Sure it was covered in some technical detail in another thread.

As Damon says, the Betz limit places a constraint on the highest efficiency you can get from a wind-driven device of around 60% (in round numbers). Current big wind turbines are around 40%, so at most there is may be another 20% to gain.

In effect, this shroud ring achieves its performance gain by increasing the effective swept area of the turbine, something that could be done more easily and with lower overall drag by using longer blades of the same diameter as the shroud ring.

http://www.greenbuildingforum.co.uk/forum114/comments.php?DiscussionID=7778

<blockquote><cite>Posted By: dickster</cite>Whilst we're on the subject of dodgy theories, on a VAWT, why don't they shield the side with the blades heading into the wind from the wind?

It's been bugging me for some time!</blockquote>

Because many designs (the more efficient VAWTs with blades) gain power from the forward moving blades, too. The principle is similar to that of a yacht sailing into wind at an angle, so for much of the into-wind bit the blades are getting some lift, it's only a small angle either side of the dead into the wind angle when they won't get anything useful and just add drag.

Dear sir,

Have you anything I can use to stop this snake squeaking?

On Facebook, there are 'like' buttons under each comment. Need two right here. Will have to content myself with a 'LOL'.

Martin.

Right, but all the lets-stick-lots-of-VAWTs-close-together folks avoid Betz by making a feature out of the fact that the wind is actually turbulent and a three-dimensional flow. So Betz answered a question, but was it the right question? Enquiring minds want to know.

Posted By: CWattersOne problem is they work best at one airspeed.

Don't turbines (large ones) tend to run a constant speed, so the tip velocity is constant and the apparent windspeed at the tips is also pretty constant because of their size.

Google found a paper..

http://130.226.56.153/rispubl/VEA/veapdf/ris-r-1543.pdf

"Aerodynamic investigation of Winglets on Wind Turbine Blades using CFD"

"Results show that adding a winglet to the existing blade increase the force distribution on the outer approx 14 % of the blade leading to increased produced power of around 0.6% to 1.4% for wind speeds larger than 6 m/s."

Sorry but I dont buy the Betz limit. A similar argument was put forward for water turbine efficiency with an upper limit set which in theory could not be broken. Unfortunately actual performance records disproved the theory which resulted in a review of the original theory and a realisation that not all forces had been accounted for in the original model.

<blockquote><cite>Posted By: renewablejohn</cite>Sorry but I dont buy the Betz limit. A similar argument was put forward for water turbine efficiency with an upper limit set which in theory could not be broken. Unfortunately actual performance records disproved the theory which resulted in a review of the original theory and a realisation that not all forces had been accounted for in the original model.</blockquote>

You're not alone, other have also questioned the validity of the Betz Limit.

It obviously can't be 100%, for the reason above (100% means no flow from the output side of the device), so there has to be a limiting efficiency, it'd be nice to know what this is if Betz has got it wrong.

What do you think is the true upper efficiency limit?

<blockquote><cite>Posted By: renewablejohn</cite>Logically if you compare airflow and water flow as being similar apart from density then water turbine technology is pushing 75% efficiency which I would think is not an unreasonable figure for airflow.</blockquote>

Unfortunately this isn't a valid comparison. The Betz limit only applies to open turbines operating in free flow (so wind turbines and underwater free water turbines using tidal power).

The Betz limit doesn't apply to closed turbines where the pressure is increased at the inlet to a value much greater than the dynamic pressure of the moving fluid. If you constrain the movement of a fluid and increase the pressure (head) then you can get efficiencies of better than 85%.

Unfortunately there's no easy way to raise the "head" of air flowing into a turbine, so no way to produce the pressure increase at the inlet needed to overcome the Betz efficiency limit.

Posted By: JSHarris

Posted By: renewablejohnLogically if you compare airflow and water flow as being similar apart from density then water turbine technology is pushing 75% efficiency which I would think is not an unreasonable figure for airflow.

Unfortunately this isn't a valid comparison. The Betz limit only applies to open turbines operating in free flow (so wind turbines and underwater free water turbines using tidal power).


Unfortunately there's no easy way to raise the "head" of air flowing into a turbine, so no way to produce the pressure increase at the inlet needed to overcome the Betz efficiency limit.

I dont see why its not a fair comparison its Betz who makes "assumptions" for his simplified model the fact that reality is more complex does not make his model correct.

As for "head" you dont need to do much turbine research to find twin rotors rotating in opposite directions are far more efficient than a single rotor. The whole aerospace industry has been built on this fact.

<blockquote><cite>Posted By: djh</cite>Jeremy, I think we're all agreeing. What you're doing is providing more explanation of the boundaries of application of Betz' limit. What John and I are saying is that there are real-world cases outside those boundaries and where the Betz limit doesn't necessarily apply. That's basically saying the same thing in two different ways.</blockquote>

I agree people are prone to express something like the Betz Limit as an absolute, without giving the specific scenario where it applies. It doesn't apply to a closed, pressurised, system, for example, so a water turbine or gas turbine can operate well over the limit that Betz proposed.

The Betz Limit should apply to a free contrarotating turbine, though, just as should apply to any device intended to extract energy from the motion of a free (unconstrained) fluid in incompressible flow.

Contrarotating props are often less efficient in general than single props, and only tend to be used where it's difficult to accommodate a larger diameter prop to absorb the available power. They are relatively uncommon now, but I did do some (amateur) experiments with using such an arrangement on a microlight aircraft years ago. Apart from the performance being poor it also made a lot of noise, indicative of poor efficiency in itself. The big problem is that the rear prop (or turbine) is operating in highly variable flow conditions caused by the front prop (or turbine). At a specific rpm these can give a positive benefit, but over most of the rpm range they just reduce efficiency.

<blockquote><cite>Posted By: renewablejohn</cite>JSH

Pity the research does not agree with your statement.

http://www.wtswind.com/home/video

Not only is the turbine more efficient but it makes the alternator more efficient as well.</blockquote>

Having just read that link I'd suggest that what they are saying agrees well with my own work on contrarotating props. They certainly don't seem to have exceeded the Betz Limit for either turbine blade, as far as I can see; both seem to be well under it.

It's hard to read the graph, but it looks very much to me as if the second tandem blade is less efficient than the first and that matches my experience with the interference effects I saw with tandem props. If they fitted the two turbine blades to separate units in the same wind speed I believe they'd get more power than with the arrangement they have, although I guess there's some convenience of having the two units on a single mast.

EDITED to add:

I have just tried to take the data from the graph on that link and work out the blade efficiency. First a caveat, even after copying, pasting and enlarging the graph I still found it hard to read off the numbers, so there is a degree of uncertainty on the base data I used of maybe +/- 50 to 100 watts.

Rotor 1 is the leading blade I'd guess, and it has the following efficiency figures:
10 mph = 36%
12 mph = 34%
14 mph = 53%
16 mph = 46%
18 mph = 42%
20 mph = 45%

Rotor 2 looks like the trailing blade and has the following efficiency figures:
10 mph = 29%
12 mph = 17%
14 mph = 16%
16 mph = 14%
18 mph = 12%
20 mph = 17%

The big effect that the leading blade has on the efficiency of the trailing blade is pretty clear, so if it was mounted in clear air it would probably perform better and result in more power.