The frequency component of flapwise

Dear Dr. Jason.

In Test25, I simulated the flapwise DOF of blade of OC4-subsemi platform,
then I made Fast Fourier transform for motion response, I got 4 frequencies,
the 1st is 0.07922, I don’t know now,
the 2nd is 0.1227 is the wave frequency for my wave period is 8.15s,
the 3rd is 0.2 for the rotation rate of blade is 12.1rpm,
the 4th is 0.3241 I guess it is the natural frequency of tower?
So can you help me what the 1st and 4th frequency represent?

Thanks for your help.
Best Regards

Dear Yuanzhao,

Yes, the fourth frequency of 0.32 Hz is the first tower-bending mode of the OC4-DeepCwind semisubmersible. I would not expect an excitation in this model at 0.08 Hz. Do you mean ≈0.01 Hz, which is the platform surge/sway natural frequency, or ≈0.04 Hz, which is the platform-pitch/roll natural frequency?

Best regards,

Dear Dr. Jonkman,

I am working on the Test25 of the semi-submersible wind turbine. My aim is to perform the structural response analysis of this wind turbine model. Before that, I need to check the natural frequencies of the whole system. I do the linearisation analysis in standstill scenario in v8.16 and use MBC matlab script and CampbellDiagram to get the frequency of tower and blade based on the Test25 files, during this process I only enable the ElastoDyn module and disabled all six platform degrees. And then using the free-decay for platform frequency analysis. I get the result below:

Rotor Speed (rpm) 0
1st Tower FA 0.36898
1st Tower SS 0.35773
1st Blade Flap (collective) 0.67000
1st Blade Edge (collective) 1.08000
1st Drivetrain
2nd Tower FA 3.73945
2nd Tower SS
2nd Blade Flap (collective) 1.80623

I have read the document of “Validation of a FAST semi-submersible floating wind turbine numerical
model with DeepCwind test data” and “Offshore Code Comparison Collaboration Continuation Within IEA Wind Task 30: Phase II Results Regarding a Floating Semisubmersible Wind System” and many posts. I could still not find the accurate value of the natural frequencies for semi-submerisible wind turbine in Test25, and thus can not assess the result of my model, can you help me with interpretation of this result?

For the platform below:
my results results; given by Alexander J etal
surge 113.1; 107
sway 114.05; 113
heave 17.55; 17.3
roll 25.6; 26.7
pitch 25.65; 26.8
Yaw 80.15; 82.7

Comparing to the results in “Validation of a FAST semi-submersible floating wind turbine numerical
model with DeepCwind test data”, they are existing some difference. How you evaluate these results and how should I adjust my input parameter in order to match the accurate result?

Best,
Charlie

Dear Charlie,

I think the natural frequencies you’ve derived for the OC4-DeepCwind semisubmersible are quite reasonable. Please note that Test25 is a model of the NREL 5-MW turbine atop the OC4-DeepCwind semisubmersible design, which was analyzed in IEA Wind Task 30 OC4 Phase II. The actual DeepCwind wave-tank tests used a scaled system with similar, but not identical, properties (at scale). So, the modeling results from Test 25 should be more similar to the results published in the IEA Wind Task 30 paper than in the Coulling et al paper.

The approach you are using to derive the natural frequencies is quite reasonable, except for the tower modes, which may be off a bit. The natural frequencies of a tower cantilevered to a floating platform are typically a bit higher than the natural frequencies of a tower cantilevered to the inertial frame, due the different tower-base boundary conditions. You can derive a more accurate frequency e.g. through free-decay of the tower with the platform DOFs (and still-water hydrodynamics and moorings) enabled, or through post-processing of a simulation with white-noise excitation (there are other posts on this forum that discuss these topics). That said, we are currently working on the addition of linearization functionality for floating offshore wind turbines within OpenFAST, which will enable full-system eigenanalysis, including the effects of platform DOFs, hydrodynamics, and moorings. We are presenting the theoretical basis for this new functionality next week at the IOWTC conference in San Francisco, CA (USA) and expect to present the verification results at the DeepWind 2019 conference next January in Trondheim, Norway.

Best regards,

Dear Dr. Jonkman,

really thanks a lot for your help, expect to say the new functionality in OpenFAST version. Now for the tower, I also do the free-decay analysis and get the FA and SS first frequency are both 0.4255 roughly. How do you think?

