Validity of this Graph?

[Baling Wire]

Does anyone know where "this" came from or how the info was derived?  Has anyone built a prop that yielded a higher TSR for it's solidity than shown from the graph?

BW

Its only fair to link to where you got said graph, or explain the source and or context in which it was presented. These vague questions just seem to waste time in quizzing the questioner for additional info.

[SamoaPower]

The graph is from "The Wind Power Book" by Jack Park. I think you misinterpret it's purpose. It's not intended to impose limits for TSR for a given solidity, but rather to show a solidity range that yields good rotor efficiency for a given TSR.

[Flux]

I first met it in correspondence with Stodhart ( Golding,s assistant at ERA)when they were active in wind power ( 1970?)

I think your version is in Jack Park's book with the tolerances.

I am fairly sure it is close enough for practical purposes. It seems reasonable to have a roughly hyperbolic relationship between solidity and tsr.

Flux

[scorman]

Generally doesn't the questions goes the other way around? ... I choose high solidity to lower the TSR to increase the efficiency, reduce noise, vibration, edge erosion, fatigue stress

Is this chart of any benefit to the conversation?

from pg175 Wind Energy Handbook by Burton

Stew Corman from sunny Endicott

[Flux]

I have far less faith in that graph than the one concerning tsr and solidity.

There is far to much difference in published results about efficiency and tsr.

One blade is crazy but was chosen I believe because it was claimed to be most efficient, but it hasn't stood the test of time. I have seen perfectly good results from fast 2 blade props but the yaw vibration makes them less attractive for larger sizes.

For 3 blades results seem to be ok for tsr 4 to 7. Beyond 7 then profile and surface finish become very critical and I agree that noise and erosion are more of an issue than actual efficiency.

Although it is possible to get very good results with lots of blades and tsr below 4 your efficiency is not significantly better in the best case ( windflower|) and in most cases of simpler construction the things fail to perform well in higher winds butt do seem ok below about 12 mph.

Unless you can load according to the cube law you will not keep the higher efficiencies at higher wind speed. For the sorts of blades I have tried the tsr for best results does seem to fall with wind speed, and it does tend to make the crude load matching more effective than it would otherwise be. To maintain best efficiency at constant tsr even at tsr 6 we may be looking at more critical profiles and finishes than most bother with, but I am happy to have a bit of peace and quiet in higher winds even if efficiency does fall a bit when power is plentiful.

Flux

[finnsawyer]

When they talk about going from say three blades to six do they mean using six blades identical to the original three?  If so, that would not be the correct thing to do.  To capture the same amount of power one would only need to scale the blades down in width and thickness by one half.  In the model that I develop in my diary the power available in the ideal case is given by the pressure difference between the front and rear of the rotor multiplied by the speed of the air through the rotor, which is a constant, times the area of the rotor:

   Powerout = (Pi - Po)xVoxA.  

None of these need depend on the width of the rotor or blades.  There will always be some pressure differential across the rotor.  Keeping the air speed through the rotor constant is another matter.  In reality, once one puts in air foils the profile of Vo between blades will not be constant.  Its average value, however, can still remain constant in certain cases.  If one then considers a differential column of air extending between two blades the power going into the column due to the effect of the pressure gradient can be shown to be proportional to the value of the pressure gradient locally and the average air speed Vo.  This power must then be equal to the power delivered locally to the blades by the air pressure difference across the air foil.  When trying to fit the usual equations for lift for an air foil to this situation I came up with the same type of behavior of the equation on rotational speed (local speed ratio) versus air speed as simply equating the lift equation to the power available by the wind in an annular ring of radius r.  But the equation gave a 2 foot width for the tip of a 5 foot radius blade at zero angle of attack and a TSR of about 4 (Cl = 0.4).

       

[Baling Wire]

Thanks! for comments fellas.  I was curious how well the information was accepted as being "The Standard".  Still like to know who and how it was composited.  May be that info is "in" the Park's book.  Will monitor thread for further input.

BW

[scorman]

GeoM,

When they talk about going from say three blades to six do they mean using six blades identical to the original three?  If so, that would not be the correct thing to do.  To capture the same amount of power one would only need to scale the blades down in width and thickness by one half.

two ways to double the solidity are to double up the # of same blades, or double the planform ie width of original blades. If you presume that at TSR of 7, that three blades capture all the wind  ( no blowthrough), then with 6 of same blades at TSR of 3.5 you have same capture effect ...but higher starting torque, more laminar flow, less turbulence ...ahhh, less turbulence as in less wasted power, also noted by less flutter which equates to less noise which is also less wasted power.

To design with three "fat" blades is simply to increase the Reynolds number which is proportional to cord width, so you function at a higher L/D ratio, but lift is increased on an absolute level as AOA is increased ...how about Cl of 1.75 at 15 degrees for NACA 4415?? (BTW don't tell me that at 15 degrees it is in stall, because this ISN'T an airplane wing ..articles confirm that in a rotating geometry, stall is probably around 30 degrees (or more) ...otherwise Bergey or Jacobs long thin blades wouldn't fly with half the lower length being in "stall").

