## OC3-Hywind RAOs

Provide feedback, request enhancements, and get help with wind-turbine computer-aided engineering tools.

Moderators: Bonnie.Jonkman, Jason.Jonkman

Carlo.Ruzzo
Posts: 5
Joined: Wed Feb 04, 2015 4:05 am
Organization: Mediterranea University of Reggio Calabria (Italy)
Location: Italy

### Re: OC3-Hywind RAOs

Dear Jason,

thank you for your reply. I've spent some time working on it and I concluded that the best thing to do for me, in order to reproduce your results, is to work in your reference system.

Indeed, if I transform the mass matrix given in the link you suggested me (it was the one I was already using, thank you for sharing with us), I don't achieve a diagonal matrix, neither using your transformation [M_cg = TransMat^T * M_swl * TransMat], nor using mine [M_cg = TransMat^T * M_swl * TransMat^-1].
Taking into account also that additional damping and stiffness have been evaluated empirically, I think it is formally better to work in the original reference system instead of using transformations.

I will keep working on it and I will let you know as soon as I have some interesting result to share.
Thank you very much,
Carlo

Joeri.Haaker
Posts: 7
Joined: Mon Jan 22, 2018 2:02 am
Organization: Tu Delft
Location: Netherlands

### Re: OC3-Hywind RAOs

Dear all,

I hope that it's not a problem that I post in this old topic, but since I have a similar problem, and most of the relevant information is within this topic I took the liberty of posting here.

I'm also trying to recreate the OC3-Hywind within (Ansys) AQWA. I found the information about the mass/inertia of the total system in this old forum post: viewtopic.php?f=3&t=748

I'm also trying to transform the mass matrix and I'm also fail to achieve a diagonal matrix. But maybe I'm doing something wrong?

If I do the transformation as mentioned in the topic (M_cg = TransMat^T*M_swl*TransMat) I get the following mass matrix:

1.0e+10 *

0.000806604815450 0 0 0 0.062916225372230 0.000008979927815
0 0.000806604815450 0 -0.062916225372230 0 0.000011226426962
0 0 0.000806604815450 -0.000008979927815 -0.000011226426962 0
0 -0.062916225372230 -0.000008979927815 5.587772915049737 0.000991477122271 -0.001744457491839
0.062916225372230 0 -0.000011226426962 0.000991477122271 5.587772971327059 0.001397033728988
0.000008979927815 0.000011226426962 0 -0.001744457491839 0.001397033728988 0.019157556316314

My second question is a question regarding the provided moments of inertia. I found a paper called 'Wave- and Wind-Induced Dynamic Response of a Spar-Type Offshore Wind Turbine' by Madjid Karimirad and Torgeir Moan in which they used the NREL 5mw wind turbine mounted on a spar platform, similar to the hywind platform. Although their platform looks similar, for some reason it is slightly heavier. These are the properties they described in their paper:

Total draft 120 m
Diameter above taper 6.5 m
Diameter below taper 9.4 m
Spar mass including ballast 7,593,000 kg
Total mass 8,329,230 kg
Center of gravity -78.61 m
Pitch inertia about the center of gravity 2:20E + 10 kg·m2
Yaw inertia about the centerline 1:68E + 08 kg·m2
Rating 5 MW
Rotor and hub diameter 126 and 3 m
Hub height 90 m
Cut-in, rated, and cut-out wind speed 3, 11.4, and 25 m/s
Rotor mass 110,000 kg
Nacelle mass 240,000 kg
Tower mass 347,460 kg

The first thing I noticed is their Pitch inertia about the CM, which is way lower than yours? When I transform the values you provided I have a pitch about the cm of 5.58E + 10 , but if I just make a quick hand calculation where I take the moment of inertia of the floater about the cm and see the tower and nacelle+ rotor as 2 point masses and add them times the length between the cm and the points squared . I 'm also in the region of 2.0E + 10. As you may understand I'm somewhat confused and I hope that someone may have an answer.

