Wind-tunnel nozzles and televisions

The power consumption of a wind-tunnel cubes with the velocity, hence an efficient tunnel design keeps the velocity as low as possible in all sections other than the working section. A nozzle is used to increase the velocity in the working section, and then a diffuser (or two) is used to reduce the velocity after the working section.

A typical wind-tunnel nozzle consists of two profiles, the first of which is concave, the second convex. It is important to avoid boundary layer separation in both parts of the nozzle, but in the case of a turbulent boundary layer, convex curvature reduces turbulent kinetic energy and skin friction, whilst concave curvature has the opposite effect (relative to a flat plate). The boundary layer over the concave surface is thicker than that over a flat plate, whilst the boundary layer over a convex surface is thinner, and therefore less prone to separation. The concave section is therefore more elongated than the convex section.

Note that the coke-bottle section on a Formula 1 car also features a convex-concave transition, although in this case the airflow is external and the convex section comes first as the sidepods taper inwards.

Meanwhile, for a wind-tunnel with a rectangular cross-section, the nozzle design is a curious echo of the external case of a late 1990s Cathode-Ray-Tube television.

An approximate macroscopic geometrical isomorphism, which was only implicate in the laws of physics, until the world of engineering made it explicate.