IEA-15-240-RWT-UMaineSemi linearization

Dear all,
I’m currently working with IEA-15-240-RWT-UMaineSemi and I’m trying to extrapolate the non-dimensional damping of the platform pitch using the linearization of OpenFAST for different wind speeds. The goal was first to create the state matrix A (considering as dofs platform pitch and its derivative + rotor speed and its derivative: 4x4 matrix) , then evaluate the eigenvalues and so the non-dimensional damping. I followed the guidelines for which in a rotating case the recommended approach was :‘it is recommended to use NLinTimes=36 (corresponding to on linearization every 10-degrees of azimuth rotation)’. The dofs activated were PtfmPDOF and GenDOF and HydroDyn still water. Once I applied that, I extracted the 4x4 A matrices from .Lin file and then I’ve averaged them for each wind speed. The results at the end are not as expected: firstly, from manual calculation I was expected a natural frequency (as conseguence of the eigenvalues) of about 0.04 Hz but I got 0.4 Hz, secondly I was expecting to have the poles related to the first derivative of the rotor speed to be in 0, but it was just close to it.
I was wondering if someone could help me to understand if I’m extracting in the wrong way the data from .lin files, in fact I encountered the following issue:
Here I write part of the .lin file
Row/Column Operating Point Rotating Frame? Derivative Order Description


      1   -8.756E-04                                 F               2         ED Platform pitch tilt rotation DOF (internal DOF index = DOF_P), rad
      2    4.721E+00                                 F               2         ED Variable speed generator DOF (internal DOF index = DOF_GeAz), rad
      3   -2.294E-07                                 F               2         ED First time derivative of Platform pitch tilt rotation DOF (internal DOF index = DOF_P), rad/s
      4    3.643E-01                                 F               2         ED First time derivative of Variable speed generator DOF (internal DOF index = DOF_GeAz), rad/s

A is a 984x984 where from the info above, I know lines 1,2,3,4 and columns 1,2,3,4 are associated to the 4 dofs i want. But looking at the matrix it seems that the first two lines are actually associated to the derivatives of the PtfmPDOF and GenDOF in opposition to what the order is telling me
0 0 1 0
0 0 0 1
-8.36600000000000 -1.22321111111111e-05 -0.125091666666667 0.00250797222222222
|-0.00313063888888889 -0.000102025277777778 -0.955677777777778 -0.0860683333333334

Here the plot of the eigenvalues:

Thank you very much.

Dear @Leonardo.Facelli,

You mention that you extracted a 4x4 submatrix from a much larger A matrix; can you clarify what additional states are in the A matrix? Are you referring to states associated with state-space hydrodynamics?

Can you clarify what eigenvalues you are obtaining?

I’m not sure I understand your question about the order of the state matrix A.

Best regards,

Thank you very much for your answer @Jason.Jonkman ,

-The large matrix has the 4 terms I mentioned + hydroDyn terms from ‘HD ExctnPtfmSg1’ to ‘HD RdtnPtfmY6’ + MoorDyn terms from ’ MD Line 1 node 1 Px, m’ to ‘MD Line 3 node 49 Vz, m/s’. I copy here part of the .lin file from which I’m extracting the infos:

Order of continuous states:
Row/Column Operating Point Rotating Frame? Derivative Order Description


