Large number of Craig Bampton modes for flexible floating systems

[RBergua]

I'm simulating one floating offshore wind turbine as follows:

The floating plaform and tower (not shown in the above image) are modeled in SubDyn. For this numerical model, I use the new rigid-body reference point available in SubDyn.

The system uses horizontal pretensioned lines included in MAP++.

When considering a wave-only condition with a regular wave applied along the x-direction, I can observe that the loads within the platform are quite sensitive to the number of Craig Bampton modes included in SubDyn. This seems to be specially true for the axial and vertical forces. See the loads at the upwind and downwind pontoons below.

Edit: the wave spectrum has been low-pass filtered with a cut-off frequency = 0.5 Hz. Time step used for the solver: Nmodes = 8 (dt = 0.01 s), Nmodes = 15 (dt = 0.01 s), Nmodes = 50 (dt = 0.01 s), Nmodes = 75 (dt = 0.0025 s), Nmodes = 100 (dt = 0.0025 s), and Nmodes = 125 (dt = 0.001 s).

I understand that the static-improvement method treats higher-frequency modes quasi-statically. As can be observed above, in this system a large number of modes (~100) has to be included to have close to a converged solution. For reference, the total number of DOFs in the structure is 180.

For these simulations I'm using the OpenFAST tight-coupling (current OpenFAST dev-tc). When accounting for a strip theory approach for the hydro, I can solve 2500 seconds of simulation in 17 h (in a powerful computer) using 100 modes in SubDyn and a time step of 0.001 s for the solver. However, for a hydro model that uses potential flow, the same simulation increases the computational time to 28 days. I understand that this very large computational time when using potential flow bodies is related to this issue: #2936 (comment).

I'm wondering if there is any workaround or solution for this.

[jjonkman]

Dear @RBergua,

I'm a bit surprised to see this sensitivity to the number of Craig-Bampton modes. What are the natural frequencies of the Craig-Bampton modes for modes 8, 15, 50, 75, 100, and 125?

Best regards,

[RBergua]

Dear @jjonkman,

Below you can find the frequencies of the Craig-Bampton (CB) modes:
Mode 8: 4.4 Hz
Mode 15: 13.4 Hz
Mode 50: 65.9 Hz
Mode 75: 158.3 Hz
Mode 100: 436.9 Hz
Mode 125: 1168.8 Hz

As commented above, the system has 180 DOFs. The Guyan modes include 12 DOFs (I use the rigid-body reference point formulation in SubDyn). So, the total CB modes are 168. Below you can see the distribution of these modes:

All these frequencies are much higher than the highest excitation in my system (regular waves with a frequency of 0.074 Hz).

What is interesting and how I realized about this sensitivity is because the axial load along the pontoon presents a phase shift when not enought modes are included in the numerical model.

If I compare the axial load at the tip vs the root for the upwind pontoon, I can see that almost the same axial load is observed in both locations when considering 8 modes (quite similar to a quasi-static approach):

However, when a large number of modes are included (e.g., 100), the axial force at these two locations presents a phase shift:

Below you can see the direct comparison between 8 and 100 modes at the pontoon root location:

Using a different software, I can see that the phase shift is indeed present and aligned with the SubDyn solution with a large number of modes. These results also agree better with experimental results.

[RBergua]

I performed a small sentivity analysis regarding using or not using the rigid-body reference point in SubDyn. The results are quite interesting...

For the numerical model without the rigid-body reference point in SubDyn, I only have the interface joint at tower top. That's the point where ElastoDyn and SubDyn are connected.

In this case, when using Nmodes = 8 in SubDyn, I have the elastic modes up to 1.08 Hz. I can see that when not using the rigid-body reference point, I have the proper phase and amplitude. Although the response is quite noisy... This is also quite surprising because the frequency range that I include now is smaller (1.08 Hz now vs 4.4 Hz before).

@luwang00 any clue what may be the difference with vs without rigid-body reference point?

[luwang00]

Hi @RBergua, thanks for documenting this. It is not immediately clear what could be causing the difference. A review of the implementation of the static improvement method in dev-tc did not raise any obvious concerns.

It is possible the introduction of additional elastic Guyan boundary modes (for unit deflection of the transition pieces) with rigid-body reference point somehow changed the rate of convergence with the number of Craig-Bampton modes retained. At the very least, we should change the recommendation on the number of CB modes to be retained and suggest a convergence test.

The noise wo/ rigid-body reference point appears to be mostly a numerical issue (the problem is numerically challenging when the interface point is at the tower top).

[luwang00]

After further discussions with @RBergua, the highest Guyan mode frequency with rigid-body reference point is found to be 71.77 Hz. This mode involves the tower axial compression/extension. When truncating the list of Craig-Bampton modes, it makes sense to retain modes up to at least the highest Guyan mode frequency for consistency since all Guyan modes are always retained. This roughly aligns with 50 modes up to 65.9 Hz. This could be a tentative recommendation pending further investigation.

In the absence of a rigid-body reference point, the Guyan modes are the rigid-body modes for a floating structure with zero frequency, so this is not a concern. Similar issue might exist for fixed-bottom structures where the Guyan modes are elastic with nonzero frequencies.

[jjonkman]

Sounds like a simple modeling recommendation, but is there a reason why it would be necessary to retain C-B modes up to the highest frequency of the elastic Guyan modes? You mention "consistency", but I'm not sure I understand why that is needed if the high-frequency C-B modes are not directly excited anyway.

[luwang00]

This is simply based on the idea that we want to strictly drop the higher frequency modes. Even though the high frequency modes are not excited externally, there is coupling between the elastic Guyan modes and the Craig-Bampton modes on the structure side. Still, I agree this requires more investigation.

[RBergua]

This parallelism with fixed-bottom structures is vey interesting. Note that structures like a monopile will have similar axial modes with pretty high frequencies. As far as I know, we tend to include relatively low Craig-Bampton modes in these systems. If we need to cover the frequency range determined by the Guyan modes, we may be forced to include a large number of modes and drop the time step for the solver. It may be good to do some tests in the future...