HW#7
Due, Friday,
February 22, 2002
We have learned that the tangential force pulling the turbine blade in its direction of rotation is:
FT = Lsinf - Dcosf
The angle f is expressed as:
f = a + g
where a =
angle of attack
g = blade set angle.
For the airfoil
section discussed on page 286 of the text, the lift and drag coefficients are:
|
a (degrees) |
CL |
CD |
|
-4 |
0.11 |
0.009 |
|
0 |
0.33 |
0.015 |
|
4 |
0.60 |
0.030 |
|
8 |
0.92 |
0.059 |
|
12 |
1.13 |
0.086 |
|
16 |
1.43 |
0.143 |
The equation above
is rewritten in terms of the lift and drag coefficients as follows:
FT = ½rVR2A(CLsinf - CDcosf)
where r = air density
VR = relative velocity (VR2
= U12 + VT2)
U1 = velocity magnitude
of air approaching the turbine blade
VT = tangential velocity
magnitude of turbine blade
A
= planform area of the section of turbine blade being considered = cDr
c
= chord of turbine blade section
Dr =
length of turbine blade section
A. For each of the following ratios of VT/U1,
find the maximum value of the tangential force coefficient (CLsinf - CDcosf), and find the angles a and g
corresponding to the maximum tangential force coefficient:
VT/U1 = 0.5, 1.5, 3.0, 5.0, 8.0, 10.0
B. Plot the maximum values of the tangential
force coefficient and the corresponding a
and g angles versus VT/U1.
C. Discuss the turbine blades (a and g)
you would use for each of the following cases:
1.
A multi-bladed
wind turbine (pumping turbine) at its tip and near its hub (axis).
2.
A two-bladed
horizontal axis wind turbine at its tip and near its hub.
Note: For parts A
and B, you should use a spread sheet for your analysis and plotting.