Comparison of two different ways of using inertance tube in a pulse tube cooler

It is well known that the pressure wave should lead the volume flow rate at the ambient end of the pulse tube for a high-efficiency operation of a pulse tube cooler. Inertance tube can provide such a phase relationship without DC flow problem. However, inertance tube is always connected with a reservoir in previous literatures. Through theoretical calculation here, inertance tube without a reservoir can also provide a rather large phase-leading effect. Thus phasor diagram is used to analyze the relationship between phase-leading requirement and the pulse tube geometry. Roughly speaking, a larger void volume of pulse tube would require a larger phase-leading effect. Comparison experiments are also done on a thermoacoustically-driven pulse tube cooler. With i.d.2 mm tube as inertance tube, the tube without reservoir yields close results in terms of lowest temperature to that of the tube with reservoir and both give much better performance than that of an orifice with reservoir. Finally, the advantages of using inertance tube without reservoir are given.