Investigations on a 2.2 K five-stage Stirling-type pulse tube cryocooler. Part A: Theoretical analyses and modeling

This paper conducts systematic theoretical analyses and modeling of a five-stage Stirling-type pulse tube cry-ocooler (SPTC) which is expected to directly reach a temperature of around 2 K and also to simultaneously achieve the cooling capacities at five temperatures varying from 2.2 K to 80 K for multiple uses. At the fourth stage it uses an active phase compressor (APC) to obtain the optimal phase relationship at the low temperatures below 12 K. A further improved electrical circuit analogy (ECA) model with the APC is developed to investigate the phase characteristics, loss mechanisms, and cooling performance of the last two stages. The structural design of the five-stage SPTC is described, in which a waveform synthesis method based on the impedance and phase analysis is proposed to clarify the effects of APC parameters on the pressure and flow in the regenerators of the last two stages. The impedance and dimensional parameters of both stages are optimized according to the system exergetic efficiency. The simulation results indicate that, with He-3, the system exergetic efficiency of the last two stages is expected to reach 2.39 %. It also indicates a five-stage SPTC alone has potential of reaching 2.2 K with simultaneously having the cooling capacities at five temperatures.