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A computational model of the flight dynamics and aerodynamics of a jellyfish-like flying machine

  • Fang Fang (a1), Kenneth L. Ho (a2), Leif Ristroph (a1) and Michael J. Shelley (a1) (a3)

Abstract

We explore theoretically the aerodynamics of a recently fabricated jellyfish-like flying machine (Ristroph & Childress, J. R. Soc. Interface, vol. 11 (92), 2014, 20130992). This experimental device achieves flight and hovering by opening and closing opposing sets of wings. It displays orientational or postural flight stability without additional control surfaces or feedback control. Our model ‘machine’ consists of two mirror-symmetric massless flapping wings connected to a volumeless body with mass and moment of inertia. A vortex sheet shedding and wake model is used for the flow simulation. Use of the fast multipole method allows us to simulate for long times and resolve complex wakes. We use our model to explore the design parameters that maintain body hovering and ascent, and investigate the performance of steady ascent states. We find that ascent speed and efficiency increase as the wings are brought closer, due to a mirror-image ‘ground-effect’ between the wings. Steady ascent is approached exponentially in time, which suggests a linear relationship between the aerodynamic force and ascent speed. We investigate the orientational stability of hovering and ascent states by examining the flyer’s free response to perturbation from a transitory external torque. Our results show that bottom-heavy flyers (centre of mass below the geometric centre) are capable of recovering from large tilts, whereas the orientation of the top-heavy flyers diverges. These results are consistent with the experimental observations in Ristroph & Childress (J. R. Soc. Interface, vol. 11 (92), 2014, 20130992), and shed light upon future designs of flapping-wing micro aerial vehicles that use jet-based mechanisms.

Copyright

Corresponding author

Email address for correspondence: ff559@nyu.edu

References

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JFM classification

Type Description Title
VIDEO
Movies

Fang et al. supplementary movie
Simulation of a hovering flyer (corresponding to Fig. 2). The black arrows denote instantaneous flow velocities. Red (positive) and blue (negative) vortices, which represent the coarse-grained vortex sheets, show the complex wake. A linearly diminishing downward background flow is added for t≤3, and turned off for t≤3. The flyer’s initial position is shown in gray as a frame reference. The “soup” of vortices stays always around the wings.

 Video (4.4 MB)
4.4 MB
VIDEO
Movies

Fang et al. supplementary movie
Response of a bottom-heavy flyer, with h=−2 (corresponding to Fig. 5 bottom row), to a transitory external torque perturbation applied at tc=3.5 (Eq. 4.2). After the torque impulse, the flyer tilts to a large angle, comes back upright, and then overshoots.

 Video (3.4 MB)
3.4 MB
VIDEO
Movies

Fang et al. supplementary movie
Response of a top-heavy flyer, with h=1 (corresponding to Fig. 5 top row), to a transitory external torque perturbation applied at tc =3.5 (Eq. 4.2). After the torque impulse, the flyer tilts slightly and then the angle keeps increasing slowly.

 Video (3.3 MB)
3.3 MB
VIDEO
Movies

Fang et al. supplementary movie
When θa increases, the flyer’s lift exceeds its weight and the flyer starts to ascend. In each stroke the flyer generates one vortex quadrapole, consisting of two symmetric near-dipoles that move sideways and downwards, carrying downward momentum (corresponding to Fig. 6a).

 Video (2.9 MB)
2.9 MB
VIDEO
Movies

Fang et al. supplementary movie
Free ascending recovery flight of bottom-heavy flyer, with h=−1.5 (corresponding to Fig. 12 left panel). An external torque perturbation (ε=400) is applied at tc=13.5 during the steady ascent of the flyer. The grey dotted line shows the flyer’s trajectory.

 Video (2.2 MB)
2.2 MB
VIDEO
Movies

Fang et al. supplementary movie
Free ascending recovery flight of bottom-heavy flyer, with h=−2 (corresponding to Fig. 12 right panel). An external torque perturbation (ε=200) is applied at tc=13.5 during the steady ascent of the flyer. The grey dotted line shows the flyer’s trajectory.

 Video (2.1 MB)
2.1 MB

A computational model of the flight dynamics and aerodynamics of a jellyfish-like flying machine

  • Fang Fang (a1), Kenneth L. Ho (a2), Leif Ristroph (a1) and Michael J. Shelley (a1) (a3)

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