Dear Sir or Madam:

I have two queries about FASTv8:

1a) Is there a way to find the natural frequency of the floater using FAST? In particular, the DeepCwind floater.

1b) I had initially thought that since the tower is connected to the floater they would act as one and hence the natural frequency of the combined system would be required(similar to a fixed-based OWT). However from the literature, I realize that the natural frequency of the tower is calculated separately from the floater. Is the concept that you would determine the natural frequency for the floater and then attach tower and determine natural frequency and that frequency of combined system is taken for the tower? This is not clear please explain

2) The different random seeds used to get in design load cases to get multiple sets of results for the same sea state variables, does this occur naturally when more than one simulation is run or do you have to change a value is FAST to activate the different seeds?

Regards,

AOAW

Dear Andre,

Here are my answers to your questions:

1a) The most direct way of computing full-system natural frequencies is through the linearization functionality of FAST / OpenFAST. But in FAST v8, full-system linearization was only available for land-based turbines (for the ElastoDyn, InflowWind, AeroDyn, and ServoDyn modules). Linearization capability for floating offshore wind turbines (including for the HydroDyn, MAP++, BeamDyn, and SubDyn modules) has been added to OpenFAST; I would suggest upgrading from FAST v8 to OpenFAST to use this capability. Alternatively, you can use white-noise waves excitation to compute natural frequencies (as discussed several times on this forum), although the results are not always easy to interpret for complicated multiple DOF models.

1b) I’m not sure what literature you are referring to, but I would say that the analysis of the combined system is required; the floating boundary condition can impact the tower natural frequencies and the flexible tower can impact the floating platform natural frequencies (particularly for TLPs).

- You need to change the WaveSeed input in HydroDyn to get different sea states for the same wave conditions.

Best regards,

Hi Jason:

Many thanks for the prompt feedback. With regard to OpenFAST I would very much like to upgrade to it. I had tried using it prior to FAST v8 but had problems setting it up. Now that I have a gained a bit more understanding I would like to find out:

- Is it possible to install the binaries for OpenFAST to my computer in a similar manner like for FAST v8 or do I have to go through the compilation process with CygWin and CMake etc? I am working with a Windows OS.

I am assuming that I have to change both random seeds for each simulation and that the value of each can be any number within the range specified. Is that correct?

I have checked another paper and it does refer to the natural frequency of the whole system. Thanks for the clarification.

Regards,

AOAW

Dear Andre,

Precompiled binary executables for Windows have been provided with each release of OpenFAST–see: github.com/OpenFAST/openfast/issues/663.

If you need to change the source code, you must recompile, but in my opinion, on Windows, it is easiest to compile OpenFAST through Visual Studio using the provided solution files (without CMake).

You can change one or the other or both wave seeds. Having two seeds provides for many different realizations.

Best regards,

Jason:

Thank you. I will install the compilers and binaries and see how it goes.

Regards,

AOAW

Hi Jason:

Going back the natural frequency of DeepCwind. In openfast I see that there is a file called “5MW_OC4Semi_Linear.FST”.

- Is this the file that is required to determine the natural frequency of the system? Please also advise me on anything else that may be required to carry out this process.

Thank you.

Regards,

AOAW

Dear Andre,

Yes, the r-test file 5MW_OC4Semi_Linear.fst is used to perform a linearization analysis of the OC4-DeepCwind semi in still water without aerodynamic loads while spinning at 12.1 rpm, from which the full-system natural frequencies and mode shapes can be extracted. The process and results are described in our DeepWind 2019 paper: iopscience.iop.org/article/10.1 … 6/1/012022.

Best regards,

Jason:

I have obtained the eigenvalues of the DeepCwind system using A=eig(Amatrix) in MATLAB. However, I am not sure which is the first natural frequency of the different degrees of freedom, surge, yaw etc. Also the output is of the format A+Bi, I do not remember how to interpret or convert to the natural frequencies in Hz as I did this a long time ago.

Would be grateful for some clarification.

Thank you.

Regards,

AOAW

Jason:

If my understanding is correct I believe the real part is the natural frequency, so if eigenvalue = A + Bi, the natural frequency is A. While the imaginary part gives information about the damping for that particular mode. However, I do not know which frequency is for which degree of freedom.

Regards,

AOAW

Dear Andre,

Interpretation of the eigensolution has been discussed many times on this forum, including a discussion of the scripts from the MATLAB Toolbox (github.com/OpenFAST/matlab-toolbox)–such as MBC3 and runCampbell–that can aid in the interpretation of the MATLAB eig() function. The derivation of the natural frequencies, damped frequencies, and damping ratios from real and imaginary components of the eigenvalues has been discussed explicitly, e.g. here, which is the approach used by MBC3.

Best regards,

Jason:

Tried to carry out the eigenanalysis using mbc. I carried out free decay test in OpenFAST and got the following file:

5MW_OC4Semi_Linear.1.lin.

However on executing the GetMats command in MATLAB I am getting the following error:

[b]Running Eigenanalysis.m using “5MW_OC4Semi_Linear.1.lin”

Please wait…

Index exceeds the number of array elements (50).

Error in GetMats (line 56)

RotSpeed = str2num( line(55:68) ); % in (rad/s)[/b]

Not sure what is happening here. If I need to modify the .lin file before executing the GetMats command. I realize that in the .lin file the number of continuous states is 138. So my AMatix is 138 x 138.

1) Could this be the source of the error? Also, not sure why 138 states are used here.