In response to Flux's comment, yes, you lose efficiency at high WS ... you would NOT consider high solidity in high WS environment, where it is easy to "top out".

The key that I see in the chart I posted is the slope of the curves (six blades is missing ...Claus's 12 isn't even thought of). Note that as the shapes "narrow" with higher solidity, they become less efficient FASTER as WS goes past optimum ..this is goodness in low WS application because it then becomes "stall regulated" and enhances the furling capability as TSR drops instead of picking up, so AOA increases with lower AOA which adds drag. Note from those curves how easy it is for 2 blades to go into runaway mode ...you run at TSR 7, wind picks up and it wants to go to TSR 10, but power available is also going up ...so it takes off!

The ideal design for low WS solidity is one where the maximum efficiency is at <14 mph say at Cp = 0.40 and at 28mph it goes down to Cp=0.10 ..the rpm only goes up 1.5x and power goes up by 2x ...not 8x as what is available in the wind and IMHO, you'll see these designs in commercial units within two years in the 2-> 3.5KW arena, and yes, they'll be 15 or 18 feet in diameter

check out the hefty blade for a 16 footer/4KW at Scoraig:

http://www.scoraigwind.com/nirvana/page2.htm

Stew Corman from sunny Endicott

[scorman]

"so AOA increases with lower AOA which adds drag"

should read:

"so AOA increases with lower TSR which adds drag"

AOA is solely dependent on TSR - inverse non-linear relationship ..stays the same for all WS if TSR is held constant

Stew

[finnsawyer]

I see you are locked into a certain way of thinking.  For a given value of the effective wind and AOA, if you double the width of the blade, you double the lift (you imply more then double) and also double the drag.  The problem is that the lift doesn't really double anyway unless the blade's efficiency increases drastically, as the power available from the air flow is fixed.  But the drag will double according to the drag equation, and most of that is directed in the direction of rotation.  So, simply increasing the planform would appear to be counter productive.

I'd like to address the question of blowthrough.  In the diary I found that the ideal case had a flow through of 53.5% of the incident wind.  Apparently you do not accept that.  It turns out the curve for efficiency is rather broad.  At a blowthrough of 35% or 70% of the incident wind the efficiency would be slightly less than the Betz Limit.  At 35% the equation for blade width that I derived would require about a 6 foot wide blade.  That is, three six foot wide blades for a ten foot diameter wind mill.  Reducing the flow through further would make the blades wider yet and would decrease the efficiency. Well, that's at a zero AOA.

I analyzed the case of zero angle of attack for the simple fact that then the air can pass through the mill unimpeded.  For a non zero angle of attack it appears that the air flow must be deflected somewhat.  Any deflection of the flow would impart some energy and power to the blades.  Another potential source of direct power to the blades comes from the pressure gradient itself as the top of the blade along a straight line through the blade in the normal direction of lift will see a slightly different pressure due to the gradient.

Can your Java Foil deal with these different physical effects?  In principle all we need to do is find the pressure distribution everywhere along the surface of the foil and integrate over that.      

[scorman]

Geom,

"For a given value of the effective wind and AOA, if you double the width of the blade, you double the lift (you imply more then double) and also double the drag."

Fine for an airplane wing section with the exception that RE number has just doubled and L/D increases as well, especially if you are at a low RE# like 100K and go to 200K (same WS, double the cord, or add 2x number of blades).

I have posted in my files 3 polar plot data sets such as the Sandia choice:

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

note that for comparing RE# = 100K vs RE# = 200K, the lift coefficient hardly changes at AOA=7 degrees, but the drag actually goes down (not up as you say) and therefore the L/D ratio increases by 15+%

"The problem is that the lift doesn't really double anyway unless the blade's efficiency increases drastically, as the power available from the air flow is fixed. "

I think your math is not on the mark ...power is a function of the torque AND the rpm, so if adding blades or solidity so that TSR is 1/2, then power out is same with the exception of greater L/D, so higher solidity = higher efficiency ...nothing "dramatically" involved here ...

question is how much change to pitch angle to get to 1/2 TSR because that moves down the polar plot AOA data ...that is why some blade profiles are better suited for low WS application as their peak L/D ratio is at 8 or 10 degrees AOA ...summary chart:

http://www.otherpower.com/images/scimages/7526/LD_ratio.jpg

http://www.otherpower.com/images/scimages/7526/Cl_vs_AOA.jpg

from these charts, you would want a NACA 4415 (or thinner NACA4412) at the tip where cord is small and AOA is small, and NACA 4425 at root where cord is wide and AOA is much larger ..this is not uncommon for tapered planforms

"I'd like to address the question of blowthrough.  In the diary I found that the ideal case had a flow through of 53.5% of the incident wind.  Apparently you do not accept that. "

nope, didn't say that

I think we are talking two different things ...my mistake if I used the wrong term.

