Estimate strength and trajectory of leading-edge vortex: a universal analytical model*

For flying animals, leading-edge vortex (LEV) in flapping flight of insects, bats and birds, is created by dynamic stall, persisting on the the upper surface of the wing at a large angle of attack (AoA) and maintaining high-lift. Current study presents a novel reduced-order analytical model that provides fast estimations in closed-form expressions for the strength and position of LEV on rotating wings at arbitrarily large AoA. Downwash-modified vorticity production at the leading edge and its subsequent outboard-directed transport are included as two competing effects in the theory of LEV development based on the case of AoA = 90^o in our previous study (Chen et al. 2017 J. Fluid Mech.). The analytical model is well validated with the corresponding experimental data and the CFD solutions in a wide range of the Reynolds number, as well as bio-inspired wing shapes of fruit fly, bumblebee and hawkmoth. Moreover, an important parameter of spanwise vorticity transport K_sp which depends only on Reynolds number at constant AoA, is found to determine the LEV trajectory in the competition of vorticity production and transport.