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First published online March 14, 2005
Journal of Experimental Biology 208, 1079-1094 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01471

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The aerodynamics of Manduca sexta: digital particle image velocimetry analysis of the leading-edge vortex

Richard J. Bomphrey^1,*, Nicholas J. Lawson², Nicholas J. Harding¹, Graham K. Taylor¹ and Adrian L. R. Thomas¹

¹ Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, UK
² College of Aeronautics, Cranfield University, Cranfield, MK43 0AL, UK

View larger version (54K): [in a new window]   Fig. 1. The three classes of leading-edge vortex (LEV) that have been described to date. (A) Class I: the Maxworthy (1979) description from his model experiments based on the `fling' of the chalcid wasp Encarsia formosa. The LEV inflects into tip and root vortices on each wing. The tip vortices connect to form a vortex ring behind the model, and the root vortices also connect so that the wake consists of one continuous vortex loop of complex shape. (B) Class II: the structure described by Luttges (1989) with a single LEV extending across the thorax of a hawkmoth and inflecting to form both tip vortices. This structure implies a free-slip critical point (a 3D focus) over the centreline of the thorax, as described by Srygley and Thomas (2002) for butterflies Vanessa atalanta. The topology is similar to that in A except that the root vortex is replaced by a continuous LEV over the thorax and there is no significant spanwise flow. (C) Class III: the structure described by Ellington and colleagues (Ellington et al., 1996; Van den Berg and Ellington, 1997a) where the LEV on Manduca is similar to that found on a delta wing. In this model there must be a surface-bound focus at the base of each wing and attached flow over the thorax. (D) Also Class III: the flow, topologically similar to C, scaled for Drosophila by Birch and Dickinson (2001). The flows in C and D differ qualitatively from A and B in the absence of the linkage between the LEVs via either wing root vortices or a continuation of the LEV across the centreline. Spanwise (axial) flow, if present, is marked by orange arrows in each case. Vertical planes show the simplified flow topology at the centreline and midwing positions.

View larger version (51K): [in a new window]   Fig. 2. Smoke wire flow visualisations of tethered Manduca sexta. The plane of the undisturbed smoke streams is coincident with the midwing position. The flow pattern is essentially indistinguishable from the results presented previously (Willmott et al., 1997; Ellington et al., 1996). There is a stagnation point on the underside of the wing, flow separates at the leading edge and reattaches towards the trailing edge, with an LEV in the separated flow region above the top surface of the wing.

View larger version (48K): [in a new window]   Fig. 3. Smoke wire visualisation of tethered Manduca sexta with the plane of the undisturbed smokestreams coincident with the thorax, close to the centreline. Flow is attached for the majority of the downstroke but separates at the end of the downstroke (images C-E); the separation has the same size and form as that containing an LEV in Fig. 2, and in previously published flow visualisations of outboard positions along the wing (Willmott et al., 1997; Ellington et al., 1996). The centreline position has not previously been analysed by flow visualisation.

View larger version (13K): [in a new window]   Fig. 4. Plan view schematic showing the windtunnel's working section and the positions of the camera and light sheet.

View larger version (73K): [in a new window]   Fig. 5. The effect of vector subtraction on streamlines. No subtraction (F): this presents the measured data free from any manipulations, therefore the frame of reference is fixed with respect to the thorax and laboratory. Free stream subtraction 0° (A): here the velocity due to the windtunnel flow has been subtracted from the measured velocity vectors so that the frame of reference is fixed with respect to a distant particle in the flow, far enough away to be unaffected by the moth. These two cases represent the simplest manipulation of the data and transform the vector fields between two equally valid frames of reference - fixed with respect to the thorax of the moth, and fixed with respect to the distant fluid. However, it is not entirely clear that either of these two global frames of reference will be locally appropriate for resolving the LEV formed by a flapping wing. For flows that occur close to the surface of the animal, a locally valid frame of reference might be expected to take into account the local geometry of the body - so for, example, where the freestream is deflected as it flows around the body it would make sense, when looking for features in that flow, to subtract the freestream modified by its deflection around the body. Vorticity is unaffected by such frame of reference corrections, but now the frame of reference is a somewhat abstract concept - being fixed relative to distant fluid flowing with the freestream once it has been deflected by the body, but unaffected by the flow induced by the flapping wings. In the case shown here, a deflection of between 10° and 20° the frame of reference is adequate to see the streamlines converge to a focus coinciding with the peak in vorticity. The focus shifts from left to right during the iterations and then disappears altogether as it is transformed into a form only visible as a shear region.

View larger version (38K): [in a new window]   Fig. 6. The late downstroke leading-edge vortex (LEV) of Manduca sexta. Flow fields resolved after subtraction of the freestream velocity (3.5 m s-1). (A,B) Vorticity and streamlines in the wake and near-wing flow field of Manduca, shown to provide context. (A) The vortex sheet is shed from the trailing edge of the wings; (B) how the streamlines spiral into a stable focus at a midwing location, just above the leading edge. (C) Two excerpts from the corresponding force trace, with the output normalised relative to body weight. The instant the three images were taken is shown by a broken line at the peak in relative upforce (2.2 times that required to support body weight).

View larger version (77K): [in a new window]   Fig. 7. Five images demonstrating the consistency of the flow structures found over Manduca. All were captured with the light sheet at the centreline of the animal and show vectors with the freestream velocity of 3.5 m s-1 subtracted. Each image shows a leading-edge vortex (LEV) over the centreline of the thorax marked by a blue vorticity maximum. For clarity only every other vector is shown (actual vector resolution is twice that presented along each axis).

View larger version (45K): [in a new window]   Fig. 8. Velocity profiles (left) and vorticity profiles (right) in vertical transects through the LEV after simple freestream subtraction. Three separate wingbeats at each of the two flight speeds (1.2 m s-1 and 3.5 m s-1) with the light sheet at the centreline and midwing positions. In each case the peak in vorticity coincides with the centre of the portion of the velocity profiles, which are associated with solid body rotation of the vortex core. Each transect represents the horizontal component of the velocity vector, i.e. the component parallel with the freestream.

View larger version (63K): [in a new window]   Fig. 9. Cartoon showing the aerodynamic features of a Class II LEV in the flow around the wings and thorax of Manduca sexta in late downstroke (top). DPIV inserts (bottom) show typical flow fields at each location with a freestream of 3.5 m s-1. The midwing insert (left) has simple (horizontal) freestream subtraction; the centreline insert (right) has local freestream subtraction of 3.5 m s-1 angled 1° below horizontal.