# Is the Reynold's number a function of the fluid flow stream or the obstruction?

I am slightly confused with this notion of the Reynolds Number. Specifically, I am looking at airfoil performance at very low Reynolds number.

I am reading a lot of papers saying things like because it is a small model aircraft, the Reynolds number will be small (so then it is to do with the shape of the obstruction in the fluid flow?). But then I see something like large turbine performance at low speeds involve low Reynolds numbers (from here I would think it is to do with the 'quality' of the fluid flow itself, whether it is laminar or turbulent, uniform etc).

If it has something to do with the fluid flow, then why do I see Reynolds numbers attributed to specific airfoils etc? Say that an airfoil has $Re=100000$, what does this mean then? If the fluid is flowing at a very low speed with high viscosity, then how can we make use of this number at all?

Do correct me if I'm wrong, I am only beginning to learn these things!

• This answer explains what affects the Reynold's number. Basically speed, size of obstruction, and gas properties. – fooot Nov 26 '14 at 19:07
• One nice thing about Reynolds number is it is dimensionless. So you could test a big wing in air at high speed by using a smaller wing in water at lower speed and if the Reynolds number is the same it gives the same results. – zeta-band Apr 17 '18 at 18:49

Maybe it helps to see the Reynolds number as the ratio of inertial to viscous forces. High flow speeds mean high inertial forces, and so lead to high Reynolds numbers. Viscous effects are strongest when the airflow hits the obstacle, and become less strong the longer the air flows around a body, so a short flow path has a low Reynolds number.

In the end it does not matter if the length of the flow or its speed drive the Reynolds number up. It is the combination of both. I am neglecting the gas properties here, because I assume we talk about air at moderate temperature and do not want to make the issue more complex.

Airfoils have no Reynolds number per se, flow conditions have. The Reynolds number of a measurement can be doubled by making the chord of the airfoil twice as long at the same airspeed, or by doubling the airspeed at the same chord. The wing of an airplane operates in a range of Reynolds numbers, depending on flight speed. That is why polar diagrams normally contain the results of several test runs rsp. computations, each at a different Reynolds number.

Sometimes you see airfoils which are optimized for a particular Reynolds number. To avoid early separation, the recompression area of an airfoil must become proportionally longer the smaller the Reynolds number is at which the airfoil is supposed to function well. At higher Reynolds numbers such an airfoil will still work, but will produce more drag than one which is optimized for a higher Reynolds number. The Reynolds number allows the aircraft designer to pick an airfoil that works well at the combination of speed and chord length for which that airplane is designed.

• Would I then be right in saying that there is no such single Reynolds number, but rather depending on where in the flow field we are looking at, we get a variety of Reynolds numbers? (If so, then is the quoted Reynolds number some sort of an average value?) – midnightBlue Nov 26 '14 at 22:24
• @midnightBlue: Yes and no. If you look at boundary layer phenomena like laminar-to-turbulent transition, a local Reynolds number is useful. If there is no pressure gradient, transition happens around Re = 400,000. But if you compare full airfoils, you need to take the Reynolds number for the full chord, or the comparison is meaningless. The quoted number is always that at full length. – Peter Kämpf Nov 26 '14 at 23:07

The best way to understand what a Reynold's number means is to look at the formula:

R# = velocity of fluid * characteristic length / kinematic viscosity of the fluid

Velocity = speed through the air, characteristic length = the length of the airfoil along the chord, kinematic viscosity = how gooey!) the air is

You can see that the Reynolds number depends on the airfoil shape as well as the conditions under which it is being examined. A higher Reynolds number means you are testing a longer airfoil at a higher speed in "thicker" air, or some subset.

It is useful when trying to predict performance. NASA uses pressurized wind tunnels in certain circumstances to affect viscosity, allowing a small model to better predict the performance of a full size wing.

Here is a calculator you can play around with:

http://airfoiltools.com/calculator/reynoldsnumber