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Aerodynamics

1. The document presents equations for calculating wind turbine performance parameters such as induction factor, flow velocity, rotor radius, thrust force, and torque. 2. Given a wind speed of 4m/s after wake expansion, the axial induction factor is calculated to be 0.25. With optimal induction, the flow velocity through the rotor is calculated to be 5.333 m/s. 3. For a turbine to produce 1.5MW at the given inlet speed, the required rotor radius is calculated to be 50.688m.

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424 views4 pages

Aerodynamics

1. The document presents equations for calculating wind turbine performance parameters such as induction factor, flow velocity, rotor radius, thrust force, and torque. 2. Given a wind speed of 4m/s after wake expansion, the axial induction factor is calculated to be 0.25. With optimal induction, the flow velocity through the rotor is calculated to be 5.333 m/s. 3. For a turbine to produce 1.5MW at the given inlet speed, the required rotor radius is calculated to be 50.688m.

Uploaded by

ghan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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m kg 10 2

V0 8 1.225 = 1.047
s m 3
60

13 a
a'
4 a1
r
x
V0
16 a 3 24 a 2 + a 9 3 x 2 1 + x 2 0

The flow angle is given as


( 1 a) V 0 a' r
tan () tan ()
((1 + a')) r a V0

The tangential force Pt is given as

Pt L sin () D cos ()

Torque is given by

Pt r

1. The wind speed after the wake expansion is measured to be 4m/s .


What is the axial induction factor (a)?

m
u1 4
s
solve , a 1
u1 (1 2 a) V0 = 0.25
4

2. What would the flow velocity through the rotor be if it was run with optimal induction? Give
the result in m/s.

1
a
3


2
256 m 2 m
V (1 a) V0 2 = 5.333
2
9s s
3. What rotor radius (and thus approximate blade length) should the turbine have to produce
1.5MW at the given inflow speed? Give the result in m.

16
P 1.5 10 6 W Cp = 0.593
27


2P
r = 50.688 m
Cp V0 3

4. Assume now a rotor diameter of 2r=116m. What is the thrust force on the rotor in kN ?

m
r4 116 = 58 m
2
1
a
3

CT 4 a (1 a) = 0.889
1
T r4 2 V0 2 CT = 368.247 kN
2

5. What is the main limitation of 1D momentum theory

Ans. Its assumes no energy is lost

1. Which values of a and a' correspond to optimum operation at r=40m ? (choose the right
option) Hin t:calculate the value for x,a,a' . keep in mind that the value of a should be within
the interval of 0<a<1
r6 40 m
rad
r6
s 1
x = 5.236 s
V0 s

x 5.236

solve , a6 0.3324505183493627492 0.332


3
16 a6 24 a6 2
+ a6 9 3 x 1 + x
2 2
2.8874432018671743787 = 2.887

1.7198937202165371279 1.72

a6 0.332
1 3 a6
a' = 0.012
4 a6 1

correct ANs a=0.332 and a'=8.03x10^-3

2. Compute the flow angle at r=40m . State the result in degrees

180
8.03 10 3 1.047 40

tan () = 7.255
0.332 8

try 82.15 or 7.255

3. I did not work it out


4. Compute the drag in kN/m too. What is the tangential force component Pt per unit length in
N/m? (recommended to write answer in 0.1 approximation)
Nm
8.7 10 3
m N
= 217.5
40 m m

5. Ans is 8.7x10^3 Nm/m

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