Author Topic: "Ideal" propeller (Read 10293 times)

TomG · « **on:** March 23, 2007, 11:22:59 AM »

I came across this image on the very helpful Otherpower "Small Wind Turbine Basics" page:

My question is: why can't the "ideal propeller" approach Betz when the TSR drops? I understand why "high speed propellers" lose efficiency as their TSR drops, but what about the design of the "ideal propeller" causes the same effect? I would have thought that if a propeller (shouldn't that be "rotor"?) was designed to run at low TSR, it would be able to approach Betz...

finnsawyer · « **Reply #1 on:** March 23, 2007, 07:12:43 AM »

But the question is, "Does the High Speed Propeller curve represent the output of one propeller designed for a single TSR versus the operational TSR or a series of propellers each designed for a different TSR?" A single Propeller will give the type of curve shown, so what needs to be done is to plot the curves for a number of propellers each designed for a different TSR and then connect the maximum values to form the curve that you are looking for. It is not clear what was done here.

TomG · « **Reply #2 on:** March 23, 2007, 07:25:57 AM »

Going on the figures I've seen from people's machine on this board, I'd guess the High Speed Propeller curve represents the output of one propeller designed for a single TSR. Some people's blades seem to peak at TSR anywhere from about 4.5 up to about 7!

But what I was really asking is why the "Ideal Propeller" curve says that an ideal propeller, designed to run at TSR=1, can only achieve about Cp=0.42? That's about 70% of Betz - why can't it approach Betz' limit?

Is this the same Ideal Propeller that the blade design programs use?

finnsawyer · « **Reply #3 on:** March 23, 2007, 07:52:28 AM »

O.K., that is an interesting question. First of all, we need to know what they think is an ideal propeller. With a TSR of one the angle of twist at the tip would be 45 degrees with no attack angle. It would increase toward the root. At the tip 45% of the lift would be in the direction of rotation, and the fraction would increase toward the root. So, it would seem the blade should get narrower toward the root. Perhaps, this doesn't happen for the "ideal" blade, so drag and other losses would be overstated. I guess the bottom line would be to find out just what "ideal" is, and what the derivation of the curve is.

TomG · « **Reply #4 on:** March 23, 2007, 08:57:13 AM »

"So, it would seem the blade should get narrower toward the root."

Following your logic, that seems to be true of every blade, no matter what TSR we're aiming for...

But as we get closer to the root, the apparent wind speed also drops fairly dramatically, so we need a wider chord to compensate for that.

Blade design programs are supposed to produce the ideal propeller, so someone must know the answer. Anyone?

The Otherpower page says the diagram came from http://www.windturbine-analysis.com/, but that website is long gone...

SamoaPower · « **Reply #5 on:** March 23, 2007, 12:09:29 PM »

The "ideal" rotor (yes, it is "rotor") has no "design". It is a mathamatical model only.

Betz determined that it is necessary to slow down a moving mass of air in order to extract power from it. This is the job of the rotor.

He further determined that the maximum power possible for a lift type rotor is when the downwind velocity equals one third the upwind velocity.

Without going into the math derivation, I think we can say that as the TSR is decreased, the rotor looses the "ability" to sufficiently slow down the air mass to extract maximum power.

This would seem to indicate that the higher the TSR, the better, as indeed, the curve shows. However, second order loss effects are increasing at a faster rate, hence a peak in the curves.

TomG · « **Reply #6 on:** March 23, 2007, 03:54:56 PM »

"Without going into the math derivation, I think we can say that as the TSR is decreased, the rotor looses the "ability" to sufficiently slow down the air mass to extract maximum power."

As I understand it, Betz' derivation didn't involve a rotating rotor at all, simply a disk capable of maintaining a pressure discontinuity. And there's no reason why TSR should cause that to fail. If the problem is the air "slipping between the blades", why don't low-TSR designs simply add more blades (like the American Multiblade)? Or increase the chord of the blades? The increased surface area shouldn't be prohibitive, because drag decreases quickly at low TSRs.

finnsawyer · « **Reply #7 on:** March 24, 2007, 07:06:59 AM »

Another factor affecting the blade width is the fact that the amount of power available in an annular ring cut out by the blades drops toward the root. To match the blades to this available power would also dictate a narrower blade toward the root, if the angle of attack is constant. A narrower blade has less drag, so it would hold the efficiency. Of course, blade strength would be severely affected by too narrow a blade. As far as the blade design programs are concerned, I wouldn't assume they are optimized. Perhaps you should design your own, since you are interested in this question.

