berkeman said:
OK, let's take a look...
The goal of a wind or water turbine
Convert the force of a fluid passing through a given area into electrical or mechanical force.
The Betz limit is discussed
here.
OK, true enough, but I'm already having my woo senses start to tingle. Let's see what this Betz discussion is...
The Betz law applies to all Newtonian fluids. It defines the maximum theoretical efficiency that a wind turbine can achieve as 59.3%. This is based on the total available energy of the wind at a given speed. All current commercial wind turbines are designed based on this same assumption and most wind turbines are considered to be 34% to 45% efficient.
This is a huge mistake
The Betz limit is based on the obvious assumption that extracting energy from wind will reduce the speed of the wind. Betz only applies to the point of extraction. What the Betz limit ignores, or more correctly, what resultant design assumptions throughout the global wind industry have ignored, is that you can also increase the speed of the wind prior to extracting energy with no penalty. Double the wind speed and the available energy increases by 8 times.
Betz applies to *all* incompressible external flows that you're trying to extract power from. This "gotcha" that he's trying to claim here is false - any design involving some kind of a concentrator (like the mountain ridge he mentions in the following paragraph) still must ultimately follow the Betz limit, you're just increasing the effective collection area. Yes, this increases wind energy available, because increasing collection area always does, but it's not a magical "get out of the Betz limit free" card.
Currently, only the outer 30% of a typical wind turbine blade produces any meaningful torque and that blade area is less than 5% of the total disk area. In addition, tip loss occurs at the maximum point of leverage. Aerodynamic efficiency is utilized but no attempt is made to divert or accelerate the air prior to or after extraction. In other words, the drag side of the equation is completely ignored.
Oh dear.
This is all basically 100% wrong. Torque is produced along the entirety of the blade length, though of course the outer 30% is the most important because that's about half the total collection area, and you have more efficient airfoils out there because you can make them thinner with better L/D because the root airfoils have more stringent structural concerns.
However, the root 70% still makes a bit less than half the power on a modern turbine, and it's not ignored. Also, low rotor solidity (the "only 5% of the total disk area is occupied by blade" part) doesn't mean that you only affect a small portion of the wind passing through. It's just a design factor. With a low solidity blade, you run a higher tip speed ratio, so you need to balance those factors when optimizing the design, but you still absolutely interact with all the air passing through the disk.
This is not necessarily intuitive of course - it looks like a ton of air is passing between the blades, but the reason this works is because the blades are traveling at a high multiple of the wind speed - usually around 10x or so. Because the blade is traveling 10x faster than the wind, air that passes through the large opening will still shortly have the blade pass right behind it or will have had the blade pass right in front of it shortly before it went through the opening, and thus the turbine still effectively interacts with the entire disk of air.
There's a really cool video that helps visualize this here:
Note how little the air from one blade passage has moved before the next blade comes by?
Returning back to the original page (there's a lot more wrong on that Betz limit page, but I'm trying to not write too much of a novel here).
Current designs maximize aerodynamic efficiency like an aircraft. This results in long thin wings that comprise less than 5% of the total disk area in the region of maximum torque (the tip). Much of the air passes through unaffected or in a region that contributes low torque (the root). Only the tip of the blade maximizes leverage.
I've already explained why this is wrong.
Now, with the Waters design:
There are two choices for accelerating flow. Divert around an object or constrict through a narrower path. Diverting flow to the outside provides more leverage for a given size object and enables a simpler design. Generally, large costs more than small. Complex costs more than simple. Here is a basic design that meets the criteria.
In the above illustration, all of the flow has to go around the back plate, accelerating in the process. A band of blades is mounted around the perimeter at both the maximum point of leverage and maximum flow velocity. As a result, all of the fluid is utilized and accelerated to maximum velocity prior to use.
