Bistability in the rotational motion of rigid and flexible flyers. (26th June 2018)

• Record Type: Journal Article
• Authors: Huang, Yangyang; Ristroph, Leif; Luhar, Mitul; Kanso, Eva
• Is Part Of: Journal of fluid mechanics. Volume 849(2018)
• Page Start: 1043
• Page End: 1067
• Publication Date: 2018-06-26
• Subjects: aerodynamics, -- flow-structure interactions, -- swimming/flying; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.446
• Languages: English
• ISSNs: 0022-1120

Abstract

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 $\wedge$ -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 $\wedge$ -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 ( $\wedge$ ) and concave-up ( $\vee$ ) 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.