Strange behaviour in FAST.Farm floating wind farm loads spectra

[andzanna00]

Hi everyone,

I’m working on FAST.Farm version 3.5, simulating a floating wind farm made of 2 small-scale turbines (D=1.2 m, rotor height=0.825 m) in line, where the first, upstream, can move, while the downstream one is fixed. I simulated several scenarios, moving the first turbine platform with SubDyn (I tested surge, pitch, yaw, surge+sway and roll+pitch) with a sinusoidal law of motion at 0.5, 1 or 2 Hz. The distance between the turbine is 6D (7.2 m), and then I simulated the same scenarios but with distance equal to 9D (10.4 m). While analyzing the thrust force spectra (through FFT) on the second rotor, what I expected was some resonance peaks at the frequency of the first turbine motion, or at some multiple of that frequency (for example, if the first turbine moves at 1 Hz, I would expect a peak on the thrust force FFT at 1 Hz or 2 Hz, 3 Hz, ...). Instead, this is what happens:

• For surge, pitch and surge+sway motion there is resonance on the thrust force FFT at half the frequency of the motion (for example, if the first turbine moves at 1 Hz, there is a peak on the FFT at 0.5 Hz) for both distances
• For roll+pitch and yaw, it happens the same thing at 6D, but if I increase the distance between the turbines (from 6D to 9D, i.e. from 7.2 m to 10.8 m) it starts to work “correctly” (resonance in the FFT at the same frequency of the first turbine motion)

The values I changed from their “DEFAULT” values in the wake dynamics parameters are k_vAmb=0, k_vShr=0.012 and C_HWkDfl_OY=0.1 and f_c=10 Hz.
I’m using 110 planes and the grid is defined as follows:

0.05 DT_Low Time step for low-resolution wind data interpolation; will be used as the global FAST.Farm time step (s) [>0.0]
0.025 DT_High Time step for high-resolution wind data interpolation (s) [>0.0]
81 NX_Low Number of low-resolution spatial nodes in X direction for wind data interpolation (-) [>=2]
71 NY_Low Number of low-resolution spatial nodes in Y direction for wind data interpolation (-) [>=2]
41 NZ_Low Number of low-resolution spatial nodes in Z direction for wind data interpolation (-) [>=2]
0 X0_Low Origin of low-resolution spatial nodes in X direction for wind data interpolation (m)
-3.5 Y0_Low Origin of low-resolution spatial nodes in Y direction for wind data interpolation (m)
0.025 Z0_Low Origin of low-resolution spatial nodes in Z direction for wind data interpolation (m). In this way the hub is coincident with the grid.
0.25 dX_Low Spacing of low-resolution spatial nodes in X direction for wind data interpolation (m) [>0.0]
0.1 dY_Low Spacing of low-resolution spatial nodes in Y direction for wind data interpolation (m) [>0.0]
0.1 dZ_Low Spacing of low-resolution spatial nodes in Z direction for wind data interpolation (m) [>0.0]
31 NX_High Number of high-resolution spatial nodes in X direction for wind data interpolation (-) [>=2]
31 NY_High Number of high-resolution spatial nodes in Y direction for wind data interpolation (-) [>=2]
30 NZ_High Number of high-resolution spatial nodes in Z direction for wind data interpolation (-) [>=2]

While I would understand that the wind would “pulsate” on the downstream turbine at some multiples of the frequency of the upstream turbine motion, I don’t understand why there is resonance systematically at half that frequency.
Do you have any idea why this is happening? I’d like to specify that the time-averaged thrust forces of the cases where the first turbine moves don’t change particularly, compared to when the first turbine is fixed.

Thanks in advance!

[jjonkman]

Dear @andzanna00,

Can you share figures that illustrate what you are referring? It would help to see the motion you are imposing on the upstream turbine, the thrust seen by the upstream turbine, and the thrust seen by the downstream turbine. Wake visualizations would also be useful.