TomG · « **Reply #8 on:** March 24, 2007, 09:18:59 AM »

"As far as the blade design programs are concerned, I wouldn't assume they are optimized. Perhaps you should design your own, since you are interested in this question."

That is indeed what I'm attempting to do. Thus why I was seeking the equations for interblade interactions. The propeller design programs seem exactly what I'm looking for, except they don't allow negative numbers(!) so not very useful for wind turbines.

wdyasq · « **Reply #9 on:** March 25, 2007, 12:41:50 PM »

"Another factor affecting the blade width is the fact that the amount of power available in an annular ring cut out by the blades drops toward the root. To match the blades to this available power would also dictate a narrower blade toward the root, if the angle of attack is constant. A narrower blade has less drag, so it would hold the efficiency."

Gee, as I interpret the energy developed by a blade it is the direct wing plus the artificial wind developed by rotation of the blades. The inner part of the disc just doesn't have the speed of the outer part. The effect of Reynolds numbers need to be taken into account as well as the area.

If I am wrong here, I'd like to get it corrected now as it is pretty fundamental to understanding the aerodynamics of turbines.

TIA,

Ron

willib · « **Reply #10 on:** March 25, 2007, 07:05:23 PM »

Try this .

http://www.alton-moore.net/wind_calculations_english.html

or warlocks

http://warlock.com.au/bladecalc-abstract.htm

both are very good wind turbine tools

TomG · « **Reply #11 on:** March 25, 2007, 08:37:15 PM »

The first is good, but doesn't take account of drag (Cd) or torque-related rotational losses in the wake. It just requires you to know the "prop efficiency". Do we know any tools for calculating _that_?

Also, why does it vary the thickness percentage? That will change the carefully calculated aerodynamic characteristics like lift! And one last little niggle - it doesn't allow you to specify "shrouded" or tip-plated blades. I'm not sure if it takes tip-vortex losses into account.

The second won't run on my (W2K) machine. Says files are out-of-date, tries to install them, reboots, then complains that they're still out-of-date.

SamoaPower · « **Reply #12 on:** March 25, 2007, 10:30:26 PM »

Yes, these calculators have their limitations. but they probably satisfy the wants of many who only want a contemporary rotor and don't want to be involved with optimization.

I'm guessing Cd is accounted for in the efficiency input, probably assuming some nominal L/D such as 50. At least, Cl can be entered.

The efficiency (Cp) input is the real kicker. Since efficiency depends more on L/D than anything else, it's a real guessing game since you can't input that. Using that L/D chart I put in your other post to get an efficiency number and using the Cl from the airfoil polars, it would probably do reasonably well.

Of course, the efficiency input only effects the power and torque output calculations and doesn't impact the chord and blade angle calculations which is what most people are concerned with to carve their blades.

The chosen AOA is another matter. Since different airfoils have different AOA at max L/D, this will directly impact the blade angle calculations. Fortunately, the range of AOA typically encountered is small, but is still a source of error.

I have to wonder if they include the correction factor for blade aspect ratio.

I don't believe that tip vorticies are a significant loss issue at these low Reynolds numbers.

Yes, the recommended thickness changes are a bit worrisome and is probably done for structural reasons. Better, is to use two different, known airfoils, one for the root area and one for the rest of the blade.

The program doesn't seem to be overly concerned with airfoil aerodynamic considerations, but neither do most of the users.

There are better design methods, but these programs are probably useful, if not completly accurate, for many.

They're a good starting point.

wdyasq · « **Reply #13 on:** March 26, 2007, 04:47:11 AM »

Check out "Propid", UICU. I think you will find the dynamics of a wind turbine 'interesting' - as in 'the old Chinese curse'. "May you live in interesting times." The curse is not Chinese but is indeed a curse.

Ron

SparWeb · « **Reply #14 on:** March 26, 2007, 11:56:35 AM »

Tom,

Sounds like you're doing more math than I expected. Have you used the "blade-element-theory" to model your prop? (sorry, "rotor") It's how I would suggest setting up a program, but it will require you to sit down and write explicit functions that the computer can integrate with respect to radius: chord, twist, lift coefficient, drag coefficient, Reynolds number, etc. and then combine the separate functions into one humungous integral that can be solved numerically by the computer.

Two integrals, really, one for "Lift" Torque (+) and "Drag" Torque (-).

I would suggest MathCAD as a tool (I prefer it over actual programming languages).

In addition, I did well learning aerodynamics from John Anderson, Introduction to Flight, 3rd Edition, 1989 (it may be revised again by now).

TomG · « **Reply #15 on:** March 26, 2007, 05:34:11 PM »

Hmm, "blade element theory"...