Also can you please give me the exact value of Full-system natural frequencies in still water, i.e. the exact value in Figure 3 of your paper “Offshore Code Comparison Collaboration Continuation Within IEA Wind Task 30: Phase II Results Regarding a Floating Semisubmersible Wind System”?

Best regards,
Charlie

Dear Charlie,

Yes, the tower frequencies you’ve identified for the OC4-DeepCwind semisubmersible through a free-decay analysis are quite reasonable.

The simulation results from all participants of IEA Wind Task 30 OC4 Phase II are available here: drive.google.com/drive/folders/ … 73PUVBJ6ZX).

Best regards,

Hello Dr. Jonkman,
I am trying to calculate the natural frequencies of the surge, sway, heave, roll, and pitch of the OC4 platform using the data in the ‘Definition of the Semisubmersible Floating System for Phase II of OC4.

  1. The stiffness Kp of the platform is composed of the mooring stiffness (Cm(1,1)=Cm(2,2)=7.08e4 N/m, Cm(3,3)=1.91e4 N/m, Cm(4,4)=Cm(5,5)=8.73e7 Nm/rad, from Eq. (5-15)) and hydrostatic stiffness (Ch(1,1)=Ch(2,2)=0, Ch(3,3)=3.836e6 N/m, Ch(4,4)=Ch(5,5)=-3.776e8 Nm/rad, from Eq.(4-3)).
  2. The mass of the platform is mt(1,1)=mt(2,2)=mt(3,3)=1.3473e 7 kg in the surge and sway directions, and the roll and pitch inertia is mt(4,4) =mt(5,5)=6.827e9 kg-m2 for the pitch and roll motions.
  3. The added mass A(1,1)= A(2,2)=6.49e6 kg, A(3,3)=14.7e6 kg, A(4,4)= A(5,5)=7.21e9 kg.
    The angular natural frequency at the individual direction is wi=sqrt((Cm+Ch/(mt+A)) and is fi=wi/(2*pi) in Hz.
    The calculated frequencies in Hz are
    surge 0.0095; [0.0093]
    sway 0.0095; [0.0088]
    heave 0.0589; [0.0578]
    roll 0.0229; [0.0375]
    pitch 0.0229; [0.0373]
    where the second column shows the reference results by Alexander Jeta which are very closed to these in the Fig3 of ‘Offshore Code Comparison Collaboration Continuation Within IEA Wind Task 30: Phase II Results Regarding a Floating Semisubmersible Wind System’.
    It shows the results in the surge, sway, and heave directions are acceptable, while, the roll and pitch motion frequencies are incorrect. Do you have any idea and suggestion about this? Thanks in advance.

Dear Feng,

I agree with your numbers, but you seem to be missing three important effects:

  • The influence of the platform center of mass (from (0,0,0) on the roll and pitch inertia of platform;
  • The influence of the supported wind turbine mass, center of mass, and inertia; and
  • The coupling between platform DOFs (off-diagonal terms in the matrices, including surge-pitch and sway-roll).

Best regards,

Dear Jason,
Thank you very much for your quick reply. Regarding the influence of the platform center of mass and the turbine mass(I guess also nacelle, motor, and hub), on the roll and pitch inertia of the platform, if you mean I should use the 6x6 mass matrix of the full system given in the marin_semi.frc file (mentioned in this discussion http://forums.nrel.gov/t/oc4-deepcwind-semisubmersible-wamit-files/2203/1).

Yes, this seems to work well to reduce the surge motion frequency a little be to 0.0093 Hz, which perfectly agreed with the existing result, and also a reduction in the heave motion frequency. But, the natural frequencies of pitch and roll are also reduced and still incorrect.
Could you please give me more comments and suggestions.
Thanks again.

Best regards,

Feng

Dear Feng,

Yes, that is the correct full-system mass matrix. Have you now included the coupling between platform DOFs (off-diagonal terms in the matrices, including surge-pitch and sway-roll)–not just for the mass matrix, but also for the added mass matrix and mooring stiffness matrix?

Best regards,

Dear Jason,
Yes, I have taken the coupling between the surge and pitch motions, and the sway and roll motions into account by including the off-diagonal elements of the added mass matrix and the mooring stiffness matrix given in the ‘Definition of the Semisubmersible Floating System for Phase II of OC4’. I tried to do free decay simulation to calculate the frequencies too after considering the coupling. The results are also very close to the ones obtained from the above-mentioned diagonal elements of total mass and stiffness matrixes.
Thanks.

