Environmental Engineering Reference
In-Depth Information
43.
J. Paquette, J. van Dam, and S. Hughes. 2007. Structural testing of 9 m carbon fiber wind turbine
research blades. Paper presented at Wind Energy Symposium. www.nrel.gov/wind/pdfs/40985.pdf.
44.
D. J. Malcolm and A. C. Hansen. 2006.
WindPACT turbine rotor design study June 2000-June 2002
.
Subcontract Report NREL/SR-500-32495. www.nrel.gov/wind/pdfs/32495.pdf.
45.
J. Jonkman. FAST, an aeroelastic design code for horizontal axis wind turbines.
http://wind.nrel.gov/
46.
J. Schmid and W. Palz. 1986.
European wind energy technology, state of the art of wind energy con-
verters in the European community
. Solar Energy R&D in the European Community, Series G Wind
Energy, Vol. 3. Dordrecht Boston: D. Reidel Publishing.
47.
National Wind Technology Center, NREL. Lancaster Tokyo: Furling Workshop presentations.
http://
48.
J. M. Jonkman and A. C. Hansen. 2004.
Development and validation of an aeroelastic model of a small
furling wind turbine
. NREL/CP-500-30589. www.nrel.gov/docs/fy05osti/39589.pdf.
49.
M. Bikdash. 2000. Modeling and control of a Bergey-type furling wind turbine. NREL and Sandia
50.
B. Vick et al. 2000. Development and testing of a 2-kilowatt wind turbine for water pumping. AIAA-
2000-0071. In
19th ASME Wind Energy Symposium
, p. 328.
51.
B. Vick and R. N. Clark. 2000. Testing of a 2-kilowatt wind-electric system for water pumping.
In
Proceedings
,
Windpower 2000
. CD.
PROBLEMS
1. A blade is 12 m long, weight 500 kg, and the center of mass is at 5 m. What is the torque
if the force is 320 Nm?
2. Find the power loss for three struts on a HAWT. Struts are 4 m long, 2.5 cm in diameter. Rotor
speed is 180 revolutions per minute. Use numerical approximation by dividing strut into 1 m
sections and calculate at midpoint of section. Then add the values for each section.
C
D
1.
3. Calculate the power loss for the struts on a VAWT. Center tube, torque tube, diameter 0.5 m.
Struts are at the top and bottom, 2 m long from torque tube to blades, diameter 5 cm, rotor
speed is 80 rpm.
C
D
1. Calculate numerically (see problem 2) or use calculus.
4. For those who know calculus, find the value of
u
(speed of drag device) that produces the
maximum
C
P
for a drag device. Use Equation 6.10, where
v
0
is the wind speed at infinity.
For those who do not know calculus, find the value of
u
that produces the maximum
C
P
for a
drag device by plotting the curve (Equation 6.12) for different values of
u
(between 0 and 1).
5. Aerodynamic efficiency can be maintained for different solidities of the rotor. If solidity
increases, will you increase or decrease the tip speed ratio?
6. Explain the difference in performance of a wind turbine if it
a. Operates at a constant tip speed ratio.
b. Operates at constant rpm.
7. What is the maximum theoretical efficiency for a wind turbine? What general principles
were used to calculate this number?
8. If the solidity of the rotor is very small, for example, a one-bladed rotor, what is the value
of the rpm for maximum
C
P
compared to the same size rotor with higher solidity?
9. For those who know calculus, calculate the value of axial interference factor for which
C
P
is a maximum for a lift device. Then show that this gives a maximum
C
P
59%.
For those who do not know calculus, find the value of
]
that produces the maximum
C
P
by plotting the curve (Equation 6.20) for different values of
]
.
10. A rotor reaches maximum
C
P
at a tip speed ratio of 7. Calculate rotor rpm for four
different wind turbines (diameters of 5, 10, 50, and 100 m) at wind speeds of 10, 20, and
30 m/s.
11. A wind turbine that operates at constant rpm will reach maximum efficiency at only one
wind speed. What wind speed should be chosen?
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