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Fluid machines year project 2013-14 presentation
Desing of an horizontal axis wind turbine
Luca Bazzucchi
Filippo Campolmi
Florian Zatti
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Desing of an horizontal axis wind turbine
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Operating conditions:
•V0 = 12 m/s (uniform);
• T0 = 15 °C;
• z = 1300 m; P = 0.87 bar ρ = 1.05 kg/m^3
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Design mechanical power at the turbine shaft
Target power = 80 kW we decided to use a three blades rotor
λ=7;
cp=0.49;
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For a=1/3 we have the maximum value of
the trend
a coefficient trend
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First attempt
cp =
Section: S = 179.9662 m^2
Diameter: D = 15.1374 m
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v1=8;
r_est = 7.5687 m;
r_int = 0.2* r_est = 1.5137 m;
h ( =“blade height” ) = 6.0549 m;
ω ( =“angular speed” ) = 11.0984 rad/s
we divide the blade into 20 parts:
u = ω*r
W_m=v1; W_t=-u W1= sqrt(W_m^2 + W_t^2)
β = atan ( W_t / W_m)
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u w β
16.8000
20.3368
23.8737
27.4105
30.9474
34.4842
38.0211
41.5579
45.0947
48.6316
52.1684
55.7053
59.2421
62.7789
66.3158
69.8526
73.3895
76.9263
80.4632
84.0000
18.6075
21.8538
25.1784
28.5541
31.9647
35.4000
38.8536
42.3209
45.7989
49.2852
52.7783
56.2768
59.7798
63.2866
66.7966
70.3092
73.8242
77.3412
80.8599
84.3801
-64.5367
-68.5266
-71.4742
-73.7297
-75.5061
-76.9390
-78.1177
-79.1037
-79.9401
-80.6584
-81.2816
-81.8275
-82.3094
-82.7379
-83.1214
-83.4666
-83.7789
-84.0628
-84.3221
-84.5597
Velocity triangles
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Velocity triangles
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Velocity triangles
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Velocity triangles
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Selection of the profiles (NREL)
• Root (40%) S808
• Primary (75%) S805A
• Tip (95%) S806A
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ROOT
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MID
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TIP
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Example of convergence analisys for the
calculation of the chord at the root section
At the beginnig, we suppose a Reynold number of 1.5e6.
We want the angle of attack that maximize the ratio between cl
and cd
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Angle of attack Cl Cd
2 0.625 0.0099
3 0.73 0.0104
4 0.835 0.011
5 0.938 0.0116
6 1.041 0.0124
7 1.142 0.0133
8 1.24 0.0144
9 1.336 0.0156
10 1.427 0.0172
11 1.51 0.0189
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Chord
new_Re = = 1.1525e6
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Linear interpolation in order to get
the values of cl and cd as function of
Re
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New values of cl and cd:
cl = 1.236
chord Re = 1.1560e6 convergence!
cd = 0.0152
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Linear interplation in order to get the values of
cl and cd along the blade height
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Chord
0.9131
0.7984
0.7118
0.6450
0.5925
0.5505
0.5165
0.4886
0.4657
0.4468
0.4312
0.4183
0.4079
0.3996
0.3932
0.3860
0.3804
0.3762
0.3732
0.3715
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Angle of attack
Approximation: we suppose that the angles of attack constant are constant for each profile
Root Primary Tip
Angle of attack 8 6 5
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γ= β- α Stagger angle
-72.5367
-76.5266
-79.4742
-81.7297
-83.5061
-84.9390
-84.1177
-85.1037
-85.9401
-86.6584
-87.2816
-87.8275
-88.3094
-88.7379
-89.1214
-88.4666
-88.7789
-89.0628
-89.3221
-89.5597
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Power
91989 kW
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Since the power calculated is bigger than the design
mechanical power, we reduce the diameter
Old
D= 15.1374 m
New
D = 14.2730 m
The Re numbers calculated in the previous
case at root, primary and tip section are
very simlilar to the new ones
We will use the same values of cl and cd
previously calculated
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New values
r_est = 7.1365 m;
r_int = 1.4273 m;
h = 5.7092 m;
ω = 11.7705 rad/s
β, u , w don’t change!
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New chord
0.8609
0.7528
0.6712
0.6082
0.5587
0.5191
0.4870
0.4607
0.4391
0.4213
0.4066
0.3945
0.3846
0.3768
0.3707
0.3640
0.3587
0.3547
0.3519
0.3502
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New power
81783 kW
cp
0.5634
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Off desing conditions: V0=10 m/s
a = f ( r, cl, cd, β, V1) but cl, cd, β, V1 depend on a
iterations
is the mean value
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Example of iteration at the root section
We start from
Using the new value of a, we can restart the iteration
The angle of attack changes!
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Linear interplation in order to get the
values of cl and cd with respect to the
angle of attack
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Power
V0=10 m/s
4.4247e+04 kW
Cp = 0.5268
V0=14 m/s
1.2049e+05;
Cp = 0.5227
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Velocity triangles V0 = 10 m/s
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Velocity triangles V0 = 10 m/s
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Velocity triangles V0 = 10 m/s
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Velocity triangles V0 = 14 m/s
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Velocity triangles V0 = 14 m/s
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Velocity triangles V0 = 14 m/s
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Mechanical Vibrations year project
THE END
Thank you for the attention