# Numerical Simulation of Flapping Airfoil Aerodynamic Characteristics
###### Abstract
Meanwhile, the C modification (optimizing the angle of attack curve) is the closest to the hovering state with the lowest energy consumption. When birds, insects, and bats fly, their wings undergo bending and twisting deformation, which is considered as flexible deformation of flapping airfoils. However, there is little research on the flexible deformation of flapping airfoils, and further improvement is needed in the theory of flapping airfoil flexibility [20]. The influence of flexibility on the aerodynamic characteristics of flapping airfoils was studied by [PERSON] [21] through numerical methods. Research has identified that the Strouhal number is proportional to the total fluid force on the airfoil. The momentum impulse and additional mass term of the fluid are influenced by the Strouhal number. As the Reynolds number and reduced rate rise, the fluid force felt on a moving object is controlled by an additional mass term, which is proportional to the acceleration of the object's motion, and the optimal frequency ratio for propulsion efficiency is 0.41 of the natural rate of the airfoil. The influence of the flexibility of flapping airfoils on their hovering and forward flight characteristics was discovered by [PERSON] [22] through numerical methods. Research has detected that the increase in thrust with increasing flapping frequency is partly due to the flexibility of flapping airfoils, and the advanced ratio is the reason for the reduced thrust of flexible flapping airfoils with high flapping frequencies. The unsteady aerodynamic loads of flapping airfoils were calculated by [PERSON] [23] using the unsteady vortex lattice method. The flexibility of flapping airfoils has been discovered to improve their aerodynamic performance. By calculating the changes in aerodynamic forces of flexible flapping airfoils with parameters such as flapping angle and inclination of flutter, the flapping motion laws of flying birds at different stages are explained. The effect of active bending deformation on the aerodynamic performance of forward-flapping airfoils was studied by [PERSON] [24], and it was found that moderate bending deformation can increase the aerodynamic efficiency of forward-flapping airfoils. Some insects in nature have more than one pair of wings, such as dragonflies, butterflies, etc. The impact of multiple pairs of wings on aerodynamic performance has attracted the attention of many scholars. The influence of three-dimensional effects of flapping airfoil motion on flapping airfoil performance in a tandem layout was researched by [PERSON]'s [25] study. It was found that the aspect ratio AR is 2 or 4, and the interaction mechanism between the front and rear airfoil vortex structures is similar in both three-dimensional and two-dimensional cases. However, the average thrust generated in the three-dimensional case of a finite airfoil span is lower than that in the two-dimensionalcase of an infinite airfoil span. This decline will rise with the rise in theaspec ratio, and this decline is more pronounced on the rear airfoil. The aerodynamic performance of a single airfoil/tandem airfoil layout was compared and analyzed by [PERSON] [26] using unsteady numerical analysis methods. It was detected that compared to the single-airfoil layout, the thrust coefficient and propulsion efficiency of the longitudinal airfoil layout increased by 28.7% and 5.7%, respectively, when the nondimensional horizontal spacing between the flapping airfoil and the tail airfoil was 0.5 times the chord length of the airfoil. The current study of fluttering airfoil motions is dominated by the presence of incoming flows, while there is relatively little research on the aerodynamic characteristics of flapping airfoils without incoming flow. To elucidate the flapping airfoil kinematics free from incoming flow effects, a numerical approach was employed. The impact of flapping motion parameters and structural characteristics on aerodynamic properties was investigated.