Bistability in the rotational motion of rigid and flexible flyers

Yangyang Huang, Leif Ristroph, Mitul Luhar, Eva Kanso

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1043-1067
Number of pages25
JournalJournal of Fluid Mechanics
Volume849
DOIs
StatePublished - Aug 25 2018

Fingerprint

hovering
pendulums
Pendulums
Fluids
fluids
apexes
oscillating flow
free flight
Oscillating flow
vortex sheets
Free flight
flapping
pyramids
two dimensional models
aerodynamics
inertia
aircraft
stiffness
Aerodynamics
flexibility

Keywords

  • aerodynamics
  • flow-structure interactions
  • swimming/flying

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Bistability in the rotational motion of rigid and flexible flyers. / Huang, Yangyang; Ristroph, Leif; Luhar, Mitul; Kanso, Eva.

In: Journal of Fluid Mechanics, Vol. 849, 25.08.2018, p. 1043-1067.

Research output: Contribution to journalArticle

Huang, Yangyang ; Ristroph, Leif ; Luhar, Mitul ; Kanso, Eva. / Bistability in the rotational motion of rigid and flexible flyers. In: Journal of Fluid Mechanics. 2018 ; Vol. 849. pp. 1043-1067.
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