Asymmetric Hovering Flapping Flight: a Computational Study

In the early 90’s, Micro Air Vehicles (MAV’s) appeared as a possible solution for missions of reconnaissance in constrained environments. The American Defense Advanced Research Projects Agency (DARPA) initiated workshops on the concept and, in 1997, raised funds to conduct a multi-year programme whose objective was to develop a low cost, high autonomy unmanned aircraft, with a largest dimension limited to 15 centimeters (6 inches). In terms of aerodynamics, this typical size specification places the corresponding airflow in the range of low Reynolds number flows, typically between 102 and 104. Several prototypes were tested, based on the conventional fixed and rotary wing concepts. However, at such low Reynolds numbers and notably supported by the researches carried on the analysis of insects’ flight, the flapping wing concept appeared as an alternative answer, suggesting enhanced aerodynamic performances (lift, efficiency), flight agility, capability to hover coupled with a low noise generation. The latter arises from the complex wing motion defined by superimposed translating (downstroke and upstroke) and rotating (supination and pronation) motions. Pioneer works relying on the aerodynamics of flapping wings were proposed by biologists whose objective was to evaluate the amount of lift generated by insects. After several attempts based on the quasi-steady approach, it was admitted that unsteady aerodynamic mechanisms are essential to keep an insect aloft, especially while hovering (Jensen, 1956; Weis-Fogh, 1973; Ellington 1984). Precisely, three phenomena may be distinguished: 1. The presence of a leading edge vortex (LEV or dynamic stall mechanism) during the translating phases, acting as a low pressure suction region on the extrados of the wing. Due to its importance in aeronautics, this phenomenon was extensively studied experimentally (Walker, 1931) and analytically (Polhamus, 1971) before its evidence was demonstrated and analysed in the context of flapping wings (Maxworthy, 1979; Dickinson & Gotz, 1993). 2. The Kramer effect, assimilated to the supplementary air circulation resulting from the combined translating and rotating motions (Kramer, 1932; Bennett, 1970; Dickinson et al, 1999). 3. The wake capture mechanism, occurring as the wing encounters and interacts with its own wake generated during previous phases (Dickinson, 1994; Dickinson et al, 1999). One should keep in mind that the spatial and temporal behaviours of such unsteady phenomena highly depend on the wing kinematics. Thus, when analysing the flow