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Wind Tunnels

Laminar Flow, Turbulent Flow, Reynolds Numbers
Dynamic Similitude
Norman O. Poff NASA/AESP 85

When this epistle on a "simple" explanation of wind tunnels started, it became obvious that the explanation would only be simple if you first knew something about fluid dynamics. So first things first. Well, sort of, anyway. Actually the topics will be introduced when something needs explaining.

Laminar flow:

One can think of a fluid as being able to flow smoothly in layers (lamina). You can think of the flow as stream-lines of fluid where there is no mixing of molecules between layers. This means also that there is no exchange of energy and momentum and all that stuff. Examples are water flowing slowly from a faucet, or smoke when it first rises from a (choke, choke) cigarette in an ashtray.

Turbulent flow:

This occurs when the fluid does not flow in layers, when there is mixing of clumps of fluid, when there is intermixing of energy and momentum and all that stuff. Examples are water flowing at a brisk speed from a faucet and cigarette smoke at the end of the laminar stream where the smoke swirls and mixes with the surrounding air.

Reynolds Numbers:

In 1883, Osborne Reynolds experimented with laminar and turbulent flow. His basic experiment was to inject a dye in a small section of fluid flowing in a tube and find where the flow changed from laminar to turbulent flow. He found that the flow could change abruptly and always happened where the following ratio occurred.

ratio when flow changes abruptly

(The length for Reynolds was tube diameter but can be any characteristic length such as wing chord.)

(The viscosity of a fluid is the tendency to resist shear deformation. It is then the friction resistance to distortion of shape.)

If the right set of units is chosen, then this ratio is dimensionless, and is called a Reynolds Number.

Reynolds Number

This ratio is also proportional to the ratio of inertial forces to viscous forces or:

ratio of internal forces to viscous forces

Dynamic Similitude:

Two experiments involving fluid dynamics are DYNAMICALLY SIMILAR if and only if the Reynolds Numbers are equal. This means that it is possible for an experiment with a helium-filled balloon 100 cm in diameter rising in air to be dynamically similar to a 9.60 cm plastic ball falling in water if the Reynolds Numbers are the same. But an experiment with an exact scale three-meter model of a Boeing 747 in a wind tunnel --- IS NOT DYNAMICALLY SIMILAR ---- to a real, flying Boeing 747 if the Reynolds Numbers are not equal.


For experiments in wind tunnels, the principle of dynamic similarity allows interpretation of the test, and the test becomes applicable to the real aircraft. It would be even better if you could make a wind tunnel that had full-scale R.N. capability or a full-scale wind tunnel where you can test the full-size aircraft. Full-scale Reynolds Numbers have been a goal of tunnel designers almost from the beginning. There are other problems, such as wall interferences effects, but they are explained well in "Wind Tunnels of NASA SP 440."

NASA has two full-scale tunnels: a 30' x 60' full-scale tunnel at Langley: a 40' x 80' full-scale tunnel, and a 80' x 120' tunnel add on at Ames.

Langley also has the National Transonic Facility, and even though the test section is only 2.5 meters, it achieves full-scale Reynolds Numbers by being able to increase the density to 9 atmospheres, and decrease the viscosity by reducing the temperature with the use of cryogenic nitrogen at -300 degrees Fahrenheit. Increased density increases the numerator of the R.N. formula, while decreased viscosity decreases the denominator together raising the Reynolds Numbers achieved.

References: Wind Tunnels of NASA SP 440, Baal, Corliss Shape and Flow, Ascher H. Shapiro, Anchor S-2 1.


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