Three-dimensional effects in hovering flapping flight

Abstract

This paper aims at understanding the influence of three-dimensional effects in hovering flapping flight. Numerical simulations at a Reynolds number of 1000 are performed to compare two types of flapping kinematics whose plunging phase is characterized by either a rectilinear translation or a revolving motion. In this way, we are able to isolate the three-dimensional effects induced by the free end condition from that induced by the spanwise incident velocity gradient (and the associated implicit Coriolis and centrifugal effects). In the rectilinear translation case, the analysis of the wake and of the aerodynamic loads reveals that the wingspan can be compartmented into three distinct regions whether it is predominantly subjected to an unstable two-dimensional flow, a stable three-dimensional flow or both two-dimensional and three-dimensional effects. It is found that this partitioning exhibits common features for three different aspect ratios of the wing. In conjunction with the previous results of Ringuette, Milano & Gharib (J. Fluid Mech., vol. 581, 2007, pp. 453-468), this suggests that the influence of the tip vortex over the wingspan is driven by a characteristic length scale. In addition, this length scale matches the position of the connecting point between leading and tip vortices observed in the revolving case, providing insight into the connecting process. In both translating and revolving cases, leading edge vortex attachment and strong spanwise velocities are found to be strongly correlated phenomena. Spanwise velocities (that mostly confine at the periphery of the vortices), together with downward velocities, do not only affect the leading edge vortex but also act as an inhibitor for the trailing edge vortex growth. As a consequence, crosswake interactions between leading and trailing edge vortices are locally limited, hence contributing to flow stabilization.

On the persistence of memory: do initial conditions impact vortex formation?

“…The resulting spatio-temporal evolution of all three vorticity components is provided in figure 10. In accordance with the reports of Jardin et al (2012), neither streamwise (tip) nor plate-normal vorticity are significant in the midplane region, which supports the previous assumption of two-dimensional LEV formation.…”

“…In the two-dimensional analysis of the plate's near-midplane region, as defined by Jardin et al (2012), it has been shown that the effective velocity U eff of the feeding shear layer is the appropriate characteristic velocity rather than the more commonly used plungeḣ or free stream U ∞ velocities. It is therefore proposed that the non-dimensionalization for various plate kinematics should be based on the effective feeding shear-layer velocity since it dictates vortex growth and thus overall force histories.…”

“…FIGURE 1. (Colour online) Sketch of separated flow over a finite-aspect-ratio plate, including (a) the classification of the two-dimensional and three-dimensional regions according to Jardin et al (2012) and indicating (b) free stream velocity U ∞ and effective shear-layer velocity U eff as the two characteristic velocities for vortex formation and corresponding circulation Γ .…”

“…In addition, it was observed that the LEV circulation decreased at spanwise positions closer to the tip. Accordingly, Jardin, Farcy & David (2012) showed that two major regions exist for accelerating, finite-aspect-ratio plates: a near-midplane region with nominally two-dimensional flow; and a near-tip region with strongly three-dimensional reorientation of vorticity (see figure 1a). Furthermore, they demonstrated that this distinction of the flow topology between two-dimensional and three-dimensional is largely dominated by the chord length rather than by the aspect ratio of the plate.…”

An Application of GPU Acceleration in CFD Simulation for Insect Flight

“…The present results show that there existed a strong spanwise flow on the flapping wing in hovering flight. As suggested by previous studies [5,7], the spanwise flow that may drain energy from the LEV, and thus limited its downstream chordwise development and prevented the wings from stalling. However, the increase of non-dimensional spanwise velocity, u * span , from the wing root to the middle wing-span also suggests that the spanwise flow may stretch the LEV along the wing and hence helped to prolong the attachment of LEV [8].…”