake configuration was subsequently reconstructed from the planar PIV measurements by two different approaches: (1) a spatiotemporal wake reconstruction obtained by convecting the time-resolved, three-component velocity field data of a single measurement plane with the free-stream velocity; (2) for selected phases in the flapping cycle a direct three-dimensional spatial wake reconstruction is interpolated from the data of the different measurement planes, using a Kriging regression technique. Comparing the results derived from both methods in terms of the behavior of the wake formations, their phase and orientation indicate that the spatiotemporal reconstruction method allows to characterize the general three-dimensional structure of the wake, but that the spatial reconstruction method can reveal more details due to higher streamwise resolution. Comparison of the wake reconstructions for different values of the reduced frequency allows assessing the impact of the flapping frequency on the formation and interaction characteristics of the vortical structures. For low values of the reduced frequency, it is observed that the vortex structure formation of instroke and outstroke is relatively independent of each other, but that increasing interaction occurs at higher reduced frequencies. It is further shown that there is a phase lag in the appearance of the structures for increasing flapping frequency, which is in correlation with the generation of the forces. Comparison of thrust generated during the instroke and the outstroke phases of the flapping motion in conjunction with the development of the wake structures indicates that wing–wing interaction at the start of outstroke (peel motion) becomes a dominant feature for reduced frequencies greater than 0.62.

Appendix: Performance assessment of the Kriging regression technique

For this purpose, a particular data set with 24 measurement planes with a distance of 5 mm between each other was used. Initially, the complete wake of the flapping wings was reconstructed from these 24 available measurement planes. The Kriging regression technique was utilized at this stage only to fill the gaps in the individual measurement planes, which originate from masked regions in the PIV data. On the other hand, the same wake was reconstructed again from a down-sampled data set, by using every other measurement plane (12 measurement planes), and with the Kriging regression technique used to interpolate one plane in between the measurement planes, which results in the same spatial resolution in the streamwise direction as in the original data set. The resultant wake structures for both cases are visualized with isosurfaces of the Q criterion colored by the vorticity component parallel with the free-stream (ω _z ) in Fig. 14. It is clear that the Kriging regression technique performs well in this case, and apart from the small scale details, the most prominent features of the vortical structures are captured.

Fig. 14

Isosurfaces of $Q/{f^{2}}$ = 20 colored by ${\omega_z}/f$ at the end of outstroke for the case of f = 10 Hz and U _∞  = 3 m/s (side view). a Wake reconstruction by the use of 24 measurement planes with 5 mm spatial resolution in the streamwise (z) direction. b Wake reconstruction by the use of every other plane with 10 mm distance and Kriging regression technique with local error estimate to interpolate one plane in between to achieve 5 mm spatial resolution in z-direction