A high-speed two-blade wind turbine operates with a tip speed ratio of 14.
It produces 1.0 MWe in a 12 m/s wind. What is the rotor diameter?

Question

Quizplus · Accepted Answer

The Answer is The power is

P = \left( 0.602 \mathrm {~kg} / \mathrm { m } ^ { 3 } ight) imes A \eta v ^ { 3 }

where the area is given in terms of the rotor diameter as

A = \pi d ^ { 2 } / 4

So combining and solving for

d

gives

d = \left[ \frac { 4 P } { \left( 0.602 \mathrm {~kg} / \mathrm { m } ^ { 3 } ight) \pi \eta v ^ { 3 } } ight] ^ { 1 / 2 }

From Figure

10.12

the efficiency for a three blade turbine with a tip speed ratio of 14 is

41 \%

. Substituting appropriate values gives

d = \left[ \frac { 4 imes 10 ^ { 6 } \mathrm {~W} } { \left( 0.602 \mathrm {~kg} / \mathrm { m } ^ { 3 } ight) imes ( 3.14 ) imes ( 0.41 ) imes ( 12 \mathrm {~m} / \mathrm { s } ) ^ { 3 } } ight] ^ { 1 / 2 } = 23.3 \mathrm {~m}

A High-Speed Two-Blade Wind Turbine Operates with a Tip Speed