Pitch natural frequency shift

Hi Jason
I was trying to model the semi-sub with turbulent wind. I found with turbulent wind+wave conditions, the platform pitch natural frequency has an offset. I have tried steady wind+wave, the natural frequency matches well with reference. According to my knowledge, the system natural frequency has nothing to do with the excitation. But i was wondering how it happens.

Besides, i have calculated the theoretic solution for RAO for the whole wind turbine without mooring. But when it comes to moored turbine, it seems there is a need to recalculate the center of gravity? i have no idea how to consider the mooring part, except the Fi^lines in the definition of the semisubmersible floating system.

Also for the turbsim, I generated full-field wind field with IECKAI model. I get the time series for wind velocity from turbsim as well as the output from inflowWind, I don’t know whether it is reasonable to have some bumps at f>2Hz. And the spectrum at low frequency is not quite flat. For f*Sw, there is not a significant peak. Is it reasonable?

Thank you for your dedicated help.

Best regards
Lulu

Dear @Lulu.Liu,

Regarding the change of pitch natural frequency with wind loads, I would guess this has to do with the thrust of the wind turbine causing a mean offset of the semi (e.g., in surge and pitch), which results in different mooring stiffness due to the geometric nonlinearity of the mooring system.

I’m not sure I understand your question regarding RAO without moorings.

Regarding your Turbsim results, the oscillations around the target spectrum are likely the result of resampling, e.g., not outputting the full time series (resulting in a different delta frequency) or a change in the time step between the TurbSim calculation and OpenFAST output.

Best regards,

Hi Jason

For the first questions, it means that the platform pitch natural frequency may vary when subjected to turbulent wind. Is it right?

About the turbine without mooring, I mean I calculated the center of gravity considering the platform,tower and tower-top mass and the mass matrix. Then i solve the equation of motion for RAO using the hydrodynamic coefficient from wamit output files. When it comes to the wind turbine with mooring system( to make the solution more accurate), I add the term Fi^lines, which includes the pretension force at the fairleads and restoring matrix from the literature" Definition of the Semisubmersible Floating System for Phase II of OC4". In this case, I think the wind turbine may have a new center of gravity,which means the mass matrix need modification? I feel that the turbine reach a new equilibrum state, but i have no idea how to solve it. From the plot, the heave response seems incorrect at very low frequenciws.

Yes, the delta frequency is the same. But the time step between the TurbSim calculation and OpenFAST output is different. But i cannot understand the strange bump starting from f=2Hz

Best regards

Dear @Lulu.Liu,

Regarding the first question, I would say the frequency changes because of the displacement of the floater and impact on the mooring stiffness. The displacement comes from the thrust load, whether from turbulent or steady wind.

Normally RAOs are computed with the full system mass matrix in its undisplaced condition, although, you could figure out the influence of the displaced condition on the matrices and compute RAOs about that. The moorings would influence the displaced condition, but you should not need to include the mooring mass in the full-system mass matrix because the mass contribution from the moorings is typically minimal.

Regarding the wind PSDs, my answer is unchanged.

Best regards,

Hi Jason,
Thank you. I solved my problem. I originally believe the center of platfrom and the tower would be different when with mooring system or without mooring system. But i realized that for the undisplaced position, the pretension at the fairleads balance the weight of the mooring line not resting on the seafloor in water. It seems the center of gravity for the whole system wouldn’t change and can be obtained through simple algebraic calculation. Thank you for your help.

Best regards

Hi Jason
When you say this, do you mean that the mooring stiffness matrix is a function of time, rather than a constant? I have seen some topics about obtaining the mooring stiffness matrix. Unlike the hydrodynamic coefficient which is a constant input from WAMIT, the mooring stiffness matrix is calculated by the relation between the load and the displacement of the platform. So it varies with time series? I am not sure my understanding is correct. I have chosen the moordyn in the glue-code, and didn’t find something i can do to change the output file format or output a summary file for the Moordyn. Currently the only output information is fairlead and anchor tension.

Best regards

Dear @Lulu.Liu,

I’m saying that the mooring stiffness can change with platform displacement due to the geometric nonlinearity of the mooring system.

Best regards,

Hi Jason
I was wondering in the Fast code mooring stiffness would change with platform displacement or it was only calculated once for the undisplaced position?

Best regards

Dear @Lulu.Liu,

Yes, if you’ve enabled one of the mooring modules in FAST / OpenFAST, the mooring stiffness will depend on floater displacement, which is why your results are as you’ve shown.

Best regards,