Rapid Pitch-Up

The LEV-based lift-enhancement mechanism seems to be a main feature during the translational motion of the stroke. In addition, the flapping wings experience rapid wing rotation at the ends of the down – and upstroke, which can enhance lift force in flying insects.

Kramer [288] first demonstrated that a wing can experience lift coefficients above the steady stall value when that wing is rotating from low to high AoAs, which is now termed the Kramer effect. The unsteady aerodynamic characteristics associated with the time-dependent AoA, including hysteresis, are shown in Figure 3.4. Dickinson et al. [201] used their Robofly along with a varied rotational pattern, illustrated in Figure 3.9, to investigate the interplay between kinematics and lift generation. They identified two aerodynamic force peaks at the end and the beginning of each

stroke (pronation and supination). The first force peak can be explained based on the rotational circulation. The resulting force enhancement is influenced by the timing of the wing rotation while translating. They found that an advanced rotation produces a mean lift coefficient CL = 1.74, which is almost 1.7 times higher than that of a delayed rotation (CL = 1.01), whereas a symmetric rotation can attain a value of CL = 1.67. These peaks were confirmed by the numerical simulations of Sun and Tang [289] and Ramamurti and Sandberg [290]. In addition, Sun and Tang [291] further investigated three mechanisms responsible for lift enhancement via unsteady aerodynamics: (i) rapid acceleration of the wing at the beginning of a stroke, (ii) delayed stall, and (iii) fast pitch-up rotation of the wing near the end of the stroke. In advanced rotation, the wing flips before reversing its translational direction as illustrated in Figure 3.9, and the leading edge rotates backward relative to the translation. Based on their computational analysis, Sun and Tang [289] suggested that the first peak is due to the increase in rapid vorticity that occurs when the wing experiences fast pitch-up rotation. The pitch-up rotation and the associated vorticity increase are plotted in Figure 3.13f and g. Sane and Dickinson [292] attributed this first force peak to the additional circulation generated to reestablish the Kutta condition during the rotation. Overall, the findings reported by Sun and Tang [289] and Sane and Dickinson [292] are in agreement. The second peak, termed wake capture, is related to the wing-wake interaction and is discussed next. Together, these two peaks contribute to lift enhancement. Because both pitch-up and wake

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Figure 3.14. Illustrations of the wake-capture mechanism [201] [296]. (a) Supination, (b) beginning of upstroke, and (c) early of upstroke. At the end of the stroke, (a), the wake shed in the previous stroke denoted by CWV is en route of the flat plate. As the flat plate moves into the wake (b-c) the effective flow velocity increases and additional aerodynamic force is generated. The color of the contour indicates the spanwise component of vorticity. CWV and CCWV indicate clockwise and counterclockwise vortex.

capture are strongly influenced by flapping kinematics, more discussion is provided later to help elucidate the parametric variations of these factors.