I'm not quite following, since you quoted my entire post: what is only unconditionally true for the free stream?
The last sentence, that power is proportional to the cube of wind velocity. Inside the venturi, you have to account for the robbing of Peter to pay Paul: the thing held constant in the freestream wind power calculation, density, is now a variable. And it will drop to conserve energy as velocity rises. Power (energy) will remain the same (ideally) even though the speed goes up, because since there are so many fewer air molecules to transport that energy, the speed becomes irrelevant. Hence I said the statement "power goes as the cube of velocity" is unconditionally true in the free stream where density remains constant. Inside the venturi, the statement is conditioned on introducing a way to overcome the pressure (density) drop. And that requires an external power source.
Look guys, I know there are secondary effects here that I (and they) have not discussed, but the most obvious thing about a Venturi is the fact that velocity differences between points are proportional to the area differences: At a spot where the area is halved from another spot, the velocity is double that of the other spot. That's all I'm saying and that's all that is claimed here.
Well, since their claim relates to power, I was just bringing the issue of pressure (density) home to roost. It can't produce a net gain without energy added to drop the backside pressure.
It must be happening otherwise the device would have to be inflating like a balloon or pressurizing like a scuba tank!
There is no definitive data that suggests that anything of the kind (power boost) ever happened. They give one data set that looks to me like anemometer readings in front of and inside the venturi. Those consistently measured velocity increase but no work was being done. The second case was with the turbine installed, in which the data is all over the place. And in that set the velocity differences are between the pole mounted turbine and the one in the venturi. So there's no way to confirm the idea that the body of the structure blocks the wind sufficiently to get a net energy gain.
The shape's explicitly stated purpose is to funnel the air to increase the airflow speed. The pressure drop is merely a consequence.
My point is you can't have one without the other. There is not a venturi effect without a pressure drop. And if that pressure drop is not sustainable due to backpressure, then nothing happens. Air just flows through at nominal speed, right? I'm saying 'ideally', ignoring compressibility and everything else.
What improvement? I just told you that when you look at their numbers, the actual claim is a reduction in energy extracted of 25%!
Apples and oranges. Yes, that part of the claim (2:1 speed should correspond to 8:1 power, not 6:1 power) -- that's the apples. Here are the oranges: on one day during a week of testing the turbine inside the venturi showed a 9:7 velocity improvement over the pole-mounted one. The enclosure therefore showed an improvement, but only briefly. There is no power data given, hence no way to calibrate oranges to apples. Besides, that's wind power, which has to be derated according to efficiency to even hope to get the apples to line up with the oranges. It's virtually useless. All we really need to see are the electrical power data.
Their language is just a smokescreen comparison of apples to oranges: you have to look at the actual numbers. They are claiming that by funneling the air to increase its velocity, they get a 6-fold increase in power versus a turbine of the same size in the freestream. The part in bold and what that means is what they gloss-over in the language.
I'm on page with you as far as the smokescreen, but after looking a little more closely at the data than you may have done (I'm only guessing; it looks like you didn't) I'd have to disagree in the sense that it was not consistent, there was one day when the freestream turbine was better, etc. I was just trying to clear that up, recognizing that you're on top of your game here as far as the science goes.
Now, the aerodynamics of that is definitely more complicated, but only marginally relevant. Still, we can discuss:
-Bernoulli's equation/conservation of energy applies.
-Venturi effect applies.
-Air outside/in front of the device is slowed by the drag from the device, converting velocity pressure into static pressure via Bernoulli's principle. That's the trick: air entering the cone is not freestream air, it has already been decelerated and had its pressure increased before it even enters the device. It is this increased static pressure that drives the air through the device.
-The result is that this device captures less air than its dimensions imply it should. The variable speed ratio in their graph is a result of that issue: a 2:1 speed ratio implies the area ratio is 2:1 (Venturi equation), but in reality, it has to be larger than that and be variable since pressure is a square function of velocity.
That last statement is certainly true. Pressure at any cross-section is ½ρv². The pressure drop as you know is the difference of those two quantities, at the mouth of the venturi vs. inside.
I'm only saying that if the back pressure won't sustain that lower amount, nothing happens. Or else nothing much happens. For this reason, if they were designing for net gain, they would need some way to create a vacuum at the tail end (like some posters magically produce in perpetual motion machines).
You suggested that this is possible from the aerodynamics of the outer surface of the contraption, and I doubted that, since it wasn't designed for that purpose. My point is that lower backpressure has to be designed into this to get a net gain in wind power in a venturi that runs exclusively from wind energy. Therefore the venturi can only produce more power than the pole mounted turbine if some vacuum-creating aerodynamic surface can be designed in. Theoretically, that is, and subject to the limited scope of what I just laid out.
