Reynolds Numbers?

[TGoodwin]

Hello I was wondering if anyone could explain to what exactly a Reynolds Number is and what is its function when selecting an airfoil????

Thanks in advance.

Ted

[NightSwan]

And you had me thinking this was all about the famous Reynolds Wrap ;) :D :eek:

[Sparky Paul]

From "Fluid Mechanics" R.C. Binder 1955:
"...for flow in which bodies are completely immersed in a fluid.. the inertia and viscous forces are the only ones which need to be taken into account. Mechanical similarity exists if, at points similarly located with respect to the bodies, the ratios of inertia forces to the viscous forces are the same. The force triangle at a point in one flow must be similar to the force triangle at the corresponding point in the other flow...
"buncha equations follow"..
...If viscous and inertia forces determine the flow for a prototype, then mechanical similarity between model and prototype is realized when the dimensionless Reynolds number for the model equals the Reynolds number for the prototype....
A small Reynolds number indicates that viscous forces predominate, whereas a large value of Reynolds number indicates that inertia forces predominate...
Frequently a model is tested in a fluid which is the same as that of the prototype flow. If the Reynolds number for each is the same and the kinematic viscosity of each fluid is the same, then similarity is given by the relation (velocity x length) for the model equals (velocity x length) for the prototype."
That's what a Reynolds number does.
It permits selecting an airfoil for a given condition of speed, related to chord from a database.
A model built to the same precision as the tested prototype can be expected to perform the same, at the test conditions.

[Sparky Paul]

Here's an example of a wind tunnel test on a Selig-Donovan 6060... note the behavior at the Re's below 100,000.. this is the viscous area mentioned above. Where the inertial forces become predominant the behavior becomes more consistent.
Attached is a typical computation for a Reynolds number.. at 35 ft/sec, and a chord of 6 inches.
The equivalent Re for any other airspeed or chord can be computed by computing the ratio of the difference and multiplying this Re by that ratio:
i.e., 70 fps is twice as fast, the Re will be twice as large..

[DaveSawers]

Reynolds number is calculated using the equation:

Re = Rho * V * D / Mu

Where: Rho is the fluid (air) density
V is the velocity
D is the important dimension (in our case wing chord)
Mu is the fluid (air) viscosity

Use consistent units throughout and the resulting Re is dimensionless.

[Pierre Audette]

Since models run at lower Re than their full size counterparts, they are not as efficient in creating lift, and generate more drag. This is why the best airfoil for a model is not the necessarily the one used in a full size plane if you're building a scale model. Add vortex effects and induced drag, makes you wonder how we get any models to fly. Just throw enough power to overcome these losses and you're flying. So basically models are not very energy efficient compared to their full size counterparts. This why the work of Selig & Donovan is significant to us, as it relates to parameters for model designs.

[desertwind]

One of the historically interesting points about Reynolds numbers is that for many years, decades, actually, the standard wind tunnel model had a chord of 200mm. That's 7.8 inches, very much a model size. That was the chrod used for each and every NACA airfoil tested in the 1930s. Those 200mm chord numbers are what people like Taylor, Piper, Cessna, Beech, etc., used when designing their planes. It is not a case of models scaling down big data. It is a case of real airplane designers scaling up model size data. To keep the surface flow as good as possible, however, those 200mm wind tunnel wing panels were like mirrors they were so smooth. Look for the info on the wing data graphs that gives the "sample size" and you will often be amazed.

[TGoodwin]

OK I am not sure I understand how this helps me to choose an airfoil? I think I understand how it relates to finding equivilent performance in a larger scale. So for model airfoils we are looking at the lower reynolds numbers only?

Thanks Ted

[TGoodwin]

So if I was compare a clark Y with a MH43 with reynolds numbers around 100000.

[TGoodwin]

Would the 100000 reynolds number be the correct one to use?

[Texas Buzzard]

Just to keep it simple ... A full size piper Cub with a 5 foot chord and flying at 85 mph has a much higher Reynolds Number than:
A model haveing a wing with a chord of 8 inches and an airspeed of 30 mph.

High Reynolds numbers are good, small are not good.

