OC3-Hywind RAOs

Dear Carlo,

The reference point for the rotations and integration of the hydrodynamic moments in those papers is the intersection of the undisplaced spar centerline and the still water level (SWL).

Viscous drag on the spar was neglected in the paper by Ramachandran et al, but the ROAs presented do include the so-called “additional linear damping” in surge, sway, heave, and yaw mentioned in the first paragraph of the “CASE STUDY” section on page 3.

Yes, the "-5.E9 Nm/rad only includes the effects of the hydrostatic pressure; the restoring effect from the center of gravity is taken into account elsewhere.

Best regards,

Dear Jason,

thank you very much for your reply.

I will keep working on it.

Best regards,

Dear all,

I have built my model in AQWA, using data found in the papers mentioned above. All the hydrodynamic quantities (added mass, damping and wave excitation forces) agree very well.

Similarly to Minxi, I added linear additional matrices and I got my RAOs but these were different from those in the paper of Ramachandran and Jonkman (rigid wind turbine with no wind).

Here are my RAOs (including linearized mooring line effect) in surge, heave and pitch (reference system centered in s.w.l.). As it can be seen, heave RAO is OK both in frequency and amplitude, while pitch RAO is completely wrong and affects also surge RAO in the second peak frequency.

I tried also to run analysis in AQWA’s reference system (centered in C.o.G.) where pitch is different in definition. I obtained a very similar (correct) RAO in heave, while RAO in pitch was equal to the one of the paper in peak frequency (about 0.034 Hz) but showed again very large amplitude. In surge I had correct frequencies too but wrong amplitude of the surge peak (I expected this RAO to be equal to the one of the first analysis but it was not so).

Can anyone help me in understanding why such differences (between my two models and the one of the paper mentioned) arise?
I have also a couple of specific questions that may be very useful for me:

• Is there any procedure to compare directly RAOs from different reference systems?
• Can I find in literature RAOs without mooring line effect, i.e. for the free floating body? (before using mooring linearization pitch amplitude seems to be good)

I would really appreciate it if anyone could help me!
Thank you in advance for your kind answers,

Dear Carlo,

I don’t recall seeing a publication where the OC3-Hywind spar ROAs are reported without moorings present.

Changing the origin of the platform will change the interpretation of the translational DOFs (not the rotational DOFs) and change the magnitude of the moments. For example, consider the linear system:

(M_swl + A_swl)qdd_swl + B_swlqd_swl + C_swl*q_swl = F_swl

where q_swl = [ surge, sway, heave, roll, pitch, yaw ]^T are the platform displacements, and F_swl are the platform loads, relative to the platform centerline at still water level (SWL) (0,0,0). The same equations can be written in terms of displacements and loads about the center of gravity located at (x_cg, y_cg, z_cg) using the following transformation:

q_cg = TransMatq_swl
F_cg = TransMat^T

TransMat =
[ [ 1 0 0 0 -z_cg y_cg ];
[ 0 1 0 z_cg 0 -x_cg ];
[ 0 0 1 -y_cg x_cg 0 ];
[ 0 0 0 1 0 0 ];
[ 0 0 0 0 1 0 ];
[ 0 0 0 0 0 1 ] ]

TransMat^T =
[ [ 1 0 0 0 0 0 ];
[ 0 1 0 0 0 0 ];
[ 0 0 1 0 0 0 ];
[ 0 z_cg -y_cg 1 0 0 ];
[ -z_cg 0 x_cg 0 1 0 ];
[ y_cg -x_cg 0 0 0 0 1 ] ]

Thus, the transformed system is:

(M_cg + A_cg)qdd_cg + B_cgqd_cg + C_cg*q_cg = F_cg

M_cg = TransMat^TM_swlTransMat
A_cg = TransMat^TA_swlTransMat
B_cg = TransMat^TB_swlTransMat
C_cg = TransMat^TC_swlTransMat

Are these the transformations you’ve applied between the two systems?

Best regards,

Dear Jason,

I am very grateful for your immediate reply.

If I understand correctly, the mass matrix I should use in my reference system is:

M_cg [kg; kg*m2] =
[ [8066048, 0, 0, 0, 629151756 , 0];
[0, 8066048, 0, -629151756, 0, 0];
[0, 0, 8066048, 0, 0, 0];
[0, -629151756, 0, 117099814443, 9913521, -8687816];
[629151756, 0, 0, 9913521, 117096372256, 6965877];
[0, 0, 0, -8687816, 6965877, 191573001] ]

Similarly, I transform Additional Linear Damping, while Additional Stiffness remains the same. Before your reply I missed transformational of Additional Damping Matrix.