      1   -8.756E-04                                 F               2         ED Platform pitch tilt rotation DOF (internal DOF index = DOF_P), rad
      2    4.721E+00                                 F               2         ED Variable speed generator DOF (internal DOF index = DOF_GeAz), rad
      3   -2.294E-07                                 F               2         ED First time derivative of Platform pitch tilt rotation DOF (internal DOF index = DOF_P), rad/s
      4    3.643E-01                                 F               2         ED First time derivative of Variable speed generator DOF (internal DOF index = DOF_GeAz), rad/s
      5    0.000E+00                                 F               1         HD ExctnPtfmSg1
      6    0.000E+00                                 F               1         HD ExctnPtfmSg2
      7    0.000E+00                                 F               1         HD ExctnPtfmSg3
      8    0.000E+00                                 F               1         HD ExctnPtfmSg4
      9    0.000E+00                                 F               1         HD ExctnPtfmSg5
     10    0.000E+00                                 F               1         HD ExctnPtfmSg6
     11    0.000E+00                                 F               1         HD ExctnPtfmSg7
     12    0.000E+00                                 F               1         HD ExctnPtfmSg8
     13    0.000E+00                                 F               1         HD ExctnPtfmSg9
     14    0.000E+00                                 F               1         HD ExctnPtfmSg10
     15    0.000E+00                                 F               1         HD ExctnPtfmSg11
     16    0.000E+00                                 F               1         HD ExctnPtfmSg12
     17    0.000E+00                                 F               1         HD ExctnPtfmSg13
     18    0.000E+00                                 F               1         HD ExctnPtfmSg14
     19    0.000E+00                                 F               1         HD ExctnPtfmSg15
     20    0.000E+00                                 F               1         HD ExctnPtfmSg16
     21    0.000E+00                                 F               1         HD ExctnPtfmSg17
     22    0.000E+00                                 F               1         HD ExctnPtfmSg18
     23    0.000E+00                                 F               1         HD ExctnPtfmSg19
     24    0.000E+00                                 F               1         HD ExctnPtfmSg20
     25    0.000E+00                                 F               1         HD ExctnPtfmHv1
     26    0.000E+00                                 F               1         HD ExctnPtfmHv2
     27    0.000E+00                                 F               1         HD ExctnPtfmHv3
     28    0.000E+00                                 F               1         HD ExctnPtfmHv4
     29    0.000E+00                                 F               1         HD ExctnPtfmHv5
     30    0.000E+00                                 F               1         HD ExctnPtfmHv6
     31    0.000E+00                                 F               1         HD ExctnPtfmHv7
     32    0.000E+00                                 F               1         HD ExctnPtfmHv8
     33    0.000E+00                                 F               1         HD ExctnPtfmHv9
     34    0.000E+00                                 F               1         HD ExctnPtfmHv10
     35    0.000E+00                                 F               1         HD ExctnPtfmP1
     36    0.000E+00                                 F               1         HD ExctnPtfmP2
     37    0.000E+00                                 F               1         HD ExctnPtfmP3
     38    0.000E+00                                 F               1         HD ExctnPtfmP4
     39    0.000E+00                                 F               1         HD ExctnPtfmP5
     40    0.000E+00                                 F               1         HD ExctnPtfmP6
     41    0.000E+00                                 F               1         HD ExctnPtfmP7
     42    0.000E+00                                 F               1         HD ExctnPtfmP8
     43    0.000E+00                                 F               1         HD RdtnPtfmSg1
     44    0.000E+00                                 F               1         HD RdtnPtfmSg2
     45    0.000E+00                                 F               1         HD RdtnPtfmSg3
     46    0.000E+00                                 F               1         HD RdtnPtfmSg4
     47    0.000E+00                                 F               1         HD RdtnPtfmSg5
     48    0.000E+00                                 F               1         HD RdtnPtfmSg6
     49    0.000E+00                                 F               1         HD RdtnPtfmSg7
     50    0.000E+00                                 F               1         HD RdtnPtfmSg8
     51    0.000E+00                                 F               1         HD RdtnPtfmSg9
     52    0.000E+00                                 F               1         HD RdtnPtfmSg10
     53    0.000E+00                                 F               1         HD RdtnPtfmSg11
     54    0.000E+00                                 F               1         HD RdtnPtfmSg12
     55    0.000E+00                                 F               1         HD RdtnPtfmSg13
     56    0.000E+00                                 F               1         HD RdtnPtfmSg14
     57    0.000E+00                                 F               1         HD RdtnPtfmSw1
     58    0.000E+00                                 F               1         HD RdtnPtfmSw2
     59    0.000E+00                                 F               1         HD RdtnPtfmSw3
     60    0.000E+00                                 F               1         HD RdtnPtfmSw4
     61    0.000E+00                                 F               1         HD RdtnPtfmSw5
     62    0.000E+00                                 F               1         HD RdtnPtfmSw6
     63    0.000E+00                                 F               1         HD RdtnPtfmSw7
     64    0.000E+00                                 F               1         HD RdtnPtfmSw8
     65    0.000E+00                                 F               1         HD RdtnPtfmSw9
     66    0.000E+00                                 F               1         HD RdtnPtfmSw10
     67    0.000E+00                                 F               1         HD RdtnPtfmSw11
     68    0.000E+00                                 F               1         HD RdtnPtfmSw12
     69    0.000E+00                                 F               1         HD RdtnPtfmSw13
     70    0.000E+00                                 F               1         HD RdtnPtfmSw14
     71    0.000E+00                                 F               1         HD RdtnPtfmHv1
     72    0.000E+00                                 F               1         HD RdtnPtfmHv2
     73    0.000E+00                                 F               1         HD RdtnPtfmHv3
     74    0.000E+00                                 F               1         HD RdtnPtfmHv4
     75    0.000E+00                                 F               1         HD RdtnPtfmHv5
     76    0.000E+00                                 F               1         HD RdtnPtfmHv6
     77    0.000E+00                                 F               1         HD RdtnPtfmR1
     78    0.000E+00                                 F               1         HD RdtnPtfmR2
     79    0.000E+00                                 F               1         HD RdtnPtfmR3
     80    0.000E+00                                 F               1         HD RdtnPtfmR4
     81    0.000E+00                                 F               1         HD RdtnPtfmR5
     82    0.000E+00                                 F               1         HD RdtnPtfmR6
     83    0.000E+00                                 F               1         HD RdtnPtfmR7
     84    0.000E+00                                 F               1         HD RdtnPtfmR8
     85    0.000E+00                                 F               1         HD RdtnPtfmR9
     86    0.000E+00                                 F               1         HD RdtnPtfmR10
     87    4.470E-05                                 F               1         HD RdtnPtfmP1
     88    4.098E-05                                 F               1         HD RdtnPtfmP2
     89   -3.689E-05                                 F               1         HD RdtnPtfmP3
     90   -3.343E-05                                 F               1         HD RdtnPtfmP4
     91    3.070E-05                                 F               1         HD RdtnPtfmP5
     92    2.857E-05                                 F               1         HD RdtnPtfmP6
     93   -2.946E-05                                 F               1         HD RdtnPtfmP7
     94   -4.147E-06                                 F               1         HD RdtnPtfmP8
     95   -3.185E-06                                 F               1         HD RdtnPtfmP9
     96    1.465E-06                                 F               1         HD RdtnPtfmP10
     97    0.000E+00                                 F               1         HD RdtnPtfmY1
     98    0.000E+00                                 F               1         HD RdtnPtfmY2
     99    0.000E+00                                 F               1         HD RdtnPtfmY3
    100    0.000E+00                                 F               1         HD RdtnPtfmY4
    101    0.000E+00                                 F               1         HD RdtnPtfmY5
    102    0.000E+00                                 F               1         HD RdtnPtfmY6
    103   -8.206E+02                                 F               2         MD Line 1 node 1 Px, m
    104    0.000E+00                                 F               2         MD Line 1 node 1 Py, m
    105   -2.000E+02                                 F               2         MD Line 1 node 1 Pz, m
    106   -8.036E+02                                 F               2         MD Line 1 node 2 Px, m
    107    0.000E+00                                 F               2         MD Line 1 node 2 Py, m
    108   -2.000E+02                                 F               2         MD Line 1 node 2 Pz, m
    109   -7.866E+02                                 F               2         MD Line 1 node 3 Px, m
    110    0.000E+00                                 F               2         MD Line 1 node 3 Py, m
    111   -2.000E+02                                 F               2         MD Line 1 node 3 Pz, m
    112   -7.696E+02                                 F               2         MD Line 1 node 4 Px, m
    113    0.000E+00                                 F               2         MD Line 1 node 4 Py, m
    114   -2.000E+02                                 F               2         MD Line 1 node 4 Pz, m
    115   -7.526E+02                                 F               2         MD Line 1 node 5 Px, m
    116    0.000E+00                                 F               2         MD Line 1 node 5 Py, m
    117   -2.000E+02                                 F               2         MD Line 1 node 5 Pz, m
    118   -7.356E+02                                 F               2         MD Line 1 node 6 Px, m
    119    0.000E+00                                 F               2         MD Line 1 node 6 Py, m
    120   -2.000E+02                                 F               2         MD Line 1 node 6 Pz, m
    121   -7.186E+02                                 F               2         MD Line 1 node 7 Px, m
    122    0.000E+00                                 F               2         MD Line 1 node 7 Py, m
    123   -2.000E+02                                 F               2         MD Line 1 node 7 Pz, m
    124   -7.015E+02                                 F               2         MD Line 1 node 8 Px, m
    125    0.000E+00                                 F               2         MD Line 1 node 8 Py, m
    126   -2.000E+02                                 F               2         MD Line 1 node 8 Pz, m
    127   -6.845E+02                                 F               2         MD Line 1 node 9 Px, m
    128    0.000E+00                                 F               2         MD Line 1 node 9 Py, m
    129   -2.000E+02                                 F               2         MD Line 1 node 9 Pz, m
    130   -6.675E+02                                 F               2         MD Line 1 node 10 Px, m
    131    0.000E+00                                 F               2         MD Line 1 node 10 Py, m
    132   -2.000E+02                                 F               2         MD Line 1 node 10 Pz, m
    133   -6.505E+02                                 F               2         MD Line 1 node 11 Px, m
    134    0.000E+00                                 F               2         MD Line 1 node 11 Py, m
    135   -2.000E+02                                 F               2         MD Line 1 node 11 Pz, m
    136   -6.335E+02                                 F               2         MD Line 1 node 12 Px, m
    137    0.000E+00                                 F               2         MD Line 1 node 12 Py, m
    138   -2.000E+02                                 F               2         MD Line 1 node 12 Pz, m
    139   -6.165E+02                                 F               2         MD Line 1 node 13 Px, m
    140    0.000E+00                                 F               2         MD Line 1 node 13 Py, m
    141   -2.000E+02                                 F               2         MD Line 1 node 13 Pz, m

