Theoretical and experimental study of a gas-coupled two-stage pulse tube cooler with stepped warm displacer as the phase shifter

A compact and high efficiency cooler working at liquid hydrogen temperature has many important applications such as cooling superconductors and mid-infrared sensors. This paper presents a two-stage gas-coupled pulse tube cooler system with a completely co-axial configuration. A stepped warm displacer, working as the phase shifter for both stages, has been studied theoretically and experimentally in this paper. Comparisons with the traditional phase shifter (double inlet) are also made. Compared with the double inlet type, the stepped warm displacer has the advantages of recovering the expansion work from the pulse tube hot end (especially from the first stage) and easily realizing an appropriate phase relationship between the pressure wave and volume flow rate at the pulse tube hot end. Experiments are then carried out to investigate the performance. The pressure ratio at the compression space is maintained at 1.37, for the double inlet type, the system obtains 1.1 W cooling power at 20 K with 390 W acoustic power input and the relative Carnot efficiency is only 3.85%; while for the stepped warm displacer type, the system obtains 1.06 W cooling power at 20 K with only 224 W acoustic power input and the relative Carnot efficiency can reach 6.5%.