IEA-15-240-RWT-UMaineSemi linearization

Wind & Water Computer-Aided Engineering Software Tools
21

Good morning @Jason.Jonkman ,
Sorry to further reply, I’ve performed different test to try understand the problem. The previous results with the free decay where obtained with AeroDyn activated. I tried to also deactivate it( keeping only ElastoDyn, MAP++, HydroDyn and Inflow file), the result in damping extraction was 2% for a wind speed of 10 m/s. (with small variations if radiation was mantained or not)
I attach the decay of the platform pitch.

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With AeroDyn I just had 2 main peaks and 3 smaller peaks in the decay before stabilizing almost completely.(with also a equilibrium point shifted from the 0).
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Since the previous results of the linearization and my model seem solid, I’m wondering if and where I could introduce an error(I performed the same approach on 5MW DeepCWind and still the same problem occurs).
I give you also additional informations about my linearizations: ElastoDyn,InflowWind,AeroDyn,ServoDyn,HydroDyn and MAP++ all activated and the results it’s giving me just a matrix 4x4 wind rotor speed, its derivative, platform pitch, its derivative.
Sorry again for the disturb.

22

Dear @Leonardo.Facelli,

I’m sorry, but I don’t really understand what your question is.

Best regards,

23

Dear @Jason.Jonkman ,
I try to explain it better. As already mentioned in this section, I’ve created a simplified model of the IEA-15-240-RWT-UMaineSemi considering only rotor , platform pitch and its derivative as dofs. At the same time I’ve also performed the linearization from openfast to perform a comparison in term of damping ratio of the platform pitch for each wind speed. The results were very close.
After this first step, I wanted to extract the same information (damping ratio) by doing free decay simulations with openfast, in which in each test the wind speed was varied and still water. (same initial condition of the platform pitch and also the only dof activated). As example the first test was initial platform pitch of 10deg, wind speed equal to 5 m/s (inflowind, aerodyn, elastodyn, map, hydrodyn activated). The duration of the simulation has been set to 600s.
I’ve then extract the damping by using the logarithmic decrement. The result was that in this case it was half of the ones I found in my model and from the linearizations.
So my question would be if you could help me in finding out if my free decay tests are set in the wrong way. Or simply, give me a feedback on the correctness of the tests (if doing them it’s really giving me the overall damping: structural + aerodynamic).
Thank you very much for your patience and availability.

24

Dear @Leonardo.Facelli,

Can you clarify how you extracting the linear damping from the free-decay? Do the damping coefficients you are extracting from the free-decay results depend on the amplitude of oscillation from one cycle to the next?

Does your model include hydrodynamic quadratic (viscous) drag, that cannot well be captured by the linear model?

Best regards,

25

Dear @Jason.Jonkman ,
The matlab function I’m using for the damping is the following:
function [B, Td, locs, pks] = CompDamping_v2(t, th, fsamp, Method, Npks, manual)

if Method == 0
    
    % Find main signal period
    [Y, ~, freq]  = fft_trasform(detrend(th, 'constant'), length(th), 1/fsamp);
    [pksH, pksF] = findpeaks(Y, freq);
    [~, maxI]    = max(pksH);
    pksF        = pksF(maxI);
    Th          = 1/pksF;
    
    % Exclude initial part
    if th(1) > 0
        th = -th;
    end
    
    % Find peaks in the selected time history
    Ths = 0.85 * Th;  % Minimum distance between consecutive peaks
    [pks, locs] = findpeaks(th, t, 'MinPeakDistance', Ths);
    
    % Discards local minima and keep only maxima
    logical = pks < 0;
    pks(logical)  = [];
    locs(logical) = [];
    
    % Start selecting peaks from the middle
    % Startpoint = floor(length(pks) / 8 );
    
    if length(pks) < Npks
        Npks = length(pks);
    end
    
    pks = pks(1 : Npks);
    locs = locs(1 : Npks);
    
    % Average signal period [s]
    Td  = mean(diff(locs));
    omd = 2 * pi / Td; % Damped frequency [rad/s]
    
    % Linear
    delta = 1 / Npks * log(pks(1) / pks(end));
    h     = 1 / sqrt(1 + (2 * pi / delta)^2);
    
    % Natural period
    omn = omd / sqrt(1 - h^2);
    Tn  = 2 * pi / omn;
    
    % Linear and quadratic
    if Npks > 2
        delta = zeros(1, Npks - 1);
        p = zeros(1, Npks - 1);
        for ii = 2:Npks
            delta(ii - 1) = log(pks(ii) / pks(ii - 1));
            p(ii - 1) = -(4 * pi / Tn) * delta(ii - 1) / sqrt(pi^2 + delta(ii - 1)^2);
        end
        PP = polyfit(16 / 3 * pks(2:Npks) / Td, p, 1);
        p1 = PP(2); % Intercept, linear
        p2 = PP(1); % Slope, quadratic
    else
        p1 = 0;
        p2 = 0;
    end
    
    % Output damping
    B = [h p1 p2]';
    
    if th(1) < 0
        pks = -pks;
        th  = -th;
    end
    
    figure(100); plot(t, th); hold on; plot(locs, pks, 'or');
else   
    ss_time = 30;
    y_inf     = mean(th(end - ss_time * fsamp:end));
    y_inf_std = std(th(end - ss_time * fsamp:end));
    
    figure(100)
    plot(t, th)
    hold on
    yline(y_inf, '--');
    yline(y_inf + y_inf_std, '-.');
    yline(y_inf - y_inf_std, '-.');

Yes the results depend slightly on the amplitude of oscillation: ex with 10 m/s, if the initial platform pitch is -1.5deg the damping is 15.59%, if 6deg 15.77% and if 15deg 16.92%.

Concerning my model, the damping term has been extracted always with the same method: free decay with no waves and no wind and initial pitch condition and the function I’ve shared. So it should have both radiation and quadratic drag terms.

Best regards,

26

Dear @Leonardo.Facelli,

Thanks for clarifying, but you haven’t said what values you are setting in the CompDamping_v2() function call, and which outputs you are extracting. Regardless, I would assume that you are extracting “h”, which seems to average across multiple peaks in the free decay, and so, somehow combines the linear damping and quadratic drag into some effective linear damping coefficient. This could be part of the problem because the linearized model is likely not properly capturing the quadratic drag in the linear damping extracted and the linear damping extracted from free-decay includes some contribution from quadratic drag.

Best regards,