# RAO calculation

Hello,everyone

I recently study the OFFshore wind turbine,but I am newer in fluid dynamic.I want to get the RAOs of the Platform motion,I don’t know how to get the RAO curves like the arcicle’Coupled Dynamic Modeling of Floating Wind Turbine Systems’. Can you tell me the ways to get the RAO curves?

Best regard!

Ruiliang.Wang

Dear Ruiliang,

We published an ISOPE 2013 paper on a comparison of RAOs between WAMIT and FAST and the influence of turbine operation on the RAOs. This paper provides a detailed description for how RAOs are derived from both software: nrel.gov/docs/fy13osti/58098.pdf.

Creating RAOs is much simpler in FAST v8 than it was in FAST v7 because the HydroDyn module of v8 directly supports a white-noise wave-spectrum model for broadband excitation of the hydrodynamic loads.

There are also several topics on this forum where the computation of RAOs using FAST has been discussed. Search for “RAO”.

Best regards,

Dear Jason,
As a newer,I want to ask a basic question about RAO calculation.I think the FAST cann’t output the RAO result directly.The method is:
How can i get the Numerator and Denominator? The Numerator is function of frequency.FAST can output the time-domin result .The Numerator is FFT transformation of FAST result ? What is the Denominator ? Is it the amplitude of wave?
Hope your help ! I will appreciate it with your nice patience!

Best Regard!
Ruiliang.Wang

Dear Ruiliang,

You can derive the RAO from the time series of the platform motion (or whatever signal you want to compute the RAO of) and the input wave time series (preferably white noise). The process is described around Eq. (3) in the ISOPE paper I referenced above.

Best regards,

Dear Jason,
Thank you for your fast reply and good patience!
In the FASTv7.02,in order to calculate the RAO ,we must set the some frequency wave,get the stabe result ,we can get the RAO and repeat the same process by varying the wave frequency if we don’t compile the white-noise routine.I think workload is large.
If I use the FASTv8,In order to get the RAOS,i just change the WaveMod to 3(White noise spectrum),and set the WaveHs=2(why is 2?) and set suitable values to WvHiCOff.We can get the time-serise of surge,roll…etc and time series of waveElev. So,we can get the Sxy(w) and Sxx(w),x is waveElev and y is result like surge.
Sxy(w) and Sxx(w) is cross-sprectrum density and anto-sprectrum density.I think we can get them by write the routine in Matlab .Do the EXCEL can get the Sxy,Sxx?
Above it is my comprehension.Is it right ?
Best Regard
Ruiliang.Wang

Dear Ruiliang,

Your understanding is correct, except that WaveHs need not be 2 m.

The Signal Processing Toolbox of MATLAB has functions to compute the cross- and auto-spectral densities from time-series data. I’m not aware of similar functions in Excel, but that doesn’t mean there aren’t any. I’m sure other software packages are available also.

Best regards,

Dear Jason,

Thank you very much!
I changed WaveMod =3 in the file HydroDyn.dat like

I simulate 600s,i set the wind turbine to rigid and have no aerodynamic and get the time series WaveElev like
I use the Matlab by the FUNCTION psd(spectrum.welch,) get the Sxx like:
i think the Sxx should be straight line.I don’t think the Sxx is correct,Can you give me some guide?

Best Regard
Ruiliang.Wang

Dear Ruiliang,

My guess is the windowing used is distorting the shape of the PSD. Instead of using MATLAB’s built-in psd function, I prefer to calculate a PSDs directly via FFT without windowing.

I also see that have WaveNDAmp set to TRUE, which will result in normally distributed amplitudes of the spectra in the frequency domain. If you really want to see a straight line, you’ll need to set WaveNDAmp to FALSE (and not use windowing when computing the PSD).

Best regards,

Dear Jason,

I have two questions: my first question is related to finding the 2nd tower FA/SS modes from the PSD of the TTDspFA field using the white-noise spectrum and setting WvLowCOff=12.566370 rad/s and WvHiCOff=21.991148 rad/s in the Hydrodyn file for the 5MW OC4 semisubmersible case. The 1st tower FA natural frequency around 0.425 Hz is obtained from PSD while the 2nd tower FA frequency is not clearly visible around 3.8 Hz as found in the reference “Offshore Code Comparison Collaboration Continuation Within IEA Wind Task 30: Phase II Results Regarding a Floating Semisubmersible Wind System”. I have also tried to zoom into the PSD plot around 3.8 Hz as the PSD values are of small magnitude (see attached). I can find 2nd tower FA (not 2nd tower SS) from the PSD of the “OoPDefl1” output field but not from the PSD of the TTDspFA. Can you please let me know why the 2nd tower FA/SS mode cannot be identified from the TTDspFA output field?

