Campbell diagram interpretation

Wind & Water Computer-Aided Engineering Software Tools
1

Hi Everyone,

I am using the MBC tool to generate a Campbell diagram for an 85kW variable speed, active pitch turbine. You can find the result below. My question is regarding the 2nd tower modes. I was surprised to see them vary so much with rotor speed. Also, the frequencies of the modes in turbulent wind simulations are fairly consistent at 4.8 Hz (FA) and 5.1 Hz (SS).

Shouldn’t the frequencies observed in turbulent wind simulations match the Campbell diagram? If so what could be causing this difference?

I’ve also generated a couple of additional diagrams where I’ve turned off the DOFs for the blade and tower separately. It is clear that it is the blade DOFs that are causing the change in the 2nd tower modes.

Any guidance would be greatly appreciated. Thanks.

northwindEngineering_campbellDiagram_rpm.PNG
northwindEngineering_campbellDiagram_rpm.PNG1198×698 73.8 KB

northwindEngineering_campbellDiagram_rpm_noBlDof.PNG
northwindEngineering_campbellDiagram_rpm_noBlDof.PNG1076×632 41 KB

northwindEngineering_campbellDiagram_rpm_noTowDof.PNG
northwindEngineering_campbellDiagram_rpm_noTowDof.PNG1085×627 60 KB

Best Regards,
Drew

–
Drew Gertz
Northwind Engineering OÜ
+372 5565 0147
drew@northwindengineering.com
northwindengineering.com

2

Dear Drew,

The second-tower bending modes typically couple with the blade-bending DOFs, so, I’m not surprised by the influence you are showing.

And yes, I would expect the frequencies in the Campbell diagram to match those form time-domain simulations.

Regarding the variation of second-tower bending modes with rotor speed, I’m not sure. Can you clarify how you deriving the Campbell diagram? Are you linearizing with aerodynamics enabled and FrozenWake = True? Are you computing a steady-state solution before linearization (and have you checked that the solution is indeed in steady state at the linearation point)? Are you linearizing at a number of azimuth steps around the rotor revolution at each rotor speed?

Best regards,

3

Hi Jason,

Thank you for your reply. To answer your questions:

  • I am linearizing with aerodynamics enabled (CompInflow=1, CompAero=2) and FrozenWake=True. The aerodynamics options are set as follows:
    1 WakeMod
    1 AFAeroMod
    1 TwrPotent
    FALSE TwrShadow
    FALSE TwrAero
    TRUE FrozenWake
    FALSE CavitCheck
    2 SkewMod
    “DEFAULT” SkewModF
    TRUE TipLoss
    TRUE HubLoss
    TRUE TanInd
    FALSE AIDrag
    FALSE TIDrag
    “Default” IndToler
    100 MaxIter

  • I am linearizing 36 times, with timing adjusted for rotor speed such that they cover one rotor revolution

  • I’ve also checked that the solution is steady state, but perhaps you can check my method. I have set it up the following way:
    CalcSteady=False
    pitch angle fixed at 0 degrees
    VSContrl=1
    VS_Rgn2K set to operate at optimal TSR
    VS_SlPc=1.5
    VS_RtGnSp and VS_RtTq set such that they are never reached
    I give the simulation 15s to reach steady state before linearizing. At this point the rotor speed is fluctuating +/- 0.0008 rpm at 5rpm and +/- 0.008 at 40rpm. See the plots below.

Thanks again for your help.

timeSeries_rpm.png
timeSeries_rpm.png3543×2362 88.5 KB

timeSeries_5rpm.png
timeSeries_5rpm.png3543×2362 182 KB

timeSeries_40rpm.png
timeSeries_40rpm.png3543×2362 218 KB

4

Here are the PSD plots of the tower base FA and SS moments from turbulent wind simulations for your reference. The red curve is 3 m/s (15 rpm nominal) and the blue is 18 m/s (32.2 rpm nominal).

psd_turbWind_TwrBsMyt.png
psd_turbWind_TwrBsMyt.png3541×2362 371 KB

psd_turbWind_TwrBsMxt.png
psd_turbWind_TwrBsMxt.png3543×2362 376 KB

5

Dear Drew,

Indeed, your approach to computing a steady-state solution and linearizing sounds reasonable. Please note that OpenFAST v2.4 includes new functionality to automate the steady-state solution (including trim of torque or pitch) to ensure that the convergence is reached before linearizing. And your approach for setting VSContrl sounds reasonable for below-rated linearization; above rated, it is more common to set constant generator torque and to trim pitch. Regardless, I would expect the results won’t change much if you make these changes.

Have you also output the linearization files with large precision (e.g., use OutFmt = “ES17.9E3”). If not, the eigensolution could certainly be impacted by numerical round-off.

Best regards,

6

Hi Jason,

Thanks again for your insight. Yes, I have also run some simulations as you describe (constant generator torque and trimming pitch) and the results didn’t change significantly, as you figured.

As for the precision, I have used a value of “ES20.12E3” which I assume is even more precise than ES17.9E3?

Can I also get your opinion on the PSD plots I posted? To me it seems quite clear that the 2nd tower FA frequency isn’t changing with rotor speed and sits around 4.8 Hz. This is why I’m so puzzled by the curve in the Campbell diagram.

Thanks again.

Best Regards,
Drew

–
Drew Gertz
Northwind Engineering OÜ
+372 5565 0147
drew@northwindengineering.com
northwindengineering.com

7

Dear Drew,

OK, it definitely sounds like you are using enough precision.

It is a bit hard to tell given the noise in the PSDs, but in general I would not expect a large impact of the rotation speed on the tower modes. I don’t see much effect in TwrBsMyt, but there is some effect seen in TwrBsMxt. The second tower modes do tend to couple with the blade bending modes, so, some effect is likely expected (especially blade pitch). It may help to smooth out the PSD a bit, e.g., by averaging the PSD across multiple time-series (multiple turbulence seeds for a given wind speed).

Best regards,

8

Hi Jason,

Okay, thank you for your input. It was very helpful.

Best Regards,
Drew

–
Drew Gertz
Northwind Engineering OÜ
+372 5565 0147
drew@northwindengineering.com
northwindengineering.com