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First published online December 1, 2006
Journal of Experimental Biology 209, 5005-5016 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02614
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Dual leading-edge vortices on flapping wings

Yuan Lu, Gong Xin Shen* and Guo Jun Lai

Full Flow Field Observation and Measurement, Institute of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, People's Republic of China


Figure 1
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Fig. 1. Dual LEV on a model dragonfly wing (AR=5.8), observed in a previous study (Y.L., G.X.S. and W. H. Su, manuscript submitted for publication). The wing was at mid-downstroke with mid-stroke angle of attack {alpha}m=60°.

 

Figure 2
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Fig. 2. Model wing planforms with a range of aspect ratios (AR). Except for the wing with AR=10 and the model fruit fly wing, which had an effective wingspan r of 154 mm and 129 mm, respectively, for all the others r=104 mm.

 

Figure 3
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Fig. 3. Sketch of flapping motion in hovering. (A) Left: spatial configuration of the flapping motion of a model wing. The thick black line denotes the leading edge; OT, translational axis; OZ, rotational axis; OD and OU, the translational extreme positions; R, model wing length; r, effective model wing length; {Phi}, stroke amplitude; {varphi}, instantaneous translational angle. Right: the motion of a section of the wing. {alpha}, instantaneous angle of attack; {rho}, instantaneous rotational angle ({rho}=90-{alpha}°); black thick line denotes wing section and solid-dot, the leading edge. (B) The kinematic curves over one period. The translational and rotational angular positions are normalized using {Phi} and {rho}m (maximal rotational angle), respectively. The black line at t/T=0.25 denotes the DPIV triggering phase.

 

Figure 4
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Fig. 4. Flow visualization by the dye release method.

 

Figure 5
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Fig. 5. DPIV setup. (A) Typical velocity vectors. The black thick line denotes wing section and the solid-dot the leading edge. The white area in front of the wing represents the shadow due to the nontransparency of the aluminum wing. Scale bar, 200 mm s-1. (B) Sketch of DPIV arrangement. The large gray arrow denotes the positioning translation of the model system. X and Z are two axes in the horizontal plane, while Y heads vertically away from the ground; z, the distance between the wing-base and the laser-sheet; r, the effective wing length. The laser-sheet and CCD were always perpendicular and parallel to Z, respectively.

 

Figure 6
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Fig. 6. (A-D) Dye flow visualization showing the dual LEV evolution over one stroke (T; AR=5.8, {alpha}m=6°, {Phi}=60°, Re=1624).

 

Figure 7
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Fig. 7. DPIV results at mid-downstroke (0.25T, the same phase as Fig. 6B). (A) A typical result at 0.29r (effective model wing length r=104 mm). The black thick line denotes wing section and the solid-dot the leading edge. Sectional streamlines are plot. The pseudocolor contour represents the spanwise vorticity. (B) Sectional flow fields at different spanwise locations. The slices were spaced by 15 mm and were all perpendicular to the spanwise direction. Plot representation as in A.

 

Figure 8
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Fig. 8. Dual LEV in various {alpha}m conditions (AR=5.8, {Phi}=60°, Re=1624). Visualization pictures were captured at mid-downstroke (0.25T). Sectional flow fields at 0.29r were measured via DPIV at the same phase as the visualization pictures. Plot representation as in Fig. 7A.

 

Figure 9
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Fig. 9. Dual LEV in various Re conditions (AR=5.8, {alpha}m=60°, {Phi}=60°). Visualization pictures were captured at mid-downstroke (0.25T). Sectional flow fields at 0.29r were measured via DPIV at the same phase as the visualization pictures. Plot representation as in Fig. 7A.

 

Figure 10
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Fig. 10. Dual LEV in various AR conditions ({alpha}m=40°). Visualization pictures were captured at mid-downstroke (0.25T). Sectional flow fields at 0.29r were measured via DPIV at the same phase as the visualization pictures. Plot representation as in Fig. 7A.

 

Figure 11
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Fig. 11. Dual LEV on model fruit fly wing (AR=3.1, {alpha}m=40°, {Phi}=150°, Re=1889). The results were captured or measured at mid-downstroke (0.25T). (A) Dye visualization picture. (B) DPIV result at 0.35r (r=129 mm). Plot representation as in Fig. 7A. (C) Sectional flow structures at different spanwise locations. The DPIV slices were spaced by 15 mm.

 

Figure 12
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Fig. 12. Global sectional flow structure. (A) DPIV result at 0.29r at mid-downstroke (AR=5.8, {alpha}m=60°, {Phi}=60°, Re=1624). Plot representation as in Fig. 7A; velocity vectors are shown. The in- and outboard blue vorticity concentrations correspond to the primary and minor vortices, respectively. The yellow and pink vorticity region behind the trailing edge is the shed trailing-edge vortex. Scale bar, 200 mm s-1. (B) Conjectured topological structure of the sectional flow field. F, focus; S, saddle; S', semi-saddle.

 





© The Company of Biologists Ltd 2006