With regards,
Joeri

Jason.Jonkman
Posts: 5882
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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### Re: OC3-Hywind RAOs

Dear Joeri,

Your 6x6 mass matrix, M_cg, includes large off-diagonal terms. Using values from your matrix, I see that your matrix is not about the cg, but includes a large 78-m offset in the z-direction i.e.

z_cg = 0.062916225372230/0.000806604815450 = 78

This will of course also impact the inertia quadrant of the matrix. Are you sure you've applied the transformation correctly?

I agree that a full-system pitch inertia about the full-system cg for the OC3-Hywind floating wind system should be closer to 2E10 kgm^2.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Joeri.Haaker
Posts: 7
Joined: Mon Jan 22, 2018 2:02 am
Organization: Tu Delft
Location: Netherlands

### Re: OC3-Hywind RAOs

Dear Jason,

Thank you for answering to my post, no I don't think transformation is correct, but for some reason it is not working. I'll try the find a solution.

Best regards,
Joeri

Lorenzo.Cottura
Posts: 56
Joined: Wed Jul 15, 2020 9:04 am
Organization: Politecnico di Torino
Location: Italy

### Re: OC3-Hywind RAOs

Dear Jason,
Using the transformations you indicated in this topic I tried to obtain the mass matrix in the center of mass (Figure 1). To obtain this matrix, I started from the SWL mass matrix you suggested in the topic viewtopic.php?t=748, applying the necessary transformations.
Does it seem right to you? Above all, I am uncertain about the inertia.
Best regards,
Lorenzo
Attachments
Schermata 2020-09-08 alle 15.08.49.png (49.87 KiB) Viewed 1312 times

Jason.Jonkman
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Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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### Re: OC3-Hywind RAOs

Dear Lorenzo,

I haven't checked all of the off-diagonal inertia terms, but at least the diagonal entries of your inertia matrix, as well as the mass and center of mass, make sense to me.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Lorenzo.Cottura
Posts: 56
Joined: Wed Jul 15, 2020 9:04 am
Organization: Politecnico di Torino
Location: Italy

### Re: OC3-Hywind RAOs

Dear Jason,
The diagonal terms return to me too, while I have doubts about the off-diagonal terms of inertias. In fact, in my model I get accelerations in x, y, z right while rx, ry, rz do not coincide very well.
Best regards,
Lorenzo.

Jason.Jonkman
Posts: 5882
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

### Re: OC3-Hywind RAOs

Hi Lorenzo,

Yes, I agree with your numbers. Here are my calculations:

