Low Reynolds Number

[graupman]

I am trying to learn some CFD to help with my model designs. What I am hoping is that someone can confirm that I am on the right track, or let me know if my results are off. I have run several simulations with airfoils and reynolds numbers that are more typical (RE=3 million or higher), so that I can compare them with wind tunnel data. Those so far have worked well. What I am working on now is very low RE simulations, RE=30,000, which is more in the foamie range. I have attached a polar showing my result of a flat plate at RE=30,000. Does anyone know if this is right?

[BMatthews]

My gut reaction from flying a couple of flatties now is that this is pretty darn close to the truth.

However little things like real thickness and whether or not the maker sanded the leading edge round or left it square likely counts for enough to make it harder to compute unless you actually run an honest test with thickness accounted for.

[kcaldwel]

Pg. 17 of this document has wind tunnel tests of a flat plate at Re = 80,000. That is the nearest data I know of to yours, but still over 2x higher:

http://www.nd.edu/~mav/belgium.pdf

Kevin Caldwell

[JetPlaneFlyer]

Looks about what I'd expect to see... Do bear in mind though that like most wind tunnel data the results are 2D i.e. based on a infinite wing (one with no tips). In the real world the Cl graph would only come close to this if you used very high aspect ratio. Typical flat plate wing models have medium to low aspect ratio and for them the lift slope would be shallower, the AoA at stall higher and the max Cl lower.

Steve

[MarkusN]

I'd be very reluctant to trust calculations at Re this low, especially considering things like CL max. Flow at this Re is unstable, to say the least.

E.g. play around with Ncrit (does your program allow this?) and you'll see that you get widely varying results.

[graupman]

Thanks for the comments - this is exactly what I was looking for.

I am not so concerned with the maximum value of CL, I am looking more at the shape of the curve. It seems that the lower the reynolds number, the smoother the transition to stall. The polar I posted has no drop in CL after stall, it just levels off.

I also ran a NACA 0012 with the same simulation, and it still had the dip after stall. So it seems the shape of the leading edge also comes into play. I am thinking that the combination of low RE and the sharp square edge are what give the polar this unique shape.

This may betray my ignorance, but what is ncrit?

[kcaldwel]

... that like most wind tunnel data the results are 2D i.e. based on a infinite wing (one with no tips). In the real world the Cl graph would only come close to this if you used very high aspect ratio. Typical flat plate wing models have medium to low aspect ratio and for them the lift slope would be shallower, the AoA at stall higher and the max Cl lower.

Steve

There is actually testing and curves there for sAR = 3 and 1 at Re = 80 k, and sAR = 3 , 1.5, 1 and 0.5 at RE = 140,000....

Kevin

[MarkusN]

Ncrit is a parameter used in XFoil to define turbulence of the stream. It affects locations of boundary layer transitions. (In free air an airfoil may be subject to laminar separation, although it may have performed well in a wind tunnel with moderately turbulent flow, because this provokes early transition to turbulent boundary layer flow. Ncrit allows to simulate these conditions.)

BTW, you might be interested in the work done by F.W. Schmitz in the fourties. He made investigations of sub- and supercritical (concerning laminar separation) flow about airfoils. He found that at low Re sharp (or rather sharp) leading edges have a definite advantage by tripping the laminar boundary layer early and thus keeping flow attached over a larger portion of the airfoil.

The problem with numeric simulation at Re this low is that the simulation relies on experimental data that is very sparse for these conditions. The model has limits there, and I don't know how well these limits are defined (or how well aware the programmers of the code were of the window of applicability of the formulae they used.)

[graupman]

Finite wing effects are another subject I am hoping to learn more about. Once I am satisfied that my 2D results are at least in the ballpark, I will move on to 3D.

I am curious to see the affects of side force generators and fences, large control surface deflections, etc. I am basically hoping to better understand what is happening to a foamie over its various flight ranges.

There seem to be a lot of people with a lot of different opinions about why foamies fly the way they do, but no one seems to really know. Not that I am going to unravel it all, but hopefully I can learn something of value...

[MarkusN]

There seem to be a lot of people with a lot of different opinions about why foamies fly the way they do, but no one seems to really know.
I'd say that pretty much sums it up. When you talk about those complex designs with differnet surfaces influencing each other, airfoil theories wont help you much. This is highly three dee, and highly instationary. Both are concepts that dont' sit well with simple calculations.

[Sail 'n Soar]

I am trying to learn some CFD to help with my model designs. What I am hoping is that someone can confirm that I am on the right track, or let me know if my results are off. I have run several simulations with airfoils and reynolds numbers that are more typical (RE=3 million or higher), so that I can compare them with wind tunnel data. Those so far have worked well. What I am working on now is very low RE simulations, RE=30,000, which is more in the foamie range. I have attached a polar showing my result of a flat plate at RE=30,000. Does anyone know if this is right?

