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Impedance Measurements of Inertance Tubes



Michael A. Lewis, Peter E. Bradley, Ray Radebaugh


The flow impedance of an inertance tube 5.74 mm inside diameter and 2.36 m long coupled to various reservoir volumes was measured and compared with that predicted by a model based on a transmission line analogy. Though data at other average pressures and temperatures were obtained this paper focuses on data taken with an average pressure of 2.5 MPa and a pressure ratio of 1.3. Frequencies of 50, 60, 70 Hz, were used, and reservoir volumes were 30, 83, 134, 334 cm3. The amplitudes and phases of the instantaneous pressure and flow at both ends of the inertance tube were measured and the resulting complex impedance and the inlet acoustic power were determined. The flow at the reservoir end was determined from the instantaneous pressure in the reservoir, and the flow at the inlet end was determined from a measurement of the pressure drop across the aftercooler consisting of copper wire mesh. The model predicted a resonance associated with the compliance of the reservoir and the inertance of the tube analogous to an electrical LC resonance circuit. At this resonance condition the imaginary part of the impedance goes to zero, the magnitude of the impedance reaches a minimum, and the inlet acoustic power becomes a maximum for a fixed pressure ratio. The experiments agreed well with the model and confirmed the existence of the resonance condition at the reservoir volume predicted by the model. For an average pressure of 2.5 MPa, a pressure ratio of 1.3, and a frequency of 60 Hz the inlet acoustic power varied from 200 W with a reservoir volume of 334 cm3 to about 800 W with a reservoir volume of 83 cm3. With a smaller reservoir volume the acoustic power decreased in agreement with that predicted by the model.
Proceedings Title
Impedance Measurements of Inertance Tubes
Conference Dates
August 29-September 2, 2005
Conference Location
Keystone, DC, USA
Conference Title
2005 Cryogenic Engineering Conference and International Cryogenic Materials Conference


Cryocoolers, cryogenics, flow impedance, inertance, pulse tubes, refrigeration, resonance, thermoacoustics


Lewis, M. , Bradley, P. and Radebaugh, R. (2005), Impedance Measurements of Inertance Tubes, Impedance Measurements of Inertance Tubes, Keystone, DC, USA, [online], (Accessed May 30, 2024)


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Created August 28, 2005, Updated October 12, 2021