Aeronautical Facilities: Assessing the National Plan for Aeronautical Ground Test Facilities (1994)

The purpose of this appendix is to provide a rudimentary explanation of aeronautical speed regimes and some of the key parameters used to define aerodynamic wind tunnels.

Many important parameters apply to the design and operation of wind tunnels. Among these are Mach number, Reynolds number, flow quality, wall temperature ratio, productivity, noise levels, and spectral signatures. Mach number and Reynolds number are especially important to the accuracy of test data, but it is very expensive to build facilities that accurately simulate these parameters for large, high-speed aircraft.

Mach number is defined as a ratio of vehicle speed to the speed of sound. It is a function of gas temperature and specific heat ratio (Equation 1). For ground tests, wind tunnel free stream velocity is used to approximate vehicle speed.

(1) Mach Number

M = Mach number

V = Vehicle speed

a = Speed of sound (nominally 750 mph at standard temperature and pressure)

γ = Specific heat ratio (of the atmosphere or test gas)

gc = Acceleration of gravity

R = Gas constant (of the atmosphere or test gas)

T = Absolute temperature (of the atmosphere or test gas)

Extremely low temperatures can produce high Mach numbers at low free stream velocities. However, wind tunnel simulation of Reynolds numbers is not achieved by raising Mach number alone (see “Reynolds Number” below).

There are four speed regimes related to aerodynamic testing. The boundaries between the speed regimes are rather vague, though each speed regime does have its own qualities that sets it apart from the others. The speed regimes are summarized as follows:

• Subsonic flight: 0 < M < 0.8

At less than about Mach 0.8, air can usually be treated as an ideal, incompressible gas for slender aircraft configurations. There are usually no shock waves to complicate design and analysis, although they can appear at velocities as low as Mach 0.3 for surfaces with high lift coefficients or in aircraft configurations that are thick or blunt or that otherwise produce a large change in pressure or velocity of the flow.

• Transonic flight: 0.8 < M < 1.0–1.2

Above roughly Mach 0.8, the aircraft or model begins to compress the air enough to generate shock waves on portions of the wing and fuselage. Some regions may have supersonic flows, while in other areas the flow may still be sonic or even subsonic. These shock waves usually begin on either the nose or the location of the peak negative pressure on the wing. However, elsewhere along the body of the aircraft or along the wing itself, areas may exist where the air is still below the speed of sound. As the aircraft velocity increases above Mach 1.0, these

shock waves tend to slope toward the wing and body surfaces.

• Supersonic flight: 1.0–1.2 < M < 5

Depending on the thickness and sweep of the wang and the slenderness of the configuration, at a speed somewhat above Mach 1.0 (typically 1.2–1.5), the general flow field becomes essentially supersonic.

• Hypersonic flight: M > 5

As velocities increase past Mach 5, test conditions for complete simulation must match additional fluid properties such as the specific heat ratio, the gas temperature, and the ratio of body-wall temperature to fluid total temperature. At hypervelocities (above about Mach 13) radiation heating and thermodynamic nonequilibrium effects become significant, and the air will start to ionize and dissociate. Interactions within the airstream and between the airstream and vehicle become much more complicated.

Reynolds number is the ratio of the inertia forces to the viscous forces that a fluid exerts on a surface as it flows past. Reynolds number is directly related to Mach number (Equation 2).

(2) Reynolds Number

Re = Reynolds number

L = Characteristic length (of the aircraft or model in the direction of flow)

ρ = Gas density

µ = Dynamic viscosity coefficient (of the test gas)

P = Gas pressure

C ≈ The ratio between µ and T^1/2 (C is itself a weak function of temperature)

See Equation (1) for definition of other variables.

During wind tunnel tests, Reynolds number should be consistent with full-scale flight conditions. Otherwise, test flows may behave differently than under actual flight conditions.

Wind tunnel models must be small enough to avoid creating flow blockages and associated wall effects. As model scale is reduced, the characteristic length of the model is also reduced, and test conditions must be altered to restore flight Reynolds number. For example, in order to test a quarter-scale model at flight Mach and Reynolds numbers, wind tunnel pressure must be increased and temperature must be decreased by a combined factor of four.

For practical reasons, few wind tunnels are designed for pressures higher than 3 to 5 atmospheres. Beyond this, atmospheric thermal effects arise, requiring large amounts of cooling in order to keep the simulation within testing parameters. The structural strength of the wind tunnel pressure vessel, the model, and the model support structure must also be increased to withstand the static and dynamic loads that high pressures generate. Thus, the construction and operational costs associated with large high-pressure facilities can be substantial.

Nonetheless, some research facilities use extremely high pressures (up to hundreds of atmospheres) or cryogenic temperatures to conduct testing at extremely high Reynolds numbers with small or moderately-sized models. Practical limitations, however, make these facilities unsuitable as development facilities. Development testing requires easy access to wind tunnel test sections to make model adjustments between test runs. High pressure facilities require long periods of time to depressurize and repressurize the test section before and after model adjustments. Cryogenic facilities require time to cool and thermally stabilize test conditions after opening the test section for human access. Furthermore, both types of facilities require specially designed models to withstand the extreme test conditions.

Some wind tunnels use nitrogen, helium, freon, or sulfur-hexafluoride (SF₆) as test gases. The higher molecular weight of gases heavier than air increases the Reynolds

number capability. In some cases, using gases other than air also makes it easier to cool the flow stream, which contributes to higher Mach and Reynolds number capability. However, use of alternative test gases complicates the interpretation of data to predict vehicle performance in air, and this process introduces uncertainty in the final results. Alternative gases may also raise safety, cost, and environmental concerns. Freon, for example, is no longer a viable option because of environmental considerations. The safety precautions needed with test gases that are corrosive or otherwise dangerous also reduce productivity. Because of these factors, gases other than air are not currently a practical alternative for large-scale development wind tunnels.

Adjusting flow velocity is sometimes used to adjust Reynolds number, but this means the data is no longer representative of actual flight speed. As free stream velocity approaches the speed of sound in the wind tunnel, compressibility effects can affect model aerodynamics in ways that will not appear on a full-scale vehicle. Experience has shown that combining data from different tests (one at flight Reynolds number, the other at flight Mach number) is not nearly as effective as conducting a single test that matches both parameters.

Wind tunnel flow quality also directly impacts the validity of test data. Highly turbulent flows will provide significantly different results than tests using low turbulence flows or smooth (or “laminar ”) flows. Laminar flows are most representative of ambient conditions in the atmosphere, but laminar flow facilities are difficult and expensive to build.

Wind tunnel productivity is usually quoted in terms of polars per occupancy hour. A polar is generally defined as a set of 25 data points, where each data point is obtained at a different value of a single independent variable. Occupancy hours include all of the time that a wind tunnel test section is dedicated to a particular test. This includes model set-up, testing, and tear-down.

Most of the time occupied in a typical wind tunnel experiment involves setting up the model in the tunnel. In most facilities, the tunnel is unable to conduct any testing while test set up, calibration, etc., is taking place. In other words, an extremely large and expensive facility may sit idle for days while a few technicians and engineers tinker with a test model. This situation contributes to the low productivity of many large wind tunnels in the United States.

The use of removable, interchangeable test carts can dramatically increase productivity. Carefully designed and engineered test carts allow experimental set up to begin in an adjacent facility while wind tunnel testing on other models can proceed without impediment. As soon as one test program is finished, the test carts can be exchanged, and testing can quickly resume on the next model. Such facilities cost more to build, but overall cost per polar is reduced if demand is high enough to take advantage of the higher productivity.

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