Numerical simulation and loss analysis on a two-stage GM cryocooler working at liquid helium temperatures

Abstract

Two-stage Gifford-McMahon Cryocoolers (GMC) working in liquid helium temperature range are widely utilized in various fields such as low-temperature superconductors, cryogenic medical instruments, and quantum computing. However, even though they have achieved mature commercialization, their current cooling capacity and efficiency remain low for a long time in the scientific and industrial applications. An in-depth analysis of the loss distribution characteristics of GM cryocooler is crucial for guiding further performance optimization. This study establishes a comprehensive numerical simulation model for a domestically produced GM cryocooler working at liquid helium temperatures. The coupling between compressor, rotary valve, and cold head is considered. Detailed investigation on the loss characteristics in different components at different cooling temperatures are carried out. Results indicate that as the cooling temperature decreases, the proportion of the loss in the compressor and rotary valve decreases, while that of the cold head increases due to the real gas effect. At cooling temperature of 4.2 K, the loss proportions of these three components are 2689.0 W (46.2 %), 1138.9 W (19.6 %), and 1879.6 W (32.3 %), respectively. In the rotary valve, more than 70 % of its total loss is caused by friction (e.g. 793.8 W at 4.2 K). To compare the effects of different loss on the 2^nd-stage cooling capacity, gross cooling capacity ${\dot{Q}}_g$ is used. When lower than 8 K, the ${\dot{Q}}_g$ of loss in the cold head is mainly due to the real gas effect (e.g. 17.53 W at 4.2 K). When higher than 8 K, the ${\dot{Q}}_g$ of 1^st-stage irreversible heat transfer loss dominates (e.g. 15.95 W at 12 K), followed by the pressure drop loss. Therefore, to improve the performance of the cold head, best to reduce the real gas loss when lower than 8 K, and adjusting the porosity and specific heat of the fillers in the regenerator should be considered.