what factors determine the upper theoretical limit for small wind turbines

[oneirondreamer]

I'm not getting any response to my posting on Reynolds #, so I thought I would repost as a new topic with a more descriptive heading.   

I've seen lots of people trying to do blade design/alternator pairing, who seem to think that a small turbine might aerodynamically perform close to the Betz limit.    I want to see what others opinions on this is, and see if we can come to an agreed number for 10ft or smaller wind turbines upper aerodynamic limits are.    In the real world the person with probably the most experience in testing micro turbines, Paul Gipe says on his website discussion of testing says that his experience leads him to believe that on a very windy day, with a very good installation of a very good commercial turbine, 20% efficiency is the best that might be achieved.

The first and largely agreed limit, is the Betz, which is a blade disk calculation proposing a turbine with no losses from drag, tip vortex's etc.     So the ceiling on the limit is 59.8 max with a perfect turbine (no drag).    The next question is what kind of efficiency would this turbine achieve?   If the blades had a 20 to 1 L/D (including an RE factor (see my previous topic, RE# and wind turbine eff)? how would that be applied to the 59.8%?   

[SparWeb]

Didn't get a chance to see the Re# thread until today.
Not many members on the site will know what you're talking about, though there are a few who do.
There's a NREL forum for questions more like that, BTW.
I'll go back and look at your question on the other thread...  see if any thoughts come to mind.

[oneirondreamer]

Can you post, or send me a link to the NREL forum you mentioned?

[fabricator]

I personally believe getting too wrapped up in stuff like Renolds numbers and upper theoretical limits for something like a home brew wind turbine is a little over the top.

[oneirondreamer]

Since this post has gotten 70 views from when I posted it this morning, and the other related post has gotten 250 views since yesterday, it seems some people find it interesting.   

It may seem a bit depressing to home builders who thought they might be able to approach the Betz limit with a small turbine, however it also may let some builders know that they have hit the nail on the head, and there's little room left to improve anything in their setup. 

 

[taylorp035]

There are a lot of other tiny factors that influence it as well:

A smooth uniform air flow
Frictionless bearings
Infinitely small hub / generator
incompressible airflow ??
air drag from the blades


Pairing the blades to the generator is going to be much more important IMO.  And that is impossible to make perfect anyways, since the power output of the generator and the blades run on different efficiency/torque/rpm/tsr curves.  If you wanted to get it right the first time, some math could be done and analyzed using a computer..... but reality will eventually set in

[SparWeb]

Fab is right, the theoretical issues are a rather moot point when you are holding a solder iron / spokeshave / welding torch in your hand.

The mathematics is fun, for some of us.  It's just not everyone's cup of tea.

https://wind.nrel.gov/forum/wind/index.php

You'll want to spend some time exploring that, and the associated databases of research reports.

[Flux]

I think I answered a lot of this on the Reynolds number post yesterday.

As nobody has yet beaten the Betz figure it stands more or less unchallenged. There have been a few attempts to show tat it may be a bit on the low side as it is based on simple momentum theory but until someone gets results even close there is little point in challenging it.

Real life results seem to indicate that large machines get over 0.4 and small ones can get a bit under this figure. I doubt that anyone has properly substantiated anything over 0.5% so your challenge is to beat that.

Cp from the prop is one thing, overall cp into a load is another. Unless the load matching is perfect you won't maintain the prop Cp over any range of wind speed. Then you need to factor in the electrical efficiency and with a small machine it is not going to exceed 80% even if built on the concept that cost is no object. Efficiency for very large electrical machines can be over 95% but they are monster power station machines connecting to the grid and running at constant speed.

When charging batteries with the non linear rectifier loads I suspect anything over 85% is approaching the impossible.
Smaller wind machines running over a limited range of wind speed may typically be in the 70% region. You won't maintain this efficiency over much of a range of wind speed without some form of load matching. if you try you will have to drop the electrical efficiency even more to keep some sort of match to the prop or your prop Cp will drop right off.

When you have solved all the problems of load matching you can start to worry about electrical efficiency and then you are left chasing the finer points of props and their aerodynamic quirks. If you don't solve the load matching problem a well matched plank will outperform the best aerofoil that is badly matched.  It normally turns out that the best performing prop is the one that best matches the load on the machine it is fitted to.

