Variable-density wind tunnel

A variable-density wind tunnel changes the density of the test gas, typically by pressurizing the circulating flow system, to control aerodynamic similarity without relying only on higher speed or larger models. It is especially useful for matching Reynolds number when the model is smaller than the full-size object.

For characteristic length $L$, speed $U$, gas density $\rho$ and dynamic viscosity $\mu$,Under an ideal-gas approximation at fixed temperature and composition, density scales with absolute pressure. If a model has one-tenth the full-size length, using ten times the density at the same speed and approximately the same viscosity restores the same Reynolds number.

An original calculation uses full-size $L=2$ m, $U=30$ m/s, $\rho =1.2$ kg/m${}^3$ and $\mu =1.8\times 10^{-5}$ Pa·s. This gives $\mathrm{Re}=4.0\times 10^6$. A 0.2 m model at density 12 kg/m${}^3$ gives the same result at 30 m/s. At ordinary density, that model would instead require 300 m/s. If the speed of sound is stipulated as 340 m/s, the two test speeds correspond to Mach numbers about 0.088 and 0.88. Density control can therefore help match viscous scaling while avoiding a large change in compressibility effects.

The historical NACA investigation of 78 related airfoil sections used a variable-density wind tunnel to study changes in thickness and mean-line form at a large Reynolds number. Its primary report describes the models, apparatus and force/moment measurements.^[ref] The systematic geometry variation illustrates why controlling flow conditions makes comparisons interpretable.

Matching Reynolds number alone is not a guarantee of complete similarity. Mach number, relative surface roughness, incoming fluctuations and model blockage remain separate issues. Changing density also changes dynamic pressure, $q=\frac{1}{2}\rho U^2$, and hence the forces a balance must measure. The pressure vessel and circulation machinery are therefore parts of both the similarity strategy and the experimental loading problem.