Phase shifting in pulse tube refrigerators

Abstract

Different types of pulse tube refrigerators are described by alternative phasor diagrams based on the volume flow rates applied at the ambient temperature inlets of the regenerator and of the pulse tube(s). This provides a simple means for finding the optimum phase shift between pressure and flow rate for PTRs operated with different kinds of phase shifters such as the orifice system, the inertance tube, and the double inlet arrangement. The basic features are discussed first for ideal systems with no losses. Then, those results are compared with experimental data of single- and two-stage pulse tube refrigerators and also with more comprehensive numerical calculations which take account of irreversible losses caused by friction as well as heat conduction and heat transfer. It is shown that for the pulse tube, the phase shift can be well estimated from the ideal model, whereas there is more discrepancy for the regenerator. Those phasor diagrams are shown to be helpful tools for the design of multistage systems.