Effect of flapping frequency on aerodynamics of wing in freely hovering flight

• Aerodynamics of flapping wing is studied with free vertical vibration.
• Supported weights by flapping wings depend on flapping frequencies.
• Vertical vibration of wing can be neglected for high flapping frequencies.
• Instantaneous change in angle of attack influences aerodynamics of wing.

Hovering flight is investigated numerically when the wing is free to vibrate in the vertical direction under the action of wing lift and insect weight in low Reynolds number regime. The two-dimensional incompressible Navier–Stokes equations are solved using the immersed boundary method. The wing is driven to translate in the horizontal direction and rotate periodically to emulate the wing motion of a fruit fly in normal hovering flight, while the motion in the vertical direction responds passively to the action of the wing aerodynamic lift and weight of the insect body. The insect body is modeled by a point mass. It is shown that flapping wing cannot produce required lift to maintain stable hovering flight in specified range with low flapping frequencies, if the insect weight is equivalent to the averaged wing lift in one cycle on the assumption of zero vertical velocity. The vertical velocity influences the instantaneous angle of attack of the hovering wing, which results in the variation in aerodynamics of the wing. The insect may experience fluctuating hovering flight with a reduced weight when the flapping frequency is low. The fluctuating amplitude decreases with increasing flapping frequency. The efficiency of hovering flight is also a problem of concern.