I also have another query:

In the .fst file under linearization, CalcSteady was set to False. However, in a particular forum I saw where you advised that it should be set to true when carrying out the free decay test.

2) Should CalcSteady be set to true when carrying out the free decay test?

Would be very grateful if you could assist.

Thank you.

Regards,

AOAW

Dear Andre,

You appear to be running the old MBC scripts for FAST v7. In FAST v8 and OpenFAST, you should use fx_mbc3.m, followed by campbell_diagram_data.m, as documented at the bottom of the page here: github.com/OpenFAST/matlab-toolbox.

OpenFAST allows you to linearize a model at any point in time, but the linear system is most useful (and able to predict a representative eigensolution) only when the model is in steady state. Enabling CalcSteady is an automated way to ensure that the solution is in equilibrium before linearizing.

A free-decay simulation is a transient event and the solution is not an equilibrium until the transients have subsided.

Best regards,

Thanks Jason. Will try that one.

Regards,

AOAW

Jason:

I have carried out the Eigenanlysis wth the new scripts and it works. However, I have a question regarding the outputs. There are 62 mode shapes. If I am understanding correctly, the first 6 seem to be the ones for the platform DOFs. With the degree of freedom being set to TRUE indicating that, the natural frequency of the system corresponds to that mode.

For example for mode number 1, ED platform horizontal sway translation DOF, m is set to TRUE and the natural frequency for that mode of vibration is 0.008866 Hz. Which is the natural frequency for the sway DOF. The same applies for the other 5 DOFs.

Please let me know if this is correct. Otherwise, what is the way to identify which mode of vibration corresponds to the respective DOFs.

Thank you.

Regards,

AOAW

Jason:

Another query;

For TowerLen and BladeLen are these the height of the tower, TowerHt (87.6 m) and TipRad (63 m) shown in ElastoDyn?

I saw in another forum where 85.41 m and 61.91 m were used for the TowerLen ad BladeLen respectively but I don’t see those values anywhere.

Please clarify.

Regards,

AOAW

Dear Andre,

By TowerLen and BladeLen, I assume you are referring to the inputs in the campbell_diagram_data.m script. These should be the length of the tower and blade that are modeled flexibly in your ElastoDyn model (i.e., BladeLen = TipRad - HubRad and TowerLen = TowerHt - TowerBsHt). However, the exact values are not critical as they are only used to normalize the eigenvectors so that each element has the same units (rad), which will help in interpretation of the mode shapes.

Often a DOF identified by TRUE in the eigensolution output from the campbell_diagram_data.m script is easy to identify as the corresponding full-system mode (yes, the sway frequency of the OC4-DeepCwind semi is 0.008866 Hz), but this is not always the case. The eigenvectors show the relative contribution of each DOF to each full-system mode. If takes experience and some knowledge of the model to interpret these eigenvectors; again, this topic has been discussed many times on the forum. The mode shape visualization functionality of OpenFAST can be used to help with interpretation

Best regards,

Jason:

I would like to raise a few more questions. I have done Eigenanalysis to find the system natural frequencies of NREL original DeepCwind model for 200 m deep water and the 100 m model using same DeepCwind platform. The sea conditions are as follows:

NREL Sea (Hs = 1.2626, Tp = 10, JONSWAP spectrum), Jamaica (Hs = 1.76, Tp = 8.0, JONSWAP spectrum)

The results are as follows:

Table 1 DOFs for the NREL 200 m DeepCwind was found to be:

Platform motion Nat frequency Hz Mode of vibration

Surge 0.008866 1

Sway 0.008869 2

Heave 0.057865 8

Roll 0.039117 6

Pitch 0.038916 5

Yaw 0.01262 3

Table 2 DOFs for the NREL 100 m DeepCwind was found to be:

Platform motion Nat frequency Hz Mode of vibration

Surge 0.050909 3

Sway 0.050919 4

Heave 0.067836 5

Roll 0.087518 9

Pitch 0.072968 6

Yaw 0.10187 12

The pitch and roll DOFs for the 100 m deep model were not picked up by ED platform roll/pitch tilt rotation but by HDExctnPtfmP3 and HDExctnPtfmR3.The pitch and roll values are also about 2 times the values of the 200 m system.

1) Does this mean there is something wrong with the 100 m deep model and it needs to be further tuned?

Table 3 200 m system natural frequency, Jamaica Sea

Platform motion Nat Frequency Mode of vibration

Surge 0.008869 2

Sway 0.008866 1

Heave 0.105887 13

Roll 0.039117 6

Pitch 0.038916 5

Yaw 0.01262 3

The heave motion was picked up as HD RdtnPtfmHv8 and not ED Platform vertical heave translation as per the others. It is also seems a bit high.

It is about twice the original heave natural frequency. Not sure what is going on here but similar to issue in question 1 above.

Table 4 100 m system natural frequency, Jamaica Sea

Platform motion Nat Frequency Hz Mode of vibration

Surge 0.039231 3

Sway 0.039328 4

Heave 0.059451 8

Roll 0.039328 4

Pitch 0.039231 3

Yaw 0.024052 1

For the 100 m system, all modes of vibration were registered as per usual. But the sway and roll; surge and pitched were picked up under the same mode of vibration. Not sure if this is good result or if this 100 m model needs further tuning as per question 1).

By the way these tables did not turn as expected. The single number at each end is the mode of vibration. The other number is the system natural frequency.

Thank you.

Regards,

AOAW