Question

Consider a wind turbine comprised of two blades, with a radius of 63 ft., which delivers maximum power when the wind speed is above 16 knots (18.4 mph). The wind turbine is designed to produce 135 hp with an efficiency of 74%. The rotor is designed to operate at a constant speed of 45 rpm in winds over 5 knots (5.8 mph) by controlling system load and adjusting blade angles.

Estimate the blade speed and power coefficient for the maximum power condition.

Answer 1

W given, in a wind turbine, Blade Radius = 63 feet = 63 Xo. 3048 meters = 19.2024 meter (I meter = 3. 28084 foot ). Wind Speed (at maximum power) = 16 knots = 18.4! per hour Con Verting it to meters per second : (1 miles per hour = 0.44704 meters per second) 18.4 mph = 8.225536 meters per second. Output power = 135 horse power ~ IkW Rotor speed = 45 rpm. now, Blade speed Blade tip speed = (rpm) notational speed xa XD hade speed Blade tip Speed 60 60 Blade speed = 45 xì x(2x19.2024) = 90.49 m/sec . Blade speed = 90.49 m/sec. power coefficient cp = Pout = Pout . Pin I SAV3 where A is the Area = r = AX (19.2024) = 1158.406 Vis the wind speed (at maximum power) = 8.225536 m/sec and I is the Air density & 1. 23 kg/m² now, Pin = txgf* *x (19.2024)*x (8.225536) 3. 100x10° x 1.23 x (3:14) x (19. 2024) & (8.225536) Cp - Pout - 100kW Pin Pin Cp 0.25222

the blade speed is calculated using the rotational speed which is given as 45rpm. Now, we can calculate the power coefficient using the wind speed and the area of the turbine which is shown in the above picture