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First published online March 28, 2008
Journal of Experimental Biology 211, 1221-1230 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.010652
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Three-dimensional flow structures and evolution of the leading-edge vortices on a flapping wing

Yuan Lu* and Gong Xin Shen{dagger}

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. The model wing and the flapping motions. (A) Left: spatial configuration of the flapping motion of the model wing. oxyz, the wing-fixed frame (y-axis vertical to the ground); D and U, the translational extreme positions; R, model wing length; r, effective model wing length; {Phi}, stroke amplitude; Formula(t), instantaneous translational angle. The thick black line denotes the leading edge. Right: the motion of a section of the wing. {alpha}(t), instantaneous angle of attack; {rho}(t), instantaneous rotational angle [{rho}(t)=90–{alpha}(t)°]. The black thick line denotes wing section and the solid-dot the leading edge. (B) The kinematic curves in one period. The translational and rotational angular positions are normalized using {Phi} and {rho}M (the maximal rotational angle), respectively. The black lines at t/T=0.125, 0.25 and 0.375 denote the DSPIV measurement phases.

 

Figure 2
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  		Fig. 2. DSPIV setup. (A) The DSPIV experimental arrangement (top view). CCD1 and CCD2 are the CCD cameras. The broken-line section of the laser-sheet represents the shadow behind the opaque model wing. The blue broken lines a, b and c around the origin o are the initial positions of 0.125T, 0.25T and 0.375T, respectively. At the instant of measurement, the wing-fixed frame oxyz coincided with the inertial frame oXYZ. The thick gray double-headed arrow denotes the positioning translation of the model system. (B) The typical raw 3D3C velocity field (at 0.25T) before spanwise interpolation. The blue region is the model wing.

 

Figure 3
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  		Fig. 3. The test of four vortex identification criteria. Data at 0.25T, when the vortical system was most intricate, were tested. The dimensionless values of the iso-surfaces (the red regions) of |{omega}|, {Delta}, Q and {lambda}2 are 0.22, 0.00015, 0.09 and 0.04, respectively. The values of |{omega}|, {Delta} and Q are normalized by their maxima (>0), whereas the value of {lambda}2 is normalized by the minimum (<0). The blue plate is the model wing.

 

Figure 4
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  		Fig. 4. Dye flow visualization of the LEVs evolution at three typical stroke phases. The model wing was translating from the left to the right with a fixed angle of attack of 60°. The dyes were released at the leading-edge. Lp, the primary vortex; Lm1, Lm2 and Lm3, the minor vortices. (Data taken from Lu et al., 2007Go.)

 

Figure 5
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  		Fig. 5. DSPIV result of the 3-D flow structures and evolution of the vortices on the model wing at three typical stroke phases. The left and right image sequences are viewed from two perspectives. Isosurfaces of the Q-value are plotted to educe the vortices. The normalized values of the external red and internal yellow isosurfaces are 0.09 and 0.36, respectively. Lp, the primary vortex; Lm1, Lm2 and Lm3, the minor vortices; T1 and T2, trailing-edge vortices (TEVs); Tr, the root of TEV; W1 and W2, wing-tip vortices (WTVs). The thick yellow curved arrows denote the rotational directions of the vortices. The white instantaneous streamlines in Lp in all images are spiraling towards the wing-tip; the magenta (released at the wing-tip) and yellow (released at the outer wing within Lm2) streamlines in 0.25T are heading towards the wing-base and meet the white streamlines at the breakdown location of Lp; the green streamlines belong to the WTVs.

 

Figure 6
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  		Fig. 6. The Q- and W-contours at different spanwise locations at three typical stroke phases. Positive Q-contours denote the vortex cores, while negative Q-contours denote the strain-dominating regions. The Q-values are normalized by the maximum in each stroke phase. Positive W indicates the spanwise flow heading towards the wing-tip, while negative W indicates the opposite direction. The values of W are normalized by the mean wing-tip speed.

 

Figure 7
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  		Fig. 7. Sketch of the evolution of the vortices on a flapping wing. The black region is the wing. Broken lines indicate the breakdown or collapse of the vortices.

 

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© The Company of Biologists Ltd 2008