Judging Airfoils from Their Polars (esp. at Low Re)

[mharms]

I'm a newbie at aerodynamics, but I've done some reading and recently started playing with Profili. I'm mostly interested in very low Re (around 30K) airfoils for use in tail-less micro planes. I searched through Profili's data base and was getting discouraged about finding/synthesizing airfoils for decent lift, low drag and near-zero Cm. Best I could do was to come up with very thin, slightly reflexed airfoils, but their useful range of AoA was quite restricted and lift was rather anemic. THEN I discovered that Profili had the ability to add turbulators. Wow, what a difference at low Re! Now for some questions...

Question 1: Can I believe any of the Profili/Xfoil results at Re = 30K, or are the math models starting to breakdown here?

Question 2: (See the image effect_of_turb_Q2.jpg) Is this improvement realizable in the real world, or is this just theoretical?

Question 3: (See the image Cl_Cd_ratio_Q3.jpg) What does one learn from the shape of the Cl/Cd (alpha) curve? Is it used as a sort of a figure of merit or efficiency indicator? I'm not quite sure what this curve is telling me.

I'm still learning to interpret and judge an airfoil by its polars, but I would like to get your comments on my thoughts, below:

A: In general, kinky curves are bad, smooth curves are good (for Cl vs. alpha, Cd v.s alpha, Cl/Cd ratio, and Cm vs. alpha). I assume that kinks represent separation and such. I would think smooth lift, drag and Cm curves would help make a plane's flying behavior be smooth across a reasonable range AoAs -- no sudden loss of lift at a certain AoA, for example.

B: (See image stall_shape_B.jpg) Looking at the Cl vs alpha plot, a smooth stall characteristic is preferable to a sharp one (which implies a sudden stall).

C: (See image Cl_Cd_vs_elev_C.jpg) A good airfoil should also have good looking curves when elevons/ailerons flaps are deflected. Otherwise I would think handling of the plane wight be affected at certain elevon deflections. For example, I used Profili to run a series of curves for various elevon deflections and I tweaked the turbulator positions to make sure the Cl vs alpha curves were smooth over the range of deflections. See image Cl_Cd_vs_elevon.jpg

D: (See image Cm_curves_D.jpg) In the case of an airfoil for tail-less planes, Cm should be near zero and constant (flat) over a wide range of AoA. Major kinks within the normal AoA range would not be good.

Comments? Again, I'm pretty new to this and appreciate anything I can learn here.

Mark

[green66]

Mark Drela, as the author of XFoil, and Stefano Duranti who authored Profili, would be the best persons to address your questions. Dr. Drela, who teaches aero at MIT, often posts into this forum so maybe he'll do so and provide a more complete response. In the meantime, I'll try to be helpful.

Question 1: Can I believe any of the Profili/Xfoil results at Re = 30K, or are the math models starting to breakdown here? Accuracy of the analysis might start to get shaky at very low Re, however I believe XFoil is the best publicly-available airfoil analysis tool w/respect to predicting drag caused by laminar separation bubbles characteristic of low Re regimes, and I believe it is the only program that considers both viscous effects as well as local flow momenta, i.e. reality-based factors that influence separation and drag.

Try comparing several polars of different airfoils obtained from wind tunnel tests Airfoil data from testing (http://www.nasg.com/afdb/list-polar-e.phtml) at very low Re to those of XFoil, then note whether the curves are similarly-shaped (regardless whether the curves are offset a bit), which would further validate the technical principles, assumptions, and computational formulary used in XFoil. If the shape of the curves is significantly different between test and XFoil, then the program probably isn't valid for that range of Re.

Question 2: (See the image effect_of_turb_Q2.jpg) Is this improvement realizable in the real world, or is this just theoretical? Turbulation can significantly reduce drag (although the inflections in your non-turb'd curve may just be computational nuances / transitions) and, not surprisingly, offers large drag reductions at low Re due to the avoidance of laminar separation bubbles and / or reduction of wake size. At higher Re, the realizable drag reduction is less since the size of the wake causing the drag is reduced due to the flow staying attached for a greater distance on the chord.

The most common everyday application of turbulation that I can think of are the dimples on a golf ball - Without them, the ball would travel like a knuckleball and with less range.

Turbulation will be more detrimental than helpful if either the turbulator is placed behind the transition point, or too far forward, or if it's applied to an airfoil that isn't conducive to turbulation, resulting in an increase in viscous drag more than the reduction of profile drag.

More on turbulation (http://www.rcgroups.com/forums/showthread.php?t=306320)

Martin Hepperle's article on turbulation at model scale: Turbulator sizing & placement (http://www.mh-aerotools.de/airfoils/turbulat.htm)

Question 3: (See the image Cl_Cd_ratio_Q3.jpg) What does one learn from the shape of the Cl/Cd (alpha) curve? Is it used as a sort of a figure of merit or efficiency indicator? I'm not quite sure what this curve is telling me. Obtaining the lift and drag forces is based on application of the Cl and Cd coefficients to the same area, therefore the indicated Cl/Cd ratio IS the lift/drag (L/D) ratio of the airfoil, but this is only for 2-dimensional flow which is, unfortunately, unreal in that it assumes a wing of infinite span or aspect ratio, thus infinitesimal tip vorticity, i.e. no spanwise flow, and ultimately no induced drag which is fully half of the total drag at max L/D.

