A three bladed wind turbine has the following geometric and aerodynamic characteristics. Number of blades, B...

 

  

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A three bladed wind turbine has the following geometric and aerodynamic characteristics. Number of blades, B = 3 Tip speed ratio, A = 7 Blade radius, R = 4.953 m. Rated wind speed, Vo = 11.62 m/sec Rotor section shape, NACA 4415 airfoil C₁ = 0.368 +0.0942a Ca = 0.00994 +0.000259a +0.0001055a² The angle of attack, a, has units of degrees Rotor 0cp = -2° СР r/Rr(m) c(m) OT 0.495 0.411 45 0.991 0.455 25.6 0.1 0.2 0.3 1.486 0.384 15.7 0.4 1.981 0.311 10.4 0.5 2.477 0.259 7.4 0.6 2.972 0.223 4.5 0.7 3.467 0.186 2.7 3.962 0.167 1.4 0.8 0.9 4.458 0.137 0.4 4.953 0.107 0.00 1.0 Given this information, apply the BEM approach to the rotor divided into the 10 spanwise segments listed in the previous table. For this, (a) Calculate and plot a and a as a function of the radial position on the rotor. Include the Prandtl tip loss factor. Comment on how it compares to the Betz optimum. (b) Calculate and plot the lift and drag coefficients as a function of the radial position on the rotor. (c) Calculate and plot the differential normal and tangential force coefficients, dFn and dFt as a function of the radial position on the rotor. ✔ (d) Calculate and plot the differential power, dP, as a function of the radial position on the rotor. (e) Calculate total power generated by the wind turbine, (dP) A three bladed wind turbine has the following geometric and aerodynamic characteristics. Number of blades, B = 3 Tip speed ratio, A = 7 Blade radius, R = 4.953 m. Rated wind speed, Vo = 11.62 m/sec Rotor section shape, NACA 4415 airfoil C₁ = 0.368 +0.0942a Ca = 0.00994 +0.000259a +0.0001055a² The angle of attack, a, has units of degrees Rotor 0cp = -2° СР r/Rr(m) c(m) OT 0.495 0.411 45 0.991 0.455 25.6 0.1 0.2 0.3 1.486 0.384 15.7 0.4 1.981 0.311 10.4 0.5 2.477 0.259 7.4 0.6 2.972 0.223 4.5 0.7 3.467 0.186 2.7 3.962 0.167 1.4 0.8 0.9 4.458 0.137 0.4 4.953 0.107 0.00 1.0 Given this information, apply the BEM approach to the rotor divided into the 10 spanwise segments listed in the previous table. For this, (a) Calculate and plot a and a as a function of the radial position on the rotor. Include the Prandtl tip loss factor. Comment on how it compares to the Betz optimum. (b) Calculate and plot the lift and drag coefficients as a function of the radial position on the rotor. (c) Calculate and plot the differential normal and tangential force coefficients, dFn and dFt as a function of the radial position on the rotor. ✔ (d) Calculate and plot the differential power, dP, as a function of the radial position on the rotor. (e) Calculate total power generated by the wind turbine, (dP)