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