# Partial Oscillation Flow Control on Airfoil at Low Reynolds Numbers
## 4 Results and Discussion
### Influence of the Oscillation Frequency  
In this segment, we examine the impact of oscillation frequency on the airfoil's aerodynamic properties through numerical simulations. The oscillating surfaces are positioned at \(P=0.1c\) and \(P=0.6c\), with an amplitude of \(0.001c\). Based on the unsteady computations of the rigid airfoil, it is revealed that the frequency of the flow field around the rigid airfoil is approximately \(5.5\) Hz. Consequently, this study elects to investigate oscillation frequencies in the vicinity of the rigid airfoil's flow field frequency, with a range of 1-10 Hz, which corresponds to Strouhal numbers \(St=0.23\)-\(2.3\). Figure 10 depicts the time-averaged lift coefficient (\(C_{L}\)), drag coefficient (\(C_{D}\)) and lift-to-drag ratio (\(K\)) for varying oscillation frequencies, where \"rig\" refers to the rigid airfoil within the illustration. Figure 10 demonstrates the significant impact of oscillation frequency on the aerodynamic properties of the airfoil. When the oscillation position is set at \(0.1c\), it is observed that as the oscillation frequency increases, the lift coefficient (\(C_{L}\)) of the airfoil initially rises before declining, whereas the drag coefficient (\(C_{D}\)) experiences a decrease followed by an increase. Consequently, the lift-to-drag ratio of the airfoil exhibits an ascending and then descending trend. At the oscillation frequency of \(f=6\) Hz, the lift-to-drag ratio attains its peak value. Relative to a rigid airfoil, partial oscillation leads to a \(4.9\%\) enhancement in the lift coefficient, a \(15.3\%\) reduction in the drag coefficient and, correspondingly, a substantial boost of \(23.8\%\) in the lift-to-drag ratio. At an oscillation  
Figure 8: Structures of the laminar separation bubble. Figure 9: Laminar separation bubble obtained from the calculation and the test. position of 0.6\(c\), similar trends in variation are noted for the airfoil's \(C_{L}\), \(C_{D}\) and \(K\) as the frequency increases, paralleling the scenario when the oscillation position is at 0.1\(c\). It is noteworthy that when the frequency hits \(f=4\) Hz, the lift-to-drag ratio attains its peak value. Under these conditions, the partial oscillation leads to a 4.9% boost in the lift coefficient, a 15.2% reduction in the drag coefficient and thereby a significant 23.7% enhancement in the lift-to-drag ratio of the airfoil. The aforementioned research demonstrates that partial oscillation can lead to a substantial decrease in the airfoil's drag coefficient. To delve into the underlying mechanisms of this drag reduction, the total drag on the airfoil is partitioned into its pressure drag and viscous drag components. At an oscillation position of 0.6\(c\), Figure 11 depicts the time-averaged pressure drag coefficient (\(C_{Dp}\)) and viscous drag coefficient (\(C_{Dp}\)) for varying frequencies. This figure reveals that, relative to the rigid airfoil, the pressure drag coefficient of the oscillating airfoil diminishes, while its viscous drag coefficient experiences an increase. These data highlight that as the oscillation frequency rises, the pressure drag coefficient of the airfoil initially dips before climbing back up, whereas the viscous drag coefficient follows a pattern of initially increasing and then subsequently decreasing. At the point where \(f=4\) Hz, the viscous drag coefficient peaks, registering an 11.6% boost, whereas the pressure drag coefficient hits its lowest point, witnessing a notable drop of 23.3%. Taking into account the fluctuations in both pressure and viscous drags, the overall drag coefficient for the oscillating airfoil sees a reduction of 15.2% in comparison to its rigid counterpart. Figure 10: Aerodynamic characteristics of the airfoil under different oscillation frequencies. **(a)** Lift and drag coefficient (\(P=0.1c\)); **(b)** lift–drag ratio (\(P=0.1c\)); **(c)** lift and drag coefficient (\(P=0.6c\)); **(d)** lift–drag ratio (\(P=0.6c\)).