Have you noticed that large sailplanes seem to fly or float better? They have a larger chord and fly faster than little ones.

[strouse]

http://jef.raskincenter.org/published/airfoil.html

I found this link pretty useful to learn about airfoils and RE...

[MarkusN]

Would the 100000 reynolds number be the correct one to use?Depends on size and weight of the model. For model gliders Re = 100 000 to 200 000 are typical. At slow speeds even less. Powered models are higher (and critical Re is less of an issue due to turbulation by propeller slipstream and vibration.) For most airfoils things start to get hairy somewhere between 200 000 and 100 000. Special low Re designs may go lower.

In metric Re is roughly speed in m/s x chord in mm x 70.

If critical Re becomes an issue in a design, turbulators help.

[ciurpita]

this might help determine the RN for your specific case
http://ciurpita.tripod.com/rc/notes/reynoldsNum.html

[luvF3b]

Here's a different approach to selecting the right foil.

Calculate the reynolds number (Re) range you'll be flying at using the formula in post#5. For example, I use the formula Re=68500xChordxspeed where chord and speed are in meters and meters/second respectively.

The lift coefficient is also a vital thing. For a given model, the lift coefficient is physically bound to the reynolds number. This is where type 2 Xfoil polars come into play, where the Re x sqrtCl is held constant. For high lift coefficient, the model is flying slowly and Re is low, and for low lift coefficient, it is flying fast and Re is high.

There is a relationship therefore between lift coefficient and reynolds number (Re). (constant=Re x sqrt Cl)

Rough experience tells me that for Re<100K, thinner foils (eg <8%) with the thickness highpoint more forward (eg<27%) work better. For Re>300K the foils can be thicker, and the maximum thickness further back. For very low Re, say<50K, very thin foils (<6%) and sharp LE radius may work better. The camber of the foil is chosen for the lift coefficient required. High Cl, more camber, and vise versa.

All of this relates to trying to reduce the foil drag to the minimum possible for the given Re and lift coefficient. As pointed out in post#4, a complex behavior of laminar to turbulent flow is happening at the typical Re range for models. For indoor models (Low Re <50k), the flow is almost purely turbulent, for high speed or larger models (Higher Re >300k) laminar flow is possible. In between 50K and 300K the behaviour of the separation bubble dominates the drag performance. For very high Re (say>1000K) the flow will be laminar until an orderly transition to turbulent flow happens with out the separation bubble (as in full size aircraft)

Laminar flow is low drag, turbulent flow is higher drag, flow with a separation bubble is higher drag still, and separated flow is the highest drag.

To return then to the opening comment about estimating the model speed, you must determine the lift coefficient corresponding to the min. speed. As sqrt 1 = 1, work out the speed at Cl=1. This can be taken from the lift formula weight=lift=0.5 rho x v^2 x wing loading. This gives you the constant for the type 2 polar (Constant=Re x sqrt Cl)

To properly identify the best foil for the job, I would suggest a programme such as Xfoil, which allows the comparison of various profiles at the appropriate Re x sqrtCL

So, you get a little taste of how difficult it is to identify the best foil for the job, because it is not a simple thing. If you could tell us the weight, wing area, average chord, and estimated flight envelope (does it have to fly both slow and fast). Given those parameters, I'm sure the group could help further.

Cheers,

John

[BMatthews]

I think you're looking for the Reader's Digest answer while most of the other replies have gotten more into the technicalities.

By now you should be seeing that our airfoils are affected by both size (wing chord) and speed in how they react with the air around them. The Reynolds number is simply a way of expressing or describing that interaction as a number so that we are all comparing apples to apples.


Does that help with understanding the other posts above at all?

[Accu157]

Isn't Reynold's number analygous to current density? A measure of the volume of air, relative to time, passing through a defined area?

A measure of the volume of peas you're dropping through a certain sized hoop in a certain time, say 300 peas per second per square foot. Only we're talking about air molecules? I may have this wrong.

[BMatthews]

It may well be more accurate to see it that way. I have to admit that I haven't studied all the aspects of Reynolds numbers.

But that is an even more confusing way of looking at it when you're an aeromodeller that just wants to know what the numbers mean for picking out an airfoil.