Coupled blade modes in FAST

Wind & Water Computer-Aided Engineering Software Tools
1

Hello to everyone,

I created blade modes with the help of BModes and applied the polynomial coefficients to my FAST model
in order to parameterize the flexible blade model. After running a few different simulations I applied
an FFT to the output results like flapwise and edgewise tip deflection. I expected to see for the
flapwise deflection the two flap mode frequencies and for the edgewise deflection the edge mode frequency.
In addition to the edgewise frequency (1.35 Hz) I also found the first flapwise frequency (0.75 Hz) in
the edge deflection results.

FFT_TipDyb1.png
FFT_TipDyb1.png1201Ɨ900 6.47 KB

This phenomen I would have expected if flap and edge-modes are coupled.
Does the blade model in FAST supports coupled modes or is there another reason for the described affect possible?

Is the blade model in FAST linear or nonlinear?

Any help is much appreciated!

Best regards,

Matthias

2

Dear Matthias,

Coupling in a real blade can be induced by the structural pretwist, offsets of the sectional mass, shear, or tension centers from the reference (pitch) axis, built-in curve or sweep of the reference axis, and the anisotripic layup of the composite laminae. The present version of FAST assumes an initially straight blade made up of an isotropic material with no offsets of mass, shear, or tension center. So, the only coupling left is what is induced by the structural pretwist.

FAST accounts for the coupling induced by structural pretwist, which is the coupling that is causing the results you are showing. The blade bending-mode degrees of freedom (DOFs) internal to FAST are not the flapwise and edgewise deflections of the blade tip, nor are they the out-of-plane and in-plane tip deflections. This is due to the blade structural pretwist. (Only if a blade had no structural pretwist would the blade DOFs equal the tip deflections in the flapwise and edgewise directions.) Instead, the DOFs are values proportional to the curvature of the blade about the pretwisted structural axes. When you integrate the curvatures along the blade to obtain the slopes, and then integrate again to obtain the deflection, the result is that flapwise and edgewise curvatures each lead to flapwise, edgewise, and axial components of deflection. While linear superposition is applied to the summation of local curvatures, the transformations and integrations made inside of FASTare all nonlinear calculations.

Because the blade flapwise stiffness is typically quite a bit less than the edgwise stiffness, the influence of the edgwise bending on the flapwise tip deflection (TipDxbi) will be much less than the influence of flapwise bending on the edgewise tip deflection (TipDybi). I suspect this is the reason why you are seeing what you expect in TipDxbi, but not in TipDybi.

I hope that helps.

Best regards,

3

Dear Jason,

thanks for your fast reply. I didnā€™t expect that in FAST the blade model will combine the
flap- and edge- modes again. I thought, that if they are parameterised independently they
will stay uncoupled in the blade model. That also explains why I expected the blade DOFs
be equal to the flapwise and edgewise deflection. As far as I understand, I should be
able to see all blade frequencies in both results (TipDxb1, TipDyb1) if the will excited.

How does FAST computes the axial deflection and the coupling of flap- and edgewise
deflection if the parameter EAStff and GJStff in the blade description are unused?

Can you recommend any article where I can find a more detailed description of the blade model used in FAST.

Best regards,

Matthias

4

Dear Matthias,

Bending is related to curvature and takes place about the local structural principle axes about which the bending mode shapes are defined. The coupling between flap and edge results by trigonometrically rotating (through the structural pretwist) the flap and edge curvatures into in-plane and out-of-plane curvatures, then integrating twice to get displacement. It is true that if the structural pretwist is nonzero that you should see flapwise and edgewise frequencies in all tip displacements. As I said in my prior post, however, because the blade flapwise stiffness is typically quite a bit less than the edgwise stiffness, the influence of the edgwise bending on the flapwise tip deflection (TipDxbi) will be much less than the influence of flapwise bending on the edgewise tip deflection (TipDybi).

Pages 3-4 of the following paper describe the basic concept behind how FAST couples flapwise and edgewise deflections with axial deflections: nrel.gov/docs/fy04osti/35077.pdf.

Unfortunately, weā€™ve never been budged the time to write an official FAST theory manual. Nevertheless, here is a quick overview of the FAST theory basis, plus links to where you can find more information.

FAST is a nonlinear time-domain model, which solves equations of motion that are of the form:

M(q,u,t)*qdd = f(q,qd,u,ud,t)

where,

M = mass matrix depending on a nonlinear combination of displacements (q), control inputs (u), and time (t)
qdd = accelerations
f = forcing vector depending on a nonlinear combination of displacements (q), velocities (qd), control inputs (u), wind inputs (ud) (input disturbances), and time (t)

The FAST model is a combined modal and multibody dynamics formulation. The equations of motion above represent the standard multibody dynamics form (with no constraints). The modal part comes in through how the DOFs for the flexible tower and blades are defined. The tower and blades in FAST are treated as elements whose flexibility is determined by the summation of shape functions (modes) scaled in magnitude (DOFs).

