The Influence of Reynolds Number and Vortex Breakdown

9th Osborne Reynolds Recent Postgraduate & Research Student Award
The Influence of Reynolds Number and Vortex Breakdown on
Insect-like Flapping-wing Aerodynamics
N. Phillips
Aeromechanical Systems Group
Cranfield University
Defence Academy of the UK
Shrivenham, Swindon, UK
SN6 8LA
Tel: 01793 78 5271 Fax: 01793 78 3192
email: [email protected]
Abstract
Currently there is no practical autonomous or remote-controlled airborne system capable of
operating in confined, indoor spaces. Such a system would be useful for search and rescue, high-risk
inspection or reconnaissance in buildings, tunnels or industrial plants. The most suitable type of
vehicle for this application appears to be a flapping-wing micro air vehicle (FMAV) based on insectlike flapping-wing flight. This mode of flight offers the abilities to sustain hover, operate at low flying
speeds and perform rapid and complex manoeuvres in confined spaces, which is seen in nature with
two-winged insects (Diptera). One of the key questions related to FMAVs is whether the stable, lift
augmenting, leading-edge vortex (LEV) generated by insect wings at the insect scale (Re on the
order of 102) is a phenomenon that extends to the FMAV scale (Re on the order of 104). Previous
researchers have shown conflicting results of the stability of the LEV at this FMAV scale, and the
existence of a critical Reynolds number of ~10000 beyond which the LEV becomes unstable has
been postulated. The present work addresses this question of whether or not the LEV is in fact stable
at FMAV-scale Reynolds numbers.
For this research, a first-of-its-kind mechanical flapping-wing apparatus that mimics insectlike flapping-wing motion has been designed and developed by the author. This apparatus features a
novel flapping mechanism which gives the wing three controllable degrees of freedom required to
produce the three separate motions necessary for mimicking an insect-like flapping-wing trajectory:
sweeping (side-to-side), plunging (up and down) and pitching (angle-of-attack variation). In this
mechanism these three motions are independently controllable. A typical trajectory of an insect wing
is one in which the wingtip traces the path of a figure-of-eight on a spherical surface with pitch
reversal (supination and pronation) at either end of the stroke as illustrated in Figure 1. The present
mechanism enables adjustable insect-like flapping kinematics to be achieved, up to a flapping
frequency of 20Hz, as pictured in Figure 2. In contrast, past mechanical flappers typically have had
fixed kinematics, wings with only two degrees of freedom, and maximum frequencies well below
20Hz.
Experiments conducted by the author utilised stereoscopic particle image velocimetry (PIV) to
perform phase-locked flowfield measurements every 1mm along the 82mm wingspan from 18% to
117% span, at various points throughout the flapping cycle. This resulted in a dense volume of threecomponent velocity data at each wing position, from which 3D vortex axis trajectories and vortex
characteristics (e.g. vortex diameter, axial vorticity etc,) were recovered, using specially-developed
algorithms. Lift measurements were accomplished with a strain-gauge force balance fitted to the
apparatus.
Over the entire Reynolds number range tested (Re = 4400 - 17800), results confirmed the
presence of a leading-edge vortex (LEV) over the wing, which feeds into the tip vortex (Figure 3).
Key results illustrated in Figure 5, detailing how the LEV and other flow structures develop and
interact over a flapping cycle at the FMAV scale, revealed that at this scale, the LEV is stable and
remains attached to the wing surface. The flow development throughout the cycle is mainly
characterised by the formation of the LEV which develops a strong axial velocity through its core and
remains attached even until the end of the half-stroke when the wing stops. Calculations determined
that the LEV is responsible for 50% of the lift generated. In addition, results revealed that over the
entire Reynolds number range tested, the LEV exhibits vortex breakdown, identified by vortex helix
angle, diameter and axial velocity (Figure 3). However, despite the presence of breakdown, the LEV
remains attached to the wing surface throughout a half-stroke and continues to augment lift as
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9th Osborne Reynolds Recent Postgraduate & Research Student Award
Reynolds number is increased, as shown in Figure 4. This reveals that this lifting mechanism
exploited by insects extends to the FMAV scale, and thus can be used by these vehicles.
Figure 1: Flapping cycle
Figure
3:
Instantaneous
streamlines
released from LEV / tip vortex axis
illustrating vortex breakdown in LEV
Figure 2: Frames from high speed
photography of flapping-wing executing a
figure-of-eight wing trajectory at 20Hz
Figure 4: Effect of increasing flapping frequency
(and, therefore, Reynolds number) on mean lift
and mean lift coefficient
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9th Osborne Reynolds Recent Postgraduate & Research Student Award
Figure 5: Top views of wing revealing flow formation throughout one half of the flapping period ‘T’,
starting when the wing accelerates from rest, followed by translation, and ending with pitch reversal and
simultaneous deceleration of the wing to rest; flapping frequency is 20Hz (Re = 15400); left column
shows vortex axes coloured with axial vorticity, and vortex core diameter (dark grey surfaces) measured
from the width of the rigid-body rotation portion of the local tangential velocity profile of the vortex; right
column shows instantaneous streamlines released from vortex axes coloured with axial velocity (along
the vortex) normalised with respect to the mean wingtip speed (8.4m/s), black streamlines released along
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the wing edge, and transparent grey isosurfaces of Q = 6 x 10 s from the vortex identification ‘Q
criterion’; positive axial direction points along a vortex axis towards the end without a white dot; LEV =
leading edge vortex; TPV = tip vortex; RTV = root vortex; STRV = starting vortex
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