[5 minute Google]

Ah! Yes, that is exactly what I've been doing! No surprise that some 19th century guy already did it. I just didn't know what it was called, so it was hard to research it! Looks like I have a century of fun to catch up on. Some of it looks pretty useful, too.

I got the lift and drag functions from an aerofoil simulator (just saved them into a text file as a big table), and wrote an "off the top of my head" function for chord and blade angle. I'm working on saving some data from prop-design programs into text files, then loading it into my program, which should be a big improvement.

Slice the blade up into 100 parts, and work out lift and drag (with directions) for each one. Convert to torque and thrust. The output currently looks like this:

TSR runs along the X-axis. The peak power for this rotor is at ~7.5.

IIRC, this was a NACA4415, with a tip blade angle of about 5 degrees, which shows you how ugly my blade curve is.

Do those curves look horribly wrong to anyone?

SparWeb · « **Reply #16 on:** March 26, 2007, 10:38:19 PM »

I considered your curves for a while, and I think they look okay, but there's no data on the axes, and I can't see what conditions you used to produce a peak power at TSR=7.5. Doesn't look quite like what I expected, but I haven't tried to plot my work in that way. Didn't set up the formulas the right way, either, so I'm not likely to try for a while.

What I can suggest, for reading material, is to go to the NACA website and start searching for old reports on propellers. I scanned through my old index and found some good material that should keep you busy for a while:

Tech Report 14 Early work on tests, good starting point

Tech Report 168

Tech Report 186

Tech Report 421

Tech Report 447 Good tests

Tech Report 639

Tech Report 640, 641, 643 Detailed tests, well covered

Tech Report 650 More good test details

Tech Report 658

Tech Report 712 Heavy math

Tech Report 749

Tech Report 775 thru 778 Series of reports, overview of work so far.

Tech Report 820

Tech Memorandum 698 Blade element theory, compares # of blades.

Tech Note 1338 Synthesis of data and theory

Don't get frustrated searching through the NACA archive - the search engine on that site is surpassed only by the one available here. Some reports mysteriously appear and disappear, depending on when you try, too.

As we've already discussed, the reports relate to propellers, not windmill rotors, but understanding this math opens the door to turning the force vectors around backward.

More to the point, have you looked up the L/D max angle for your airfoil section? It's probably about 5 to 7 degrees, right? Have you ensured that you have twisted the blade so that the entire span experiences this angle of attack at the design TSR?

SamoaPower · « **Reply #17 on:** March 27, 2007, 03:53:04 AM »

Interesting work Tom.

I guess I would have expected a TSR peak of around 4 for the 4415 with a tip blade angle of 5 degrees. I think a TSR of 7 would be closer to 0-1 degree blade angle.

I'm also not sure about the torque curve, but haven't looked at that very often.

It seems that at the moment, you're most interested in rotor performance prediction. I haven't done much in this area so I don't think I could be much help.

If you get interested in rotor design methods, I may be able to help out there.

Keep it up.

Stonebrain · « **Reply #18 on:** March 27, 2007, 04:44:55 AM »

Hi,

I don't think you can solve the question with only math.

The mat is far too complex for a 'normal guy'.Even for very qualified scientifics

it's a pain to predict the behavior of propellers and it takes a good deal of

trial and error to come to the right design.

Those calculators are not science,just based on rules of the thumb,with restricted

application.Some even might be wrong.

The French aircraft carrier "charlesDeGaule" (the only one) had only half the propulsionpower then planned because of a badly designed screw.They had to change

it.

Personally I would prefer this scrap,payed with my taxmoney,going to the bottom of the sea,But I'm getting off topic.

cheers,

stonebrain

Murlin · « **Reply #19 on:** March 28, 2007, 12:59:54 PM »

When someone comes up with the Ideal design for a turbine blade, I would sure like to know.

I have been researching the subject on the Sandia Labs website.

At first I thought they had finally come up with the perfect shape.

They called it the SG5061.

They gave all the chord lengths and it appeared that the chord at the root for a 20' rotor would be about 18" wide.

Upon further investigation, what they were calling the SG5061 did not really look like that airfoil at all.

It looked almost identical to the NC 4412 here is a pic of what they ended up with:

As you can see by my next two pics the root had a huge pitch...

But then I noticed that the report was done in 2002.

Upon further research I found a report in 2004 that used an entirely new airfoil design that looks like the NREL S823 at the root:

This Airfoil is very similar to the one Sammopower used for his alumiinum blades.

After scanning through the the report I noticed that they left out all the loft info so others could not easily duplicate it.

