Heat and mass transfer during a sudden loss of vacuum in a liquid helium cooled tube – Part II: Theoretical modeling

Abstract

A sudden loss of vacuum in particle accelerator beamlines and other cryogenic systems can lead to substantial equipment damage and possible personnel injuries. Developing a clear understanding of the complex dynamical heat and mass transfer processes involved following a sudden vacuum break is of great importance for the safe operation of these systems. Our past experimental studies on sudden vacuum break in a liquid helium cooled tube revealed a nearly exponential slowing down of the propagating gas front. However, the underlying mechanism of this slowing down is not fully explained. In this paper, we discuss a theoretical framework that systematically describes the gas dynamics, heat transfer, and mass deposition of the propagating and condensing gas inside the helium-cooled tube. The experimentally observed apparent gas-front propagation, measured as the abrupt temperature rise by the thermometers installed along the tube wall, can be well reproduced by the model simulation. We also show that following the gas front, the mass deposition rate of the gas on the tube inner wall approaches a constant. The extension of this nearly constant gas deposition zone is the key to understand the observed exponential slowing of the gas propagation. Our model also allows us to gain valuable insights about the growth of the frost layer on the tube inner surface. This work paves the way for a theoretical understanding of the physical processes involved during vacuum break in accelerator beamlines.