Code: Select all

`>> M_swl = [ [ 8.0660481545E+006 0 0 0 -78.001301464*8.0660481545E+006 -1.1132995542E-002*8.0660481545E+006 ];[ 0 8.0660481545E+006 0 78.001301464*8.0660481545E+006 0 -1.3918125391E-002*8.0660481545E+006 ];[ 0 0 8.0660481545E+006 1.1132995542E-002*8.0660481545E+006 1.3918125391E-002*8.0660481545E+006 0 ];[ 0 78.001301464*8.0660481545E+006 1.1132995542E-002*8.0660481545E+006 6.8025977471E+010 9.9135213851E+006 -8.6878157798E+006 ];[ -78.001301464*8.0660481545E+006 0 1.3918125391E-002*8.0660481545E+006 9.9135213851E+006 6.8022535284E+010 6.965876724E+006 ];[ -1.1132995542E-002*8.0660481545E+006 -1.3918125391E-002*8.0660481545E+006 0 -8.6878157798E+006 6.965876724E+006 1.9157300092E+008 ] ]M_swl =   1.0e+10 *   0.000806604815450                   0                   0                   0  -0.062916225372230  -0.000008979927815                   0   0.000806604815450                   0   0.062916225372230                   0  -0.000011226426962                   0                   0   0.000806604815450   0.000008979927815   0.000011226426962                   0                   0   0.062916225372230   0.000008979927815   6.802597747100000   0.000991352138510  -0.000868781577980  -0.062916225372230                   0   0.000011226426962   0.000991352138510   6.802253528400000   0.000696587672400  -0.000008979927815  -0.000011226426962                   0  -0.000868781577980   0.000696587672400   0.019157300092000>> TransMat = [ [ 1 0 0 0 78.001301464 1.1132995542E-002 ];[ 0 1 0 -78.001301464 0 1.3918125391E-002 ];[ 0 0 1 -1.1132995542E-002 -1.3918125391E-002 0 ];[ 0 0 0 1 0 0 ];[ 0 0 0 0 1 0 ];[ 0 0 0 0 0 1 ] ]TransMat =   1.000000000000000                   0                   0                   0  78.001301463999994   0.011132995542000                   0   1.000000000000000                   0 -78.001301463999994                   0   0.013918125391000                   0                   0   1.000000000000000  -0.011132995542000  -0.013918125391000                   0                   0                   0                   0   1.000000000000000                   0                   0                   0                   0                   0                   0   1.000000000000000                   0                   0                   0                   0                   0                   0   1.000000000000000>> M_cg = TransMat'*M_swl*TransMatM_cg =   1.0e+10 *   0.000806604815450                   0                   0                   0                   0                   0                   0   0.000806604815450                   0  -0.000000000000000                   0                   0                   0                   0   0.000806604815450                   0                   0                   0                   0                   0                   0   1.895050184890263   0.000991227154749   0.000006894335879                   0                   0                   0   0.000991227154749   1.894705909912941  -0.000003858384188                   0                   0                   0   0.000006894335879  -0.000003858384188   0.019157043867686`

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Lorenzo.Cottura
Posts: 56
Joined: Wed Jul 15, 2020 9:04 am
Organization: Politecnico di Torino
Location: Italy

### Re: OC3-Hywind RAOs

Best regards,
Lorenzo.

Lorenzo.Cottura
Posts: 56
Joined: Wed Jul 15, 2020 9:04 am
Organization: Politecnico di Torino
Location: Italy

### Re: OC3-Hywind RAOs

Dear Jason,
I report here my problem because despite using the right mass matrix my model does not work.
I noticed that in the case of offshore turbines the two predominant forcings are the loads at the base of the turbine tower and the moorings (which must compensate for the tower loads).
In my model the loads at the base and the moorings add up (with those relating to hydrodynamics, restorings, etc. which are smaller) and, divided by the mass matrix, give the accelerations, from which I get the positions to feedback and obtain the loads of the mooring (via Map ++).
The problem is that Fx and My of the tower start with a step, which if too large leads the moorings to diverge rather than converge and compensate for these loads. To demonstrate this, I tried to manually enter the average value of the forces at the base of the turbine tower, and as can be seen in Figure 1, beyond a certain value of Fx the mooring diverges (at 2 * 10 ^ 5 N converges, while at 3 * 10 ^ 5 N diverges).
Figure 1
Schermata 2020-09-15 alle 20.26.43.png (127.17 KiB) Viewed 1273 times

I asked you about the off-diagonal moments because I noticed that it is not so much the x position that makes Fx_moor diverge, but rather ry which is much higher than the value obtained with FAST.
By setting an increasing trend instead of a step (Figure 2) it is possible to reach higher values ​​of Fx (up to 10 ^ 6, a value higher than the Fx_tower values ​​of the tests carried out), however this would mean making up the first instants of Fx at the base of the turbine.
Figure 2
Schermata 2020-09-15 alle 20.24.15.png (75.71 KiB) Viewed 1273 times

How does FAST prevent this problem?
Thanks for the reply, best regards.
Lorenzo.

Jason.Jonkman
Posts: 5882
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

### Re: OC3-Hywind RAOs

Dear Lorenzo,

I'm not sure I can really comment on the results from your model, which I'm not familiar with.

What does FAST / OpenFAST do for this same load case?

Please note that FAST / OpenFAST include many nonliearities that may not be present in your model. A related discussion in the following forum topic may provide some insight: viewtopic.php?f=25&t=2522.

Best regards.
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov