Some people have the impression, that an experiment, where they can measure everything up to umpteen digits behind the decimal, are the only truth. The people who are doing the real work, i.e. performing measurements at an experimental facility, like a wind tunnel, know better. It is extremely difficult to provide well defined test conditions and to make accurate measurements, especially on airfoils at Reynolds numbers below 500'000.
Some important points are the facts, that
- the flow at low Reynolds numbers is very sensitive to external influences (turbulence, noise),
- spanwise flow may occur in airfoil tests, especially when separation occurs,
- the wind tunnel changes the flow field around the airfoil,
- the forces and pressures to acquire are very small, and
- the wind tunnel model must be built to high standards to closely represent the desired shape.
Unfortunately not all wind tunnel experiments are documented as well as the results from the tests at the University of Illinois Urbana-Champaign (UIUC). Usually only one drag polar per Reynolds number is given and the user has no idea about fluctuations or errors in the system. The following plots show the published data for the E 374, as it has been investigated at the UIUC. The symbols represent the data, as sampled at four different spanwise locations; the line connects the mean values for each angle of attack (this is what you will find in the final publication). I can assure you, that the bandwidth of these results at lowest Reynolds numbers is not unusually large and is not a sign of poor measurement techniques. It is a matter of the physics of the flow.
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At this low Reynolds number of 61'500 the data points are scattered in a wide band. |
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At medium Reynolds numbers the scatter is considerably reduced. |
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Increasing the Reynolds number moves the scatter to the corners of the laminar bucket. |
As you can see, the band width at Reynolds
numbers above 150'000 is quite narrow, as long as you focus around medium
lift coefficients. Increasing or decreasing the lift coefficient can lead
to separation, usually starting at the trailing edge and moving more or
less slowly towards the leading edge. The flow in separated regions is
neither stationary nor two dimensional, which introduces additional
scatter into the forces and pressures.
These spanwise variations of lift and drag can occur due to wind tunnel
deficiencies, non uniform model accuracy and local separation bubbles. In
most experiments the lift coefficient is determined by a force
measurement, giving a mean value for the whole model, but the drag
coefficient is measured locally. Most modern drag measurements are
performed at several spanwise locations, but not all of them. For example
the drag coefficients, published in [20], were sampled at a single
spanwise location. The reader is referred to [12], [13] and [17] for
further discussion of the problems of tests at low Reynolds numbers, as
well as to the section «MH 32: Wind Tunnel Results».
Something, which seems to be never (?) published, is the time history of the measurements, which might yield an even wider scatter band. Drag measurements can be performed by a single sensor, moving through the wake and sampling the total and the static pressure at different locations at different times, or by using a wake rake, sampling at different locations at the same time (depending on the equipment). Thus the sampling rate and sampling time will have some influence on the results, especially when periodic fluctuations of the flow occur.
Remark:
The purpose of this section is not to blame the people who
contribute to the excellent work at UIUC or other facilities - these guys
are doing excellent and hard work, which is appreciated very much by so
many all around the world. The scatter of the experimental data is just a
matter of fact, caused by the underlying physics.
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