etc…

-The eigenvalues are directly evaluated as eig(A) where A is the averaged state matrix for a given wind speed. As example for 5 m/s I have:
-0.0625583933119680 + 2.89214181454705i
-0.0625583933119680 - 2.89214181454705i
-0.0848410659622325 + 0.00000000000000i
-0.00120214741383145 + 0.00000000000000i
I was expecting lower imaginary part(around 0.2i) , and it seems to be connected with the term of the submatrix 3-1 (-8.366).

  • For what concern the order in the matrix, considering the 4x4 I know that the derivatives of platform pitch and of generator speed should have zero everywhere in their rows but in 1 in the respective columns (from an equation in state-space point of view: derivative=derivative). So i was expecting two lines with only one term egual to 1: it happened, but I don’t understand why they are in the first two rows since the ‘Order of continuous states’ is saying that the first two rows are not associated to the derivatives. I hope I expressed it better now, maybe I’'m just misuderstanding.

Dear @Leonardo.Facelli,

Thanks for clarifying. Neglecting the hydrodynamic states should be OK when calculating full-system natural frequencies, but neglecting the mooring states will obviously have some impact on some floater modes of motion.

Regarding the incorrect pitch natural frequency, I would guess this is tied to lack of surge-pitch coupling given that you’ve disabled surge, so, the floater can only rotate about the platform reference point.

Regarding the ordering of the state “A” matrix, the linear state-space equation is:

dxdot = A*dx

where dx = { dq; dqdot } and dxdot = { dqdot; dqdotdot }. Thus, the upper-right quadrant of A should contain the identity matrix, expressing the fact that dqdot = dqdot.

Best regards,

Thanks again for your answer @Jason.Jonkman ,

I’m actually trying to compare the linearization from OpenFAST with a simplified model formed by 3 states( rotor speed, platfrom pitch and derivative of the platform pitch) that I created. In the simplified model, the platform pitch’s equation has the following form: Jpthetadotdtot+Cpthetadot+Kptheta=hhT
where:
hh: hub height
Jp: equivalent platform pitch inertia given my the contribution of platform mass,tower mass and tower top mass + added mass
Rp: platform pitch damping from free decay analisys coming from openfast simulation
Kp: platform pitch stiffness given by hydrodynamic term(with C_hs(5,5) from .hst file in HydroData) + gravitational term + mooring lines term (from analysis of the slope of overall moment of mooring lines for different initial condition of the pitch)
T: thrust component that I linearized in the further passages(will have contribution on the damping and coupling with the rotor speed equation)
Given this position, you suggest then to activate surge and then extract the 4x4 (or 3x3 to fully respect my model) submatrix? For what concern the mooring states, are they a big issue?(given that I’m not considering them neither in the simple model, except for their stiffness contribution)

Regarding the state A matrix, it is my fault, I completely agree with you, thanks.

Dear @Leonardo.Facelli,

Regarding the pitch natural frequency, I’m just speculating that the pitch frequency could be off because it often couples with surge and you have not enabled that DOF.

In your simplified model, are you assuming pitch rotation is about the same platform reference point as your OpenFAST model? If so, you should be able to compare the Jp, Cp, and Kp you are using are consistent with the state “A” matrix generated by OpenFAST.

If you want only the linearized stiffness of the mooring system without all of the mooring states, I would suggest switching from MoorDyn to MAP++, in which case the mooring stiffness would be included in the OpenFAST linearization solution without associated mooring-related states.

Best regards,

Thanks @Jason.Jonkman ,
I’ve repeated all the simulation using MAP++ instead of MoorDyn and now the eigenvalues and natural frequency are very close. I didn’t include the surge dof at the end since OpenFAST was struggling to identify a condition to perform the linearization.
I’d like just to share the final result of the comparison in term of non-dimensional damping with my linear model:


I notice that between 6-7 m/s OpenFast is not reproducing the flat step as in the model(which was a direct conseguence of the linearization of the thrust force in my model), additionally after the peak at 10 m/s the h decreases very rapidly. When I performed the linearization with MoorDyn on the other hand h had a maximum of 3% but the shape was respected. Do you have some hints on how to interpret these changes? I also attach the non-dimensional damping coming with MoorDyn.

Thank you very much for your time.

Dear @Leonardo.Facelli,

I’m not sure how you are defining “non-dimensional damping” or what you mean by “h”.

Best regards,

Dear @Jason.Jonkman ,
sorry I’m using ‘h’ to speak about pitch non-dimensional damping. It’s simply evaluated as:
h=abs(real(eigenvalue))/w_n
where w_n=sqrt(real(eigenvalue)^2+imag(eigenvalue)^2) (distance from the origin in the complex plane).
Thank you very much

Dear @Leonardo.Facelli,

I see; you mean the damping ratio as calculated by the eigenvalue.

I’m glad your now obtaining the natural frequencies you expect.

I’m not sure I know enough about your simulation set up to comment on what damping terms you have included (hydrodynamic radiation, hydrodynamic viscous, aerodynamics, etc.).

