# Numerical Simulation of Flapping Airfoil Aerodynamic Characteristics
## 3 Results and Analysis
### Effects of Motion Parameters on the Aerodynamic Characteristics of Flapping Airfoils
#### 3.1.2 Impact of Flapping Frequency on the Aerodynamic Characteristics of Flapping Airfoils
This indicates that the work performed by thrust is better than the work performed by drag during one cycle of the flutter, meaning the vehicle is subjected to rightward force throughout the flutter. The flow field cloud maps of flapping airfoils with various frequencies at t = 0.45 T are displayed in Figure 12. It can be terminated that when the flapping airfoil flaps to the left, the leading edge of the upper airfoil surface is connected by leading edge vortices, and a low-pressure region is generated. The trailing edge vortex is produced at the trailing edge, and the low-pressure region is created near the trailing edge of the airfoil. As the rate of flapping airfoils climbs, the strength of the leading and trailing edge vortices of flapping airfoils also increases, and the low-pressure region corresponding to the vortices also lifts. Figure 11: Average drag coefficient for different frequency cycles. Figure 10: Curve of drag coefficient at different frequencies. The cloud diagram of the flapping airfoil flow field at different frequencies at t = 0.82 T is indicated in Figure 13. The flapping airfoils at different frequencies are flapping to the right, with leading edge vortices attached to the leading edge of the airfoil. Low-pressure regions are created on the upper airfoil surface, and trailing edge vortices are generated by the trailing edge of the airfoil. Additionally, low-pressure regions are formed at the tail of the trailing edge. A pair of trailing vortices that fell off during the previous stroke were captured at the front and rear edges of the airfoil. The low-pressure  
Figure 12: t = 0.45 T flow field contour map. Velocity contour map on the left, intermediate pressure contour map, and vorticity contour map on the right (Q criterion). (**a**) \(f\) = 25 Hz; (**b**) \(f\) = 50 Hz; (**c**) \(f\) = 100 Hz; (**d**) \(f\) = 150 Hz. area near the front edge was increased by the vortices captured at the front edge, while the low-pressure area near the rear edge was expanded by the vortices captured at the trailing edge. The strength of the leading and trailing edge vortices on the airfoil is enhanced with the growth of the flapping frequency, and the strength of the tail vortices captured by the airfoil and the corresponding low-pressure region of the vortices are also raised. Figure 13: t = 0.82 T flow field contour map, velocity contour map on the left, intermediate pressure contour map, and vorticity contour map on the right (Q criterion). (**a**) \(f\) = 25 Hz; (**b**) \(f\) = 50 Hz; (**c**) \(f\) = 100 Hz; (**d**) \(f\) = 150 Hz. From the above content, it can be discovered that as the flapping rate rises, the low-pressure area on the airfoil surface, the pressure difference between the upper and lower airfoil surfaces, and the combined force on the flapping airfoil will also be raised. Therefore, as the flapping frequency increases, the lift coefficient and drag coefficient of the flapping airfoil will all be raised. From an energy perspective, as the flapping rate increases, the kinetic energy of the flapping airfoil is boosted, and the energy transmitted to the air by the flapping airfoil is raised. This results in an increase in the pressure difference between the upper and lower surfaces of the airfoil. Consequently, the lifting effect is continuously strengthened. Although the rate rises and the aerodynamic characteristics of flapping airfoils are continuously enhanced, the lift cannot be improved by infinitely increasing the frequency. There is an upper limit to the power that insects, birds, and bats can provide for flapping, and the same is true for artificial flapping airfoil aircraft. The lifting efficiency is also shown to differ significantly as the flutter frequency of the flapping airfoil is changed.