Derivation of Relation between Angle of Attack and Effect of Leading Edge Erosion on Airfoils at the Tip of Wind Turbine Blades

Leading-edge erosion of wind turbines is caused by particles in wind. Impacts at a high velocity damage the blades severely and lower the aerodynamic efficiency. The aim of this paper is to estimate the flow rate hitting on the leading edge of the airfoil NACA4412, which forms the tip of a wind turbine blade, with the geometry referred to NREL offshore 5-MW baseline wind turbine. The methodology is to first compute the coordinates of the points on the boundary of the airfoil that is defined to be the leading edge, then with trigonometry relationships of the airfoil, the length that is passed through by wind can be found. Finally, relating them together, a differential equation is established. It reveals how the angle of attack and flow rate through the leading edge are correlated. With graphs plotted, the equation states that changing the angle of attack from 6 to 7 has 6.2% less erosion while Cl/Cd is dropped by 4.6% only. Hence, for situations where leading edge erosion and aerodynamic efficiency are considered equally important, it is better to vary the angle of attack to 7 degrees rather than the optimal 6 degrees.