Wind-tunnel airfoil test specimens, however, do provide results reflecting 2D flow because the ends of the test piece extend out to the walls of the tunnel to eliminate spanwise effects.

Yes, L/D is a direct measure of aero efficiency but, again, efficiency of an entire aircraft (not just the airfoil) would have to include all other sources of drag, induced usually being the major other. More practically, L/D of an entire aircraft, e.g. a glider, directly predicts the glide angle (arctan D/L) for shallow angles.

A: In general, kinky curves are bad, smooth curves are good (for Cl vs. alpha, Cd v.s alpha, Cl/Cd ratio, and Cm vs. alpha). I assume that kinks represent separation and such. I would think smooth lift, drag and Cm curves would help make a plane's flying behavior be smooth across a reasonable range AoAs -- no sudden loss of lift at a certain AoA, for example. I'm not certain that those kinks are actually reflected in reality. Probably most are just computational discontinuities, program grappling with boundary conditions, correction of iterative error stackups, etc.

B: (See image stall_shape_B.jpg) Looking at the Cl vs alpha plot, a smooth stall characteristic is preferable to a sharp one (which implies a sudden stall). That bump peaking the blue curve may actually represent real phenomena - There may be a critical AOA (9 deg here) where the flow, in having to negotiate the turn around the leading edge, trips into a turbulent mode and extends the duration of attached flow on the top surface, effectively exploiting more of the airfoil's camber resulting in the bumped-up Cl.

C: (See image Cl_Cd_vs_elev_C.jpg) A good airfoil should also have good looking curves when elevons/ailerons flaps are deflected. Otherwise I would think handling of the plane wight be affected at certain elevon deflections. For example, I used Profili to run a series of curves for various elevon deflections and I tweaked the turbulator positions to make sure the Cl vs alpha curves were smooth over the range of deflections. See image Cl_Cd_vs_elevon.jpg If tweaking turbulator position changed the shape of a curve, it may have been because the aft positions you tried were behind the predicted point of separation - A turbulator behind the separation point is useless, and too far forward will increase viscous drag more than reducing profile drag.

I think flaps' effect on the handling of a plane at low Re will more often be due to separation / drag effects based on the changes of airspeed (Re) caused by the flaps.

D: (See image Cm_curves_D.jpg) In the case of an airfoil for tail-less planes, Cm should be near zero and constant (flat) over a wide range of AoA. Major kinks within the normal AoA range would not be good. Assuming predicted Cm is realistic, abrupt changes would not be good at all considering the pitch sensitivity of flying wings.

Hope this helps some.

[green66]

BTW, since your emphasis is on flying wings, a few more resources, if you don't already have them:

The Hepperle site is a must:
Flying wing airfoils (http://www.mh-aerotools.de/airfoils/nf_1.htm)
Flying wing design (http://www.mh-aerotools.de/airfoils/flywing1.htm)

Also consider the Panknin Twist formula to determine flying wing washout:
Panknin Twist (http://www.b2streamlines.com/Panknin.html)

[Ollie]

Quote from Dr. Drela:
"I find the Cm curve is more typically S-shaped,
with a positive slope at small and large Cl's,
and a larger negative slope at intermediate Cl's.

(Graph is not here)

The nonzero slopes of the curve cause the stability margin to vary
considerably with Cl, or equivalently, the aerodynamic center
to shift with Cl.

The shift in the AC, as a fraction of chord, is

delta( x_AC / chord ) = (-dCm/dAlpha) / (dCl/dAlpha)

At small and large Cl's the shift is forward (destabilizing),
while at intermediate Cl's the shift is rearward (stabilizing).

The positive and negative slopes of the curve increase as Re decreases,
as Ollie mentioned. On small gliders the more troublesome forward
AC shifts are 10% of the chord or more. On large gliders, shifts
of less than 5% are more typical.

These predicted shifts closely match the differences I observe between
the AC position as computed by theory, and the AC position observed
by incrementally moving the CG backwards on the glider until
instability is reached. "Theory" here refers to the vortex-lattice
method, with correction to account for the nonlinear Cm curve.
So it is possible to pick a stability margin and very closely nail
the correct CG location and decalage before the first flight, but
this requires doing the vortex lattice and Xfoil polar calculations.


