105-2019201 Practice 2

Wind turbines 101

Question 1

One of the simplest models for understanding wind turbines is the 1-D momentum model. In 1-D momentum model, the wind turbine acts as a braking disk, that reduces the speed of incoming air from $V_{0}$ to $V_{1}$.

The kinetic energy carried by the incoming wind is

$E_{i}={\frac {1}{2}}mv_{0}^{2}$

where the mass of incoming air is

$m=\rho V_{i}$

If the wind turbine has area A, the mass of air it receives per unit time is

$\Delta V=Av_{0}\Delta t$

(a)

Calculate the incoming power (incoming energy per time)

$P_{i}={\frac {1}{2}}\rho {\frac {\Delta V}{\Delta t}}v_{0}^{2}$

solutions