###### Abstract
For example, the authors of [5] added surface roughness on the top surface of NACA4412 airfoil at 30% and 40% of the chord in wind tunnel measurements and found increased drag and delayed stall at high Reynolds number, \(Re_{C}=1.7\times 10^{5}\). The effect of surface roughness on the two circular cylinders in tandem was studied by [6] numerically in the subcritical flow regime (\(Re_{C}=6.5\times 10^{4}\)), in which the drag reduction, intermittence of vortex shedding, and wake destruction are identified. Therefore, using surface roughness to increase airfoil performance at low Reynolds numbers, i.e., \(Re_{C}<1\times 10^{5}\), has not been clear. Before this can be carried out, understanding the aerodynamic mechanism due to Reynolds number variations is needed. The airfoils of a wind turbine model tested in a typical boundary layer wind tunnel are in the low Reynolds number regime, i.e., \(\mathrm{O}\big{(}10^{4}\big{)}\). Not only for wind tunnel tests, but also the low-Reynolds number flow is found in many other applications. The wing of insects resembles airfoils in the flow of the 'ultra-low' Reynolds number regime, i.e., \(\mathrm{O}\big{(}10^{3}\big{)}\) (e.g., [7]). In Reynolds number of \(\mathrm{O}\big{(}10^{4}\big{)}\), other application examples can be micro air vehicles (e.g., [8]). In Reynolds number of \(\mathrm{O}\big{(}10^{5}\big{)}\), applications are found in the blades of small-scale wind turbines (e.g., [9]) and propellers. Sailplanes are found in the Reynolds number of \(\mathrm{O}\big{(}10^{6}\big{)}\) (e.g., [10]) and commercial aircraft are in \(\mathrm{O}\big{(}10^{7}\big{)}\) and \(\mathrm{O}\big{(}10^{8}\big{)}\) (e.g., [11]). As a result, airfoil aerodynamics have been studied in a wide range of Reynolds numbers, as well. Examples of the works that have been carried out experimentally are ([12; 13; 14; 15; 16]) or numerically are ([17; 18; 19; 20; 21; 22]). Most of the previous works focused on the flow separation above the airfoils, since it has strong connections to the surface pressures and the aerodynamic forces. Since the airfoils are generally used to generate lift, small angles of attack are usually considered in the literature, i.e., \(0^{\circ}\leq a\leq 15^{\circ}\). For large angles of attack, the flow separates regardless of Reynolds number and behaves in a similar way to a flat plate that is placed normal to the flow direction. An illustrative overview of the Reynolds number effects is given by [21]. For Reynolds of \(\mathrm{O}\big{(}10^{7}\big{)}\) or more, flow separation can be observed on the upper surface near the leading edge. Due to the high inertia of the approaching flow, the separated flow reattaches at a short distance after the separation, resulting in a small separation bubble. During the separation, the laminar separated flow transforms to turbulence, forming a reattached turbulent boundary layer. For Reynolds number in \(5\times 10^{4}<Re_{C}<10^{5}\), the laminar boundary layer before separation thickens as compared to the higher Reynolds number scenario (i.e., \(Re_{C}\geq 10^{7}\)). Since the inertia of the approaching flow becomes weaker, it is unable to force the separated flow back to the surface as quickly as in \(Re_{C}\geq 10^{7}\); therefore, the reattachment point moves toward the trailing edge, forming a larger separation on the upper surface. By decreasing the Reynolds number to the range of \(10^{4}<Re_{C}<5\times 10^{5}\)the laminar boundary layer becomes thicker and more stable. Since the reattachment point propagates further downstream, the flow may not be able to reattach in this low-Reynolds number flow. Surface pressure measurements conducted in experiments (e.g., [14; 15]) and numerical simulations (e.g., [18; 21]) show strong dependences on the behavior of the separated flow. For lower Reynolds numbers, i.e., \(Re_{C}<10^{5}\), the effects due to Reynolds number variations are more drastic than in the higher Reynolds number scenario, i.e., \(Re_{C}>10^{5}\), as also noted in [21].