Cheating Betz?

[rotornuts]

About 6 months ago I was doing some blade calculations and came to the same conclusion as some others have lately. The root acording to theory should be much wider, but I had this nagging in the back of my head that said it wasn't right(not to say my nagging feeling is). My intuition tells me the root if covered by large cord blades will be a sespool of turbulence. Could be wrong so I went on a hunt to find a turbulent wake analysis for a wind turbine and found one at the risoe site. I'm no pro at interpreting these images but they confirm what one would expect. Most turbulence is concentrated at the tips and the root with the center of the rotor area being much less turbulent. Does this mean we can get away with greater cord widths at say 30 - 40% blade length?

Doesn't a turbulent root area serve to compound the betz effect and further deminish efficiency. The faster the turbulent air behind a turbine blade reforms into smooth flow the better, right? the longer the "tail" of turbulent air the larger the cone in front and I think this is shedding too much potential power "around" the rotor rather than through it.

Here's a thought and an image after. Ditch the root and make it of a strong material with additional depth but much reduced cross section to produce as little interference with air flow as possible. Basically the exact opposite of the status quo. Place the maximum cord at 30 - 40% blade length, this is now where the effective or lifting portion of the blade starts and don't be afraid to make it much wider than normal.

Theory in my head is that the relatively unobstructed air flow through the center of the rotor area should "invigorate" for lack of a better word the center of the turbulant tail and reduce the cone ahead and the tail behind, possibly allowing the air through the effective portion of the rotor area to slow beyond the 2/3 theoretical limit, sort of like the center is becoming a venturie and pulling air through the blades rather than the air shedding around them.

Just a thought that been rattling around in my head.

 



BTW. this is why I was so attracted to the maple seed, It's cord distribution follows my theory.

[domwild]

The reason for a diminishing chord must be purely structural. A wider chord on the outside means higher centrifugal forces, this IMHO.

The water pumping sails have the max. chord on the outside but need rings to stop them from flying away.

Looking at the huge blades of the 1.7MW kind, there is an small chord at the hub, then increasing to the outside with corresponding increase in pitch, then a gradual taper and less twist and thickness of blade to the tip.

One must trust the scientists that they got it right with their supercomputers and modelling of laminar and turbulent flow, besides, those mills can vary the pitch.

[rotornuts]

I realized I should include a rough example of the front view so here it is. It was a quick job just to represent the idea.

[rotornuts]

The twist distribution would follow theory right to the hub root intersection.

[finnsawyer]

Well, if the hub is made reasonably aerodynamic (a hemisphere, for example), you get a speed up (50%) in the air at the blade plane resulting in a potential power increase (factor of 3.375).  Making the cord too narrow at the root throws away this extra power.  The speed up would also suggest a greater pitch angle than is normally used.  Have you considered these possibilities?

[windyknight]

Check out the Enercon website -their new E66 blade now has a much wider root for the reasons you give I think!

[Trivo]

I thought the bacic theory was the thicker the blade close to the center the lower wind speed it requires to start and the more torque it produces, and the greater the limit on speed the thinner the center the blade the more wind it requires to start and the less torque but the greater the speed. TSR so it is a balancing act to match up to the geni requirements?

the blade design above, i would think, would run very fast but stall under a lot of load on a big geni but a smaller one would work well

Trivo

[rotornuts]

The power available in the root area of the average turbine is minimal as the area covered doesn't represent a great deal of total rotor area, but the potential damage to the flow characteristics of the air leaving the rotor area in my mind is significant. Betz theory simply points out that you can only slow the air 2/3 through the rotor area before you start to deminish efficiency due to air flowing around the rotor area because of the pile up of air in front of and behind the blades. I don't believe that you would ever realize the theoretical advantage of directing air around the hub and across a wide root because of turbulence and the fact that the very act of directring that air into an allready taxed rotor area will inevitably displace some air around rather than across the blades.

Could be wrong though, nuts

[rotornuts]

I'd like to (actually I'm trying to) challenge the idea of wide roots close to the hub. Many people here who have flown many sets of blades seem to agree that less cord at the root than theory calls for has worked fairly well. I would advocate that there may be an opportunity to increase efficiency by nearly eliminating this seemingly ineffective portion of the rotor area so we can realize the possible benefits of reliving the pressure build up in front of the blades and the loww pressure area behind. It is as important to consider upstream and downstream flow as it is flow across the blade itself.

Once a "portion" of air has done it's work and slowed to 2/3 upstream velocity you want it to get the heck out of the way. The air passing through the inner portions of the rotor area has no effective escape route so to speak so it rolls aroud flowing downstream till enough of the tail has deminished that it has the opportunity to get back in line with his buddies moving at full velocity. These areas will consequently have an effect on upstrean velocity without providing the desired benefits. If the air behind the rotor is slowing the upstream air rather than the blades slowing the upstream air you've thrown out potential power and on a scale that I believe is much more significant than that of omitting the root.

