2. A tidal turbine has a blade length of 2 m, compute the blade power when the t

Question

2. A tidal turbine has a blade length of 2 m, compute the blade power when the tidal current is 12km/hr. Assume the power coefficient of the tidal turbine is 0.5 and water density of 1000 Kg/m^3 3. The air density at an installation site for a wind turbine has been calculated as 1.18 kg/m^3.The average wind speed is 13m/s. a) Compute the length of the blades to capture 1500kW of wind energy. b) For the TSR=5 of the turbine. Determine the rotational speed of the turbine in revolution per minute (rpm). c) If the generator is a synchronous machine with the rotor speed 011800 rpm, determine the gearbox turns ratio.

Explanation / Answer

1) Given the length of the blade L, we compute the area of the turbine:

S =pi*L^2

The power of turbine is simply (Betz Law - C is the power coefficient). 12 km/h =3.333... m/s

(http://en.wikipedia.org/wiki/Betz%27s_law#Betz.27_law_and_coefficient_of_performance)

P =(C/2)*rho*S*V^3= 0.5/2 *1000* (pi*4)*3.333^3 =116355.3 W

2)

The power of the incoming wind is simply the turbine power without the power coefficient.

P =(1/2)*rho*S*V^3 so that

S =2P/(rho*V^3) =2*1500*10^3/1.18/13^3 =1157.2 m^2

The blade length is

L =sqrt(S/pi) = 19.19 m

b)

TSR = Tip of blade speed/wind speed =V(blade)/V(wind)

V(blade) =5*13 =65 m/s

The angular speed is

w =V(blade)/L = 65/19.19 =3.387 rad/sec

The frequency F (rps or rpm) is w=2*pi*F, that is

F = w/(2*pi) =3.387/(2*pi) =0.539 rps (1/s) =0.539*60 rpm= 32.34 rpm (1/min)

the gearbox turn ratio n is

w1/w2 =F1/F2 =n2/n1 =n= 32.34/1800 =0.01797   or equivalent 1/n =55.657

(that is the output gear to the generator is smaller that the input gear from the wind turbine.)

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