The blades of a wind turbine turn a large shaft at a relatively slow speed. The rotational speed is increased by a gearbox that has a mechanical efficiency of m = 0.93. In turn, the gearbox output shaft drives an electric generator with an electrical efficiency of e = 0.95. The cylindrical nacelle, which houses the gearbox, generator, and associated equipment, is of length Ln= 6 m and diameter Dn= 3 m. The turbine produces P = 3.0 MW (rated at 12 m/s) of electrical power, and the air and surrounding temperatures are T= 25oC and Tsur = 20oC, respectively. The three identical blades are designed based on the Blade Element Theory (N = 20) using the 2D NACA 4412 airfoil, with aerodynamic efficiency, a below 0.593 (Betz Limit). Determine the blade length (R), blade profile (with a 3D CAD model), and solidity (). (a)Determine the temperature in the nacelle by making reasonable heat transfer assumptions. (b)Determine c/R, ', T, , Q, P for = 7 at r/R = 0.30 and 0.90 with hand calculations. (c)Compete for the table below using Excel or Matlab.(d)Plot Cp vs (=5- 10) for V = 3-12 m/s. (e)Create a 3-D turbine blade solid and wireframe model using SolidWorks. (f)Determine the Capacity Factor based on the velocity probability as shown on Page 4.

- a 9 C/R round transition transition NACA 4412 r/R 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 B: number of blades c: blade (airfoil) chord length o': local solidity, o' = Bc/2rtr