Very low Reynolds number causes a monotonic force enhancement trend for a three-dimensional hovering wing in ground effect

Abstract

This research reports the numerical results of the ground effect trend for a three-dimensional flapping insect wing at a very low Reynolds number (Re = 10). It demonstrates that the ground effect trend at this Re has a ‘single force regime,’ i.e. the forces only enhance as the ground distance decreases. This phenomenon is unlike the widely expected non-monotonic trend publicized in previous studies for higher Reynolds numbers, that shows ‘three force regimes,’ i.e. the forces reduce, recover, and also enhance as the ground distance decreases. The force trend in the ground effect correlates to a similar trend in wing–wake interaction or the downwash strength on the wing’s head. At very low Re (10), the very large viscosity causes diffused vortices and less advected vortex wake, while at relatively high Re, the vortices are easily separated from the wing and then advected downwards. This different development of the vortex wake caused different force trends for the flapping wing in the ground effect. Furthermore, by examining only the first stroke when there is no vortex wake, we found that the ‘ramming effect’ enhances the forces on the wing. This effect increases the pressure of the lower wing surface due to the squeezed air between the wing and the ground. The ‘ramming effect’, combined with the reduced downwash (or wing–wake interaction) effect, causes the force enhancement of the wing near the ground’s vicinity. It is further comprehended that the trend is dependent on Re. As the Re is increased, the trend becomes non-monotonic. The effect of varying angles of attack, flapping amplitude and wing planform at very low Re does not change this trend. This ground effect might help insects by enhancing their lift while they hover above the surface. This finding might prove beneficial for developing micro air vehicles.