Propulsion Performance of Multiple Pitching-Heaving Airfoils in Side-by-Side Configurations

In nature, flying animals and swimming fishes flap their wings or fins to achieve excellent movements within the low Reynolds number regime. Their complex flapping kinematics are often reasonably simplified into the pitching-heaving motion of a two-dimensional (2-D) airfoil or hydrofoil, which can be further upgraded to multiple airfoils or hydrofoils in either tandem or side-by-side configurations when insect swarms or fish schools are considered. Here, the propulsion performance of pitching-heaving airfoils in the side-by-side configuration is examined via numerical simulations. The research starts with finding an preferable propulsion status for a single airfoil and then, to further guide the practical design of a multiple-flapping-wing micro air vehicle (MAV), the biplane and triple airfoil configurations are then considered. Results show that, for a single airfoil undergoing pitching-heaving motion, high propulsion efficiency is obtained when the amplitude of the effective angle of attack is around 20°. The corresponding reduced frequency should be confined within a certain range that goes up slightly as the Strouhal number increases. When placing airfoils in the side-by-side configuration, the contribution of clap and fling motion can enlarge the thrust and efficiency, which becomes prominent when the minimal inter-foil gap decreases. The enhancement led by a single clap and fling phase is found to be relevant to a novel flow structure. The middle airfoil of the triple configuration experiences dual clap and fling phases and almost double its thrust enhancement. Compared to previous research on pitching-heaving airfoils, our findings explain the fluid-mediated interaction between multiple (>2) pitching-heaving airfoils in the side-by-side configuration without a limit of total heaving amplitude. These findings can provide insight into determining the wing number of a MAV with multiple flapping wings sharing a stroke plane.