## 4 Effect of Turbulence Intensity on Airfoil at Different Reynolds Numbers
### The Influence of Reynolds Number on the Airfoil  
The effect of Reynolds number on airfoils has been discussed a lot in the literature. The main discussion here is on the airfoil aerodynamic performance with an increasing Reynolds number in terms of the improvement of stalling angle, generation of LSB, and the earlier transition. The pressure distribution and chordwise friction drag coefficient of airfoils with an angle of attack of 10\({}^{\circ}\) in varied turbulence intensities at \(Re_{2}\) = 53,000 are shown in Figure 18.  
It can be seen that flow separation, transition, and a short LSB occur around the leading edge of NACA0012 under both turbulence intensities at \(Tu=0.6\%\), as well as SD7037. There is no appearance of separation or LSB on the upper surface of SD7037 at \(Tu=6\%\), but Figure 18b shows that the transition still exists. In addition, combined with Figures 13c and 18, it can be seen that: With the increase of Reynolds number, the high-attack-angle separation around the trailing edge on the upper surface transfers to a small separation section, and the degree of flow separation is restrained. This shows that with the increase of Reynolds number, the shear effect on the airfoil surface is enhanced, the kinetic energy is more abundant, and the ability to resist the adverse pressure gradient is enhanced, so that the airfoil aerodynamic performance and stalling angle improves.  
Figure 19 shows the transformation of chordwise friction drag coefficient at angles of attack of 8\({}^{\circ}\) under three different Reynolds numbers.  
Taking the NACA0012 at \(Tu=0.6\%\) as an example, it can be seen that with the increase of Reynolds number, an earlier separation occurs on the upper surface of airfoil, the separation point transfers from 5% to 2%, and reattaches to the wall around 22%, forming a typical structure of short LSB. When the Reynolds number increases to \(Re_{3}=212\),000, the position of the LSB transfers to 6%-13%, and the  
Figure 18: Airfoil aerodynamic performance at \(\alpha=10^{\circ}\), \(Re_{2}\) = 53,000. (**a**) Pressure distribution; (**b**) Coefficient of chordwise friction drag.  
size of the LSB becomes evidently smaller. In addition, the valley value of \(C_{f,X}\) represents the onset of laminar flow transition, and peak value after the valley of \(C_{f,X}\) represents the finish of the transition to turbulent flow. Figure 19 shows that the transition point moves forward from 42%c through 17%c to 12%c, and the reattachment point also moves forward from 80%c through 25%c to 13%c. It can be concluded that, the increasing Reynolds number results in earlier transition and reattachment, contributing to an overall decrease in separation bubble length, as stated in [38].  
In addition, the generation of the LSB affects the aerodynamic characteristics of the airfoils. The pressure distribution and chordwise friction drag coefficient of airfoils with an angle of attack of 5\({}^{\circ}\) in varied turbulence intensities at \(Re_{2}\) = 53,000 are shown in Figure 20.  
It can be seen that transition occurs on the upper surface of both airfoils and then laminar separation bubbles form at \(Tu=0.6\%\). The generation of the laminar separation bubble changes the effective shape of the airfoil, increases the curvature of the upper surface of the airfoil (Figure 20c) so that the lift coefficient of the airfoil at \(Tu=0.6\%\) is bigger than that at \(Tu=6\%\), and also causes the nonlinear phenomenon of the lift coefficient at small angle of attack as shown in Figures 9a and 10a. However, when the separation bubble size is small or forms near the trailing edge of the airfoil, it has little effect on the lift characteristics of the airfoil.