To maintain flight, insect-scale air vehicles must adapt to their low Reynolds number flight conditions and generate sufficient aerodynamic force. Researchers conducted extensive studies to explore the mechanism of high aerodynamic efficiency on such a small scale. In this paper, a centimeter-level flapping wing is used to investigate the mechanism and feasibility of whether a simple motion with a certain frequency can generate enough lift. The unsteady numerical simulations are based on the fluid structure interaction (FSI) method and dynamic mesh technology. The flapping motion is in a simple harmonic law of small amplitude with high frequency, which corresponds to the flapping wing driven by a piezoelectric actuator. The inertial and aerodynamic forces of the wing can cause chordwise torsion, thereby generating the vertical aerodynamic force. The concerned flapping frequency refers to the structural modal frequency and FSI modal frequency. According to the results, we find that under the condition that frequency ratio is 1.0, that is, when the wing flaps at the first-order structural modal frequency, the deformation degree of the wing is the highest, but it does not produce good aerodynamic performance. However, under the condition that frequency ratio is 0.822, when the wing flaps at the first-order FSI modal frequency, the aerodynamic efficiency achieve the highest and is equal to 0.273. Under the condition that frequency ratio is 0.6, that is, when the wing flaps at a frequency smaller than the first-order FSI modal frequency, the flapping wing effectively utilizes the strain energy storage and release mechanism and produces the maximum vertical coefficient which is equal to 4.86. The study shows that this flapping motion can satisfy the requirements of lift to sustain the flight on this scale.

To better understand the secret of natural flying vertebrates such as how humming-birds twist their wings to achieve superb flight ability, we presented a numerical investigation of dynamic twisting based on a hummingbird-like flapping wing model. Computational fluid dynamic simulations were performed to examine the effects of dynamic twisting on the unsteady flow field, the generation of instantaneous aerodynamic forces, and the time-averaged aerodynamic performance. This research reveals the details of leading-edge vortices (LEVs) and the underlying mechanisms behind the positive effects of wing torsion. The results demonstrated that wing torsion can effectively maintain the favorable distribution of effective angle of attack along the wing spanwise, resulting in a higher time-averaged thrust and vertical force. Further, the proper parameters of dynamic twisting can also improve the propulsive efficiency in forward flight. Dynamic twisting also showed a superior ability in controlling the airflow separation over the wing surface and maintaining the stability of the LEV. The amplitudes of effective angle of attack associated with the highest peak thrust and the maximum thrust-to-power at different advanced ratios were also explored, and it was found that the amplitudes decrease with increasing advanced ratio. To improve the efficiency during larger advanced ratio, specific modifications to the pitching of the wing were proposed in this work. The research in this paper has promising implications for the bio-inspired flapping wing.

Due to the complexity of tailoring the wing flexibility and selecting favorable kinematics, the design of flapping wings is a considerably challenging problem. Therefore, there is an urgent need to investigate methods that can be used to design wings with high energy efficiency. In this study, an optimization model was developed to improve energy efficiency by optimizing wing geometric and kinematic parameters. Then, surrogate optimization was used to solve the design optimization model. Finally, the optimal design parameters and the associated sensitivity were provided. The optimized flapping wing, inspired by hummingbirds, features large geometrical parameters, a moderate amplitude of the flapping angle, and low frequency. With the spanwise twisting deformation considered in the parameterization model, the optimization solver gave an optimized wing with a pitching amplitude of approximately 39 deg at the root and 76 deg at the tip. According to the sensitivity analysis, the length of the wing, flapping frequency, and flapping amplitude are the three critical parameters that determine both force generation and power consumption. The amplitude of the pitching motion at the wing root contributes to lowering power consumption. These results provide some guidance for the optimal design of flapping wings.

To deepen our understanding of the aerodynamics by which hummingbirds use flexible wings to hover efficiently during flapping flight, a three-dimensional wing model with dynamic morphing was developed according to the morphological and kinematic data of a hovering hummingbird’s wing. Navier-Stokes equations were solved on a dynamically deforming grid to study wing aerodynamics. In numerical simulations, boundary-based smoothing and overset methodologies were used in combination to update the interior nodes of cells in the computational domain, allowing those nodes to accommodate the motion of the flexible wall. This study showed that the leading edge vortex (LEV) attached to the wing was stable during the downstroke but extremely unstable and shed continuously during the upstroke. In the results of the downward stroke, the different vortices separated from the surface and formed a vortex ring. The difference is that the leading edge vortex induced a vortex ring near the root and a smaller and weaker vortex ring near the wingtip during the upstroke. A significant enhancement in aerodynamic forces was found during the downstroke, along with a large number of power consumptions. We found that the asymmetry in the time-averaged vertical force between the two half strokes was 3.5, and the value was higher than that reported earlier. Aerodynamic force coefficients and efficiency matched well with those of another hummingbird wing (the ruby-throated hummingbird). It is worth noting that hummingbirds can maintain a similar wingtip speed by flapping their wings, but different strategies are adapted to hover efficiently due to the differences in size and body weight. The results of this study help to better understand the aerodynamics of the hovering hummingbird.

Three-dimensional numerical simulations are performed to examine the effects of dynamic wing morphing of a hummingbird-inspired flexible flapping wing on its aerodynamic performance in hovering flight. The range analysis and variation analysis in the orthogonal experiment are conducted to assess the significance level of various deformations observed in the hummingbird wings on wing aerodynamic performance. It has been found that both camber and twist significantly can affect lift, and twist has an even higher significant impact on lift efficiency. Spanwise bending, whether out-of-stroke-plane or in-stroke-plane, has a negligible impact on lift and efficiency, and the in-stroke-plane bending can cause lift to decrease to an extent. Optimal parameters for determining the wing deformations are selected and tested to validate the conclusions drawn in the analysis for the results in orthogonal experiment. Through a comparison study between the optimized wings and the rigid wing, it is found that although the wing flexibility can cause the net force to decrease, the flexible wing used less energy to bring the net force closer to the vertical direction, thereby improving the lift efficiency. This study provides an aerodynamics understanding of the efficiency improvement of the hummingbird-inspired flexible flapping wing.