Just a though, don't know how else to explain it.

The rotor design shown adove would operate according to design and given the same area should stall no different than any other. I know people think that the additional cord located "out there" would really increase drag but I don't think so.  

I'm really curious if I've made a fatal flaw here.

[rotornuts]

Actually it's the opposite but you bring up good point. This concept I'm pushing applies to smaller machines than the grid power units. At low rpms and large rotor diameters the problems aren't the same so my theory doesn't apply.

[wdyasq]

There has been a lot of study on the details Nuts has been looking at.  Kestral actually does put a little fatter cord in the center.  IMO, the root needs the structure of a thicker airfoil and cord.  I don't think there will be much loss in rotornuts idea but few structures are as low drag as an airfoil.  The PROPER airfoil in the root region should have minimal drag and SMOOTH the flow about the center of the turbine.

I do suggest one read a few of the thousands of publications available on the problem - and perhaps learn a little about airflow and structure. Well, all my comments on this post.  

Ron

[rotornuts]

I have dozens of publications on file and have read hundreds of hours info and while I may not be all that eloquent at conveying my thoughts I do understand what's happening. An understanding is exactly why I've made the suggestion but as I'm sure you know fluid dynamics is a complex issue with no blanket theory to cover all applications, in fact many theories are required just to understand one application. With all the complexity surrounding the issue it's easy to generalize and become fish eyed in one area so I'm mearly hunting for thoughts and trying to stimulate some conversation on global air flow around a turbine as appossed to doing more googling.

[Dave B]

I'm no expert but realize that the charts for blade design indicated on several sites combine twist , taper, chord, blade thickness and length to arrive at at specific TSR. I have noticed very few who have  carved their blades to these "suggested" dimensions and rightly so, it is much more difficult than compromising the root by starting with stock only 2" thick. I tend to disagree with what seems to be the norm that the large root dimensions and drop have little affect on performance. I think these opinions are based more on the fact that what the majority are building are performing well and the alternator design is what is being tweaked to match the blades.  My opinions are based on my 12' 3 blade I carved. I carved 3" drop at the root (called for nearly 6") and tapered and twist to the tip per chart. Unloaded I have measured 420 RPM @ approx. 30 MPH wind, the amount of torque and easy startup in low wind make them very responsive because even in a steady 5 MPH wind they are already cruising at 60 RPM. It's all a balancing act and give and take. It would be very interesting to see the Dan's compare blade designs on one of their "standard" alternators. The formulas work but it ain't easy. Dave B.  

[rotornuts]

yes I'm very interested in Windstuffs alternator kits so a few people can maybe start comparing blade designs on a common alternator. till we have standard alts to use there's alot of speculation about what is best.

Nuts

[monte350c]

Interesting ideas there Rotornuts!

Reminds me of a bunch of reading I did a while ago about augmentors. There are lots of detractors out there on that scheme, and only a few proponents.

But your approach may have a lot of merit compared with an augmentor/diffuser.

And I have to wonder what aerodynamic contribution the centre third of the blade is really making. Looking at some of the calculated lift numbers close to the root it's hard to believe your idea wouldn't help. Maybe we'd be better off with a hole in there.

Ted.

[finnsawyer]

I guess the only answer is to try some different ideas.  The trouble is that making the different blade configurations would be a lot of work.  As far as the effect of the hub on the power being insignificant, it ain't necessarily so.  Mathematical solutions for the flow of fluid around a sphere exist.  They predict that making the hub diameter equal to half the blade diameter boosts the available power by 22%.  At a hub diameter of 30% of mill diameter the boost is 15%.  The reason for this may be because of the effect of the pressure wave that builds up in front of the sphere.  At least that's my take.

Betz's equation applies for a windmill in a uniform air stream.  When you start deforming the airflow all Betz's may be off.

[rotornuts]

I didn't think of it quite like that. You bring up an interesting thought of displacing this area I think is causing problems. I was thinking too small.

Gonna have to mull that over.

Nuts

[rotornuts]

Thanks for the thumbs up ted. Someday I'll get to testing the idea.

[finnsawyer]

I'm hoping,if I find the time, to try a large hub.  The trouble is, that without a wind tunnel, it's going to be hard to verify any of this stuff.  Still, there are other reasons I'm interested in such an approach.  Anyway, good luck.

[finnsawyer]

The thing is, you have about 12 degrees of pitch angle to play around with.  The drag coefficient is nearly constant for that range of angles.  So you don't necessarily have to have a wide chord at the root to get good performance (lift) if you make the pitch angle near 12 degrees.  The drag also is less with a narrower chord.  So, from an engineering stand point, you have an interplay of factors in the design and therefore compromises.  Most of the blades I've seen described on this site use a low pitch angle at the root (a 2x6 rather than a 4x6 to make the blade).  Economics rules.

[rotornuts]

I've got this problem of a maple blade to take care of first.