). This type of vortical structure, at certain high Reynolds numbers, is analogous to the spiral conical vortex generated on each leading edge of a delta wing (Birch et al., 2004). However, whereas considerable importance is attached to the force performance and power efficiency of flapping flight (Birch and Dickinson, 2003;Sun and Tang, 2002a;Sun and Tang, 2002b), few studies have addressed the detailed structure of the LEV.In a recent flow visualization of a robotic wing moving in the motion of dragonfly hovering (Y.L., G.X.S. and W. H. Su, manuscript submitted), we observed that the LEV with intensive spanwise flow did not develop along the leading edge but moved inboard, leaving a space for the formation of a minor vortex outside the primary vortex (see Fig.·1). In fact, a similar LEV pair has been reported in butterfly free flight using smokewire visualization (Srygley and Thomas, 2002). This vortical system reminds us of the dual LEV structure on non-slender delta wings, which is defined as the large and small same-sense vortices (the primary vortex and minor vortex, respectively) located close to the leading edge on both sides of the secondary separation in-and outboard, respectively (Gordnier and Visbal, 2003;Taylor and Gursul, 2004). This interesting flow behavior implies that the LEV generated in flapping motions may involve sub-structures, and merit in-depth exploration.With both visualizations the two vortices were reported to rotate in the same direction, but it is difficult to distinguish them directly from the flow images. In this paper, dye flow visualization and high-resolution DPIV measurements were conducted to reveal the detailed features of the LEV region. Based on the validation of the dual LEV, systematic investigations were performed by altering the kinematic (Re, from 160 to 3200, and ␣ m , from 10 to 80°) and geometric (AR, from 1.3 to 10) parameters. The well-known case of the fruit fly was re-examined to see whether the dual LEV had been missed in the previous studies. All measurements were obtained with the robotic wings flapping in the hovering condition.
Materials and methodsModel wing planform The planform of the simplified model dragonfly wing (AR=5.8, AR=R/c; where R is model wing length, measured from the translational axis to the wingtip; c is mean wing chord length) An experimental investigation was performed with two aims: (1) to clarify the existence of the dual leading-edge vortices (i.e. two vortices with the same sense of rotation located close to the leading edge above the leeward wing surface) observed on flapping wings in previous studies; (2) to study systematically the influences of kinematic and geometric parameters on such a vortical structure. Based on a scaled-up electromechanical model flapping in a water tank, the leading-edge vortex (LEV) cores were visualized via dye flow visualization, and the detailed substructures of LEV were revealed through digital particle image velocimetry (DPIV) with high spatial resolution. Five wing aspect ratios (AR) (1.3, 3.5, 5....