If you want to experiment with props and efficiency then you must do all your tests at the maximum power point of its curve or you will be fooling yourself.  You would most likely be better of doing the tests with some form of variable mechanical load, introducing electrics could give you the loading required but you need to measure the mechanical input power. What electrical power you get into a battery with these tests would depend entirely on your ability to convert input power to output power with the minimum loss.

I hope this helps you see why there is interest here but not a lot of response, Those who use wind for power are not really in a position to even measure the complex issue of plotting power curves let alone make all the changes on a regular basis to untangle the interconnecting issues.

Flux

[thirteen]

How effective are the vertical open framed rotating cylinder turbines going to be? According to the article I just read they have made over 900 and installed them in different places . They say they are getting more power from them in a smaller place with the upright turbines than the older style bladed ones. They claim it will be better for the birds and with less noise for us to hear. I am just wondering how efficiently they will operate. Sounds ok but time will tell.

[oneirondreamer]

Thanks for your reply Flux.   I haven't been able to find any credible claim by a small wind turbine manufacturer or independent reviewer that exceeds 25% Cp, and I see that L/D ratios drop by around 1/2 when you go from commercial scale turbines to small, and if we agree that the biggies are around 40% Cp then it seems reasonable that the small ones would be closer to 20% Cp than 30% so I think your estimate of 35% is quite high.

@thirteen
If you are talking about the "windspire" ,  which have a bunch of veritical small wings, joined by a series of hoops.   They likely have much lower efficiency than a conventional turbine of the same swept area, it would be interesting to see what they produce relative to dollars of installed solar pv.   Regardless though of initial dollars to watts, the windspire system doesn't look very robust.

[Flux]

Just to make sure we are thinking of the same thing, I was only considering the prop Cp from wind energy in to mechanical power out, I  Can't see any manufacturer quoting that. The only thing that matters to the end user is overall Cp from wind in to electricity out.

If you stick with overall Cp then I suspect you will not find anything over 25% over the full range of wind speed for battery charging machines. To achieve 25% overall the input will have to be 30% or above to deal with the quite low electrical efficiency. As I said Previously with sine wave loading of large grid machines the electrical efficiency will be much higher so with blades over 45% you may be able to get 40% or better overall.

This large difference between commercial grid connected machines and small battery charging wind machines is partly to do with blade efficiency but much more to do with other issues. Reynolds number and L/D is certainly important but doesn't affect small machine's as badly as you seem to imply.

Flux

[oneirondreamer]

I think we are talking about the same thing, just not agreeing, which is fine.   What I am saying is that I am having trouble finding credible data that says small wind turbines have a shaft power output of greater than 30% at any wind speed, and Paul Gipe, one of the worlds experts in small wind turbines believes a claim of 20% (wind to watts) is high for anything other than a turbine mounted in a very windy location.    I think this stands to reason, given that very large conventional turbines are now reaching into  the 40-50% range, and they will have L/D ratio's (basically a statement of foil efficiency) of double what a small turbine can have.   There are other reasons a small turbine is unlikely to have as high an efficiency as very large turbines, including greater sensitivity to stall, and as has been pointed out, greater sensitivity go surface finish, dirt, and bug guts.       

If you find anything solid, showing higher mechanical eff, please pass it on.

Thanks

Drew

[fabricator]

You seem to be missing an important point, the wind harvested is free, so 10,20,30,40,50% efficiency, who cares? These are small home built turbines a lot of them have blades carved by hand with hand tools, with stators with crooked coils and in some cases salvaged magnets.
Theoretical limits are pretty meaningless to home brewers.

[oneirondreamer]

I disagree fabricator, and one of the most interesting things for me about asking this question is the number of people who seem uncomfortable with the question itself.     If it weren't interesting, why would you have bothered to read it?   I don't think I have missed the point at all.   The 2 questions most people face about most decisions are "what do I have to do" and "what will I get out of it".    Many people hear are working hard at making good answers about "what can I do to make some of my own electricity",  the next question is what will people get from there work.   In the past, on these and other forums I have seen many people write that they believed achieving close to the Betz limit was possible with small turbines, hoping for 30% + energy extraction, when I see that it's much more likely they will get 15% than 30.     I agree, it's great to get anything from work of your own, and I would say it also feels great to go to the next step, and improve something you found especially if that means you can pass on that knowledge.    To know when you have hit on an improvement, you need to know where you are.   That's what I'm trying to ask here,  What is the present state of energy capture in small turbines, both in theory and practice?   What I see is that most HAWT's are likely below 20% and most VAWTS are lucky to hit 5%.    I'd like for people to help me find more exact numbers than that, if they are interested. 

