Short Quiz Wind Turbine Aeroelasticity
A short quiz to get an idea of what will be explained during a training on wind turbine aeroelasticity.
- The work done by the aerodynamic forces on a wind turbine blade is calculated for a full cycle of the first edgewise mode. If this work done has a positive value, what does this say about the damping of the first edgewise mode?
- A: Nothing, the work done during the mode shape cycle is not related to the damping of the mode
- B: The mode is positively damped by the aerodynamic forces
- C: The mode is negatively damped by the aerodynamic forces
- You have a blade design with negative aerodynamic damping of the first edgewise mode. Changing which parameter would be most effective to resolve this?
- A: Edgewise stiffness
- B: Flapwise stiffness
- C: Generator torque-speed relation
- D: Structural pitch angle (direction of stiffest and most flexible direction)
- A mode on a turbine consists of three blades flapping in the same direction: so all against the wind and then with the wind etc. If this frequency of flapping is 1.0 Hz in the rotating frame and the blades rotate at 12 RPM (0.2 Hz), which frequency or frequencies will you be able to measure in the tower?
- A. 1.0 Hz
- B. 0.8 Hz, 1.0 Hz and 1.2 Hz
- C. 0.8 Hz and 1.2 Hz.
- D. You will not be able to measure this vibration in the tower.
- If the flapwise mode of the blade is close to 1.0 Hz (including centrifugal stiffening) and the turbine is rotating at 12 RPM, which frequency or frequencies will you be able to measure in the tower?
- A. 1.0 Hz
- B. 0.8 Hz, 1.0 Hz and 1.2 Hz
- C. 0.8 Hz and 1.2 Hz.
- D. You will not be able to measure this vibration in the tower.
- You see a vibration on the blades at 0.8 Hz. The rotations speed of the turbine is, for that situation around 9 rpm. The closest natural frequency of the blade is the edgewise frequency at 0.73 Hz. Is this vibration due to resonance or an instability?
- A. The vibration is due to resonance occurring.
- B. The vibration is due to an instability occurring.
- If you want to to an aeroelastic load simulation for one case and you want to do this with some more conservative settings from an aeroelastic stability point of view, which of the following options would be options for you?
- A. Reduce the structural damping.
- B. Set a small pitch angle error for all three blades.
- C. Turn off the dynamic stall model.
- D. Increase the tower diameter for the tower shadow model, without changing its stiffness
- E. Use a smaller time step.
- You see a vibration resembling the graph below. What is going on in your turbine?
- A. No problem, just some gust passing by.
- B. An eigenmode without any damping is excited by an external force that is close to this frequency.
- C. An eigenmode has negative damping, but due to the nonlinearities in the lift curve, it does not increase indefinitely.
- D. An eigenmode with a lot of damping is excited several times by some external discrete force.
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Answer Question 1
A: Nothing, the work done during the mode shape cycle is not related to the damping of the mode
B: The mode is positively damped by the aerodynamic forces
-> C: The mode is negatively damped by the aerodynamic forces
The work done being positive means that energy is added to the motion, in other words the mode is negatively damped by the aerodynamic forces. In case the structural damping removes more energy than is added by these aerodynamic forces, the mode would still show some positive damping overall.
Answer Question 2
A: Edgewise stiffness
B: Flapwise stiffness
C: Generator torque-speed relation
-> D: Structural pitch angle
This angle defines the stiffest and most flexible directions. It varies along the blade. In plane motion has little to negative damping, out-of-plane motion usually has a lot of damping, so ensuring that there is out-of-plane motion in the edgewise mode can increase the damping of this mode.
Answer Question 3
-> A. 1.0 Hz
B. 0.8 Hz, 1.0 Hz and 1.2 Hz
C. 0.8 Hz and 1.2 Hz.
D. You will not be able to measure this vibration in the tower.
This mode shape is the same frequency in the rotating as in the non-rotating frame as the reaction force will be out-of-plane.
Answer Question 4
- A. 1.0 Hz
- B. 0.8 Hz, 1.0 Hz and 1.2 Hz
- C. 0.8 Hz and 1.2 Hz.
- D. You will not be able to measure this vibration in the tower.
The first blade flapwise mode on a three-bladed turbine will result in three different full turbine modes, one is a symmetric mode and remains at (almost) the same frequency as the blade frequency and two are whirling modes. These whirling modes result in vibrations in the tower at one times the rpm lower (backward whirling mode) or one times the rpm higher (forward whirling mode). You can view one example of a simplified whirling mode on the opening page of our website, with the resulting force acting on the tower top going in one full circle during 1 mode vibration. If you add the rotation of the rotor to this load, you will see that it will be measured in the tower at the blade frequency minus the rpm in the example on our main page.
Answer Question 5
- A. The vibration is due to resonance occurring.
- B. The vibration is due to an instability occurring.
A resonance will occur at an excitation frequency, an instability will occur at a natural frequency. On a wind turbine, the excitations are at the so-called nP values, 1P, 2P, 3P,… due to rotational sampling of turbulence and tower shadow. The given frequency is equal to 4P. The edgewise natural blade frequency is close, and edgewise modes always have little damping, therefore a resonance results in more vibrations than it would do for well damped flapwise modes. An edgewise mode close to 4P will result in a backward whirling mode close to 3P in the stand still frame and the excitation of a three bladed turbine at 3P is significant. Therefore it is very likely you will see a vibration in the tower at 3P, while it is at 4P in the blades.
Answer Question 6
- A. Reduce the structural damping.
- B. Set a small pitch angle error for all three blades.
- C. Turn off the dynamic stall model.
- D. Increase the tower diameter for the tower shadow model, without changing its stiffness
- E. Use a smaller time step.
The structural damping adds damping to the modes in the simulation, by reducing these, you perform a more conservative simulation. If the response is still stable, you know you have some safety margin, which can compensate for the fact that the calculations are never fully accurate. The dynamic stall model also adds damping to most of the vibrations modes, therefore by turning it off, you do a more conservative simulation. For some simulation tools, the time step effects the numerical damping that is present in the calculation, in those cases using a smaller time step will also provide a more conservative calculation.
Changing the pitch angle will change the flow condition on the turbine and that will change the damping of the modes, but it is not a more conservative setting. Changing the tower diameter for the tower shadow can increase the excitation on the turbine, but will not change the damping of the modes on the turbine.
Answer Question 7
A. No problem, just some gust passing by.
-> B. An eigenmode without any damping is excited by an external force that is close to this frequency.
C. An eigenmode has negative damping, but due to the nonlinearities in the lift curve, it does not increase indefinitely.
D. An eigenmode with a lot of damping is excited several times by some external discrete force.
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This is a clear illustration of so-called ‘beats’.
We hope you have found this quiz useful and perhaps entertaining. If you want to learn more about wind turbine aeroelasticity, please check out our page on training.