Abstract
We explore the rotational stability of hovering flight in an idealized two-dimensional model. Our model is motivated by an experimental pyramid-shaped object (Weathers et al., J. Fluid Mech, vol. 650, 2010, pp. 415-425; Liu et al., Phys. Rev. Lett., vol. 108, 2012, 068103) and a computational -shaped analogue (Huang et al., Phys. Fluids, vol. 27 (6), 2015, 061706; Huang et al., J. Fluid Mech., vol. 804, 2016, pp. 531-549) hovering passively in oscillating airflows; both systems have been shown to maintain rotational balance during free flight. Here, we attach the -shaped flyer at its apex in oscillating flow, allowing it to rotate freely akin to a pendulum. We use computational vortex sheet methods and we develop a quasi-steady point-force model to analyse the rotational dynamics of the flyer. We find that the flyer exhibits stable concave-down and concave-up behaviour. Importantly, the down and up configurations are bistable and co-exist for a range of background flow properties. We explain the aerodynamic origin of this bistability and compare it to the inertia-induced stability of an inverted pendulum oscillating at its base. We then allow the flyer to flap passively by introducing a rotational spring at its apex. For stiff springs, flexibility diminishes upward stability but as stiffness decreases, a new transition to upward stability is induced by flapping. We conclude by commenting on the implications of these findings for biological and man-made aircraft.
Original language | English (US) |
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Pages (from-to) | 1043-1067 |
Number of pages | 25 |
Journal | Journal of Fluid Mechanics |
Volume | 849 |
DOIs | |
State | Published - Aug 25 2018 |
Keywords
- aerodynamics
- flow-structure interactions
- swimming/flying
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics