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Old Jan 18, 2012, 05:27 PM
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Optimum planforms for low Re wings - strange XFLR5 results found

I have been doing a lot of reading on planform design. It appears the best wind tunnel testing cannot measure a difference between a rectangular wing with a square tip and an elliptical planform, even at a medium aspect ratio of 6 where the induced drag differences should be larger than on a high AR wing.

The rectangular wing with a square tip performs better than theory suggests due to vortex effects at the tip, and the elliptical planform performs worse due to 3D flows at the tips that are not accounted for in lower order analysis.

http://ntrs.nasa.gov/archive/nasa/ca...1994012101.pdf

They did measure differences between elliptical planforms with straight and swept 1/4 chords, even though simple lifting line theory, vortex lattice methods or simple 3D panel analysis with planar wakes (or XFLR5) do not predict there should be differences. The straight trailing edge elliptical chord length distribution wing seems near optimum without any low Re effects.

And then I was reading a paper where recovering an elliptical lift distribution on a constant chord wing, except at the tip where the vortex again helps, using wing twist gives better performance than adjusting the planform shape in any case.

http://oddjob.utias.utoronto.ca/dwz/...t_MDO_2008.pdf

http://oddjob.utias.utoronto.ca/~dwz...nduceddrag.pdf

When I couple all this with the negative effect on the transition points from any 3D cross flow (taper, sweep, changing airfoil, etc.) for low Re airfoils, I am beginning to think that a constant chord wing with a square tip, and some carefully tailored small amount of twist may be the optimum low Re planform.

http://dspace.mit.edu/bitstream/hand...pdf?sequence=1

This type of planform seems to avoid the performance penalties of the small chord, low Re tip. It avoids any cross flow deterioration of the transition point from cross flows from taper, sweep and changing foils along the span. It captures the performance advantage of the sharp tip vortex effect. The twist required is small enough that the higher speed performance does not seem to be compromised. A constant chord wing is easy to build and has forgiving flying characteristics.

Twist only allows recovering an elliptical distribution at one Cl, but the penalty seems very small off the design point over a typical thermal soaring sailplane speed range.

Does anyone see a down-side that I am missing? Even the 3D XFLR5 analysis is not really able to differentiate planform effects with 3D flows, non-planar wakes, etc., and is all I have access to.

Of course that split tip planform looks pretty cool, and those seagulls and albatrosses really do seem to have something figured out with their downward curved hyper-elliptical 3D planforms:

citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.117.7340&rep=rep1&type=pdf

My inverted landings would need some practice though!

Kevin
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Old Jan 18, 2012, 05:39 PM
Lift is cheap - Drag sucks
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Kevin,

Interesting presentation - thanks.

Tom
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Old Jan 18, 2012, 05:56 PM
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Constant chord wings do look ugly! I did read Alex Strojnik's stuff on the constant chord wing ages ago, but largely ignored it:

http://delta.wtr.ru/files/Strojnik%2...ar%20magic.pdf

For full size where the Re issues aren't quite as important, and the structural advantage of moving the lift centre inboard are larger, I think taper makes more sense. But at model sailplane Re, I really think a constant chord wing may well have some advantages....

Still ugly though!

It does look like those swoopy swept back tips so many sailplanes sprouted are definitely detrimental.

Kevin
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Old Jan 18, 2012, 06:02 PM
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Neat

Quote:
Originally Posted by kcaldwel View Post
I have been doing a lot of reading on planform design. It appears the best wind tunnel testing cannot measure a difference between a rectangular wing with a square tip and an elliptical planform, even at a medium aspect ratio of 7 where the induced drag differences should be larger than on a high AR wing.

The rectangular wing with a square tip performs better than theory suggests due to vortex effects at the tip, and the elliptical planform performs worse due to 3D flows at the tips that are not accounted for in lower order analysis.

http://ntrs.nasa.gov/archive/nasa/ca...1994012101.pdf

They did measure differences between elliptical planforms with straight and swept 1/4 chords, even though simple lifting line theory, vortex lattice methods or simple 3D panel analysis with planar wakes (or XFLR5) do not predict there should be differences. The straight trailing edge elliptical chord length distribution wing seems near optimum without any low Re effects.

And then I was reading a paper where recovering an elliptical lift distribution on a constant chord wing, except at the tip where the vortex again helps, using wing twist gives better performance than adjusting the planform shape in any case.

http://oddjob.utias.utoronto.ca/dwz/...t_MDO_2008.pdf

http://oddjob.utias.utoronto.ca/~dwz...nduceddrag.pdf

When I couple all this with the negative effect on the transition points from any 3D cross flow (taper, sweep, changing airfoil, etc.) for low Re airfoils, I am beginning to think that a constant chord wing with a square tip, and some carefully tailored small amount of twist may be the optimum low Re planform.

http://dspace.mit.edu/bitstream/hand...pdf?sequence=1

This type of planform seems to avoid the performance penalties of the small chord, low Re tip. It avoids any cross flow deterioration of the transition point from cross flows from taper, sweep and changing foils along the span. It captures the performance advantage of the sharp tip vortex effect. The twist required is small enough that the higher speed performance does not seem to be compromised. A constant chord wing is easy to build and has forgiving flying characteristics.

Twist only allows recovering an elliptical distribution at one Cl, but the penalty seems very small off the design point over a typical thermal soaring sailplane speed range.

Does anyone see a down-side that I am missing? Even the 3D XFLR5 analysis is not really able to differentiate planform effects with 3D flows, non-planar wakes, etc., and is all I have access to.

Of course that split tip planform looks pretty cool, and those seagulls and albatrosses really do seem to have something figured out with their downward curved hyper-elliptical 3D planforms:

citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.117.7340&rep=rep1&type=pdf

My inverted landings would need some practice though!

Kevin
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Old Jan 18, 2012, 08:38 PM
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Thanks for the interesting thoughs. It got me thinking on a few things, and I have a few questions.

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Originally Posted by kcaldwel View Post
The rectangular wing with a square tip performs better than theory suggests due to vortex effects at the tip, and the elliptical planform performs worse due to 3D flows at the tips that are not accounted for in lower order analysis.
Here is a good article on crescent wings and how elliptical planforms don't produce exactly elliptical lift distributions because of tip effects.
--Smith, S. C. & Kroo, I. M. Computation of induced drag for elliptical and crescent-shaped wings, Journal of Aircraft, 1993, 30, 446 - 452

Quote:
Originally Posted by kcaldwel View Post
They did measure differences between elliptical planforms with straight and swept 1/4 chords, even though simple lifting line theory, vortex lattice methods or simple 3D panel analysis with planar wakes (or XFLR5) do not predict there should be differences.
I'm not sure I agree. A vortex lattice method will show a typical swept wing will produce less lift at the root and more at the tip (as compared to a similar unswept wing).


Quote:
Originally Posted by kcaldwel View Post
Twist only allows recovering an elliptical distribution at one Cl, but the penalty seems very small off the design point over a typical thermal soaring sailplane speed range.
I've actually been looking at this recently. The penalty for flying at an off-design CL depends on how much twist the wing has an how far away the CL is from CLdes. For CLdes = 0.2, a CL=0.8 will cause a few percent loss of efficiency. For CLdes=0.4 and CL=0.8 that penalty is pretty small. A planform with a taper ratio around 0.4 will require the least amount of twist (as it already has a lift distribution close to elliptical). (I say least in a loose sense)

David
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Old Jan 18, 2012, 08:45 PM
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Give that wing a nice tip and a lot of the ugly can go away....

