Question

A newly-designed vertical axis wind turbine with a diameter of D=1.25 m spins the air around with a tangential velocity (in polar coordinate system) of Vo=(1/π)Dω at its tip, where ω is the angular velocity of the turbine.

a) Calculate the circulation for this turbine when it rotates at N=65 rpm in a field that air pressure and temperature are 101250 Pa and 7 oC, respectively.

b) If the turbine height is H=8 m, find the lift force produced by the turbine where the wind velocity is 12 m/s.

Answer 1

Ans:

1. The circulation is given by:
   U_tan = (2π)(n/60)(D/π) = nD/30 m/s

The circulation around a cylinder is the integral of the tangential velocity about its perimeter, So

Γ =

          =

          = nπD²/30

Where D = diameter (m)

          n = Rotational speed (rpm)

Γ = 10.63 q.e.d

1. Lift force per unit length is given by:

L = ρUΓ

          = (1.225)(12)(10.63)

          = 156.26 N/m

The total lift force is thus 156.26*8 = 1250.08 N