I was referring to the verbiage that if one uses 4 blades rather than 3 at the same pitch angle and rpm, that the extra blade "catches up" to air of the next blade and therefore extracts no more power, but simply adds drag. This may be an oversimplification for the case at same TSR , but my point was simply that if you changed the pitch angle also, to allow a TSR of one half, then the above argument for "blowthrough" is met ...all the blades "see" all the air and function properly.

"At 35% the equation for blade width that I derived would require about a 6 foot wide blade.  That is, three six foot wide blades for a ten foot diameter wind mill."

that is kinda wide ..I just uploaded an xls calculator based on Hugh's equation:

http://www.otherpower.com/images/scimages/7526/cordwidth.xls

plug in your numbers and see what you get ...(BTW, tell me if you found I did the equation incorrectly ..think I double checked it)

Scoraig built a 2 ft wide root on that 16 foot turbine I referenced in previus post.

"Can your Java Foil deal with these different physical effects?  In principle all we need to do is find the pressure distribution everywhere along the surface of the foil and integrate over that"

Not that simple ...mass-flow simulation is great for airplane wings, and there are supposedly better finite element analysis software that supposedly take into account the rotation effects and do what you request...BUT, when I plug in Allison's weird triangular blade ..the numbers don't jive ...if you design a hypothetical tapered twisted blade whose AOA is constant at a particular TSR (choose TSR=6?) and therefore the RE# is constant, and ignor tip vortex effect, you might come close ..but IF it really runs at TSR 5.5 or TSR 7 all bets are off. Me personally think that modelling is a good start, but building a working unit tells the tale. That is why I build with tubular spars, so i can reset the pitch angle at will.

At least I have Claus Nybroe's design as a stake in the ground at Cp=0.47 at TSR=3.6

Stew Corman from sunny Endicott

[finnsawyer]

You need to read what people say.  I specifically stated for a given value of effective wind.  In that case doubling the blade width will not double the lift, but will double the drag.  And that is because you can not get any more power out than is available in the wind at the given radius.  With the blades rotating at the same rate and no change in the available power the component of the lift in the direction of rotation must stay the same (the torque doesn't change either).  The fact that the lift equation for a foil predicts a doubling of the lift force is irrelevant.  Nature adjusts the pressures and flow rate such that the same power is taken from the wind.  I think this open ended lift force part of the air foil theory causes a lot of confusion.  The drag force, of course, robs some of that power from lift.

My six foot blade width result was for a zero AOA, a Cl of .4, a radius of five feet, a pass through of 35% of the incident wind, and a TSR of about 4.  For a TSR of 7 the blades would be narrower.  I don't know how any of this relates to Hugh's designs.  I'm not particularly happy about the result as it predicts rather wide blades which get wider toward the root.

I now think people are wrong about what happens when adding another blade.  To some extent the air flow is channeled between two blades.  With the requirement that the average velocity be constant as the air passes through the rotor the channeling would be 100%.  In other words there are no wakes.  Adding the extra blade simply means the channels get narrower.  So, each blade gets less of the power, but the total power going to all the blades stays the same.  But power robbing drag will increase.

I think this channeling effect may account for your belief that one can get usable power from the rotor for AOAs in excess of the normal stall angle.  Basically, the channeling of the flow would tend to delay separation of air flow along the low pressure side of the blade or air foil.  But this puts the mode of operation of the air foil in a range and situation for which the wind tunnel results may not apply.  How does one get some numbers to use in design for that case?

The problem, of course, is that we are not modeling airplane wings.  While we only need the pressure distribution over a working wind mill blade, getting there is the problem.  I've pretty much discounted Betz' analysis simply because he only looks at kinetic energy, rather than the total energy of the air flow.  In most cases involving getting power from a gas the internal energy of the gas changes.  Why should it be any different for a wind turbine?  Allowing that to happen led to the analysis in my diary.  It's pretty straight forward, and the result is simple,  The available power is equal to the pressure drop across the mill times the speed of the air flow through the mill, kept constant.  Trying to place a physical air foil in that model and matching the air foil parameters to the power available is proving to be anything but easy.      

[palomarbob]

keep your design between the lines on the graph , for max power
=================================================================
reply to #5 8 years ago                                         
 note: each 1% error drops power ~1%                             
       if total of all % errors is 100% or more it just wont work
                                                                 
airfoil naca cyh                                                 
s.ratio      4.000  ; design tsr , run at 5 tsr for 100%     
w.angle      9.357°                                           
s.radius           1524mm ; 5ft radius blade                       
s.bccl      509.7                                           
#.blades           2                                            
p.angle      9.357°    ; pitch angle at tip of blade                 
a.angle      0.000°    ; aoa from airfoil data [not pitch at tip]
s.lift              0.4022    ; cL @ aoa from airfoil data             
s.chord      634mm   ; 25in chord at tip                       
r.number           1,812,517                                       
s.drag      .01064                                           
e.ratio      38                                             
                                                                 
=================================================================