Many years back in an issue of Model Airplane News they did an article on the optimum wing planform for models. There was some small amount of math and aerodynamics and in the end they came to the same conclusion as you did. That a basic "Hershey bar" wing isn't such a bad compromise for a model airplane. It has the other advantage that it wants to stall from the center out as well. A rather nice feature that goes away with as little as something around a taper ratio of 0.8 as I seem to recall.
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Old Jan 18, 2012, 09:28 PM
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Originally Posted by DPATE View Post
Here is a good article on crescent wings and how elliptical planforms don't produce exactly elliptical lift distributions because of tip effects.
--Smith, S. C. & Kroo, I. M. Computation of induced drag for elliptical and crescent-shaped wings, Journal of Aircraft, 1993, 30, 446 - 452
Yep, I have all the Kroo/Smith papers - there are several others. There is lots of good stuff in them. That was the first place I saw the split wing tip design, and good analysis showing advantages over other planforms. I suspect low Re effects will kill the split tip planform at our Re, but I'd love to be proved wrong

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Originally Posted by DPATE View Post
I'm not sure I agree. A vortex lattice method will show a typical swept wing will produce less lift at the root and more at the tip (as compared to a similar unswept wing).

David
VLM methods will show some effects for swept wings and dihedral. VLM is a linear fist-order, inviscid, camber-line only analysis that will not show the effect of a non-planar wake (vertical structure in the wake, wake is in the plane of the panel 1/4chord, not the X-Y plane like LLT), wake roll-up, LE tip vortex effect on the tip, 3D flow at the tips, or even the effect of the trailing edge shape on the wake. VLM does not include viscous effects. VLM analysis does not show the effects of the planforms presented in the Smith/Kroo papers, or the papers I have referenced above. Even the 3D methods used by van Dam for his crescent shaped wing papers had numerical problems that showed a much larger effect than there actually is. It takes some pretty sophisticated CFD techniques to properly analyze planform differences accurately.

Three different VLM codes all give quite different results for simple planforms (AVL, XFLR5, and Tornado)

"Smith’s work with the split-tip confguration illustrates a serious
drawback with linear theory: the static-wake assumption. This
assumption is adequate for a first-order analysis of most geometries,
but the split-tip example demonstrates that higher-order effects must
be included for accurate induced drag prediction.
Wake shape is one way that nonlinearity can impact the induced
drag. Another important higher-order effect is induced lift, which,
unlikewake shape, is unique to nonplanar confgurations. Induced lift
is generated on nonplanar geometries by the vertical component of the
bound vortex, which increases or decreases the streamwise velocity
on parts of the geometry."

http://oddjob.utias.utoronto.ca/~dwz...nduceddrag.pdf

Kevin
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Old Jan 18, 2012, 10:04 PM
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Kevin,

The answer to this question depends a lot on what Re you want the wing to operate at. How low a Re are you interested in?

Steve
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Old Jan 18, 2012, 10:52 PM
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I'm glad to see someone with common interests :-)
I agree about the wake roll-up points, but I think that the vortex lattice will capture the fact that for a swept wing the bound vortex from one side will create downwash on the other side. This is strongest at the root which is why the lift distribution dips down there.

In the end it doesn't really matter because I don't think we're looking at much sweep anyway.

I recently saw a talk by someone showing very different moment/neutral point predictions comparing AVL and Tornado.


I'd really enjoy seeing some analysis comparing the viscous drag to the induced drag for different chord distributions.
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Old Jan 19, 2012, 06:46 AM
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Interesting read, but I can't access the first paper from Kevin's post. Is it available elsewhere or will I have to contact wikileaks?
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Old Jan 19, 2012, 11:52 AM
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Originally Posted by JaRaMW View Post
Interesting read, but I can't access the first paper from Kevin's post. Is it available elsewhere or will I have to contact wikileaks?
The NASA server seems to be having some problems today. I can't see it in a browser window, but if I "Save Page As" in Firefox it still downloads.