Best regards,

1 Like

Thank you very much for your time and your help @Jason.Jonkman

Best regards

Dear @Jason.Jonkman ,
I’m further analyzing the non-dimensional damping of the platform pitch, and I tried to extract it (again varying the nominal wind speed) from free decay tests: PtfmPitch dof activated, still water, very small initial platform pitch(-1.5 deg), costant values of rotor speed and blade pitches as in steady-state for the given speed,no ServoDyn and MAP++ to respect the linearization.
From the PtfmPitch time history, I used the logarithmic decrement method for my purpose.
As I moved into the results I’ve noticed that the values are half of the ones from the OpenFAST linearization. I tried to use MoorDyn or change the initial pitch, but the results were almost the same. I also tried skip the first 50-60s from the analysis to avoid large displacement non-linearities, but it was still quite hard to get the expected results.(as example: for 12 m/s I cut the initial 60s and I’m able to get to 22% damping ratio, 11 m/s cutting 50s I get 27% but 10 m/s whatever I’m cutting I’m at 15-17%. So I’d say it’s not the right path to follow)
Since the previous results are robust, I was wondering if I’am missing something important in the simulations settings. Or if you have any suggestions.
As example I attach one typical PtfmPitch output:
image
(The red dots are the peaks values I’m using to get the damping ratio)
Thank you very much for your time again.

Dear @Leonardo.Facelli,

Can you clarify your simulation set-up in terms of hydrodynamic damping contributions (radiation, viscous), both for linearization and for your free-decay simulations? If the hydrodynamic damping is dominated by viscous effects, the linearized damping is likely not representative, as implied by the following known issue related to how viscous effects are linearized in HydroDyn: Feature Request: Improve How Viscous Drag is Linearized in HydroDyn · Issue #1210 · OpenFAST/openfast · GitHub.

