Hovering efficiency comparison of rotary and flapping flight for rigid rectangular wings via dimensionless multi-objective optimization

In this work, a multi-objective optimization framework is developed for optimizing low Reynolds number (Re) hovering flight. This framework is then applied to compare the efficiency of rigid revolving and flapping wings with rectangular shape under varying Re and Rossby number (Ro, or aspect ratio). The proposed framework is capable of generating sets of optimal solutions and Pareto fronts for maximizing the lift coefficient and minimizing the power coefficient in dimensionless space, explicitly revealing the trade-off between lift generation and power consumption. The results indicate that revolving wings are more efficient when the required average lift coefficient (C) over bar (L) is low (< 1 for Re = 100 and <1.6 for Re = 8000), while flapping wings are more efficient in achieving higher (C) over bar (L). With the dimensionless power loading as the single-objective performance measure to be maximized, rotary flight is more efficient than flapping wings for Re > 100 regardless of the amount of energy storage assumed in the flapping wing actuation mechanism, while flapping flight is more efficient for Re < 100. It is observed that wings with low Ro perform better when higher <(C)over bar>(L) is needed, whereas higher Ro cases are more efficient at (C) over bar (L) < 0.9 regions. However, for the selected geometry and Re, the efficiency is weakly dependent on Ro when the dimensionless power loading is maximized.