Wind energy

[FALCON_12]

Ok. Can you explain to me why we cannot consider that the blade experiences a wind of speed V0-V1 and use this formula?

Don't get me wrong, I'm not disputing it, I just need to understand what's going on. It is impossible for me to admit what I do not understand.

Let's say that from the start, you and I do not think on the same approach.

My view is orderly flow with 90° deflection of the fluid stream.

Your point of view is an undeflected flow at 90° which "dissipates" as it goes around the blade in a turbulent manner, you are in the domain of aerodynamic drag (and not a momentum balance).

So under this assumption we can use your calculations using the relative wind to estimate the force. The Cx of a plate facing the wind is around 2 I believe.

Ok. There remains this counter-intuitive result for me which says that with this system the maximum efficiency is less than that predicted by the Betz limit for a wind turbine with equal surface area (surface swept by the wind turbine equal to the surface that I 'opposes the wind) and even for the largest existing Cx: 1.5 (parachute).

Indeed, I found Emax=4/54.Ro.Cx.S.V0^3.T for my system, while the Betz limit for a wind turbine says: Emax=1/2.Ro.S.V0 ^3.T, so it's 4/54.Cx in front of 1/2 or approximately: 0.11 in front of 0.5 for the max Cx available on the planet: 1.5. I can't explain that to myself.

On the other hand, surprisingly, I found that you have to let the surface move back to V0/3 to have Emax, and Betz's theory says that the wind leaving the wind turbine must also advance to V0/3! Amazing similarity.

[phil59]

https://fr.wikipedia.org/wiki/Limite_de_Betz

Around 60% yield at best, if it's comparable.

60% is already huge. Only hydraulics do better, in pure electrical production.

Yes, and no, 60% is just the wind turbine, without a generator, which will further reduce the output.

60% is the maximum that the wind turbine can take, the maximum wind, slowed down by the next blade, which slows down, in a way....