aeroelastic damping

Dear all,
could anybody please provide me with some references where I can learn more on how the aeroelastic damping is modeled in FAST ?
Thank you very much!

Enzo

Dear Enzo,

I’m not exactly sure what type of information you are seeking. The structural model of FAST interacts with the aerodynamic model of AeroDyn at every time step. “Aeroelastic damping” refers to aerodynamic forces that depend on structural velocities. How structural velocities enter the aerodynamic force computation is described in the AeroDyn Theory Manual: wind.nrel.gov/designcodes/simula … Theory.pdf. Do you need clarification beyond the information presented in this manual?

Best regards,

Hello Jason,

I have recently been looking into the aerodynamic damping that occurs when the structural and aerodynamic model are coupled. I have found few sources of information that gives different ways to calculate a simplified aerodynamic damping. For what I have seen the aerodynamic damping for the flap-wise blade motion is much stronger than the structural damping, however I quantify much stronger by a aerodynamic damping ratio of 0.1(or 10%) which is much more than the structural one around 0.0048 (or 0.48% of critical damping) as given in the blade file. So I am interested in finding a better approximation by analyzing the fast output data ofthe 5MW wind turbine.

For this purpose, I deactivated most of the DOFs except the blades Flap-wise and Edgewise DOFs to analyse the blade deflection response decay. When I deactivate aerodynamic force calculation then I obviously end up with a vibrating blade with very small structural damping. However, what’s troubling me is that when I activate the Aerodynamic coupling it seems as if the damping significantly increases much more than a damping ratio of 10%. Could it be that other forces reducing flap-wise motion are involved? I have attached the simulations output figures for clarifications.

Simulation details: I wanted to minimize the influence of other forces so I set the axial wind speed of 0.1m/s and an rpm of 11.45 with a pitch=0. I’m not 100% that it is the best simulation set up.
Could I easily do it another way using Fast, for example waiting for steady state and create a special impulse event or by deactivating all forces except the one produces by blade vibrations?

I sorry I forgot the axis labels, this is obviously meters and time (seconds).
Thanks for your time and answers.
Regards,
Terence.

Hi Terence,

I’m not exactly sure what you are doing but I’m surprised that the use of 0.1 m/s wind makes such a difference. Have you disabled the control system that the rotor speed and blade-pitch angle are fixed?

Did you deactivate aerodynamic forcing by setting CompAero = False (effectively resulting in a simulation of a turbine in vacuum) or by setting the wind speed to zero (still air). It may be interesting to see how the still air case compares to 0.1 m/s.

One method to derive the damping would be to deriving the damping would be to give the blades an initial displacement and measure the free-decay response.

Best regards,

Hello Jason,

Thanks for your reply.

I agree with you on this

, My problem is more to be sure than there are no other forces acting on the blades.

I have run few more simulations that may make things clearer, for clarity sake the details of the simulations are also on the pictures. I’m going to split this post into 2 to keep the pictures and questions together. (Sorry I haven’t found another way)

[size=150]I] [/size] First I have a question about the next Figure. The only active DOF are Flap-wise and Edge-wise blade vibrations and there is no pitch angle, compaero = false and gravity set to 0. I therefore expected that by setting the edgewise initial condition to 1m tip displacement and 0m for Flap-wise I would observe 0 flap-wise displacement. My first question is what is that forces or coupling inducing Flap-wise motion in this case?

[size=150]II][/size] Now is the part that troubles me. In the next figures the initial displacement for Flap-wise is set to 1m and 0 for Edge-wise. Moreover, the rotational speed is changed and its effect on the aerodynamic damping is visible. After the first test I realized that the damping was not changing significantly with the axial velocity but with the rpm. I’m fine with the small difference in natural frequency that is caused by the centrifugal stiffening however the huge differences in damping surprises me. Because of the assumption that I have made here, I was expected that for fixed speed, constant pitch and high tip speed ratio wind turbines (high rpm) the aerodynamic damping would be directly related to the slope of the lift coefficient but not to the rpm. However, the significant changes in aerodynamic damping and the change in mean values as for rpm=12 require another explanation.

Can you think of any explanation for these results?

Thanks for your time and reply.
Regards,
terence.

Dear Terence,

Regarding your first question, the structural pretwist of the blade in FAST leads to coupling between the edgewise and flapwise motions. Please see the forum topic found here for more information: http://forums.nrel.gov/t/coupled-blade-modes-in-fast/314/1 (particularly, the Dec 13, 2010 post).

Regarding your second question, what aerodynamic options have you enabled when CompAero = True? That is, does StallMod = STEADY or BEDDOES; does InfModel = EQUIL or DYNIN?

Best regards,

Hello Jason,

Thanks a lot for your advises.

I have been reading your master thesis, especially Section 3 where you explain the structural coupling between Flap-wise and Edge-wise motion. I just would like to summarize it to see if my understanding is correct. Could you please let me know if the following are correct:

1 - The Flap-wise and Edge-wise direction are not defined for the entire blade. They are local principal axis of a section of the blade.

2 - Since Aerodynamic and Structural twist are equals for the 5MW wind turbine blades, the local Flap-wise direction is normal to the local chord line.

2 - The Flap-wise and Edge-wise deflection are only independent per section. For instance, a blade tip Edge-wise displacement induces Flap-wise displacement at other span location where the structural twist is different.

3 - For computing the general deflection, the Flap-wise and Edge-wise local contributions are translated in the Out of plane, In plane axis via the twisted mode shapes.

