Three-dimensional wing structure attenuates aerodynamic efficiency in flapping fly wings

Abstract

<jats:p>The aerial performance of flying insects ultimately depends on how flapping wings interact with the surrounding air. It has previously been suggested that the wing's three-dimensional camber and corrugation help to stiffen the wing against aerodynamic and inertial loading during flapping motion. Their contribution to aerodynamic force production, however, is under debate. Here, we investigated the potential benefit of three-dimensional wing shape in three different-sized species of flies using models of micro-computed tomography-scanned natural wings and models in which we removed either the wing's camber, corrugation, or both properties. Forces and aerodynamic power requirements during root flapping were derived from three-dimensional computational fluid dynamics modelling. Our data show that three-dimensional camber has no benefit for lift production and attenuates Rankine–Froude flight efficiency by up to approximately 12% compared to a flat wing. Moreover, we did not find evidence for lift-enhancing trapped vortices in corrugation valleys at Reynolds numbers between 137 and 1623. We found, however, that in all tested insect species, aerodynamic pressure distribution during flapping is closely aligned to the wing's venation pattern. Altogether, our study strongly supports the assumption that the wing's three-dimensional structure provides mechanical support against external forces rather than improving lift or saving energetic costs associated with active wing flapping.</jats:p>

Wing Design in Flies: Properties and Aerodynamic Function

“…In corrugated wings of gliding dragonflies, slowly rotating vortices only develop at small angles of attack but flow broadly separates from the wing surface at larger angles (Re = 34,000 [ 53 ], Re = 1400 [ 136 ]). By contrast, a recent numerical study on root-flapping wings shows that corrugation valleys in fruit flies, house flies, and blowflies are unable to trap vortices at Reynolds numbers up to 1623 ( Figure 5 ) [ 83 ]. Thus, small-scale corrugation, low Reynolds number, spanwise flow advecting vorticity and high angle of attack make vortex trapping less likely in flapping insect wings.…”

“…There is a wide variety of aspect ratios found in insect wings ranging from approximately 1.5 to 5.8 [ 118 , 119 , 120 , 121 , 122 ]. In Diptera, previous studies reported aspect ratios of 2.91–3.14 for Drosophila [ 121 , 122 ], 2.88 for Musca [ 83 ], and 2.62–2.93 for Calliphora [ 119 , 121 ]. The highest aerodynamic forces in hovering, root-flapping insect-like wings are produced at an aspect ratio of approximately 3.0 [ 123 ].…”

“…For this review, we additionally calculated the aerodynamic quantities of revolving ( Figure 3 ) and flapping ( Figure 4 ) wings of a blowfly, as well as simple rectangular and ideal-shaped wings in order to compare their performance. The ideal wing shape was calculated according to the estimation by Prandtl–Betz in Figure 2 e. The numerical simulations were performed using a previously published numerical model [ 83 , 125 ] combined with a wavelet-adaptive solver [ 126 ], and efficiency was calculated as Rankine–Froude efficiency [ 127 ]. Table 1 shows that revolving rectangular and fly wings perform similarly, producing approximately the same amount of lift.…”

“…Upward camber and a downward oriented leading wing edge tend to create more lift than a flat wing flapping at similar angle of attack. Chordwise camber and the shape of the leading edge are thus comparable to a change in the effective angle of attack of an insect wing [ 56 , 83 ].…”

“…In the third section, we consider the wing’s three-dimensional morphology. A recent numerical study, for example, showed that the three-dimensional shape of rigid fly wings attenuates both lift production and aerodynamic efficiency rather than enhancing these measures compared to a flat wing [ 83 ]. In the last section, we focus on the aerodynamic consequences of elastic deformation in morphological complex wings.…”