Best
Drew

[fabricator]

Good luck, a lot of the folks here are busy building turbines, not worrying about a few percentage points of efficiency.

[RP]

Usually efficiency is a issue when you pay for a thing and convert it to another thing with some loss.  Efficient means minimal loss of the thing you paid to convert.

Automobiles have some efficiency at converting fuel dollars into transportation with the rest wasted.  A plywood factory converts tree dollars into lumber with some waste leftover.

We don't usually talk about how efficient a window is at lighting a room because we're not paying for the sunlight.  We simply choose one big enough to tap into enough light to do the job without worrying if one kind of glass is 98% clear versus 99% for instance.  I'm ignoring insulation benefits, etc. here and just focusing on a window's primary purpose (lighting).

Wind turbines and solar voltaics for that matter tap into a free stream of energy so it's more meaningful to talk about Return On Investment or Dollars spent / Kilowatt.  There have been many discussions here about efficiencies of various turbine blade designs but in the end, adding a couple inches to the length of the blades can add more power (by tapping more into the wind) than micro-polishing the surface or using an ultra-complicated airfoil shape.

Most of the value of a solar panel is in the warranty.  Virtually all commercial solar cells have roughly the same energy conversion efficiency.  The money you spend on a quality panel is hopefully enough to guarantee that the panel will not ruin itself by corrosion, water leakage, broken internal connections, etc. before you've had a chance to get your Kwh value from it.  Again, there have been lots of discussions here on how to make your own panels but in many cases, it's just cheaper in the long run to buy them because the warranty means you won't have to throw it away in 1 year or 4 years.

Think about it in terms of haw many KWH can I get in 1 year per dollar spent rather than how many KWH captured per KWH that slipped by.

Hope this helps...

[finnsawyer]

Take a look at "The Betz Limit - Again" in my diary section.  Let me know what you think.

[TomW]

Take a look at "The Betz Limit - Again" in my diary section.  Let me know what you think.

That guy is a real pain in the ...

He gets his cut just as surely as the gubermint redistributes  money via taxation. Neither is a fair deal, either!

Thanks for bringing him up.

Tom

[oneirondreamer]

@RP, what the conversion eff a turbine may be able to reach, or the difference between 2 turbine blade sets, or two different turbines, directly relates to ROI.   If one turbine reaches .1 Cp, and another reaches .2, but both took the same resources to make, then ROI or kWh/yr is massively impacted, as is the fact that most conventional turbines reach their max Cp only at very high velocities.  Small Low velocity (the prairie pumper) turbines were abandoned more because their very low shaft speeds made them unsuitable for electricity generation (at the time shaft speed was a very large factor, gears were expensive, as were the crappy magnets they had available and few knew about Axial Flux alt configurations) then because their Cp was low.  Yes the wind, and the sun are free (if you have real estate), but the cost of converting varies very widely.    I think a lot of small turbine owners are lead to expect Cp's of .3-.4, when it looks much more like .1 to .15 is likely.   Expectations should be realistic, both in what the cost of access will be, and the return will be.   It's interesting to note that most small turbine manufacturers are backing away from making claims about Cp these days.

@finn and TomW,  I am a builder more than a theorist, however the Betz limit, as stated by Betz does make some sense to me, and I have seen no evidence of anyone actually coming even close to reaching it (botched wind tunnel work aside).   This makes me think that even if there is some error in the Betz postulate, any more accurate postulate is as likely to be lower than higher.   I have argued that the Betz as stated doesn't apply well to high solidity VAWT's, especially to high TSR units that eject exhaust sideways as much as rearward, however I am not saying that turbines like mine can exceed it, just that it doesn't apply. 

