Improving the Efficiency of a Gifford–Mcmahon Cryogenic Refrigerator

A numerical study of the performance of a single-stage Gifford–McMahon refrigerator was performed. A description of the mathematical model of the refrigerator operating with an unsteady flow of helium is given. Adequacy of the mathematical model was confirmed by comparing its results with published reliable data on tests of a refrigerator with cooling capacity of 30.2 W at 80 K. Using the wave approach, a method was developed that made it possible to study the time behavior of helium temperatures at direct and counter-flow helium blow at the regenerator inlet and outlet, as well as packing in its middle part. It is shown that for small amplitudes of temperature fluctuations, it is possible to reduce the length of the regenerator by 20–25% without diminishing its performance indicators. From the analysis of the operation of a single-stage cryogenic refrigerator, it is established that the main source of thermodynamic losses in it is the substantial non-equilibrium heat exchange between helium in the cold cavity and the wall of the working cylinder. A two-fold increase of heat transfer surface in the cold cavity will increase the cooling capacity of the refrigerator by 25%, i.e., up to 37.9 watts.