Laminar Flow, Turbulent Flow, Reynolds Numbers
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
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.
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.
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.
(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
If the right set of units is chosen, then this ratio
is dimensionless, and is called a Reynolds Number.
This ratio is also proportional to the ratio of inertial
forces to viscous forces or:
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.
WHAT HAS ALL THIS GOT TO DO WITH WIND TUNNELS??
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.