# Partial Oscillation Flow Control on Airfoil at Low Reynolds Numbers
## 4 Results and Discussion
### Influence of the Oscillation Position  
In this segment, we examine the impact of oscillation position on the aerodynamic properties of the airfoil, maintaining a constant oscillation frequency of \(f=5\) Hz and an amplitude of \(A=0.001c\) throughout the study. The aerodynamic attributes of the airfoil subject to various oscillation positions are illustrated in Figure 15. This graphical representation highlights that when the oscillation position is at \(P=0.1c\) and \(P=0.6c\), the airfoil experiences a reduction in its drag coefficient, concurrent with a significant boost in both the lift coefficient and the lift-to-drag ratio. Specifically, when \(P=0.1c\), there is a \(4.87\%\) increase in \(C_{L}\), a \(15.29\%\) decrease in \(C_{D}\) and a remarkable \(23.79\%\) augmentation in \(K\), all in comparison to the rigid airfoil. With \(P=0.6c\), there is a notable augmentation of \(4.94\%\) in \(C_{L}\), a substantial reduction of \(15.15\%\) in \(C_{D}\) and a considerable surge of \(23.68\%\) in \(K\). From the foregoing analysis, it is evident that the changes in the aerodynamic coefficients exhibit similar patterns when \(P=0.1c\) and \(P=0.6c\), thus substantiating that partial oscillations at both \(0.1c\) and \(0.6c\) exert comparable flow control effects. Figure 14: Shape of the LSB on the airfoil (\(P=0.6c,f=4\) Hz). Figure 15: Influence of the oscillation position on aerodynamic characteristics of airfoil. **(a)** Lift and drag coefficient; **(b)** lift–drag ratio. From Figure 15, it is discerned that the time-averaged location of laminar separation lies at \(0.506c\), while the time-averaged reattachment point is situated at \(0.721c\). Consequently, the oscillation position at \(0.6c\) is proximate to the centroid of the LSB on the airfoil. The research demonstrates that when oscillation occurs in close proximity to the leading edge or the central region of the LSB, the enhancement in lift and the reduction in drag resulting from partial oscillation are most pronounced. Figure 16 presents time-averaged streamline patterns and velocity distributions for the oscillating airfoil at various positions. Time averaging entails computing the temporal mean of flow field parameters over multiple cycles, yielding a result that represents the averaged conditions. This approach serves as a pivotal technique widely adopted in the study of unsteady flows at low Reynolds numbers [23]. From this figure, it is discernible that multiple LSBs exist across the upper surface of the rigid airfoil within the span of \(0.506c\) to \(0.721c\). Under a Reynolds number of \(3\times 10^{5}\), the cumulative length of these LSBs measures \(0.215c\). At \(P=0.5c\), a significant extent of laminar separation persists. However, when \(P\) assumes values of \(0.1c\) and \(0.6c\), multiple smaller separation bubbles coalesce into a single larger bubble within the laminar separation region on the upper surface of the airfoil, resulting in a visibly reduced separation area. On the other hand, these velocity contours reveal that when the oscillation positions are at \(0.1c\) and \(0.6c\), the acceleration of airflow over the upper surface of the airfoil is reduced compared to the rigid airfoil case and the scenario where oscillation occurs at \(0.5c\). Concurrently, the formation of low-velocity regions indicative of recirculation is diminished. These  
Figure 16: Streamlines and velocity distributions of airfoil. (**a**) Rigid airfoil; (**b**) \(P=0.1c\); (**c**) \(P=0.5c\); (**d**) \(P=0.6c\). observations suggest that local oscillation at positions \(0.1c\) and \(0.6c\) exert a controlling effect on the laminar separation bubble over the upper surface of the airfoil.