But it looks like to me that it does not have the extreme pitch at the root.

I know on the first rotor it was designed for a semi vairaible pitched blade for Jacobs, where overspeed was corrected by counter weights.

The 2004 report was surley designed for a full blown variable pitched rotor.

While I almost had the 2002 blade drawn up in CAD, I am going to scrap it and go with the NE S823 with the NC 4415 from about 60% of the radius to the tip. This seems to be about what has been done on all the new turbine blades being manufactured at the present time. I am using Proe for the design and the TSR, pitch and chordal scale can be all be easily modified.

The over all plan view shape of the rotor blades has not changed since 2002, so I think the groundwork is already done. It is documented in the Sand2002-3101 report.

One just needs to be able to sift through the massive amount of data out there to come up with a solution.

I will be machining a mold out of laminated basswood to make the foam core, fiberglass skinned blades.

hvirtane · « **Reply #20 on:** March 28, 2007, 01:16:39 PM »

I wanted to point out that there is a mistake in that well-known chart concerning the efficiencies of various wind machine types. The mistake is explained in the book by Gary Johnson.

http://www.eece.ksu.edu/~gjohnson/

The correct chart is here:

- Hannu

TomW · « **Reply #21 on:** March 28, 2007, 01:32:33 PM »

Murlin;

Pretty good info, i guess. I must point out that the next time you post a herd of huge pictures the post will get removed.

Very unfriendly to the folks on a slow link.

We have only explained this big file size thing 4,593 times.

As Editor, but too lazy to log out then back in

TomW

Murlin · « **Reply #22 on:** March 28, 2007, 02:57:26 PM »

Ok buddy I deleted them. Thanks for your kind words.

I thought I resized them I was in a hurry and made a mistake. I appologize.

Thats good info "I guess"? WTF is that? BTW that's a rhetorical question....

I guess since you don't think the pics have any merit, there is no need to repost them.

TomW · « **Reply #23 on:** March 28, 2007, 03:11:18 PM »

Murlin;

Nothin personal at all.

"I guess" is because I am not actually following the thread very close.

It has nothing to do with merit, simply file sizes that are unfriendly large.

I won't go into it again but its a policy thats been active for a long time.

T

hvirtane · « **Reply #24 on:** March 29, 2007, 09:05:35 AM »

I thought I resized them I was in a hurry and made a mistake. I apologize.

Why not resizing them and uploading with exactly the same names. Then they would work again.

A good program for resizing is 'Gimp'. If still using some non-free operating systems, 'Gimp' exists for them, too.

- Hannu

Murlin · « **Reply #25 on:** March 29, 2007, 10:33:24 AM »

Thanks man but I just forgot to resize them as I was in a hurry to leave work.

All that the Admin need to do was just ask me to resize which I would have done within an hour of posting as I logged back on when I got home.

I posted 5 pics from 140k to 190k. The three pics that were over the size limit were only amounted to less than 70k...big woopie...

IMO Tom was rude and condecending.

It was not like I posted a whole bunch of high res pick over a meg a piece, he was just throwing his weight around.

I refuse to lay down and take that crap.

Ya its your site Tom and you can just delete my whole diary if you wish I backed it up...I am out of here...just call me Casper....

Murlin teh out!

hvirtane · « **Reply #26 on:** March 29, 2007, 11:40:02 AM »

IMO Tom was rude and condecending.

It was not like I posted a whole bunch of high res pick over a meg a piece, he was just throwing his weight around.

I refuse to lay down and take that crap.

I think that Tom is sometimes just tired, not really rude. It isn't probably so easy job to take care of this big website.

- Hannu

BigBreaker · « **Reply #27 on:** April 04, 2007, 11:55:33 AM »

Perhaps it is better to put a large nose cone on the turbine and redirect the wind that would otherwise hit the root to a section of the airfoil with less cord/angle/etc.

scorman · « **Reply #28 on:** April 18, 2007, 06:33:31 PM »

OK,

We have just so many tools available to us, so we can think we know what is going on.

Hugh Piggot claims that a straight, non-tapered, non-twisted blade doesn't really perform much worse than the fancy stuff.

I have spent considerable time reading the Sandia report on optimum designing a moldable blade:

http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/2002/023101.pdf

I know there was a thread by paradigmdesign where he is building a plug to create a scaled down version of that blade profile.

So I went to UIUC database to get some profile data and imported them into JavaFoil to see what is going on.

The ultimate profile from Sandia that is supposed to beat the original Jacobs 20KW blade is an SG6050, whereas the Jacobs is an USNPS4.

