# Numerical Simulation of Flapping Airfoil Aerodynamic Characteristics
###### Abstract  
Flapping airfoil flight technology is widely used in defense and civilian fields, and huge economic benefits can be created. The bionic flapping airfoil is the research object of this paper. The influence of flapping frequency, flight trajectory, different airfoil types, and various flapping layouts on the aerodynamic characteristics of the flapping airfoil is investigated through numerical calculation. It is found that an increase in the flutter frequency can lead to an increase in the lift and drag of the flutter airfoil, as well as the strength of the flutter airfoil leading edge vortex, thereby improving the aerodynamic characteristics of the flutter airfoil, but the increase in the frequency leads to the decrease in the lifting efficiency. With the same symmetry of the trajectory of the flapping airfoil, the flapping airfoil lift characteristics are the same, but the drag characteristics may be different. If the symmetry of the flapping airfoil trajectory is distinct, the lift and drag characteristics of the flapping airfoil are different, and it is also found that the best lifting efficiency occurred in the \"\(\infty\)\" trajectory. If the curvature and thickness of the airfoil are different, the aerodynamic characteristics of the flapping airfoil are distinct. Finally, the effect of different layouts on the aerodynamic characteristics of the flapping airfoil is examined. It is found that both tandem and parallel layout flapping airfoils can effectively increase the lift drag, but both tandem and parallel layout flapping airfoils lead to a decrease in the lifting efficiency. flapping airfoil; flexibility; numerical simulation; aerodynamic characteristics 22 May 2025  
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revealed by many scholars through analyzing the flutter motion function. The effect of Rossby number (R\({}_{0}\)) on the aerodynamic characteristics of flapping airfoils during forward flight was investigated by [PERSON] [5]. The peak lift coefficient was found to increase with increasing Rossby number, and the peak average drag coefficient was established to reduce with growing Rossby number. The influence of flapping airfoil kinematic function on insect aerodynamics was investigated by [PERSON] [6] through numerical simulation and experimental methods, and the effective boost in flap lift is affected by taking a smaller value of K and a larger value of C\({}_{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text  
and 3D by [PERSON] [16]. The lift and power performance of the flapping airfoil can be significantly affected by the wingtip vortices, and the lift is influenced by the interaction of the wingtip vortices with the leading edge vortices but there is no additional power requirement. The three-dimensional flow field of a rectangular flapping airfoil with a low spreading ratio was studied by [PERSON] [17] using a large vortex simulation. The lift performance is continuously enhanced with an increasing reduction rate. Beyond the dimensionless time 0.2, the lift-resistance performance of the flapping airfoil pitching motion is not much impacted by the reduction frequency. The effect of distinct types of flapping airfoil interactions on a miniature flapping airfoil vehicle was investigated by [PERSON] [18]. The highest lift and least power is generated by a spreading rigid, chordwise flexible airfoil, and higher lift is created by more airfoils, but more drag is generated and more power is demanded. The aerodynamic characteristics of a butterfly airfoil model in different motion modes were experimentally investigated by [PERSON] [19]. The results show that increasing the angle of attack in the uplift phase significantly increases the lift but also raises the power consumption. The AB motion modification (increasing the angle of attack in the uplift phase + decreasing the angle of attack in the backward phase) produces the maximum thrust but reduces the lift accordingly.