FAST: Model linearization

Dear Lain,

You are getting C66 = 1.099E8 Nm/rad because the OC3-Hywind model includes an additional yaw spring, i.e. C66 = 98,340,000 Nm/rad + 11,560,000 Nm/rad. The reason you are not getting the correct values for C33, C44, and C55 from your FAST v7 linearization is because of the influence of the hydrostatic stiffness and system weight (gravitational restoring) terms. The procedure for deriving the linear 6x6 stiffness matrix associated with the mooring system (without the hydrostatic and weight terms) from FAST v7 is explained in my Oct 30, 2012 post in the following forum topic: Questions about the HydroDyn Module.

BModes does not include the influence of system weight on the modal calculation. Body weight is important for the pitch and roll restoring of deep-drafted floating platforms, such as spar buoys. As such, The “OC3Hywind.bmi” model uses an adjustment to the (4,4) and (5,5) elements of the mooring system stiffness to augment the overall restoring in pitch and roll.

I hope that helps.

Best regards,

Dear Jason,

first of all thank you for the quick reply and for the work you are doing in the forum, with the software development and the investigation.
I used as described in the post viewtopic.php?f=4&t=732 the zero valued hydrostatic and hydrodynamic matrices. I get now the matrix I attach as “K – Stiff” where the difference with the matrix of the paper 47535 are negligible in C66, and a 5% difference remains in the C44=C55 as you describe in your answer in order to take account of the mass of the spar buoy. I now get as you can see in the attached file a difference of around 20% in C15 and C24. 4 new parameters appear which are maybe not negligible and do not appear in “OC3Hywind.bmi” Cij matrix.

My question is if still I am doing something wrong in my calculation or it is well done. If it is well done then C26, C35, C46 and C64 are negligible and the difference in C15 and C24 has not much influence in the modal calculation. If it is badly done then there is/are remaining parameter/s I did not check in my calculation which I fear. In this last case I already checked the azimuth influence being negligible for the calculation and other more tests but I run out of ideas maybe you can help with some.

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Laín Nieto Gómez
PhD Student in the UPV/EHU University of the Basque Country
Escuela Técnica Superior de Ingenieros de Bilbao
Departamento de matemática aplicada
Spain
lnieto001@ikasle.ehu.eus

K_Matrix.txt (2.32 KB)

Dear Lain,

Did you follow all of the steps from the forum post I linked above (Questions about the HydroDyn Module)? If you did, I would expect that you’d match the 6x6 stiffness matrix of the mooring system from NREL/TP-500-47535 exactly. The resulting matrix would not include the body-weight terms.

Best regards,

Dear Jason,

Could I please know are there any example models of linearization (or detailed steps on how to use) for finding out the natural frequencies and modeshapes of the system corresponding to wind and wave loads (Aerodyn and Hydrodyn). I am using OpenFAST v3.0.

Thanks,
Satish J

Dear Satish,

I would not expect the natural frequencies to depend directly on wind and wave loads, although mean loading can effect the steady-state operating point and/or rotor speed, which can effect the natural frequencies.

This test of the NREL 5-MW baseline turbine atop the OC4-DeepCWind semisubmersible is the floating linearization test that we have made available: github.com/OpenFAST/r-test/tree … emi_Linear.

And there is general guidance for generating a Campbell diagram here and visualizing the mode shapes here: github.com/OpenFAST/matlab-toolbox.

Best regards,

Dear Jason,

Thanks for your reply.

Are there any documentations for linearisation in OpenFAST (Steps to follow) and on how to use Campbell diagram matlab script and visualizing the mode shapes.

Thanks,
Satish J

Dear Satish,

The last link in my prior post provides the guidance that we’ve developed.

Best regards,