Regarding a Structural Model For a Wind Turbine Tower

Hi Everyone,
I am a Masters student doing my thesis on wind turbine structural analysis, specifically on wind turbine towers. In order to do that, I built a model in a FEM tool. I obtained geometry from a wind farm operator for a 6 MW wind turbine tower. I assumed the foundation to be fixed, the tower as a variable shape and thickness cylinder from top to bottom, and the blades as uniform thicknesses, as I didn’t have any information about them.
I started with a modal analysis, and I got the first side-to-side mode about 0.146 HZ while the one at the site is about 0.145 hZ, makes me think my model is somehow reasonable.
I calculated the wind loads on the tower and for the blades I used the thrust force equation i.e. the actuator disk. F= 1/2Aswept area Ct*V^2. This gives me a value of 818 kN.
The problem arises when i apply this thrust force as a point load on my wind turbine tower, as I get a deflection of about 2.5 meters, which is definietely not realisitic. I couldnt find a solution to this problem. DOes anyone here provide a insight on how to solve this issue.

Dear @KanwarOsama.Zulfiqar,

What wind speed (V) and thrust coefficient (Ct) are you using? How tall is your tower? Are you modeling a wind turbine that is similar to one of the reference wind turbines, such as the NREL 5-MW baseline wind turbine?

Note that your equation for thrust is missing the air density.

Best regards,

Yes, I forgot to put the density in the equation but while I am calculating thrust, I did use the air density.
With regards to the air speed, I am using 10 m/s and a Ct of about 0.635. The wind speed and thrust values are choosen by me, I dont have the thrust coeffcient from the manufacturer.
My idea is to calculate the stress and deflection when tje wind turbine is at rated speed. Also, the tower is 149 meters, the bottom diameter is 5.6m and bottom thickness is 43 mm while the top diameter is 3.7 m and the thickness is 18 mm.
I have thought about changing the wind speed to a lower value like 6.9 m/s because this is the average wind speed at site. But I am not sure if this 6.9 m/s will produce the maximum power.
I am looking for some suggestions to improve the calculation of thrust force or my model (i dont think i should change in my model as the modal analysis is really close).


Based on the tower dimensions provided (tower height = 149 m, external diameter at the bottom = 5.6 m, thickness at the bottom = 43 mm, external diameter at the top = 3.7 m, and thickness at the top = 18 mm), the system is quite slender. This is also denoted by the relatively low first tower bending mode (around 0.145 Hz).

A deflection around 2.5 m is not surprising for the loading applied at tower top (818 kN).

Similar results can be obtained with a cantilever beam approach.

I hope that helps.

Thanks for the comment. Actually, I tried to ask the farm operator and I came to know that under the rated conditions, the deflection generally stays under a meter. What can be the reason for this huge discrepancy in the deflection that I calculated and the one that is in reality.
Is this assumption that thrust load acts as a point load on tower top reasonable? or should I change it to something else? like a pressure?


Also, just to add that I verified my modes of vibration with the operator. it seems really close. One problem is that I only know the diameter of rotor and nothing else. Can there be some situations that can reduce the thrust force?

The deflection that you get only depends on the tower geometry defined and the load applied. Applying the thrust force as a point load at the tower top is the proper approach. You can tilt that load according to the wind turbine tilt angle (usually around 6 degrees). But the result will be very similar. If you are expecting smaller tower top deflections, there are only two plausible explanations:

  1. The tower is in reality stiffer. This would mean that the dimensions used are not representative of the real system. But this would also mean that you will get a higher first tower bending frequency that won’t match the measured value (assuming that the rotor-nacelle-assembly characteristics that you were using to obtain the system eigenfrquencies were the proper ones).
  2. The maximum rotor thrust force is in reality significantly lower (around a third) than you are considering. You may want to check the force that you are using against thrust forces that are publicly available for similar designs…

I hope that helps.