That said, the case you are considering may not be well captured by FAST.Farm in its present form. Our experience using FAST.Farm for floating offshore wind turbines--as discussed in the following paper: https://wes.copernicus.org/articles/9/1827/2024/--has shown that the wake pulsations associated with floater motion are likely not captured well by FAST.Farm. This is an area where we plan to improve FAST.Farm in the future. Until then, your case may be better handled by other software, such as OLAF within the standalone AeroDyn driver or AMR-Wind (large-eddy simulation).

Best regards,

[andzanna00]

Dear @jjonkman,

I checked the computation of the FFT, and found an error regarding the sampling frequencies. I corrected it, and now the FFT actually works correctly (for both turbines), so thank you for that!

The only issue I still have is about the yaw cases: at 6D, there are no significant peaks, and the spectra are very similar to the fixed case; at 9D, instead, the resonance appears at double the frequency of motion. While I don't have particular problems with peaks at double the frequency of the motion, I don't quite understand the behaviour at 6D (the black dots are the fixed case spectrum):

The other cases, for the same distance between the turbines, instead, show much clearer resonances:

Do you have any idea about why this happens?

Best regards,

[jjonkman]

Dear @andzanna00,

I'm glad you corrected the FFT and the results now make more sense to you.

For yaw, I would expect thrust to oscillate at twice the frequency of the yaw motion because thrust will decrease from its value for aligned yaw whether the yaw angle is positive or negative. The reduction in thrust with yaw is not linear and the wake response and its impact on the thrust of the downstream turbine are not linear either though, so, I would expect harmonics to show up in the FFT of thrust for both the upstream and downstream turbine. My expectation is that this behavior would be independent of turbine spacing and/or yaw amplitude/frequency. I see a lot of noise in your results, so, what you are seeing could be numerical artifacts that would reduce if you increased the simulation length or decreased the time step.

Best regards,

[andzanna00]

Dear @jjonkman,

I tried changing some parameters (time step and simulations length), but the results are pretty much the same. However, the general trend for yaw is that the time-series results are usually affected by noise.
Instead, one last thing that conerns me is the roll+pitch motion: while at 6D it follows the behaviour of the other motions (excpet yaw), meaning resonance at the frequency of motion, with higher distance (at 9D) a second peak at double the frequency of motion appears, as if it behaves halfway through the other motions and the yaw.

If you could help me understand this last thing it would be great.

Best regards,

[jjonkman]

Dear @andzanna00,

Due the nonlinearities I mentioned previously, I would expect peaks to show up at harmonics of the oscillation frequency in the thrust signal of both turbines for different motions. So, seeing peaks at twice the oscillation frequencies does not surprise me. The magnitude of the peaks will depend on the degree of nonlinearity for the specific case.

Best regards,

[andzanna00]

Dear @jjonkman

I thought about what you said about the reasons the yaw causes resonance at double the frequency of motion:

For yaw, I would expect thrust to oscillate at twice the frequency of the yaw motion because thrust will decrease from its value for aligned yaw whether the yaw angle is positive or negative.

I tried to simulate cases with sway and roll motions alone, in order to see if the DOFs similar to yaw (the ones that move transversely to the wind, i.e. along the y axis) exhibit the same trend, since the behaviour you described for yaw should be valid also for those motions. The result is that the behavioru is very similar to that of the yaw:

At 6D, the peaks are not so high and sometimes at multiples of the frequency of motion; at 9D, the resonances are more obvious and at ouble the frequency of motion, exactly like what seen in the yaw cases. The results for sway at 9D are not clear for 0.5 and 1 Hz because the 2 Hz (yellow plot) covers them, but the behaviour is the same, even though the peaks magniude are lower than those at 2 Hz.

In conclusion, I guess that when the first turbine moves along the y axis, the thrust will decrease whether the motion (yaw angle, roll angle or sway translation) is positive or negative, like in the yaw cases, and as a result the thrust spectra show resonance peaks at double the frequency of the motion.

Thank you for your time, it was really heplful talking to you!

Best regards,