Best regards,

Dear @Jason.Jonkman,
here it is my HydroDyn settings for both cases:
------- HydroDyn v2.03.* Input File --------------------------------------------
IEA 15 MW offshore reference model on UMaine VolturnUS-S semi-submersible floating platform
False Echo - Echo the input file data (flag)
---------------------- ENVIRONMENTAL CONDITIONS --------------------------------
“default” WtrDens - Water density (kg/m^3)
“default” WtrDpth - Water depth (meters)
“default” MSL2SWL - Offset between still-water level and mean sea level (meters) [positive upward; unused when WaveMod = 6; must be zero if PotMod=1 or 2]
---------------------- WAVES ---------------------------------------------------
0 WaveMod - Incident wave kinematics model {0: none=still water, 1: regular (periodic), 1P#: regular with user-specified phase, 2: JONSWAP/Pierson-Moskowitz spectrum (irregular), 3: White noise spectrum (irregular), 4: user-defined spectrum from routine UserWaveSpctrm (irregular), 5: Externally generated wave-elevation time series, 6: Externally generated full wave-kinematics time series [option 6 is invalid for PotMod/=0]} (switch)
0 WaveStMod - Model for stretching incident wave kinematics to instantaneous free surface {0: none=no stretching, 1: vertical stretching, 2: extrapolation stretching, 3: Wheeler stretching} (switch) [unused when WaveMod=0 or when PotMod/=0]
3000.00 WaveTMax - Analysis time for incident wave calculations (sec) [unused when WaveMod=0; determines WaveDOmega=2Pi/WaveTMax in the IFFT]
0.025 WaveDT - Time step for incident wave calculations (sec) [unused when WaveMod=0; 0.1<=WaveDT<=1.0 recommended; determines WaveOmegaMax=Pi/WaveDT in the IFFT]
1.10 WaveHs - Significant wave height of incident waves (meters) [used only when WaveMod=1 or 2]
8.52 WaveTp - Peak spectral period of incident waves (sec) [used only when WaveMod=1 or 2]
DEFAULT WavePkShp - Peak-shape parameter of incident wave spectrum (-) or DEFAULT (string) [used only when WaveMod=2; use 1.0 for Pierson-Moskowitz]
0.1 WvLowCOff - Low cut-off frequency or lower frequency limit of the wave spectrum beyond which the wave spectrum is zeroed (rad/s) [unused when WaveMod=0, 1, or 6]
0.5 WvHiCOff - High cut-off frequency or upper frequency limit of the wave spectrum beyond which the wave spectrum is zeroed (rad/s) [unused when WaveMod=0, 1, or 6]
0.00 WaveDir - Incident wave propagation heading direction (degrees) [unused when WaveMod=0 or 6]
0 WaveDirMod - Directional spreading function {0: none, 1: COS2S} (-) [only used when WaveMod=2,3, or 4]
1 WaveDirSpread - Wave direction spreading coefficient ( > 0 ) (-) [only used when WaveMod=2,3, or 4 and WaveDirMod=1]
1 WaveNDir - Number of wave directions (-) [only used when WaveMod=2,3, or 4 and WaveDirMod=1; odd number only]
90 WaveDirRange - Range of wave directions (full range: WaveDir +/- 1/2WaveDirRange) (degrees) [only used when WaveMod=2,3,or 4 and WaveDirMod=1]
-561580799 WaveSeed(1) - First random seed of incident waves [-2147483648 to 2147483647] (-) [unused when WaveMod=0, 5, or 6]
RANLUX WaveSeed(2) - Second random seed of incident waves [-2147483648 to 2147483647] (-) [unused when WaveMod=0, 5, or 6]
TRUE WaveNDAmp - Flag for normally distributed amplitudes (flag) [only used when WaveMod=2, 3, or 4]
“none” WvKinFile - Root name of externally generated wave data file(s) (quoted string) [used only when WaveMod=5 or 6]
1 NWaveElev - Number of points where the incident wave elevations can be computed (-) [maximum of 9 output locations]
0 WaveElevxi - List of xi-coordinates for points where the incident wave elevations can be output (meters) [NWaveElev points, separated by commas or white space; usused if NWaveElev = 0]
0 WaveElevyi - List of yi-coordinates for points where the incident wave elevations can be output (meters) [NWaveElev points, separated by commas or white space; usused if NWaveElev = 0]
---------------------- 2ND-ORDER WAVES ----------------------------------------- [unused with WaveMod=0 or 6]
False WvDiffQTF - Full difference-frequency 2nd-order wave kinematics (flag)
False WvSumQTF - Full summation-frequency 2nd-order wave kinematics (flag)
0 WvLowCOffD - Low frequency cutoff used in the difference-frequencies (rad/s) [Only used with a difference-frequency method]
0.737863 WvHiCOffD - High frequency cutoff used in the difference-frequencies (rad/s) [Only used with a difference-frequency method]
0.314159 WvLowCOffS - Low frequency cutoff used in the summation-frequencies (rad/s) [Only used with a summation-frequency method]
3.2 WvHiCOffS - High frequency cutoff used in the summation-frequencies (rad/s) [Only used with a summation-frequency method]
---------------------- CURRENT ------------------------------------------------- [unused with WaveMod=6]
0 CurrMod - Current profile model {0: none=no current, 1: standard, 2: user-defined from routine UserCurrent} (switch)