The general shape looks to be OK, but the transition point from CL proportional to alpha is too high. Page 172 of the 1983 reprint of "Model Aircraft Aerodynamics" by Martin Simons provides low turbulence level wind tunnel measurements of Cl vs. alpha for the Gottingen flat plate. Those curves for Re = 42,000 indicate a Cl transition point from high to low slope at Cl ~ .52 and alpha ~5.7 degrees. Cl, max was between .7 and .75.

Increasing the Re to 168,000 raises the transition point to Cl between .55 and .6, but Cl max is about the same.

[graupman]

After some experimenting, I have settled on what I think is about as good a result as I am going to get...

The work done by F.W. Schmitz (thank you to MarkusN for directing me to this) has been quite helpful. Unfortunately the data in the paper I have is all 3D. His tests were using a rectangular plan form with an aspect ratio of 5. I was able to compare to the wind tunnel data from Mueller (also referenced earlier). This was 2D and seems to match reasonably well.

The two key things I found were grid resolution (fairly obvious) and the turbulent energy of the free stream. If there is any existing turbulence in the free stream, the flow stays attached much longer, and results in a higher CL curve.

I think the next step is to start comparing different leading edge shapes, plate thicknesses, and then move on to 3D.

Any other suggestions?

[Sail 'n Soar]

After some experimenting, I have settled on what I think is about as good a result as I am going to get...


Any other suggestions?

First of all, I assume you are doing this exercise to design a real model with some finite aspect ratio wing. It is relatively easy to translate the SD AR 5 data to the local CL value analytically, at least up to the point you have significant separation (what is considered significant is a matter of judgement.) For the data you give, the CL vs. alpha slope change at alpha = ~7.5 degrees appears to be that point for the two Schmidtz curves shown in your chart. Up to ~7.5 degrees you can then compare the CL @ centerline to the Mueller data. I would consider the wing effectively stalled where ever that point is. The given that CL @ centerline as your CL max value, you can calculate the CL average at stall for whatever your wing AR and planform is. The 2D data is only good for identifying when the airfoil is likely to stall locally. The CL value that should be used to calculate when a wing will stall will be lower than that. i.e., don't use either the Mueller measurement or your calculated value in your wing stall speed calculation.

[graupman]

Eventually, yes, I will be using this for design work... not for a specific model, but just generally to try new things and see how they affect a model.

For example: What is the best shape and angle for a vortex generator? How big should it be? At what angle? How far apart should they be spaced? Will it's benefit be large enough to overcome weight and complexity?

Obviously the best way to answer these questions would be a wind tunnel since it is difficult to get good results when simulating viscous flow like this. The problem is I don't have a wind tunnel, or access to one. More than once I have considered signing up for some classes at a local university, but until I am actually willing to commit the time and funds to that, I have my laptop to solve these problems. Its not the best tool, but its all I've got.

2D is more or less an exercise for me to learn and compare my results against real world data. I would not use any of the 2D data for 3D results.

Once I have tested a few different shapes in 2D, I will start testing those same sections with a finite wing to see if all the correlations are consistent.

One of my primary goals is to find shapes that are not necessarily the most efficient, but have a smooth transition to stall. Since a foam or 3D model spends a lot of time above or near stall, I think finding shapes with a predictable, gentle stall that is relatively insensitive to reynolds number would be helpful.

[Sail 'n Soar]

One of my primary goals is to find shapes that are not necessarily the most efficient, but have a smooth transition to stall. Since a foam or 3D model spends a lot of time above or near stall, I think finding shapes with a predictable, gentle stall that is relatively insensitive to reynolds number would be helpful.

Smooth transition to stall is one thing, perhaps more importantly is the lift distribution, which will determine where the wing stalls first, which, in turn, will influence if the stall occurs straight ahead or results in a hopefully recoverable spin. If you are not worried that much about efficiency, go with a constant cord wing with moderate camber and don't worry about the rest.

Still, the computer thing is a fun exercise.

[Flyingwingbat1]

Serrated LE's seem to smooth out the stalls on my foam-plate gliders. A caveat; the serrations in my design are generally 25-40% of chord depth. Also, the stall speeds went down as a result, too, at the penalty of slightly lower L/D. One very light foam design can be released from horizontal standstill, and it will drop and recover to a steady glide within 18" (span is 12" for that model).

One advantage of the serrations; you don't have to add extra parts to the wing.

[graupman]

This is exactly the type of thing I am trying to learn!

I built a foamie with serrations as well, but did not notice a large improvement. My serrations were not nearly as large as yours, so it seems likely that mine were too small. On my list of things to try in a simulation is serrations. How big, how long, how far apart, what angle, etc.

Also, that is the type of performance I am looking for. My ideal plane is just as stable and controllable when completely stalled as it is in normal forward flight.