Question

A wind turbine is located in an area with air density of approximately 1.2 kg/m³ and the wind is blowing at 10 m/s.

1. What is the wind power density?
2. Suppose the coefficient of performance is related to the TSR by the following equation:

C_p = - 0.1 TSR² + 0.4 TSR - 0.05

Find the maximum wind power density the turbines can capture.

Answer 1

Given datas :

Air density, = 1.2 kg/m³

wind speed, v = 10 m/s

So, wind power density,

or, (ANS)

Now we know,

C_p = (Power captured by the wind turbine) /  (Wind power density)

So,

(C_p)_max = (Maximum power captured by the wind turbine) /  (Wind power density)

Let, Tip seed ratio, TSR = x

Given:

or,

For (C_p)_{max ,}

or, x = 2

Hence (C_p)_max

As (C_p)_max = (Maximum power captured by the wind turbine) /  (Wind power density)

or, Maximum power captured by the wind turbine = 0.35 * Wind power density = 0.35*600 = 210 watts/m²(ANS)