0 CurrSSV0 - Sub-surface current velocity at still water level (m/s) [used only when CurrMod=1]
“DEFAULT” CurrSSDir - Sub-surface current heading direction (degrees) or DEFAULT (string) [used only when CurrMod=1]
20 CurrNSRef - Near-surface current reference depth (meters) [used only when CurrMod=1]
0 CurrNSV0 - Near-surface current velocity at still water level (m/s) [used only when CurrMod=1]
0 CurrNSDir - Near-surface current heading direction (degrees) [used only when CurrMod=1]
0 CurrDIV - Depth-independent current velocity (m/s) [used only when CurrMod=1]
0 CurrDIDir - Depth-independent current heading direction (degrees) [used only when CurrMod=1]
---------------------- FLOATING PLATFORM --------------------------------------- [unused with WaveMod=6]
1 PotMod - Potential-flow model {0: none=no potential flow, 1: frequency-to-time-domain transforms based on WAMIT output, 2: fluid-impulse theory (FIT)} (switch)
2 ExctnMod - Wave Excitation model {0: None, 1: DFT, 2: state-space} (switch) [only used when PotMod=1; STATE-SPACE REQUIRES .ssexctn INPUT FILE]
2 RdtnMod - Radiation memory-effect model {0: no memory-effect calculation, 1: convolution, 2: state-space} (switch) [only used when PotMod=1; STATE-SPACE REQUIRES .ss INPUT FILE]
60.0 RdtnTMax - Analysis time for wave radiation kernel calculations (sec) [only used when PotMod=1; determines RdtnDOmega=Pi/RdtnTMax in the cosine transform; MAKE SURE THIS IS LONG ENOUGH FOR THE RADIATION IMPULSE RESPONSE FUNCTIONS TO DECAY TO NEAR-ZERO FOR THE GIVEN PLATFORM!]
“DEFAULT” RdtnDT - Time step for wave radiation kernel calculations (sec) [only used when PotMod=1; DT<=RdtnDT<=0.1 recommended; determines RdtnOmegaMax=Pi/RdtnDT in the cosine transform]
1 NBody - Number of WAMIT bodies to be used (-) [>=1; only used when PotMod=1. If NBodyMod=1, the WAMIT data contains a vector of size 6
NBody x 1 and matrices of size 6
NBody x 6
NBody; if NBodyMod>1, there are NBody sets of WAMIT data each with a vector of size 6 x 1 and matrices of size 6 x 6]
1 NBodyMod - Body coupling model {1: include coupling terms between each body and NBody in HydroDyn equals NBODY in WAMIT, 2: neglect coupling terms between each body and NBODY=1 with XBODY=0 in WAMIT, 3: Neglect coupling terms between each body and NBODY=1 with XBODY=/0 in WAMIT} (switch) [only used when PotMod=1]
“HydroData/IEA-15-240-RWT-UMaineSemi” PotFile - Root name of potential-flow model data; WAMIT output files containing the linear, nondimensionalized, hydrostatic restoring matrix (.hst), frequency-dependent hydrodynamic added mass matrix and damping matrix (.1), and frequency- and direction-dependent wave excitation force vector per unit wave amplitude (.3) (quoted string) [MAKE SURE THE FREQUENCIES INHERENT IN THESE WAMIT FILES SPAN THE PHYSICALLY-SIGNIFICANT RANGE OF FREQUENCIES FOR THE GIVEN PLATFORM; THEY MUST CONTAIN THE ZERO- AND INFINITE-FREQUENCY LIMITS!]
1 WAMITULEN - Characteristic body length scale used to redimensionalize WAMIT output (meters) [only used when PotMod=1]
0.0 PtfmRefxt - The xt offset of the body reference point(s) from (0,0,0) (meters) [1 to NBody] [only used when PotMod=1]
0.0 PtfmRefyt - The yt offset of the body reference point(s) from (0,0,0) (meters) [1 to NBody] [only used when PotMod=1]
0.0 PtfmRefzt - The zt offset of the body reference point(s) from (0,0,0) (meters) [1 to NBody] [only used when PotMod=1. If NBodyMod=2,PtfmRefzt=0.0]
0.0 PtfmRefztRot - The rotation about zt of the body reference frame(s) from xt/yt (degrees) [1 to NBody] [only used when PotMod=1]
20206.34889 PtfmVol0 - Displaced volume of water when the platform is in its undisplaced position (m^3) [only used when PotMod=1; USE THE SAME VALUE COMPUTED BY WAMIT AS OUTPUT IN THE .OUT FILE!]
0 PtfmCOBxt - The xt offset of the center of buoyancy (COB) from the platform reference point (meters) [only used when PotMod=1]
0 PtfmCOByt - The yt offset of the center of buoyancy (COB) from the platform reference point (meters) [only used when PotMod=1]
---------------------- 2ND-ORDER FLOATING PLATFORM FORCES ---------------------- [unused with WaveMod=0 or 6, or PotMod=0 or 2]
0 MnDrift - Mean-drift 2nd-order forces computed {0: None; [7, 8, 9, 10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero]
0 NewmanApp - Mean- and slow-drift 2nd-order forces computed with Newman’s approximation {0: None; [7, 8, 9, 10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero. Used only when WaveDirMod=0]
0 DiffQTF - Full difference-frequency 2nd-order forces computed with full QTF {0: None; [10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero]
0 SumQTF - Full summation -frequency 2nd-order forces computed with full QTF {0: None; [10, 11, or 12]: WAMIT file to use}
---------------------- PLATFORM ADDITIONAL STIFFNESS AND DAMPING --------------