I think a hard thing to grasp when considering air as a fluid, is it's incredible viscosity, relative to water,  even though it has a much lower density than water, which makes this difficult to observe the effects of in normal life.   Air is much more like molasses than water, but because it's so light we don't notice.   I think this leads a lot of people to underestimate the effects of blockage especially upstream, air can pile up much more dramatically than water.   The CFD work on VAWT's I have seen I do not think matches reality well, due to the problems CFD has in accurately reflecting vortex shedding and the effects of turbulence on a foils performance.   I got an opinion from a Phd CFD researcher who convinced me of this, and they believe it will be a few more years before CFD is able to make good predictions of VAWT performance, especially ones like mine with highly 4D flows (4D because it's flow characteristics change widely with turbine angular position).   CFD is fairly useful for conventional turbine blades which see relatively consistant flow over the foil (except as they pass the tower, which is rarely considered).   In low solidity VAWT modeling the flettner effect of the rotating shaft, the non planar flow of air, the drag of supporting structures is rarely reflected in CFD work, it's more than most computers can handle.   

[fabricator]

Ahhh, I see it all now, you are saying small hawts are really not getting the efficiency people think they are which in effect causes vawts to be much more competitive with hawts.

[bob g]

personally i think Flux has it summed up nicely, however i would venture a guess
that most of these alternators will never achieve much over 50% efficiency with any
regularity no matter what the manner of build, save for those that use some sort of
load matching electronics (which is or has been up till recently quite rare).

couple this reality with the betz limit of something around 58% from the blade set, which is for practical argument sake gospel, and which assumes a perfectly made blade set which is just as rare as any other part of the system.

so in my opinion the realistic betz limit for a hand carved set of blades is likely closer to 40% and when factored by the 50% efficiency of the typical alternator, the net overall efficiency is probably going to be damn close to what paul gipe reports as being about 20%.

and in my opinion there is nothing wrong with that, either.

accepting this level of efficiency allows most folk a reasonable return on investment
(time and money) wherein trying to increase the efficiency in a marked way is going to be an exercise in what is known as the point of diminished returns.

there is an old saying, it goes something like this...

" you get 90% of the result with 10% of the investment in time and money, and...
to get into the last 10% of the result you will spend 90% of the overall time and money."

wind power is no exception in my opinion.

once on understands and appreciates certain realities, he can then move forward in an informed manner and determine just how much energy he wants to expend trying to get another percentage point in efficiency.

i would not be at all surprised to find out that it quadrupled the cost of the machine just trying to get from 20% up to 25% overall efficiency.

it might well be there is some mathematical law that will become apparent, much like the "square" and "cube" laws of wind power, where diameter and windspeed have there relationships clearly defined by these laws. it might be some relationship will become apparent and be able to be mathematically expressed in relation to cost (time and money) vs. overall efficiency gains.

in any event i bet the relationship is not linear!

fwiw, which ain't much these days.

bob g

[oneirondreamer]

@ fabricator,  not quite what I am saying, as many VAWT's also have the small small chord = low Reynolds number = low lift to drag ratio + poorer stall characteristics + poorer dirty blade surface characteristics, relative to very large turbines.   I'm hoping in the future to be able to make a fair comparison between the type of turbines I've been working on, and conventional, and as well, I just don't like to drink the cool aid, so when things don't add up, I ask questions.  Not everybody's cup of tea, but I don't mind doing it.   What I am seeing is that the numbers regularly used to characterize small conventional HAWT's performance don't seem solid.   Telling me to take them like "gospel" is like throwing gasoline on a fire.

So, though bob g seems to think the numbers bandied about are "for practical argument sake gospel" I'm more of a questioning man, than a religious man,

I disagree with Bob G about alt eff and home built quality as well.   I built an alt, the poorly designed (by me), mismatched bastard thing that it is, does over 70% eff as measured by me and a retired electrical engineer at the speeds a conventional HAWT would be running (sadly not so good at the rpm's I was hoping for performance out of it, there closer to 20% ;-(  ..... )    And in terms of design theory, yep sure 90/10 though I perfer the 80/20 flavor, but only in terms of the design work not the fabrication end of things that people here are doing.    I think with the crowdsource program here, that a whack of smart people are nibling away at that difficult to obtain final 10 to 20%, of the hard side of design, and the people who are asking for and taking advice from the real knowledge base here are likely building turbines with higher eff's than commercial stuff.  

