OC3 Hywind Structural Properties

Wind & Water Structural Analysis
1

Hi,

I am trying to model OC3 Spar FWT with 14 DOFs (6DOF for blades, 2 for tower, 6 for platform). The frequencies of the translational motion agrees with frequencies provided in literature (Surge= Sway = 0.008, Heave = 0.0324). However, I don’t get the correct frequencies in roll and pitch degrees of freedom. I checked the forum and saw that the mass matrix is given in this topic: Inertial Moments of OC3-Hywind Components.

Comparing the mass matrix, I can see that there is a difference in my mass matrix in rotational terms.
The mass matrix in rotational terms should include: I_t + I_s + (M_RNAh^2) + (M_t^2h_t^2), where I_s = 4.2292e9, M_RNA = (240e3 + 56780 + m_blades), M_t is the integrated mass of the tower = 249720, h is the distance from yaw bearing to CG of the system = 89.9155 + 87.6, h_t is the distance from the tower center to CG of the system = 43.2373 + 89.9155, and I_t is the moment of inertia for the tower at towers CM = 9.1072e5.
So, by summing all these values I get 1.9763e10 which is different from the value given in the mentioned post IXX: 6.8025977471E+010 kg-meter**2.

I wanna know, is there anything that I am missing or calculating it wrong?

2

Dear Vahid,

I see a few problems with your math:

  • M_t in your equation should not be squared (perhaps the ^2 is a typo?)
  • As mentioned in the forum post you referenced, the CG of the full turbine + tower + spar for the OC3-Hywind system is 78-m below SWL, not 89.9155 m below SWL
  • Because the spar CG and full-system CG are not the same thing, several of your values need to change
  • The RNA CG will be centered higher than the yaw bearing
  • The value of IXX reported in the forum post you referenced is about the tower centerline at SWL, not at the full-system CG, so again, several of your values need to change

I hope that helps.

Best regards,

3

Dear Jason,

Thanks for your complete response.
Yes ^2 for M_t is a typo in my equations and I have mistakenly considered the system CG to be located at -89.9155. Even, changing the h value to 78 m does not help me find the correct frequencies in roll and pitch directions. I believe my calculations for Ixx is not correct and that is the reason for it.

By calculating these values again, the only value that changes should be h = 78 + 87.6 (m) and h_t = 43.2373 + 78 (m)(Let’s approximately consider RNA CG at the yaw bearing). By summing all the values mentioned at the first comment and applying the correct position of system’s CG I get Ixx = 1.7565e10 kg-m^2.

I wonder what is the Ixx value at the full system CG and not tower centerline? If you don’t have that value, how can I calculate it by using FAST or any other related program?

Best Regards,

4

Dear Vahid,

As I mentioned in my post from July 23 above, the value of IXX reported in the forum post you referenced is about SWL, not at the full-system CG. You can convert this inertia to the full-system CG by subtracting from it the ( full system mass ) times ( 78 m )^2. Performing this math gives a result that is close to yours.

As discussed on this forum, the linearization functionality of FAST v7 (but not FAST v8 or OpenFAST) could be used to return the 6x6 rigid-body mass matrix of the full system; from this mass matrix, one can derive the full-system mass, CG, and inertias.

Best regards,

5

Dear Jason,

Thank you for your response, probably there should be a mistake in another place and I need to check and see why my frequency in pitch and roll DOFs do not agree with the ones in literature.
thank you