What he's missing here is that due to the high blocking caused by this design, a large proportion of the air will just flow around the entire turbine. This doesn't "utilize all the fluid", it actually will force a large proportion of the air to just bypass the turbine entirely. In addition, he continuously makes the mistake of assuming drag doesn't matter, but the direction drag operates at the blade tips or in his blade ring is nearly directly opposing the desired torque. Drag is opposite the relative wind, and because the turbine spins, that means drag *opposes this spin*. Wind turbines are designed for maximum L/D for very good reasons, and not just because the designers are naively following aircraft design principles.
I originally designed the Waters turbine to prove a point for a lecture I gave regarding Open System Physics and Thermodynamics. At the time I had little interest in wind turbines but had been involved in aviation and aerodynamics most of my life. The wind industry made an easy, somewhat devastating example.
As a general rule, if you're not in a given field, and you look at that field and think "obviously they're doing everything wrong", it's
vastly more likely that you're missing something than that everyone in that field's history has been an idiot.
(
Relevant XKCD)
Compressing air increases temperature. Lowering pressure reduces temperature. This is basically how an air conditioner works. The Waters turbine uses drag to create 3 different pressure zones in addition to ambient. As kinetic energy is extracted, temperature drops.
Even a small thermal differential represents a considerable amount of energy potential if designed correctly. With the 4 month physicist study, optimizing this showed a COP of up to 20 which means we were tapping a second thermal energy source. At first glance this appears to be a case of asymmetric thermodynamics but in reality the kinetic differential is just being exploited more efficiently.
This is a strange aside - at normal wind speeds and pressure coefficients you'd encounter at those speeds, temperature changes within the flow are totally negligible. I'm not sure why he's trying to even bring thermal changes into this at all, but we can absolutely disregard all of this. Bringing a 20 m/s flow to stagnation causes a temperature rise of less than a quarter of a degree celsius, and 20m/s is faster than most of his claimed windspeeds anyways.
In my tests, the conventional design was a molded precision product with an accurate airfoil. Mine was far from optimized, using no airfoils (concrete vent) in order to establish the source of the efficiency gain that was in addition to aerodynamic gains.
Comparing my 4' design against a stock 5' three blade under the same load, the conventional product starts at over 7 mph and produces very little torque or rpm at that speed. My turbine, under the same load starts at under 1 mph. If the square force relationship is used that is 49 times more force required to turn the conventional design. If the cube rule is used the difference is 343 times. Then there is a size difference. The actual formula is more complex and varies with wind speed but the results are interesting. Startup velocity is just one factor but this shows that a much broader wind velocity range can be utilized.
Under extreme shaft load, the conventional turbine would not turn even at 28 mph. My design in the same conditions self starts at 11 mph.
I strongly suspect his reference turbine here has a fixed blade pitch. This means that at low RPM, the blade will be nearly entirely stalled, and producing next to no power. It's unsurprising that under load, it would struggle to self start. For proper comparison, the turbine needs some kind of RPM control on it, adjusting back torque to keep it at approximately a fixed tip speed ratio (ratio between tip speed and incoming wind speed to maintain good angle of attack across the whole blade).
If he actually allowed the HAWT to unstall, he'd find that it would make substantially more power than his design. You need to let it spin up before you apply substantial load, particularly for a fixed pitch turbine. As a result, his test results are totally useless. It's also well known that if your goal is low-RPM torque, particularly stall torque, you do want a pretty high solidity rotor (having more of the disk area occupied by blades) - a good example of this is your classic US western "windmills" that drive water pumps for livestock and such. This gives more starting torque, but actually less peak power because you have more drag as you try to increase RPM.
Also, larger scale wind turbines use pitch controlled blades to help alleviate this starting problem - they do still perform optimally at fairly high RPM (relative to their diameter and incoming wind speed), but to aid starting, they can pitch the blades more towards feather so they are not stalled as they start up. As the rotor accelerates, the blade pitches more and more towards operation, maintaining a good non-stalled angle of attack the entire time. You can see that clearly in this video here, for example:
Basically, his design might work well in some small niches, but it'll always make less power than a well designed horizontal axis 3 blade turbine, as long as that 3 blade is actually operated properly and not just forced to sit there with its blades stalled the whole time.
