Problem 1 (20 pts) A 0.5 meter long blade element on a four bladed wind turbine,

Question

Problem 1 (20 pts) A 0.5 meter long blade element on a four bladed wind turbine, located 23.5 m from the axis of rotation has a pitch angle of 2.27 degrees and a chord length of 1.7 meters. The rotor of this wind turbine is spinning at 25 rpm in a 13 m/s wind. Using Method I analyze this section of the blade assuming wake rotation and no drag determine a) b) c) d) the axial induction factor the angular induction factor, the torque on the element, and the power produced by the element Take the density of the air to be 1.225 kg/m3 and the lift coefficient data on the airfoil is shown below Lift attack Coefficient Angle of (degrees) 0.064 0.043 0.151 0.258 0.366 0.473 0.58 0.685 0.786 0.884 0.975 1.056 0 1 4 7 7.88

Explanation / Answer

Power = 0.5 x Swept Area x Air Density x Velocity3*K* C....K=0.0001333, C=0.25

Swept area =ND2/4=(1.7-0.5)^2*3.14/4 =1.1304 m2.

b.) Axial and tangential induction factors

Axial factor:- a=6Cn/((4Sin^2Q)+(6Cn))

Cn= 1.7Cos(Q)------Drag Force =0

Degree = 2.27

Ct=1.7 Sin 2.27

Ct= 0.051

Axial Induction Factor= 0.9979

Tangential induction factors:

b= 6Ct/((4SinQX CosQ)-(6Ct))

   =-2.57

Angular Factor= 1/(4 sinQCosQ/Sigma Ct)-1

Torque=0.5*DensityXNo.of Blade x velocity^2x(1-a)^2XCn*C/Sin^2 Q.

           

             =5.25

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