Then, once I obtain RAOs in my reference system, if I understand correctly, I should have:

SurgeRAO_swl = SurgeRAO_cg + zG * RollRAO_cg - yG * YawRAO_cg

At last I can compare my transformed RAOs with those of the paper.

Am I right?

Best regards,
Carlo Ruzzo

Dear Carlo,

I don’t believe your M_cg is correct. The mass matrix about the cg should be basically a diagonal matrix (with maybe some small nonzero off-diagonal terms in the lower-right inertia quadrant). The mass matrix of the OC3-Hywind spar system about the SWL is given in my Nov 16, 2012 post in the following forum topic: http://forums.nrel.gov/t/inertial-moments-of-oc3-hywind-components/610/1.

I’m not sure what you mean when you say the “additional stiffness remains the same”, but as my prior post explains, the mass (M), added mass (A), damping (B), stiffness (C), force (F), and displacement (q) all get transformed between SWL and CG.

To convert RAOs from the CG to the SWL, you could write:

q_swl = TransMat^-1*q_cg

TransMat^-1 =
[ [ 1 0 0 0 z_cg -y_cg ];
[ 0 1 0 -z_cg 0 x_cg ];
[ 0 0 1 y_cg -x_cg 0 ];
[ 0 0 0 1 0 0 ];
[ 0 0 0 0 1 0 ];
[ 0 0 0 0 0 1 ] ]

Your equation is almost correct, except that “roll” should be changed to “pitch”.

Best regards,

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,

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: http://forums.nrel.gov/t/inertial-moments-of-oc3-hywind-components/610/1

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^TM_swlTransMat) 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 configuration 3 blades
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,

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,

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,

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 Inertial Moments of OC3-Hywind Components, applying the necessary transformations.
Does it seem right to you? Above all, I am uncertain about the inertia.
Best regards,

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,

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.
Can you please check them?
Thanks for your help,
Best regards,

Hi Lorenzo,

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

[code]>> M_swl = [ [ 8.0660481545E+006 0 0 0 -78.0013014648.0660481545E+006 -1.1132995542E-0028.0660481545E+006 ];
[ 0 8.0660481545E+006 0 78.0013014648.0660481545E+006 0 -1.3918125391E-0028.0660481545E+006 ];
[ 0 0 8.0660481545E+006 1.1132995542E-0028.0660481545E+006 1.3918125391E-0028.0660481545E+006 0 ];
[ 0 78.0013014648.0660481545E+006 1.1132995542E-0028.0660481545E+006 6.8025977471E+010 9.9135213851E+006 -8.6878157798E+006 ];
[ -78.0013014648.0660481545E+006 0 1.3918125391E-0028.0660481545E+006 9.9135213851E+006 6.8022535284E+010 6.965876724E+006 ];
[ -1.1132995542E-0028.0660481545E+006 -1.3918125391E-0028.0660481545E+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_swlTransMat

M_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[/code]
Best regards,

Thanks a lot for your prompt reply.
Best regards,

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).

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.

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

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: http://forums.nrel.gov/t/hydrodynamic-implementation/2284/1.

Best regards.

Hi everyone

I’m a Ph.D. student studying concrete floating offshore wind turbines. (using WAMITv7 and OpenFAST.)

I quite don’t understand the 2nd process.
(2)Redefine the added mass and damping as zero in the file named “spar.1”

As the spar.1 is the output from WAMIT, does this mean the zero values of added mass and damping will be input at WAMIT *.frc files then do the analysis again, or it will be input at PLATFORM ADDITIONAL STIFFNESS AND DAMPING of OpenFAST HyDroDyn?

Thank you in advance for your kindly answer.

Dear Wichuda,

The steps outlined by Minxi where to obtain the rigid-body mass matrix of the system, not including hydrodynamic added mass. In OpenFAST, it is possible to zero out the added mass completely, but this was not possible in FAST v7. So, the workaround was to specify WAMIT output files with all coefficients set to zero. These are not obtained by running WAMIT; instead, the files were created by hand to look like they were WAMIT-generated. I’ve attached the files to my post dated Oct 30, 2012 in the following forum topic: http://forums.nrel.gov/t/questions-about-the-hydrodyn-module/596/4.

Best regards,

Dear Jonkman

Thank you very much. Now I got it.