Self-propulsive Performance of Tandem Flap**-Fixed Airfoils at Low Reynolds Number: A Case Study

Abstract

Tandem airfoils or hydrofoils have been extensively observed in both natural flyers or swimmers and aircraft. Dragonflies can achieve excellent flights by adjusting the phase difference and wake interaction of their tandem flap** wings. A similar phenomenon also exists between individual fishes in a school formation. Specifically, the flap**-fixed configuration of tandem airfoils with a narrow inter-foil gap was revisited by us recently, and it was proved that the lift performance of this configuration can be improved by the strong fluid-mediated interaction at an expected propulsion performance. As a follow-up, the self-propulsive performance of this configuration is further examined using numerical simulations, and the analysis is focused on three typical cases, i.e., a high-thrust (HT) case, a high-lift (HL) case, and an enhanced high-lift (EHL) case by tilting the flap** plane. The Lattice Boltzmann method is employed to conduct the simulations and the code has been well-validated in our previous work. Results show that, compared to the fixed Strouhal number condition, the self-propulsive solution of tandem flap**-fixed airfoils can release their thrust margin and lead to a higher cycle-averaged forward speed. The forward speed also fluctuates corresponding to the dynamic thrust generation within a flap** cycle. This release of extra thrust can boost the forward speed of the HT case up to almost 1.5 times and the conventional triple vortex streets in the wake are compressed in the lateral direction to form a highly staggered wake pattern. For the HL and EHL cases, the increase in forward speed is not significant and thus the lift enhancement is marginal. The wake topology is mostly retained at the self-propelled equilibrium while the downstream convection of vortices is at a higher speed. Moreover, the lift efficiency of both HL and EHL cases can be enlarged by 10–15% at the self-propelled equilibrium. The impact of the density ratio between the airfoils and the fluid is also investigated and the aerodynamic performance is barely changed until the density ratio decreases to 10, below which an increase of cycle-averaged forward speed and lift generation is observed for both HL and EHL cases. This research presents a more practical solution for the tandem flap**-fixed airfoils within a low Reynolds number regime since micro air vehicles of this compound layout should cruise at the self-propelled equilibrium. Despite that, a further consideration of the MAV body and other components can include extra drag, these conditions can also be easily investigated using the current solution.