From what I see on these boards, the electrical design people outweigh the blade design people by a long shot in terms of professionals and given that conventional HAWT's run at a relatively narrow range of speeds, I bet many of the home built alts do pretty well.

 I suspect the home built turbines we are seeing here are probably more efficient than a lot of the commercial stuff out there, which frankly from what I have seen is often snake oil junk!   My estimate at this time falls in line with Paul Gipe's testing, that a conventional HAWT is doing well to hit 20% wind to Watts eff in very high velocity winds, the blade sets are likely in the 20%-30% range at very high wind speeds, and at those high rpm's the better alts are closing on 80%.  

[ghurd]

I have no idea where this fits into this discusion, but it is small.
And I am happy with the numbers.
Figure bearing losses, iron losses, etc, and it still looks pretty good to me.
http://fieldlines.com/board/index.php/topic,138380.0.html

[bob g]

oneiron:

at the risk of being argumentative...



my point boils down to this,
you will never get close to the betz limit with a home built machine, or for that matter
with a factory machine either, most especially in the 10ft class doing battery charging  duty in the typical install location seen by most people...

further,
it is doubtful that most folks will ever get close to half the betz limit under such conditions...

your point in re to crowd sourcing fails to account for the collective cost of both time and money, and the problems associated with any project that is done by many folks, in many locations, under many differing conditions, materials and capabilities. just ask boeing about their experience when it comes to this problem.

all i am saying is this, start with an accepted number from someone that ought to know, such as paul gipe, hugh piggot, the dan's book, flux, and numerous others here and find a range, then pick a realistic number to accept as a baseline, then...

as you work on your unit, be very careful to document everything, triple check every test, and be "very, very, very" suspect if your results are much more than a percentage point or more over that of the accepted baseline number as established earlier.

doing this sort of work requires all sorts of stuff most folks either don't have access too or have little interest in doing in the first place. things like 2 or 3 separate volt meters to cross check even the accuracy of the voltage output can sometimes explain errors in your findings.

don't  get me wrong, i have no problem with your interest in testing and improving efficiencies, however just remember it is overall efficiency that counts. be prepared to run back to back testing over and over again to determine if your gains in efficiency are truly gains and not some other factor that is skewing your results.

also it makes me little difference whether you are an amateur or an electrical engineer, i have seen faulty numbers from both, just as i have seen good numbers from either. the point being results from an engineer are just as suspect to me as those from jon doe out in his garage.

i will close with this assertion,
it is doubtful after 150 years of generator development, over 100 years of airfoil development, and over a half century of work from everyone between jacobs to boeing, from hugh to flux, from you, me and everyone else that dabbles in this stuff that there will be some radical improvement in the basic machine as is typically built by folks here. raising the efficiency of a typical 10ft class of machine by more than a couple percentage points is going to be a very costly endeavor in my opinion.

but don't let me stop you, you might well be smarter or luckier than others, and come up with a real game changer, however doubtful i think it might be.

i write this not to be rude or to pour cold water on you or anyone that wants to do what you are proposing, i just want you to be aware of the true costs of development. i have been in the research and development game myself for the last 4-5 years with micro cogeneration, and i can tell you this...

i have more time and money invested in the test cell than most folks will ever have in their home built cogenerator or windgenerator for that matter.  i have seen changes in efficiency come in with a 5 point gain, only to find out later that it can be explained by a fault somewhere in measurement or calculations.  these faults are much easier to find in an engine driven generator than one driven by wind where windspeed can be so variable that getting accurate numbers can be very tricky.

also be aware that it will likely be something less than 1% of all the folks that build windgenerators that will be committed to this level of testing, research and development.

that makes crowdsourceing a very small group indeed.

good luck.

bob g

ps. my comment in re to alternator efficiency coming in at 50% or so is as applied, that is you may well build an alternator that tests on the bench to be 70 or more percent efficient, but how efficient it is when applied to battery charging is where the rubber meets the road.  who cares if a car has a 400 hp motor if it only gets 200 hp to the tires and to the road?  who cares if it makes 400hp at 8k rpm if it is a grocery getter and will be driven at an average rpm of 2k rpm?

this is my problem with claimed efficiency numbers, i can tweak any single component to give me any number i want, however it is the overall efficiency doing what the unit is designed to do, under the conditions it will be used under that is of the only importance.

at least that is how i see it.

