# Partial Oscillation Flow Control on Airfoil at Low Reynolds Numbers
## 4 Results and Discussion
### The Performance of Laminar Flow Separation on the Rigid Airfoil  
An unsteady numerical simulation approach has been employed to investigate the laminar separation bubble on a rigid airfoil, complemented by a corresponding water tunnel test conducted under identical conditions.  
At a Reynolds number of \(3\times 10^{5}\) and an angle of attack set at \(3^{\circ}\), the structural configurations of the laminar separation bubble, as derived from both the water tunnel testing and numerical simulations, are depicted in Figure 8. The results of the water tunnel testing reveal a distinct flow pattern where the streamline along the leading edge of the airfoil initially appears as a narrow and straight streak, indicative of a laminar flow regime. It is further elucidated that the flow field in the central region of the model maintains its two-dimensional characteristics, remaining largely unaffected by three-dimensional effects. Subsequently, this streak broadens and darkens, signifying the onset of laminar flow separation followed by the emergence of reverse flow. Thereafter, the staining line exhibits chaotic behavior, marking the transition to turbulent flow. Ultimately, the evidence of backflow dissipates, and the fluid once again adheres to the airfoil surface. The LSB is characterized as the zone stretching between the laminar separation point and the point of reattachment. As illustrated in Figure 8, the LSB phenomenon on the airfoil at low Reynolds numbers is distinctly observable through the water tunnel testing, and the numerically simulated structure of the LSB aligns well with the experimental findings.  
Figure 9 illustrates the time-averaged positions of laminar separation and turbulent reattachment. In the given figure, LS denotes the position of laminar separation, while TR represents the location of turbulent reattachment. The region encapsulated between the laminar separation (LS) point and the turbulent reattachment (TR) point constitutes the laminar separation bubble. As evidenced by this figure, it is apparent that at low Reynolds numbers, a distinct laminar separation bubble exists on the upper surface of the airfoil. In comparison to the experimental outcomes, the calculated errors are sufficiently minute, thereby validating the high accuracy of the unsteady numerical simulation method employed in this study for predicting the locations of laminar separation and turbulent reattachment at low Reynolds numbers. The calculation result shows that when the angle of attack is \(3^{\circ}\), the time-averaged length of the laminar separation bubble is \(22.2\%c\). The  
\begin{table}
\begin{tabular}{c c c c} \hline  & \(C_{\mathrm{L}}\) & \(C_{\mathrm{D}}\) & \(K\) \\ \hline Refined grid & 1.2347 & 0.01737 & 71.0823 \\ Initial grid & 1.2342 & 0.01750 & 70.5257 \\ Relative error & \(-0.0405\%\) & 0.748\% & \(-0.783\%\) \\ \hline \end{tabular}
\end{table}
Table 1: Calculation results of refined grid and initial grid.  
substantial extent of the laminar separation bubble suggests a significant impact on the airfoil's aerodynamic performance.