A numerical study on the free hovering flight of a model insect at low Reynolds number

• Hovering flight on fixed periodic wing kinematics is weak in quasi-static stability.
• NS solver is integrated with Newtonian flyer dynamics and a generic control algorithm.
• Sustained stable quasi-periodic free hovering is simulated.
• Results are in good agreement with published works.
• Free flight simulation offers physical realism and a promising research direction.

The typical insect employs a flapping-wing mode of flight. In this paper we present numerical simulations on the low Reynolds number free hovering flight of a model fruit fly. A heuristic analysis shows that insect hovering flight tends to be poor in static stability. Stable quasi-periodic free hovering is achieved through active adaptation of wing kinematics during flight. The numerical model integrates the computational fluid dynamics of the flow with the three-dimensional Newtonian dynamics of the flyer and a generic PID-type kinematic control algorithm. The resultant wing and body motion of the flyer, which is evolved dynamically from variations to a basic set of sinusoidal wing kinematics, is quasi-periodic and quasi-steady. Two types of wing control are implemented here: an outer kinematic mode based primarily on the rotation of the wing stroke plane, and an inner kinematic mode based on adjustments of intra-stroke parameters. They allow the flyer to hover on a nearly horizontal stroke plane (normal hovering) and to hover with nearly horizontally poised body on a tilted stroke plane. The study is focused primarily on longitudinal stability (positional and pitching) in free hovering flight. The results obtained show good consistency and agreement with available published results. The present computational approach offers a promising line of investigation that could complement physical experiments in a wider study of the free flight aerodynamics of insect-like flyers.