Iā€™ve provided a few references below which expand on this information:
*Chapters 2-4 of my Masterā€™s thesis provide a good overview of the basic aerodynamic and structural dynamic theories, although not all of the information is up-to-date (it is about 8 years old), it doesnā€™t cover everything, and there a few errors: nrel.gov/docs/fy04osti/34755.pdf.
*This paper provides a basic, 10-pg overview of the FAST code and the changes we made to it about 6-7 years ago: nrel.gov/docs/fy04osti/35077.pdf.
*The aerodynamic theory is also described in AeroDynā€™s theory manual: nrel.gov/docs/fy05osti/36881.pdf.
*The new theory pertaining to hydrodynamics and mooring system responses is described here: www3.interscience.wiley.com/cgi- ā€¦ 5/PDFSTART.

Although the above references are not entirely up-to-date, I think they should provide the information you are seeking. However, if you still want more information, such as the detailed derivation of the equations of motion as currently implemented, we do have this information available. However, it is written down in a series very large MS Word documents containing mostly equations and very little explanation. We hope to eventually publish this information as the official FAST theory manual (if weā€™re ever budgeted the time). But if you need this information as well, we can provide this too.

Best regards,

5

Hi all,

with regard to the discussion above I have a question.

If I want to simulate blades with coupled (bend-twist) modes, how can I do it with Fast?

Considering for example coupling due to an anisotropic layup, so without the necessity
of a curved blade aerodynamic modelling. I can obtain the coupled modes from a FE
analysis, but how I input these into Fast? I remark that I have never used Fast before,
so sorry If Iā€™m asking something trivial.

Regards

Marco

6

Dear Marco,

The simple answer is that you canā€™t (at least not yet).

From my post above dated December 13, 2010 it should be clear that FAST only includes coupling between flapwise and edgewise bending in the blade. Couplings associated with offsets of the sectional mass, shear, or tension centers from the reference (pitch) axis, built-in curve or sweep of the reference axis, or the anisotripic layup of the composite laminae are currently neglected by FAST. Additionally, FAST currently has only 3 degrees of freedom (DOFs) available per blade: 2 flapwise bending modes and 1 edgewise bending mode per blade. There is currently no blade torsion DOF in FAST.

We are initiating the effort this year to replace FASTā€™s flap and edge mode DOFs with coupled flap-lag-twist mode DOFs. But this is a fairly big project that will likely take a bit of time to complete.

Best regards,

7

Dear Jason,

thanks a lot for the answer, but at this point one question arises automatically:
if there is not DOF for the blade twist, how the aeroelastic coupling is considered
within Fast ? I thought that the main source of aeroelastic coupling in WT blades
was due to the elastic twist.
Anyway,is it possible to insert the bend-twist coupling effect in Fast by some simple
modifications of the code? Would it be possible to link the value of the flap-bending DOF
to a correction of the blade twist distribution which is input into aerodyn?

Regards

Marco

8

Dear Marco,

In many wind turbines, the natural frequencies of blade twisting are far higher than the blade bending modes and wind- and structural-excitation frequencies. In these systems, the blade twisting does not have a prominent roll in the system dynamics and the present FAST model is likely suitable. The present FAST model accounts for the aeroelastic effects associated with blade bending and other turbine motions. When blade torsion is important for the system dynamics, FAST in its present form would not be suitable.

Iā€™ve heard others suggest making the blade twist deflection a simple function of the bending deflection or pitching moment. But frankly, I would be concerned that this approach will neglect important dynamics of the twisting. Thus, we have not pursued this approach at NREL. Insteadā€“as I stated in my prior postā€“our plan is to replace FASTā€™s flap and edge mode DOFs with coupled flap-lag-twist mode DOFs (with the pertinent dynamics included). This will be far more challenging, but will be more accurate.

Best regards,

9

Dear Jason,

your answer is very clear and useful, thanks.
As I told you previously, Iā€™m investigating the capabilities of bend-twist coupled blades. I have seen that
people inside NREL are doing the same by using Fast. So, how is it possible? Are they modifing the code?
If you can not provide me this information, donā€™t worry.
Below I explain why Iā€™m asking you all these questions:
I developed a code for the static aeroelastic analysis of WT blades, by coupling a BEM code and a structural code
based on composite beams FEs. So, the structural code is able to capture the elastic coupling; but from this point the
effort necessary for the implementation of a dynamic aeroelastic analysis code would be really high. Therefore, Iā€™m trying to see if I
can use an open source code, because my work is focused on the concept investigation rather than on the tool development.

Would you, inside NREL, be interested in the development of Fast in order to make possible the use of (coupled) beam finite elements?