Best regards,

Feng

Dear Feng,

Your equation for the natural frequencies above applied to mass and stiffness values written as scalars (or only consider separate terms uncoupled). How are you calculating the natural frequencies with 6x6 matrices? Are you forming the first-order state-space matrix (A) and computing its eigensolution?

Best regards,

Dear Jason,
I calculate the eigenvalues of the system using the total mass and stiffness matrixes. I didn’t consider the yaw motion, so the matrix is 5x5. I attached the code and the results as the following. It seems there are negative eigenvalues because of the large negative hydrostatic stiffness of the roll and pitch motions.
%%Full mass matrix%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
M=[1.407E+07 0.000E+00 0.000E+00 0.000E+00 -1.392E+08
0.000E+00 1.407E+07 0.000E+00 1.392E+08 0.000E+00
0.000E+00 0.000E+00 1.407E+07 0.000E+00 1.448E+05
0.000E+00 1.392E+08 0.000E+00 1.270E+10 -1.094E-01
-1.392E+08 0.000E+00 1.448E+05 -1.094E-01 1.269E+10];
%%%%%%%Added Mass%%%%%%%%%%%%%%%%%%%%
Ainf(1,1)=6.49e6; Ainf(1,5)=-85.1e6;
Ainf(2,2)=6.49e6; Ainf(2,4)=85.1e6;
Ainf(3,3)=14.7e6;
Ainf(4,2)=85.1e6; Ainf(4,4)=7.21e9;
Ainf(5,1)=-85.1e6; Ainf(5,5)=7.21e9;
%%%%Mooring line stiffness%%%%%%%%%%%%%%%%%%%%%%%%%%%%
CM(1,1)=7.08e4; CM(1,5)=-1.08e5;
CM(2,2)=7.08e4; CM(2,4)=1.08e5;
CM(3,3)=1.91e4;
CM(4,2)=1.07e5; CM(4,4)=8.737e7;
CM(5,1)=-1.07e5; CM(5,5)=8.737e7;
%%%%% Hydrostatic stiffness%%%%%%%%%%%%%%%%%%%%%%%%%%%
CH(3,3)=3.836e6; CH(4,4)=-3.776e8; CH(5,5)=-3.776e8;
KT=CM+CH;
MT=M+Ainf;

Eigen=eig(KT, MT);
Omg=sqrt(Eigen);
Freq=sort(Omg/(2*pi));

Freq =

0.0094 + 0.0000i
0.0094 + 0.0000i
0.0000 + 0.0203i
0.0000 + 0.0203i
0.0583 + 0.0000i
I checked all the matrices with the definition of semisubmersible and they all seem no problem. The first two should be the natural frequencies of surge and sway, while the last one is the frequency of heave motion. But the negative eigenvalues and the resultant complex numbers are really odd.
Thanks.

Best regards,

Feng

Dear Feng,

I see the problem. I don’t see that you’ve included the restoring in roll and pitch associated with the influence of the full system body weight / center of mass. Effectively, you must add to KT(4,4) the contribution of gravity*M(2,4); likewise for KT(5,5).

Best regards,

Dear Jason,
Thank you very much for the suggestion. I am still confusing about how to consider the influence of the full system bodyweight/center of mass on the restoring stiffness in roll and pitch. Is this related to the CM and CB of the platform, which I actually tried to look into them? I am also curious about the connection between the full mass matrix and the mass provided in the Definition of the Semisubmersible, which only includes the mass of the floating platform and ballast. Is there any reference that is helpful to figure this information, so that I can have a more clear understanding of the origin of these data?
Thanks.

Best regards,
Feng

Dear Feng,

The hydrostatic stiffness matrix (CH in your example) includes the effects of waterplane area and center of buoyancy, but it does not include the effects of full system body mass and center of mass.

The full system mass matrix linked in the forum topic linked above (M in your example) includes the full system mass (upper-left quadrant), center of mass (upper-right and lower-left quadrants) and inertias (lower-right quadrant).

So, you can derive the restoring in roll (4,4) and pitch (5,5) from body mass / center of mass from the gravity times the M(2,4).

Best regards,

Dear Jason,
Thank you very much for your help. I think the natural frequencies are right now, which are 0.0093, 0.0093, 0.0396, 0.0396, and 0.0583.
Thank you again.
Best regards,
Feng