Inertance Tube Optimization for Pulse Tube Refrigerators

Abstract

The efficiency of regenerative refrigerators is generally maximized when the pressure and flow are in phase near the midpoint of the regenerator. Such a phase relationship minimizes the amplitude of the mass flow for a given acoustic power flow through the regenerator. To achieve this phase relationship in a pulse tube refrigerator requires that the flow at the warm end of the pulse tube lag the pressure by about 60 degrees. The inertance tube allows for the flow to lag the pressure, but such a large phase shift is only possible with relatively large acoustic power flows. In small pulse tube cryocoolers the efficiency is improved by maximizing the phase shift in the inertance tube. This paper describes a simple transmission line model of the inertance tube, which is used to find the maximum phase shift and the corresponding diameter and length of the optimized inertance tube. Acoustic power flows between 1 and 100 W are considered in this study, though the model may be valid for larger systems as well. For large systems the model can be used to find the minimum reservoir volume that in combination with the inertance tube provides a phase shift of 60 degrees. This transmission line model is compared with some experimental results on a small‐diameter inertance tube and found to agree quite well provided some heat transfer is taken into account. Design graphs for a frequency of 60 Hz and an average pressure of 2.5 MPa are presented for different pressure ratios and for both adiabatic and isothermal conditions.