Wednesday, July 02, 2014

Formula 3 airflow restrictors and black holes

The July issue of RaceTech magazine contains a decent article by Marco de Luca and Angelo Camerini on the principles behind airflow restrictors, such as those used to limit engine power in endurance racing and Formula 3.

The authors explain that as the RPM of the engine increases, the suction of the engine lowers the pressure in the downstream portion of the air intake duct. With an airflow restrictor, this duct consists of an inlet, a converging section, a throat, and (in some cases, but not in F3) a diverging section. As the downstream pressure lowers, the airflow velocity through the throat increases until, eventually, supersonic speeds are reached. In this condition, the flow in the duct is 'choked'.

Under normal conditions, when the RPM of the engine increases the pressure drop is communicated by means of pressure waves travelling upstream to the external atmosphere at the speed of sound. When the flow velocity becomes supersonic in the throat of the intake duct, these pressure waves can no longer breach the throat, and the engine's demand for greater mass-flow is unsatiated.

What the RaceTech authors sadly omit to mention, however, are the similarities between such airflow regimes and the event horizons of black holes. 

Physicists have been aware for some decades that fluid flow can influence the propagation of sound in the same way that black holes can influence the propagation of light. The classic example of such an analogy is perhaps the Laval nozzle. This contains a converging section, which accelerates a subsonic upstream flow so that it reaches the speed of sound in the throat of the nozzle. Then, (unlike the case of the air restrictor), the airflow is maintained in a supersonic condition downstream. 

The subsonic region of the 'acoustic geometry' corresponds to the exterior of the blackhole spacetime geometry; the throat corresponds to the event horizon; and the supersonic region corresponds to the interior of the black hole. 

Sound waves propagating upstream in the subsonic region are doppler shifted to longer wavelengths, just like the light escaping from the clutches of a black hole. Moreover, all sound waves in the supersonic region are swept further downstream, just as light is unable to escape the interior of a black hole. (See this Scientific American article by Theodore A. Jacobson and Renaud Parentani for an accessible introduction to the field of acoustic black holes.)

I look forward to a subsequent article by Marco, which explains the analogies between exhaust systems and white holes.