Regards

Marco

10

Dear Marco,

I donā€™t know of anyone at NREL modeling blades with flap-twist coupling using FAST.

That said, FAST has two modes of operation. First, it has its own structural dynamics model that can be used for simulation (with no ability to model flap-twist coupled blades), as described above. Second, FAST has a preprocessor capable of creating MSC.ADAMS datasets of wind turbines. The FAST-to-ADAMS preprocessor, as it is known, uses the turbine configuration specified for the FAST model, plus additional structural inputs, to build a higher-fidelity model of the turbine for simulation with MSC.ADAMS. One of the additional structural inputs is the blade flap/twist coupling coefficient. The FAST-to-ADAMS preprocessor also includes the AeroDyn-ADAMS interface to enable aeroelastic calculations. So, FAST in its present form can be used to model flap-twist coupled blades, if used in conjuction with MSC.ADAMS. Perhaps this is the approach youā€™ve heard of?

Our longer-term plans for FAST include the ability to model the blades with finite elements as an alternative to assumed modes. However, these would have to be nonstandard finite elements that take into account the centrifugal, coriolis, and other effects important to spinning rotor blades. But, unfortunately, we donā€™t have the budget to work on this topic at the moment.

Best regards,

11

Hi Jason,

thanks for the answer. I think you are right, these people of NREL (or Sandia Lab) probably were using Fast only as pre-processor for Adams.
At this point I do not understand one thing. If the twist DOF is not included in Fast dynamic structural modelling, why within the blades input file
the twist stiffness is assigned?

Regards

Marco

12

Itā€™s only used by the ADAMS preprocessor in FAST.

13

I understand, thanks for the answer.

Marco

14

Hi everybody! Iā€™d like to ask about one thing about the coupled mode shapes:

I refer to Jonkmanā€™s Report from December 2003 about Fast_AD. As far as I know this is a predecessor of todayā€™s FAST.
As far as I understood the elastic behaviour of the blades is dependent on the defined mode-shapes. The mode-shapes are normalized and the generalized coordinate for the modes is the tip-deflection.
I am interested in the total deflection shape, which is presented from page 36ff. on. I would like to calculate the whole shape but I canā€™t find the variables q1 (Tip-Deflection for 1st bending mode) and q11 (Tip-Deflection for 2nd bending mode). I assume q13 to be equal the edgewise tip deflection.
As the ā€žrealā€œ flapwise deflection is the combination of both shapes, I was wondering how I could use the variables q1 and q11. I couldnā€™t find this information in the FAST User guide.

Any help is very appreciated. My Version of FAST is 7.0
Cheers,

Kai

15

Dear Kai,

Iā€™m not sure I understand your questions. What do you mean when you say that you ā€œcanā€™t find the variables q1 and q11ā€? What do you mean when you ask ā€œhow [you] could use the variables q1 and q11ā€?

FYI: In the latest version of FAST, v7.01.00a-bjj, the internal DOFs (including their first and second time derivatives) and the local blade flap, edge, and axial deflections (available at up to 9 stations along the blade) are available for output. You should be able to see the 3D shape of the deflected blade from the local blade flap, edge, and axial deflections.

Best regards,

16

Dear Jason,

thanks a lot for your reply. The Variables q1 and q11 are mentioned in you report from December 2003 on page 31. They are defined as the tip deflections for either the natural mode 1 or 2.

At the bottom of page 36 it is explained how to get the deflection in dependency of the modes and the generalized coordinates (which is the tip deflection).

I assume, that the variable, I can acces in FAST (Flapwise Tip-deflection) is the summation of those variables (q1, q11) - simmilar to the deflection of the tower (explained at the bottom of p.32) I really hope I donā€™t get anything wrong from the report.

I guess I will have to do an update for my version of FAST because I am really interested in blade deflection.

Thank you very much for your help.

Cheers,

Kai

17

Dear Kai,

As shown in Eqs. (3.24), (3.25), and (3.27) of that report, the out-of-plane, in-plane, and axial blade deflections in FAST each depend on all three of the blade-bending (2 flap and 1 edge) DOFs (due to how the structural pretwist couples flapwise and edgewise bending).

As I mentioned in my prior post, the total tip deflection, as well as the contributions from each blade-bending DOF, are available outputs in the latest version of FAST, v7.01.00a-bjj.

Best regards,

18

Dear Jason,

thank you very much. I will upgrade my version then.

Cheers,

Kai

19

Dear Jason Jonkman,

These days I am studying the FAST source code and writing down in pencil the equations (especially the ā€˜RtHSā€™ routine). I just read your post above dated 15 dec 2010 above where in the last line you mention a word document that contains all these equations and their derivation. Could I read that doc as well? It would help me a great deal I think

Thanks
Gerrit

20

Dear Gerrit,

Please send me an e-mail and I will reply back with the ā€œUnofficial FAST Theory Manual.ā€

Best regards,