4 - If the structural twist is constant over the blade span, one can translate from the Flap-wise mode shape to the twisted mode shape by a simple factor. (integrals of Equations 3.16 to 3.21 simplify)

5- q1, q11 … are the Flap-wise DOF or modal coordinates. Each modal coordinates is associated with a particular mode shapes. Moreover the linear combinations of Flap-wise mode shapes represent the general Flap-wise motion.

6 - The modal coordinates are time dependent but space independent → q1(t).

7 - q1(t) and q11(t) can be calculated by solving a Finite Element model of the blades using the Flap-wise blade properties given in the 5MW definition PDF.

9 - q1 (Flap-wise modal coordinate) and q13 (Edge-wise modal coordinate) can be calculated independently.

8 - Once the modal coordinates for Flap-wise and Edge-wise are calculated one can use Equation 3.24 and 3.25 to translate the deflections in the Out of plane, In plane axis.

Thanks for your time.
Regards,
terence.

Dear Terence,

Here are my responses:

Correct.

This is what is stated in my MS thesis, but they way FAST is now implemeted is that the twisted shape functions are computed without the blade-pitch angle (removing theta_p from Eqs. (3.16) - (3.21)). The out-of-plane and in-plane deflections are calculated separately via rigid-body rotations of the blade-pitch angle. The “Unofficial FAST Theory Manual” mentioned in other forum posts describes the equations in the correct form as implemented.

Correct.

No. The modal DOFs (q(t) for each blade mode) are calculated by FAST at run time by solving and integrating the FAST equations of motion. All DOFs are coupled within FAST and cannot be solved independently.

Yes, except for the difference in the way the blade-pitch angle is implemented, as discussed under Q3 above. This calculation is implemented directly within FAST.

I hope that helps.

Best regards,

Hello Jason,

Thanks for your reply, it really helps me.

Regarding the blades only, would it not be easier to actually calculate the whole blade principal axes and resolve in that plane instead of using the localised principal axis?

Regards,
terence.

Dear Terence,

If I understand what you are proposing, this approach would not lead to a coupling between the flap and edge motions induced by the structural pre-twist. The structural pre-twist-induced coupling is a physical effect that is important to resolve.

Best regards,

Hello Jason,

after a long time of absence I finally decided to focus my effort one more time on the structural modelling of wind turbine blades. I think I now have a better understanding of the way fast integrate the flapwise/edgewise coupling through the twisted mode shapes. According to the user guides of FAST and MODES I read that FAST requires the mode shape of the untwisted and un-pitched blade. My own code agrees very well for this particular case, however, I am now interested in integrating the flapwise/edgewise coupling. For that purpose, I generalise the flapwise and edgewise stiffness distribution along the blade span to the In-Plane and Out-Of-Plane axis ( similarly to MODES when using the real pretwist distribution). More precisely :

  • I first calculate the local flapwise and edgewise beam element stiffness matrices for the entire blade. These elements cannot directly be assembled together because of the structural pretwist.

  • I, therefore, combine the flapwise/edgewise stiffness matrix and use a rotation matrix, dependent of the pretwist distribution along the blade span, to resolve it in the IP and OOP axis. At this point I obtain a large size matrix composed of three submatrices :
    1 - The OOP stiffness matrix (K_oop)
    2 - The IP stiffness matrix (K_ip)
    3 - The coupling matrix (K_iop) and its transpose ( K_iop’ )

which form the following matrix:
| K_oop K_iop |
| K_iop’ K_ip |

Since the rotation matrix varies with the blade radius, a flapwise force at the blade tip introduce both a flapwise and edgewise components at other locations along the blade span.

Question : While I know that non-linear effect are not yet considered in my model, do you think that this approach is viable ?

As always, thank you for being so helpful.

Regards,
terence.

Dear Terence,

Yes, for a bending-only model, the transformation you’ve implemented will account for the structural twist in the off-diagonal terms of the stiffness matrix.

Best regards,

Hello Jason,

Once again, thank you for your reply.

I now came across something interesting. I have, recently, been playing with the input values used for the NREL 5 MW wind turbine blades in FAST. Let’s say I multiply the blade flap-wise stiffness by 1.5, this change should directly impact the blade :

  • Natural frequencies
    and
  • Twisted Modes-shapes (amplitude and direction)

Based on this reasoning, if the Twisted Modes-shapes direction changes and I apply the same force for both cases then I expect a change in both the tip displacement and root bending moment. However, when I try this in FAST I do notice a change in tip displacement only.

In details :
1 - I set up a simulation with the original wind turbine blade parameters, run it and saves the flapwise and edgewise tip displacements and root bending moments.

2 - I multiply the flapwise stiffness by 1.5 over the entire blade span and run the exact same simulation.

3 - As one would expect, a greater flapwise stiffness (dominating the first vibration mode) results in a lower flapwise tip displacement. However, I do not observe any significant change of edgewise tip displacement, flapwise and edgewise root bending moments. I was expected a fairly noticeable change in edgewise tip deflection due to the change in twisted mode shape direction and a rather small change in root bending moments. Fast does not, however, show any noticeable variations.

Do you think my reasoning is correct ? or is FAST correct?

Thank you for your time.
Regards,
terence.

Dear Terence,

The twisted shape-functions in FAST depend directly on the specified flapwise and edgewise mode shapes and distributed structural twist angle, not on the distributed stiffness values. However, a change to the flapwise stiffness should impact the flapwise mode shape that you enter in FAST (this effect is not automatically calculated by FAST, but it is up to the user to update the mode shape based on the desired mass/stiffness).

I hope that helps.

Best regards,