Inertance Tube Models and Their Experimental Verification - Luo, Ercang; Radebaugh, Ray; Lewis, Michael (Advances in Cryogenic Engineering; Volume 49B, 2004)
The inertance tube is a relatively new phase shifter that can avoid the DC-flow loss that commonly occurs in a pulse tube refrigerator with a double-inlet loop. The impedance of an inertance tube is a result of its resistance, inertance, and compliance effects. Previously, simple lumped-parameter models have been used to predict the phase shifting performance, but with limited accuracy. Other realistic effects, such as turbulent flow and heat transfer between gas and solid wall must be considered in improved models. Verification of inertance tube models has been difficult because systematic experimental data on inertance tubes are very limited. This paper presents a laminar-flow thermoacoustic transmission-line model and a turbulent-flow thermoacoustic model that accounts for both turbulent flow and heat transfer. The laminar-flow transmission-line model is solved analytically whereas the turbulent thermoacoustic model must be solved numerically. To verify the accuracy of the models, experimental measurements were conducted with frequencies between 20 and 90 Hz and with acoustic power flows less than about 50 W. The turbulent-flow model agrees reasonably with the experimental results for most of the experimental conditions investigated here.