Environmental Engineering Reference
In-Depth Information
For problems 12-18, speciications for a wind turbine are induction generator (rpm 65),
ixed-pitch, rated power 300 kW, hub height 50 m, rated wind speed 18 m/s, tower
head weight 3,091 kg; rotor: two blades, mass of one blade 500 kg, hub radius 1.5
m, rotor radius 12 m.
12. How fast is the tip of the blade moving?
13. How fast is the blade root (at hub radius) moving?
14. Put the mass at the midpoint and calculate the kinetic energy for one blade. Assume the
mass of the blade is distributed evenly over ten sections. What is the kinetic energy for
one blade?
15. At rated wind speed, calculate the torque since you know power and rpm (remember
angular velocity, rad/s).
16. At 10 m/s, what is the thrust (force) on the rotor trying to tip the unit over? Calculate for
that wind speed over whole swept area.
17. If the unit produced 800,000 kWh/year, calculate output per rotor swept area.
18. Calculate the annual output per weight on top of tower, kWh/kg.
For problems 19-25, speciications for a wind turbine are induction generator (rpm 21),
variable-pitch, rated power 1,000 kW, hub height 60 m, rated wind speed 13 m/s,
tower head weight 20,000 kg; rotor: three blades, mass of one blade 3,000 kg, hub
radius 1.5 m, rotor radius 30 m.
19. How fast is the tip of the blade moving?
20. How fast is the blade root (at hub radius) moving?
21. Place the mass at the midpoint of the blade and calculate the kinetic energy for one blade.
Assume the mass of the blade is distributed evenly over ten sections. Now what is the
kinetic energy for one blade?
22. Calculate the torque at the rated wind speed. You know the power and rpm (remember
angular velocity, rad/s).
23. At 15 m/s, what is the thrust (force) on the rotor trying to tip the unit over? Calculate for
that wind speed over the whole swept area.
24. If the unit produces 2,800,000 kWh/year, calculate the specific output, annual kWh/rotor
area.
25. Calculate the annual output per weight on top of tower, kWh/kg.
26. For a 12 m blade, center of mass at 5 m, weight 500 kg, calculate the angular momen-
tum if the rotor is operating at 60 rpm.
27. For the blade in problem 26, the angular momentum is around 8 * 10 4 kg m 2 is Calculate
the torque on the blade at that point if the angular moment of the rotor is stopped in 5 s.
Use Equation 6.24. Then estimate the force trying to bend the blade.
28. Why are the blades for large wind turbines made from fiberglass-reinforced plastics?
29. Why are yaw rates limited on large wind turbines or yaw dampers installed on small
wind turbines?
30. How does furling work on small wind turbines?
31. For loss of load on small wind turbines connected to the utility grid, how long can it take
for overspeed shutdown?
32. For megawatt-size wind turbines, what is the most common configuration?
33. Go to the Proven Energy website for blade design. Make a paper model of the blade to see
the principle for passive control.
34. List two methods of nondestructive testing and briefly describe them.
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