Universal scaling law of inertance tube phase shifter

An inertance tube is a long thin tube that is now frequently used as the phase shifter for a pulse tube cryocooler. Developing a scaling law suitable for the inertance tube shifter is the objective of this work. Different pulse tube coolers need different inertance tube phase shifters which can be characterized by their acoustical power transmission and phase shifting capabilities. In other words, the acoustical power at the inlet of inertance tube reflects the gross cooling capacity of pulse tube cryocooler and the phase angle at its inlet that required by pulse tube cryocooler for efficient operation. To obtain the universal operating behavior of inertance phase shifter, a series of dimensionless groups are needed, including dimensionless diameter, dimensionless length of inertance tube, and dimensionless acoustical power. Two limiting cases of inertance tube phase shifter configurations, infinitely large reservoir volume and zero reservoir volume are highlighted in modeling. Oscillating turbulent flow is incorporated, which makes universal scaling law describe the practical operating behavior of real inertance tube shifters. Charts are provided to quickly choose an optimal inertance tube phase shifter.