[Antero]

I have tested windgenerators several years.
I have wrote about that;

http://translate.google.fi/translate?sl=fi&tl=en&js=n&prev=_t&hl=fi&ie=UTF-8&layout=2&eotf=1&u=http%3A%2F%2Fwww.poikkis.net%2Findex.php%3Ftopic%3D5033.0

My experience is, that the height of the mast is the most critical.
Blade diameter allso.

Antero Rantanen
Finland

Attached file for the effect of the mast height;

[finnsawyer]

The higher efficiency of the large wind turbines may just be a consequence of geometry.  If one divides the circumference of a circle by the area of the circle, the result is 4 divided by the diameter.  As the diameter increases this ratio gets smaller.  what this would seem to imply is that a greater percentage of the air entering at the front of the large turbine would reach the rear and not be deflected radially.  This would give a greater efficiency based on my analysis.  Solution?  Put a band around the circumference of the small wind turbine.

[Lloyd]

Hi BobG.

Hello All,

My first post...but I know B..G...now that I have my cup of coffee.

Back to topic, I know nothing of the wind.

I know precious little about building alternators, and most of that I know from B..G.

But what I do know is the world revolves around balance.

I have been reading about wind(the engine), mostly here.

What I have read about the engine(=screws) noone ever talks about the balance.

Balance is much like a ships propeller, and even a ships hull.

Now for the good screw,  like a ships hull, a screw in balance has no power, it has to overcome that balance to make forward movement.

Efficiency is where the thrust is greater leaving, than entering the screw(but reverse for wind).

In the case of wind, a vacuum leaving the screw, would upset the balance.

vertical or horizontal!

Lloyd



A propeller is a type of fan that transmits power by converting rotational motion into thrust. A pressure difference is produced between the forward and rear surfaces of the airfoil-shaped blade, and a fluid (such as air or water) is accelerated behind the blade. Propeller dynamics can be modeled by both Bernoulli's principle and Newton's third law. A propeller is often colloquially known as screw both in aviation and maritime

The superiority of screw against paddles was taken up by navies. Trials with Smith's SS Archimedes, the first steam driven screw, led to the famous tug-of-war competition in 1845 between the screw-driven HMS Rattler and the paddle steamer HMS Alecto; the former pulling the latter backward at 2.5 knots (4.6 km/h).

The twisted airfoil (aerofoil) shape of modern aircraft propellers was pioneered by the Wright brothers. While both the blade element theory and the momentum theory had their supporters, the Wright brothers were able to combine both theories. They found that a propeller is essentially the same as a wing and so were able to use data collated from their earlier wind tunnel experiments on wings. They also found that the relative angle of attack from the forward movement of the aircraft was different for all points along the length of the blade, thus it was necessary to introduce a twist along its length. Their original propeller blades are only about 5% less efficient than the modern equivalent, some 100 years later.

contra-rotating propellers, where two propellers rotate in opposing directions on a single shaft, or on separate shafts on nearly the same axis

[Lloyd]

How about a little design failure

[TomW]

How about a little design failure

Can you say "PhotoShopped"?

Tom

[Lloyd]

How about a little design failure

Can you say "PhotoShopped"?

Tom

Actually Not PS.

I meant to put the link in the original post, so here it is.

lloyd

http://www.hprcc.unl.edu/articles/index.php?id=241

[bob g]

hi'ya Lloyd

you have come to the right place if you want to learn the very real differences between
an airplane prop, a ship screw and a windgenerator

these guys will surely educate  you in those differences



as for the linked picture

anytime you have a windfarm you will have times when the wind direction will interfere
down wind of the leading machine, the trick is siting so that this alignment is not in the prevailing winds.

or do your best in limiting this type of exposure, either by proper siting or by controlled shutdown of down wind units should there be strong winds that are directed such that downwind units might be damaged.

the big boys can do all these things and more, its unlikely that they subject their machines to turbulence that would damage downwind units.

bob g