###### Abstract
As a result, this work tries to understand the mechanism of the Reynolds number effects on the airfoil aerodynamics in the low Reynolds number region. At low Reynolds numbers, i.e., \(Re_{C}<10^{6}\), relatively few works have been carried out to study the effects of Reynolds number variations. The authors of [18] applied INS2D to numerically simulate the unsteady flow passing Eppler 387 airfoil at \(Re_{C}=6\times 10^{4}\), \(1\times 10^{5}\), and \(2\times 10^{5}\) as well as \(0^{\circ}\leq\alpha\leq 7^{\circ}\). Their results showed that the size of the time-averaged separation bubbles decreases as the Reynolds number increases. Nearly uniform distributions of pressures can be found along the windward portion of the bubbles, while adverse pressure gradients can be observed near flow reattachments. The PIV measurements by [14] on the GA (W)-1 airfoil at \(Re_{C}=7\times 10^{4}\) and \(6^{\circ}\leq\alpha\leq 12^{\circ}\) showed that the transition process of the laminar separated shear layer to turbulent reattachment is through Kelvin-Helmholz vortices. Utilizing smoke flow visualization, hot wire velocity measurements, and surface pressure measurements on the NACA0025 airfoil at \(5.5\times 10^{4}\leq Re_{C}\leq 2.1\times 10^{5}\) as well as \(\alpha=0^{\circ},5^{\circ}\), and \(5^{\circ}\), the authors of [15] further categorized the separated flows into two regimes: (i) At lower Reynolds numbers, i.e., \(5.5\times 10^{4}\leq Re_{C}\leq 1.1\times 10^{5}\), the flow separates from the upper surface without reattachment; (ii) at higher Reynolds numbers, i.e., \(1.75\times 10^{5}\leq Re_{C}\leq 2.1\times 10^{5}\), the flow separates and reattaches, forming separation bubbles. By comparing the flow visualization and the velocity energy spectrum, they found that the most energetic peaks are associated with the shear layer roll-up vortices and speculated that the merging of the roll-up vortices is associated with the other subharmonic peaks. As the Reynolds number increases, the length scales of the roll-up vortices and the wake vortices reduce and the flow structures become more irregular. Recently, the authors [21] examined the performance of various airfoils (NACA0009, NACA0012, Clark-Y, Flat plate, Cambered plates) at \(10^{4}<Re_{C}<10^{5}\) and \(0^{\circ}\leq\alpha\leq 30^{\circ}\) using the in-house time-averaged turbulence solver TURNS2D. As the Reynolds number increases, the performance of the airfoils increases due to the increased lift coefficients and reduced drag coefficients. Moreover, they noted the non-linearity of the lift coefficient curve below the stall angles, which is usually assumed to be linear for high Reynolds numbers. These non-linearities are attributed to the movement of the separation bubbles induced by the variations of attack angles. As the angle of attack increases significantly beyond the stall values (e.g., \(\alpha\geq 30^{\circ}\)), the PIV and force measurements of NACA0012 by [16] showed that the airfoil aerodynamics are nearly independent of the variations of Reynolds numbers, i.e., \(5.1\times 10^{3}\leq Re_{C}\leq 5.3\times 10^{3}\). Although the mentioned works provided great implications from the velocity measurements, they were not directly linked to the wind loads. For example, the decreased airfoil performances are generally associated with the formation of the separation bubbles at low Reynolds numbers (e.g., [14; 15; 16; 18; 21]). However, no further explanation was provided for why the separation bubbles are detrimental. Therefore, to contribute to the detailed connections between the ambient flow fields and the overall loads, this work adds the vorticity and the pressure fields for explanation. As shown in Section 2.2, the velocity and vorticity are both responsible for the suction on the upper surface, generating the lift forces for the airfoil. One of the best ways to simulate the shear layer vorticity numerically is the vortex method. Therefore, the two-dimensional (2D) vortex particle method (VPM), as proposed in [23], is utilized in this work.