It also was available from several other sources, do a search of "Wind-Tunnel Investigation of Aerodynamic Efficiency of Three Planar Elliptical Wings With Curvature of Quarter-Chord Line". Some of the copies are much better the NASA's, but lack some of the drawings and charts.

http://www.cs.odu.edu/~mln/ltrs-pdfs/tp3359.pdf

Kevin
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Old Jan 19, 2012, 12:01 PM
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Kevin,

The answer to this question depends a lot on what Re you want the wing to operate at. How low a Re are you interested in?

Steve
Steve,

I am presently just looking at 2m and DLG sized RC sailplanes - not very low Re by today's standards. Below Re = 20k, things are very different, and I have little idea what happens there, besides completely laminar flow generally.

I was surprised how difficult it is to measure the planform shape effects in wind tunnels, and how complicated it really gets when high order analysis is used. XFLR5 spits out all sorts of pretty graphs showing planform shape performance changes, but I think they are largely meaningless.

I am starting to run a comparison of the three XFLR wing analysis tools to the wind tunnel testing in the NASA report. It will be interesting to see how they compare.

One thing I have noticed about XFLR5 wing results is that it is extremely easy to get span efficiency factors over 1 for a planar wing. This is clearly wrong, and the guide says the mesh needs to be improved. If the mesh is incorrect for span efficiency, then the results for all the other results must be too?

I have an extremely hard time changing the mesh to get the span efficiency below 1 and still getting it to converge. How would I know when it was close to right? Keep changing the mesh until the span efficiency stops dropping?

Kevin
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Old Jan 19, 2012, 02:45 PM
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I have run some XFLR5 simulations of the wing planforms from the NASA wind tunnel test I referenced in the first post. I made them as close to the same as I could. I used the NASA NLF(1)-0416 airfoil, the same wing dimensions, and adjusted the flow speed to obtain Re = 1.5*10^6. I used 10 station wings to approximate the elliptical wings, and used the 10 stations on the constant chord wing for consistency in the meshing.

I did increase the tip chord on the elliptical planforms from 0 to 10mm to allow convergence. The effect of this change should be small.

I am still pondering on how to best present the results, and where to go with a comparison. I'd appreciate any suggestions.

At first glance, the results do not correspond with the results of the wind tunnel testing very well. The Constant Chord wing shows lower efficiency than the Straight 1/4c Elliptical planform, which was not what they saw in the wind tunnel testing. I suppose this is to be expected, since none of the analysis techniques model the tip vortex effect that helps the CC wing, and likely hurts the elliptical wing.

All three analysis methods - LLT, VLM, and the XFLR5 3D panel method - give different results. The VLM and 3D panel methods are closer than the LLT results.

The straight TE elliptical platform, and the swept elliptical planform both show span efficiency over 1, which is not correct. It seems very difficult to get them below 1, and I am not sure how you would know that the mesh is correct after achieving a value of span efficiency below 1 in any case?

Comments?

Thanks,

Kevin

Edit: These graphs are actually with trips at the 0.075c chord point top and bottom on the airfoil. They ran that configuration in the wind tunnel test also, so this corresponds with that testing. I had forgotten that the trips get stuck on in this version of XFLR5, even after you un-check the trip boxes.
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Old Jan 19, 2012, 03:15 PM
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Are these twisted wings?

What spacing are you using for your stations (uniform, half cosine,...)?

One way to assess convergence is to plot your metric vs. your detail. In this case I guess you would have e vs. Nstations. It's not perfect but it helps.
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Old Jan 19, 2012, 07:06 PM
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They are untwisted wings as were used in the wind tunnel tests in the first paper I referenced.

I've tried all sorts of mesh settings, from the default to anything I can get to vaguely work. The default settings seem to give the best results.

I only seem to be able to make the results further from reality, with efficiency getting more over 1, or 0. And now I seem to have broken XFLR5 entirely. It is just giving me nonsense even after trying to re-set everything to defaults. Guess I'll have to re-install.

I am less enamoured by XFLR5 results by the moment.

I'll post the wpa file if I can get it to work again.

Kevin
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