The AC shifting has practical implications to the more casual RC glider pilot.
A glider which is stable in cruise (stable intermediate-Cl region),
can become unstable and tuck into a dive if the speed is increased
until the positive-slope left part of the Cm curve is entered
Having the CG below the wing, like on a poly glider, also contributes
to the tuck-in behavior, as does a flexible wing and/or tailboom.
In any case, one needs sufficient stability margin to overpower
the combined destabilizing effects of the nonlinear Cm curve,
poly/dihedral, and elasticity. The "dive test" is useful in that
it represents the worst-case situation where all these destabilizing
effects gang up, and hence it reveals the farthest-forward
AC position that the glider will ever see.


The existence of the "stable" middle part of the curve can be
demonstrated with a small flat plank of balsa with ballast on
the leading edge. This plank can be made to glide slowly at moderate Cl
even though it has no reflex camber (not possible with a flat Cm curve).

Free-flight HLG's and some paper airplanes make use of this phenomenon.
A FFHLG has nearly zero decalage to allow a high non-looping launch.
If there was no stabilizing Cm curve, such a glider would not be able
to glide slowly after launch.


>What is the cause?

The culprit is the variation of the boundary layer thickness
and the movement of the separation bubble with Cl.
The boundary layer and bubble changes the effective camber shape
of the airfoil, which then causes the Cm to change. The effective
shape of the airfoil is plotted in Xfoil under the Cp vs x/c plot.

As you increase the Reynolds number the boundary layer and the
bubble get thinner, so the modifications to the camber line
get smaller. Hence the Cm variations get smaller as well.

- Mark


Center of pressure location is
x_cp = 0.25 - cm/cl

Aerodynamic center location is
x_ac = 0.25 - (dcm/dalpha)/(dcl/dalpha)"

[mharms]

green66 and Ollie,

I've been traveling and did not have a chance to check this thread for a while. Thank you for your replies. Much good info to digest here. These forums are such a great resource -- thanks to folks such as yourselves.

Mark

[Arvid K. Gromhol]

green66:

Please indicate to me where a tubulator should be placed on a ClarkY 15% thickness for Reynolds number around 170 000. Also indicate size of tubulator. The average wing cord is 240 mm.

[Sparky Paul]

Why do you feel a Clark Y would benefit from a turbulator at any location?
What airplane is it to be used on?

[Batmanwpg]

green66:

Please indicate to me where a tubulator should be placed on a ClarkY 15% thickness for Reynolds number around 170 000. Also indicate size of tubulator. The average wing cord is 240 mm.

Computer analysis shows a slight improvement with a turb at 60% and only really helps at lower cl's below .6 For the size of the turb goto http://www.mh-aerotools.de/airfoils/index.htm click on the Aerdynamics tab then Turbulators. There is a chart there on selecting the size for chord position and Re.

Bear

[Arvid K. Gromhol]

Sparky Paul:
Up to this point in time, I did not know anything about turbulators, so I thought I should ask the question.
The model I have in mind is my own design:
Wing area 0, 43 m2, aspect ration 8.3, ClarkY 15%, model weight 4,3 kg or so,
.91 4 stroke engine.
It has become a little heavy, so I am looking for methods to counter this.

[green66]

Hi Arvid,

As Sparky and Batmanwpg imply, there will be little benefit turbulating the Clark Y at Re = 170k.

The graphs below show results from a Profili analysis of the standard Clark Y (11.7% thk) and the Clark YM-15 (15% thk) and neither look like they'd benefit from turbulation. Assuming your 170k Re occurs when flying at an efficient AoA (Cl around .85), you also won't get the apparent low-Cl benefit since the airspeed will be higher at low Cl, thus higher Re, so the transition point will be farther back, effectively putting the turbulator farther forward.

I don't think it's worth chancing increased drag for what appears to be very little or no benefit. If you feel compelled to try turbulation, put a strip at 60% like Batmanwpg suggested (corresponding to the black curve) which will be 145 mm behind your leading edge, and from the Hepperle site, the thickness should be about .29 to .33 mm.

I'm only aware of turbulation commonly used on gliders, because it typically is only useful at one airspeed, e.g. while thermalling. Below that speed, the turbulator is useless since it will be behind the transition point, i.e. in the wake region, and above that speed it's too far ahead of the transition point, tending to increase viscous drag more than reducing profile drag. So you can see that getting the turbulator placed correctly even with a specific airspeed (Re) in mind can be pretty iffy. With a powered model flying over a broad range of speeds, I'd say forget turbulation.

P.S. Edited my 1st post to clarify - got mixed up re turbulator location and transition location.

[Arvid K. Gromhol]

Thanks.
Are the curves you show from profili? I have Profili 2.10, does that veron have this facility, if so, where?

[Ollie]

See:
http://www.profili2.com/eng/default.htm
Include turbulator in new airfoil creation by using external shape.

[biber]

Deleted: I´d better learn reading posts of others more carefully... :rolleyes:

biber

[green66]

Are the curves you show from profili? I have Profili 2.10, does that veron have this facility, if so, where? The turbulator analysis capability may have been added after ver 2.10, so you might need to download the latest version (2.19). If turbulator analysis is in ver 2.10, click on menu item "Polars," then "Drawing Polars: free criteria - advanced (type 4)"