Transcript Design of a small horizontal axis wind turbine, HAWT

WATERPOWER LABORATORY
Design of a small horizontal
axis wind turbine, HAWT
WATERPOWER LABORATORY
Design parameters
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Power Output, P:
Wind velocity, c:
Tip Speed Ratio, TSR:
Assumed efficiency, h:
Number of blades, z:
Wing profile:
Angle of attack, a:
Lift coefficient, CL:
Drag coefficient, CD:
300 W
8 m/s
5
30 %
2
NACA 23015
8o
0,8
0,01
Radius of the turbine
D
WATERPOWER LABORATORY
1
P       c 3 h
2

R
Where:
A
c
h
P

R
P2
    c 3 h
=
=
=
=
=
=
Area
Wind velocity
Efficiency
Power
Density
Radius


[m2]
[m/s]
[-]
[W]
[kg/m3]
[m]

2
   R 2  c 3 h
300 2
1,2    83  0,3
 1,02 m
Speed of the turbine
WATERPOWER LABORATORY
c  TSR  60
n

2   R
n  2 

60
Where:
c
n

R
=
=
=
=

8  5  60
 374 rpm
2   1,02
374  2  
60
Wind velocity
Speed
Angular velocity
Radius
[m/s]
[rpm]
[rad/s]
[m]
 39,2 rad
s

Power through a section of the
turbine blade
WATERPOWER LABORATORY
1
P       c 3 h
2

P 


2
A  r  r   r 2
z

r  r   r    c
2 z

2
2
3
h
dA

Torque force, dFT from a section
of the turbine blade
WATERPOWER LABORATORY
r 

P  FT   r    
2


P
FT 
r 

 r   
2

dA
dFT
Wing profile
WATERPOWER LABORATORY
Chord Length, Lchord
1
FL  C L     V 2  A
2
FL
1
FD  C D     V 2  A
2
WATERPOWER LABORATORY
FD
a
Where:
A
=
a
=
CD =
CL =
FD =
FL =
LChord =

=
V
=
Area
Angle of attack
Drag Coefficient
Lift Coefficient
Drag Force
Lift Force
Chord Length
Density
Relative velocity
v
[m2]
[degrees]
[-]
[-]
[N]
[N]
[m]
[kg/m3]
[m/s]
LChord
4
Peripheral velocity
Wind velocity = c

WATERPOWER LABORATORY
u R
Relative velocity = V
V
u
c
u
WATERPOWER LABORATORY
a
q
u = ·r
v
c
FL
FD
F
1
FL  C L     V 2  A
2
a
WATERPOWER LABORATORY
1
FD  C D     V 2  A
2
q
u = ·r
F
v
c
u
F
v
c
FL
FD
F
FL (Torque )  FL  sin F 
WATERPOWER LABORATORY
FD (Torque )  FD  cosF 
a
q
F
v
c
u
F
u = ·r
FL(Torque)
FD
v
c
FD(Torque)
FL
F
a
q
u = ·r
WATERPOWER LABORATORY
F
v
c
FT
FD
FT  FL  sinF - FD  cosF
FL
WATERPOWER LABORATORY
FT 

2
 LChord  r V  C L  sinF - C D  cos F 
2
v
FT
Chord Length, Lchord
FT 

2
Lchord
 LChord  r V  CL  sinF - CD  cosF 
2
WATERPOWER LABORATORY

LChord
2  FT

  r V 2  CL  sinF - CD  cosF 
u
T anF  
c
u


c
  r  dr 2

F


c
F  t an 
   r  dr
2

1






c
v
WATERPOWER LABORATORY
Output data
r
dA
dP
dT
dFT
u
v
F
LChord
[m]
[m ]
[W]
[Nm]
[N]
[m/s]
[m/s]
[degrees]
[m]
0,099
0,196
0,293
0,389
0,486
0,583
0,679
0,776
0,873
0,970
0,03422
0,05953
0,08891
0,11829
0,14766
0,17704
0,20642
0,2358
0,26518
0,29456
3
5
8
11
14
16
19
22
24
27
0,080
0,140
0,209
0,277
0,346
0,415
0,484
0,553
0,622
0,691
0,81
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
3,9
7,7
11,5
15,3
19,1
22,9
26,7
30,5
34,3
38,1
8,9
11,1
14,0
17,3
20,7
24,3
27,9
31,5
35,2
38,9
64,0
46,1
34,8
27,6
22,7
19,3
16,7
14,7
13,1
11,9
0,246
0,175
0,139
0,114
0,096
0,082
0,072
0,064
0,058
0,052
2