Real gas features on the performance of pulse tube cryocoolers

Abstract

The working helium gas in a pulse tube cryocooler operating at temperatures down to 80 K is mainly assumed to be an ideal gas. Therefore, the time-variations of the temperature profiles and the position of the gas element traveling with pressure oscillations inside the pulse tube can be readily determined by the law of Poisson function. However, this is certainly invalid for the pulse tube cryocooler operating at temperature range of liquid helium, in which the thermal properties of the helium gas change drastically. The temperature profiles in the regenerator and the pulse tube are strongly affected by the real thermal properties of the helium gas. We derive in this paper, the respective expressions to follow the tracks of the gas elements as they move in the pulse tube, and to reveal the time dependence of the temperature profiles and the position of gas elements traveling with the pressure oscillations inside the pulse tube. The approach is based on the thermodynamic equations for the real gas. We will show that contrary to the ideal gas case there is another term which determines the dynamic behaviors of the temperature distributions and the position of the gas elements. A typical calculation is presented for visualizing the time dependence of the cooling-down processes of the temperature profiles in the pulse tube of a 4K two-stage pulse tube cryocooler from room temperature down to low temperature.