Analysis of a Wind Turbine

Figure 3.32: Analysis of a Wind Turbine

 

A wind turbine (Fig.3.32) extracts energy from an air stream while a propeller adds energy to the air stream. The analysis follows the same lines. The wind turbines are smaller in size compared to the propellers. For the wind turbine too we have the result that

$$V_2~ =~{{V_1~+~V_4} \over 2 }$$

$$=~F~V_1~=~\dot{m}~(V_4~-~V_1)~V_1$$ (3.110)

Now the efficiency is given by the Kinetic energy extracted divided by the kinetic energy in the free stream. Thus,

$$\eta_{Th}~= {{{1 \over 2} \rho A~V_2 (V_1^2~-~V_4^2)}\over {{1 \over 2} {(\rho~A~V_1)~V_1^2}}}~=~{{(V_1~+~V_4)~(V_1^2~-~V_4^2)} \over {2~V_1^3}}$$ (3.111)

The above expression has a maximum when V₄/V₁ = 1/3. The maximum theoretical efficiency is 59.3%.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney