Dynamics of liquid helium boil-off experiments with a step change in pressure

Abstract

The results of dynamic analysis of the effect of pressure variations during helium boil-off experiments are presented. A general solution of the diffusion equation with a time-dependent boundary condition is employed to describe the dynamic response of the liquid helium system under variable pressure conditions, and a solution is obtained for the special case when the system is subjected to a step change in pressure. The calculated temperature response of the liquid indicates that most of the experiments were not likely to have reached equilibrium as a result of the low thermal diffusivity of liquid helium. The initial rate of evaporation or condensation is large, and the rate decreases sharply with time. A method is proposed to account for the transient effect that is observed during calculation of the heat loss rate from a helium boil-off experiment. By assuming that there is no mixing at all, the present analysis provides an estimate of the upper (condensation) or lower (evaporation) bound of the heat loss rate as a result of a pressure increase or decrease in the system. A previously reported equilibrium analysis is expected to apply to situations where complete mixing occurred in the bulk liquid and provides the opposite limits.