Propagation of nitrogen gas in a liquid helium cooled vacuum tube following sudden vacuum loss – Part II: Analysis of the propagation speed

Abstract The propagation of near-atmospheric nitrogen gas entering a liquid helium (LHe) cooled vacuum tube following an accidental loss of vacuum will be strongly influenced by condensation of the gas on the tube wall. Our previous experimental study revealed that in presence of condensation, the propagation speed of the gas front decreases nearly exponentially as the front advances in the tube. In the present paper, the exponential decrease is studied semi-analytically. We reduce the analytical model of the front speed, using assumptions, to show its derivative in the direction of propagation to be proportional to the mass deposition rate near the front. The deposition rate is then obtained at discreet locations along the tube from the condensation heat transfer rate at these locations. We find the deposition rate to diminish nearly exponentially along the tube so that the spatial derivative of the speed will show the same effect. In this special case, the front speed will also fall exponentially along the tube. Within the experimental and procedural uncertainty, the exponential decay length-scale of the mass deposition rate also agrees reasonably with the empirically determined exponential decay length-scale of the propagation speed.