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SNL-WaterPower / WecOptTool-MATLAB

WEC Design Optimization Toolbox
GNU General Public License v3.0
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Flapping device #207

Closed H0R5E closed 1 year ago

H0R5E commented 3 years ago

Description

Continuation of #170

Fixes #156

Checklist:

ryancoe commented 3 years ago

Can you put together a MWE along the lines of this?

[Aw, Bw, Fexc, P_cc] = flapper_mwe(depth)

H0R5E commented 3 years ago

So, these are the results from modifying the depth of Giorgio's flap from 15m (minimum depth) to 30m in 5m intervals.

                AvgPow        |MaxPow|     PowTHD_dBc    MaxTheta    MaxOmega    MaxTauPTO 
              ___________    __________    __________    ________    ________    __________

    15.0 m    -2.7235e+05    1.2862e+06       NaN        0.051194    0.028945    4.8244e+07
    20.0 m    -3.0834e+05     3.752e+06       NaN         0.18056     0.10012    6.1384e+07
    25.0 m     -3.378e+05    6.8582e+06       NaN         0.26963     0.14805      8.24e+07
    30.0 m    -3.5975e+05    1.1169e+07       NaN         0.36094     0.19639    1.0558e+08

model_results

The input values for added mass, damping and excitation are shown in the plots below:

added_mass damping excitation

H0R5E commented 3 years ago

I never got a chance to discuss it in our meeting, but I've been looking at this some more, and my current thoughts are that this is either a quirk of the maths (and therefore is maybe a matter of adding a constraint?) or something fishy in the outputs of NEMOH.

So, fundamentally, for the CC controller (and unconstrained PS, by design) the optimal complex velocity is the ratio of the excitation force to the real part of the impedance matrix (i.e . the radiation damping). So for the result, the absolute size of these values is irrelevant. What is happening in the NEMOH results is that as the depth of the flap is increasing, the radiation damping is getting smaller faster than the excitation force, and thus the optimal velocity and power are increasing.

It seems to me that this is going to quickly exceed the upper limit on the extractable power from the wave, so I'm not sure what assumption is being broken to allow this to happen. Is there some relationship between the radiation damping and the excitation force that is being broken by NEMOH? It would be interesting to see what capytaine does with this case, also.

EDIT: Is the wave's complex velocity increasing? Say, if we have

<img src= "https://render.githubusercontent.com/render/math?math=%5Cdisplaystyle+%5Ccolor%7Bred%7D%5Chat%7BF%7D+%3D+%5Chat%7Bu%7D%28B+%2B+i%5Comega+A%29" alt="\color{red}\hat{F} = \hat{u}(B + i\omega A)">

Then for \color{red}\hat{F} to reduce more than \color{red}B , it would seem to me that \color{red}\hat{u} must be increasing. Would that be expected due to the change in water depth?

EDIT2: Yeah, I think that's it. The wave celerity increases with depth for shallow water and then the wave power is proportional to the celerity. So, in this case the WEC is getting deeper, but the available power is increasing also. Is it really shallow water though? For all the frequencies. Is NEMOH doing something funny?