# Rotor aerodynamics while OFWT is moving

Hi,
I am a freshman in aerodynamics of wind turbines.
Now, I am writing a simple model of offshore floating wind turbine (OFWT) in MATLAB for control design. I would like to calculate the aerodynamics by using the BEM model recommended by “AeroDyn Theory Manual”.
Compared with land-based wind turbines, OFWTs have another 6 DOFs (surge, sway, heave, roll, pitch and yaw) which may affect the relative wind velocity.
For simplification, the wave and wind are both horizontal and yaw motion is neglected. Therefore, only surge and pitch motion of OFWT are considered: the surge velocity is always in the same or opposite direction of the wind velocity; and the pitch velocity is always perpendicular to the rotor plane.
However, I do not know how to deal with these velocities. I only have an idea as follows.

1. Surge and pitch velocities are added to the wind velocity (vector).
2. The resultant velocity is treated as new wind velocity “V new” with new direction “Th new”.
3. Calculate the aerodynamics by using BEM model with “V new”.
4. The new wind velocity is not perpendicular to the rotor plane because of the pitch motion and “Th new”. Therefore, skewed wake correction should be used which is similar to the solution of yaw motion.
Is it OK?

Or, how does FAST+AeroDyn deal with the same problem? I plan to verify my controller in FAST, therefore I prefer the same solution.

Thank you very much.

Best regards,
Lei Duan

Essentially, FAST vectorially adds the motion of the segment of the blade whose aerodynamics are being computed by BEM to the three components of the wind field at that point. The motion of the blade segment include that which is caused by a moving foundation, tower flexibility, yaw motion, rotor rotation, and blade flexibility. In other words, it computes the motion in inertial space and adds that to the motion of the wind to determine the relative speed of the wind flowing past the blade segment and then uses BEM to determine the lift and drag.

Jason may be able to explain it in more detail, but that is essentially it in a nutshell.

Dear Lei,

While I agree with Marshall, there is one subtlety that you should be aware of. When AeroDyn computes the relative wind speed for use in the dynamic pressure and angle of attack calculations, the computed induction factor applies only to the free stream wind speed, not the relative wind speed between the free stream wind and blade element velocities. That is, in equation form, AeroDyn effectively uses:

Urel = Uwind*(1-a) + Ustruct

where,
Urel = Relative wind speed normal to the disk
Uwind = Free stream wind speed relative to the inertia frame
Ustruct = Structural velocity normal to the disk relative to the inertia frame, positive into the wind
a = axial induction factor

This is in contrast to an approach which treats wind and structural velocities equally:

Urel = (Uwind + Ustruct)*(1-a)

The method used by AeroDyn comes from the assumption that structural velocities are likely the result of structural vibrations of high frequency such that the they would have little effect on the induced velocity. However, if the structural velocity results from low-frequency floating platform motion, this assumption is questionable.

Instead of choosing between one of the two equations above, we’ve discussed the option of filtering both the wind and structural velocities such that the low-frequency velocites impact the induced velocity and the high-frequency velocities do not. We would like to look at this issue some point in the future.

Best regards,

Hi, Jason,
Thanks for your answer. And I am sorry for late reply because your website is always prevented by the network of our university.

Now, I can understand how does AeroDyn work.

For compare, I would like to try the second equation you mentioned above in MATLAB. But I am still puzzled by using BEM theory in OFWT.
I have an idea. Could you do me a favor to check it and answer some questions?

1. First, the velocities of the element because of the platform are vectorially added on the wind velocities.
Vplat+Vwind=Vnew
Here, Vnew is not normal to the rotor plane.

2. In addition, Vnew is using as the free stream velocity in BEM code with skewed correction without considering any in-plane velocity.

3. Question. Which velocity should be used in calculating the angle of attack.
arctg(phi)=Vnew(1-a)/[omegaR(1+a’)]
or
arctg(phi)=Vnew’(1-a)/[omega
R(1+a’)]
Vnew’ is the normal part of Vnew to the plane.

4. Question. Which velocity should be used in calculating the thrust force.
Vtotal^2=[Vnew(1-a)]^2+[omegaR(1+a’)]^2
or
Vtotal^2=[Vnew’(1-a)]^2+[omega
R(1+a’)]^2

Using Vnew may be right by Aerodyn theory manual. The only difference is using Vnew instead of Vwind. But I am worry about the effect of the skewed correction.
Using Vnew’ may be easily understood, but the total in-plane wind velocities are ignored.

Could you answer my questions or give me some suggestion on my idea?

Best wishes,
Lei DUAN

Dear Lei,

I’m not really sure I understand your questions.

The equations for ATAN(phi) and Vtotal are vector relationships, so, they must use velocity components normal and tangential to the rotor disk (identified with _n and _t in the rest of my post below).

I should clarify one point from my earlier post. While AeroDyn currently uses Vrel_n = Vwind_n*(1-a) + Vstruct_n for the relative velocity normal to the rotor plane (as stated in my post above), it uses Vrel_t = (Vwind_t + Vstruct_t)(1+ap) for the relative velocity tangential to the rotor plane, where Vwind_t is the local undisturbed wind speed tangential to the rotor plane and Vstruct_t is the local structural velocity tangential to the rotor plane, including ( omega x radius ) and structural vibration terms. This is in contrast to what is stated in Eq. [2] of the AeroDyn thoery manual where it is implied that Vrel_t = omegaradius*(1+ap) + Vstruct_t: wind.nrel.gov/designcodes/simula … Theory.pdf. (Note: Vtotal^2 = Vrel_n^2 + Vrel_t^2.)

I hope that helps.

Best regards,

Dear Jason,