# Aerodynamic Sensitivity Analysis for a Wind Turbine Airfoil in an Air-Particle Two-Phase Flow
## 4 Aerodynamic Sensitivity Analysis to Particles for S809 Airfoil
### Effects of Particle Concentration  
The particle concentration \(m\) is related to a specific environment. It may be less than 0.5% and more than 2% under the sandstorm and rain conditions, respectively. In this subsection, three particle concentrations of 0.5%, 1% and 2% are considered at \(Re=1\times 10^{6}\). As displayed in Figure 9, a higher concentration leads to a greater influence. The maximum lift and drag coefficient increments are respectively \(-2.6\%\) and \(10\%\) at \(m=0.5\%\), and they are \(-9.7\%\) and \(37.4\%\) at \(m=2\%\). The most sensitive  
Figure 8: \(Re\) effects on location and moving distance of separation point on S809 airfoil: (**a**) Location of separation point; (**b**) moving distance of separation point.  
Figure 7: Velocity profiles for S809 airfoil flow at \(\alpha=4.1^{\circ}\) and \(Re=1.5\times 10^{6}\).  
angle of attack maintains a fixed value of \(9.1^{\circ}\) for three particle concentrations, which means that the particle concentration does not affect the most sensitive angle of attack.  
Figure 10 shows the effects of particle concentration on the surface pressure distribution. The pressure difference between these particle concentrations is slight at \(\alpha\) = \(4.1^{\circ}\), while it is significant at \(\alpha\) = \(9.1^{\circ}\) since a larger concentration leads to a more extensive flow separation.  
Figure 11 gives the moving distance of separation point at three particle concentrations and \(Re\) = \(1\times 10^{6}\). Likewise, a larger particle concentration causes a larger moving distance. The maximum upstream-moving distance increases from 5% at \(m\) = 0.5% to 17.2% at \(m\) = 2%. For three particle concentrations, the angle of attack corresponding to the maximum moving distance also equals a constant value of \(8.1^{\circ}\), which is \(1^{\circ}\) smaller than the most sensitive angle of attack of \(9.1^{\circ}\). So, this angle difference is not influenced by the particle concentration, which has been verified to be independent of \(Re\) number in Section 4.1.  
Figure 10: Particle concentration effects on pressure coefficient distribution over S809 airfoil at \(Re\) = \(1\times 10^{6}\): (**a**) \(\alpha\) = \(4.1^{\circ}\); (**b**) \(\alpha\) = \(9.1^{\circ}\).  
Figure 9: Particle concentration effects on lift and drag coefficient increments of S809 airfoil at \(Re\) = \(1\times 10^{6}\): (**a**) Lift coefficient increment; (**b**) drag coefficient increment.  
A wind turbine generally operates around the maximum lift-to-drag ratio. Figure 12 illustrates the lift-to-drag ratio of the S809 airfoil at different particle concentrations and \(Re=1\times 10^{6}\). As can be seen, the lift-to-drag ratio decreases with increasing particle concentration, the peak angle of attack is between \(6.1^{\circ}\) and \(7.1^{\circ}\) approximately, which is about \(3^{\circ}\) smaller than the most sensitive angle of attack of \(9.1^{\circ}\). Hence, the aerodynamic performance of a wind turbine is susceptible to particles considering its operating state, environments as well as pitch control.