A comparative study of the hovering efficiency of flapping and revolving wings

Direct numerical simulations are used to explore the hovering performance and efficiency for hawkmoth-inspired flapping and revolving wings at Reynolds (Re) numbers varying from 50 to 4800. This range covers the gamut from small (fruit fly size) to large (hawkmoth size) flying insects and is also relevant to the design of micro- and nano-aerial vehicles. The flapping wing configuration chosen here corresponds to a hovering hawkmoth and the model is derived from high-speed videogrammetry of this insect. The revolving wing configuration also employs the wings of the hawkmoth but these are arranged in a dual-blade configuration typical of helicopters. Flow for both of these configurations is simulated over the range of Reynolds numbers of interest and the aerodynamic performance of the two compared. The comparison of these two seemingly different configurations raises issues regarding the appropriateness of various performance metrics and even characteristic scales; these are also addressed in the current study. Finally, the difference in the performance between the two is correlated with the flow physics of the two configurations. The study indicates that viscous forces dominate the aerodynamic power expenditure of the revolving wing to a degree not observed for the flapping wing. Consequently, the lift-to-power metric of the revolving wing declines rapidly with decreasing Reynolds numbers resulting in a hovering performance that is at least a factor of 2 lower than the flapping wing at Reynolds numbers less than about 100.