A major problem in wind-tunnel model testing arises if we rely solely on increasing the speed to correct the Reynolds number. Since the chord c of the model is smaller, we must make (pV )/u larger. This in turn means that, unless we do something about the density and viscosity, a 1/10 scale model would need to be run at 10 times the full-scale speed.
Unfortunately aircraft are large objects, and we often wish to make models of 1/10 scale or less. To simulate 100 m/s at 1/10 scale, we would need to
run the tunnel at 1000 m/s which is nearly three times the speed of sound at sea level! Clearly, the resulting supersonic conditions would ensure that the flow around the model was nothing like that for the full-size aircraft.
One way to avoid this difficulty, is to use a pressurised wind-tunnel. By increasing the pressure in the tunnel, the density and hence the Reynolds number may be increased at any given air speed. A similar effect can be obtained by using a so-called cryogenic tunnel where the air is cooled (usually with liquid nitrogen) to decrease the viscosity coefficient p. Gases, unlike liquids, become less viscous as they are cooled. The density is also increased.
In order to obtain similar flow characteristics between model and full scale (a condition known as dynamic similarity), it turns out that there are other quantities that need to be matched in addition to the Reynolds number. For aeronautical work, the other really important one is the Mach number, the ratio of the relative flow speed (or aircraft speed) to the speed of sound. As we shall see, the speed of sound depends on the temperature, and thus quite a bit of juggling with speed, pressure and temperature is required, in order to get both the Reynolds and the Mach numbers in a test simultaneously matched to the full-scale values.
Although less important, we should really try to match the levels of turbulence in the oncoming air stream, which can be difficult, because in full scale, the aircraft can sometimes be flying through still, and hence non-turbulent air.
For fundamental investigations, and exploratory test programmes, it is still customary to use simple unpressurised tunnels. When the low speed characteristics of the aircraft are being investigated, the Mach number mismatch is unimportant. The Reynolds number error can sometimes be reduced by sticking strips of sandpaper on the surface to provoke transition at the correct position, which can either be estimated, or determined from flight tests.
For tests at supersonic speeds the Mach number must be matched, which is quite easy, and the Reynolds number effect is often less important. Unfortunately, most airliners, and quite a few military aircraft spend most of their time flying faster than 70 per cent of the speed of sound, where both the Mach and Reynolds numbers are important. Wind-tunnels in which the pressure, temperature and Mach number can be controlled accurately to suit the size of model are expensive to build and run, especially for speeds close to the speed of sound, but they are essential for accurate development work.