0.0 AddF0 - Additional preload (N, N-m) [If NBodyMod=1, one size 6*NBody x 1 vector; if NBodyMod>1, NBody size 6 x 1 vectors]
0.0
0.0
0.0
0.0
0.0
0 0 0 0 0 0 AddCLin - Additional linear stiffness (N/m, N/rad, N-m/m, N-m/rad)
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0 AddBLin - Additional linear damping(N/(m/s), N/(rad/s), N-m/(m/s), N-m/(rad/s))
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
9.23E+05 0.00E+00 0.00E+00 0.00E+00 -8.92E+06 0.00E+00 AddBQuad - Additional quadratic drag(N/(m/s)^2, N/(rad/s)^2, N-m(m/s)^2, N-m/(rad/s)^2)
0.00E+00 9.23E+05 0.00E+00 8.92E+06 0.00E+00 0.00E+00
0.00E+00 0.00E+00 2.30E+06 0.00E+00 0.00E+00 0.00E+00
0.00E+00 8.92E+06 0.00E+00 1.68E+10 0.00E+00 0.00E+00
-8.92E+06 0.00E+00 0.00E+00 0.00E+00 1.68E+10 0.00E+00
0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 4.80E+10
---------------------- AXIAL COEFFICIENTS --------------------------------------
1 NAxCoef - Number of axial coefficients (-)
AxCoefID AxCd AxCa AxCp
(-) (-) (-) (-)
1 0.0 0.0 1.0
---------------------- MEMBER JOINTS -------------------------------------------
0 NJoints - Number of joints (-) [must be exactly 0 or at least 2]
JointID Jointxi Jointyi Jointzi JointAxID JointOvrlp [JointOvrlp= 0: do nothing at joint, 1: eliminate overlaps by calculating super member]
(-) (m) (m) (m) (-) (switch)
---------------------- MEMBER CROSS-SECTION PROPERTIES -------------------------
0 NPropSets - Number of member property sets (-)
PropSetID PropD PropThck
(-) (m) (m)
---------------------- SIMPLE HYDRODYNAMIC COEFFICIENTS (model 1) --------------
SimplCd SimplCdMG SimplCa SimplCaMG SimplCp SimplCpMG SimplAxCd SimplAxCdMG SimplAxCa SimplAxCaMG SimplAxCp SimplAxCpMG
(-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-)
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
---------------------- DEPTH-BASED HYDRODYNAMIC COEFFICIENTS (model 2) ---------
0 NCoefDpth - Number of depth-dependent coefficients (-)
Dpth DpthCd DpthCdMG DpthCa DpthCaMG DpthCp DpthCpMG DpthAxCd DpthAxCdMG DpthAxCa DpthAxCaMG DpthAxCp DpthAxCpMG
(m) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-)
---------------------- MEMBER-BASED HYDRODYNAMIC COEFFICIENTS (model 3) --------
0 NCoefMembers - Number of member-based coefficients (-)
MemberID_HydC MemberCd1 MemberCd2 MemberCdMG1 MemberCdMG2 MemberCa1 MemberCa2 MemberCaMG1 MemberCaMG2 MemberCp1 MemberCp2 MemberCpMG1 MemberCpMG2 MemberAxCd1 MemberAxCd2 MemberAxCdMG1 MemberAxCdMG2 MemberAxCa1 MemberAxCa2 MemberAxCaMG1 MemberAxCaMG2 MemberAxCp1 MemberAxCp2 MemberAxCpMG1 MemberAxCpMG2
(-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-)
-------------------- MEMBERS -------------------------------------------------
0 NMembers - Number of members (-)
MemberID MJointID1 MJointID2 MPropSetID1 MPropSetID2 MDivSize MCoefMod PropPot [MCoefMod=1: use simple coeff table, 2: use depth-based coeff table, 3: use member-based coeff table] [ PropPot/=0 if member is modeled with potential-flow theory]
(-) (-) (-) (-) (-) (m) (switch) (flag)
---------------------- FILLED MEMBERS ------------------------------------------
0 NFillGroups - Number of filled member groups (-) [If FillDens = DEFAULT, then FillDens = WtrDens; FillFSLoc is related to MSL2SWL]
FillNumM FillMList FillFSLoc FillDens
(-) (-) (m) (kg/m^3)
---------------------- MARINE GROWTH -------------------------------------------
0 NMGDepths - Number of marine-growth depths specified (-)
MGDpth MGThck MGDens
(m) (m) (kg/m^3)
---------------------- MEMBER OUTPUT LIST --------------------------------------
0 NMOutputs - Number of member outputs (-) [must be < 10]
MemberID NOutLoc NodeLocs [NOutLoc < 10; node locations are normalized distance from the start of the member, and must be >=0 and <= 1] [unused if NMOutputs=0]
(-) (-) (-)
---------------------- JOINT OUTPUT LIST ---------------------------------------
0 NJOutputs - Number of joint outputs [Must be < 10]
0 JOutLst - List of JointIDs which are to be output (-)[unused if NJOutputs=0]
---------------------- OUTPUT --------------------------------------------------
False HDSum - Output a summary file [flag]
False OutAll - Output all user-specified member and joint loads (only at each member end, not interior locations) [flag]
1 OutSwtch - Output requested channels to: [1=Hydrodyn.out, 2=GlueCode.out, 3=both files]
“ES11.4e2” OutFmt - Output format for numerical results (quoted string) [not checked for validity!]
“A11” OutSFmt - Output format for header strings (quoted string) [not checked for validity!]
---------------------- OUTPUT CHANNELS -----------------------------------------
“Wave1Elev” - Wave elevation at the platform reference point ( 0, 0)
“WavesF1xi”
“WavesF1zi”
“WavesM1yi”
“WavesF2xi”
“WavesF2zi”
“WavesM2yi”
“WavesF2xi”
“WavesF2yi”
“WavesF2zi”
“WavesM2xi”
“WavesM2yi”
“WavesM2zi”
END of output channels and end of file. (the word “END” must appear in the first 3 columns of this line)

