Long-term two-dimensional analysis of the flow field around a hovering flapping flat-plate wing

A flapping wing is considered as one of the most effective aerodynamic systems for micro air vehicles (MAVs). Many numerical studies have been attempted to investigate the flow field around a flapping wing; nevertheless, the long-term flow characteristics, which can cause a non-negligible effect on long-term hovering operations of MAVs have not been adequately clarified owing to the high computational cost involved. This study numerically investigates the long-term flow characteristics around a flapping flat-plate wing during hovering flight at a chord-based Reynolds number of 2.5 × 104. Based on the finite-volume method with the arbitrary Lagrangian-Eulerian (ALE) method, two-dimensional laminar flow analyses were performed for 40 periods of flapping motions with stroke inversion angles of β = 30°, 45°, and 60°. The results showed that the lift coefficient CL was not completely periodic despite the periodic motion. To identify the CL characteristics for each β case, a half-stroke-period-based phase-average of CL was calculated over different time segments. Then, the phase-averaged CL using the fifth to 30th periods sufficiently provided converged aerodynamic characteristics: the β = 30° and 45° cases had a single peak of CL, whilst the β = 60° had double peaks; the second peak taking the maximum CL in the β = 60° case was delayed compared to others. The results of this study provide a guideline for the number of periods required in the numerical estimation of the CL characteristics and associated flow fields around flapping-type MAVs, which contributes to their further improvement of them.