When running a polar in JavaFoil I get the following data:

http://www.otherpower.com/images/scimages/7526/usnps4polar.txt

http://www.otherpower.com/images/scimages/7526/sg6050polar.txt

and I have already built some NACA4425 tapered, non-twist 10'+ blades

http://www.otherpower.com/images/scimages/7526/NACA4425polar.txt

Now, when I look at the lift coefficient Cl, the Lift/Drag ratio at EVERY AOA at EVERY RE#, I see the "optimum blade" not performing as well as the Jacobs and the NACA4425 being the best overall. What gives

Either I am missing something basic here, or the Propid models they use is not giving the same numbers as JavaFoil. They claim that the optimum blade is 10%+ better than the Jacobs .....how???

Stew Corman from sunny Endicott

BTW, I am a mechanical engineer and know what RE# really are.

TomG · « **Reply #29 on:** April 19, 2007, 02:59:08 AM »

Did you experiment with different finish, stall model and transition model? Not that that seems likely to reverse the results, but it might do something...

finnsawyer · « **Reply #30 on:** April 19, 2007, 08:20:11 AM »

When you redirect that "wind" with a nose cone it speeds up. The speed up would be 50% with a hemisphere rather than with a cone. It actually wouldn't pay in that case to try to streamline (air foils have blunt noses). You need to redo the the blade twist and AOA to get the best results.

scorman · « **Reply #31 on:** April 19, 2007, 09:03:03 AM »

I came to realize, and correct me if I am wrong, that the original Jacobs blades were non-tapered and non-twist. Whereas their Propid designed optimum blade panform used a linear taper and calculated twist for a TSR of 7 (which defines the AOA at each station)to accomplish the 10%+ improvement in efficiency. That said, I would like to see a Propid modeling of the same parameters with the non-taper,non-twist Jacobs USNPS4 profile, which I don't think they did as a comparison??

"First it should be remarked that the airfoils are somewhat thinner than those used on the baseline blade. The selection of thinner airfoils avoids the poor performance of thick airfoils operating at the low Reynolds numbers, which are experienced by the baseline blades." So the same planform or "shape" is altered by making it thinner or are they defining both the profile shape and the cord taper or just the cord dimensions?

Perhaps someone can clarify exactly what they mean by the term "planform" within the context of this report.

then:

"Two blade-planform families cases were considered. In the first case, the original planform of the Jacobs turbine was retained. The resulting improvements in performance are therefore due to changes in the blade twist distribution and better airfoil performance. The second case did not include the planform constraint, offering the advantages of changes in both chord and twist." This is where they choose the SG6050 at the end of the decision tree.

they modeled the Jacobs with twist, etc?:

"For the fully twisted/tapered blades, a desired lift coefficient and axial induction factor distribution were specified at a wind speed of approximately 16 mph...... To achieve these desired aerodynamic characteristics along with the rotor power constraint, the blade chord and twist distributions were determined automatically by PROPID1. For the case when the blade planform was fixed to that of the Jacobs blade as described below, only the lift coefficient distribution was prescribed, and the twist was automatically adjusted in PROPID to achieve the prescribed lift coefficient."

Above is confusing since they might be comparing apples to oranges. I still cannot see how with CL and L/D superior to SG6050, they can derive their ultimate choice.

To choose a thinner blade, then the cord width must be smaller, so choice of higher Cl is required and the SG6050 doesn't do it.

Stew Corman from sunny Endicott

scorman@stny.rr.com

SamoaPower · « **Reply #32 on:** April 19, 2007, 10:40:51 AM »

Stew,

From my original reading of this report some time ago, I seem to recall that their baseline rotor is the contemporary Jacobs not the original Jacobs.

"So the same planform or "shape" is altered by making it thinner or are they defining both the profile shape and the cord taper or just the cord dimensions?"

I believe their use of "thinner" and "thicker" refers only to the airfoil profile dimension, not to a planform dimension (chord).

"Perhaps someone can clarify exactly what they mean by the term "planform" within the context of this report."

As I read it, their use of "planform" is conventional, i.e., a two-dimensional projection of span and chord onto a surface. It does not include airfoil thickness.

"To choose a thinner blade, then the cord width must be smaller ..."

Here again, I think you are confusing airfoil thickness with planform chord.

I believe a lot more goes into an airfoil selection than just Cl and L/D, particularly for a fixed pitch rotor. For a stall regulated machine, the "softness" of the stall characteristics are also important. Construction considerations are also significant.

I'm not necessarily supporting their choice, but am trying to understand it as you are.

News:

Author Topic: "Ideal" propeller (Read 10293 times)