Secondly, I observed the PSD of the Wave1Elev is showing frequency components outside the WvLowCOff and WvHiCOff range (see attached) for WvLowCOff=12.566370 rad/s and WvHiCOff=21.991148 rad/s. I don’t think WvHiCOff is too high to lead to any nonphysical effects as mentioned in the Hydrodyn manual. I did not see any unwanted frequencies in the PSD of the Wave1Elev for the white-noise spectrum with WvLowCOff=0.314159 rad/s and WvHiCOff=1.570796 rad/s. I have also found the “Wave1Elev” PSD is normally distributed even after setting WaveNDAmp to FALSE. I am not sure what is wrong with my Hydrodyn file. What input parameters lead to a normally distributed PSD. By-the-way, I calculated the PSD directly from FFT without any windowing as you suggested in the forum.

Regards,

Dear Srinivasa,

I’m not sure I really understand what you are doing. It sounds like you are trying to use white noise to excite the tower, but the frequency range you’ve selected (2-3.5 Hz) is not in the range of the tower frequencies you are trying to identify. Only nonlinearities in the system will excite frequencies outside the excitation range.

Regarding your second question, your wave-elevation plot does not really look like white noise between 2-3.5 Hz (your solution cuts off at around 3 Hz); I’m not sure I understand based on what you are describing. Regarding energy appearing outside the range of the first-order wave cut-offs, have you enabled second-order wave kinematics? The PSD can also be impacted if you are not outputting the full time series at the full resolution that the wave kinematics are generated. Are you outputting the time series at WaveDT up to WaveTMax?

Regarding WaveNDAmp, enabling this flag will randomize the wave spectrum (following a normal distribution) about the target spectrum.

Best regards,

Dear Jason,

Yes you understood it right. I am trying to excite the tower modes using a band-limited white noise spectrum. Also you are right the frequency range I selected (2-3.5 Hz) is not in the range of the tower frequencies. In fact I did try with a frequency range 2-5.5Hz but I obtained a similar PSD as shown in my previous post. I see here (RAO OC3Hywind Turbine), the one sided spectrum equation is given by: WaveS1Sdd = WaveHsWaveHs/(8( MIN( Pi/WaveDT, WvHiCOff ) – WvLowCOff ) ). I think this equation does not allow me to use wave high frequency > Pi/WaveDT. Is this right?

Yes, I agree with you that my “Wave1Elev” PSD cut-off at 3 Hz but I don’t understand why it does that way even when I set different cutoffs for lower and higher wave frequencies. Yes, I have disabled second-order wave kinematics. Also, I am outputting the time series at WaveDT up to WaveTMax. I am using TMax=4600, DT=0.0125, and DT_Out=0.05 in fst input file. See attached the HydroDyn.dat file (Here I used WvLowCOff= 12.56637 and WvHiCOff= 34.55752 rad/s).

Can you please suggest how I can obtain band-limited PSD for the “Wave1Elev” field?

Regards,

Dear Srinivasa,

HydroDyn computes the wave-elevation time series by computing an inverse FFT of the frequency-domain spectra with random phases. The highest frequency in this spectra is determined by WaveDT, i.e., the maximum frequency (in rad/s) is Pi/WaveDT. Setting WvHiCOff higher than this will not change the result. In your case, Pi/(0.2 s) = 15.71 rad/s = 2.5 Hz, so everything about 2.5 Hz will be cut-off.

You are outputting the wave-elevation time series at a higher sample rate (0.05 s instead of 0.2 s), so, HydroDyn will simply interpolate to output the wave elevation at the higher sample rate. This interpolation will impact the PSD a bit. To see the true PSD, set DT_Out = WaveDT.

And if you want wave energy at higher frequencies, reduce WaveDT (and DT_Out accordingly).

Best regards.

Dear Jason,

Thanks for your reply. I could now see the band-limited white noise spectrum (wave frequency range is 2 to 5.5 Hz) for the Wave1Elev field by setting WaveDT=DT_Out=0.0625. Now I think the 2nd tower modes will be excited. However, I see there is lot of noise in the PSD of the TTDspFA to clearly identify the 2nd tower FA and SS. I believe playing with the WaveDT can help me reduce the noise in the PSD. Can you please suggest if there is any better way to identify the 2nd tower modes from the PSD of the output fields as they are too noise in the high frequencies?

Regards,

Dear Srinivasa,

You can try smoothing the PSD by binning it into larger frequency steps, or by splitting the time series into small sections, computing the PSD of each section, then averaging. Either way, you should ensure TMax and WaveTMax are large enough to get the frequency resolution you desire after smoothing.

Best regards,