Thanks for your help

Dear @Leonardo.Facelli,

I see that you have both state-space-based wave-radiation damping and an additional quadratic drag matrix enabled in your model. The damping you calculate via eigenalysis from the resultant linearized model will not be accurate because (1) you are neglecting the radiation states in the process of calculating damping and (2) the linearization of the additional quadratic drag matrix is not handled properly by HydroDyn in the absence of forward speed (mean velocity) per the OpenFAST issue I mentioned above. Thus, I would not rely on the damping ratio as “representative” from this linearized solution.

Best regards,

Dear @Jason.Jonkman ,
I tried some linearizations (under rated,rated and above rated wind) with the new settings, but the results are really really close to the one before, I would not relate the difference from the free decay to this. Should I try to do the inverse? Deactivate them in the free decay tests?

I’m not really sure I understand what you are asking.

I was simply trying to not consider radiation and quadratic drag in the free decay tests. I tried, but it just worsened the differences.

Can you clarify what you changed in the HydroDyn input file and what results you obtained (linearization versus free-decay)?

The initial results (also addying the changes in HydroDyn) are the following:


(Blue line is my simplified model, red is from free decay and yellow from linearization)

In HydroDyn given your suggestions, I put 0 at ‘ExctnMod’ and ‘RdtnMod’.
When I tried to do free decay test with them deactivated, the damping ratio was getting very low (about 2-3%).

Thank you