Atomic recombination in a hypersonic wind-tunnel nozzle

TLDR

The study examines the flow of an ideal dissociating gas through a nearly conical nozzle. The authors derive the shape of an optimum nozzle to minimize departure from equilibrium. They numerically solve one‑dimensional motion equations with a simple rate equation and develop an approximate method exploiting rapid freezing to estimate equilibrium deviations across a range of conditions. The calculations show that chemical equilibrium can be widely disrupted, leading to rapid freezing that keeps the dissociation fraction nearly constant, and that such non‑equilibrium conditions are expected in hypersonic wind tunnels and shock tubes, slightly altering post‑shock flow but reducing blunt‑body heat transfer and drag by about 25%, while making shock shape more sensitive to equilibrium departures.

Abstract

The flow of an ideal dissociating gas through a nearly conical nozzle is considered. The equations of one-dimensional motion are solved numerically assuming a simple rate equation together with a number of different values for the rate constant. These calculations suggest that deviations from chemical equilibrium will occur in the nozzle if the rate constant lies within a very wide range of values, and that, once such a deviation has begun, the gas will very rapidly ’freeze’. The dissociation fraction will then remain almost constant if the flow is expanded further, or even if it passes through a constant area section. An approximate method of solution, making use of this property of sudden ’freezing’ of the flow, has been developed and applied to the problem of estimating the deviations from equilibrium under a wide range of conditions. If all the assumptions made in this paper are accepted, then lack of chemical equilibrium may be expected in the working sections of hypersonic wind tunnels and shock tubes. The shape of an optimum nozzle is derived in order to minimize this departure from equilibrium. It is shown that, while the test section conditions are greatly affected by ’freezing’, the flow behind a normal shock wave is only changed slightly. The heat transfer rate and drag of a blunt body are estimated to be reduced by only about 25% even if complete freezing occurs. However, the shock wave shape is shown to be rather more sensitive to departures from equilibrium.