Experimental Investigation and Modeling of Inertance Tubes

Abstract

Three models describing and predicting the inertance effect in inertance tubes for pulse tube refrigerators are presented in this thesis. All models take the inertance, the compliance, and the resistance associated with oscillating gas flow in the inertance tube into account. The first model is based on electrical transmission line theory, the second is based on lumped components in which the resistance, compliance, and inertance are each represented by a single, lumped component in a network. The third model, introduced for the first time here, divides the inertance tube into a number of smaller tubes with each smaller tube represented by a resistance, compliance, and inertance element. The distributed lumped components can be combined in a network and used to predict mass flow, pressure, and their phase in the inertance tube. To verify these models, the mass flow rate and pressure characteristics are measured for a number of different inertance tube geometries at different experimental conditions. The instantaneous pressure at various locations and the mass flow rate at the terminating end of the inertance tube can be measured relatively easily. The mass flow rate at the pulse tube end of the inertance tube presented a challenge and several techniques were used to measure this quantity. A commercially available, hot film anemometer was modified in order to measure the rather high mass flow into the inertance tube and withstand the high operating pressure. Unfortunately this modified anemometer failed to measure the true mass flow under oscillating flow conditions. Two methods of indirectly measuring the mass flow exiting the compressor were introduced. Although these two methods were shown to be capable of measuring the mass flow correctly under certain limiting conditions, they failed to accurately measure the mass flow rate consistently over a range of operating conditions. Therefore, the models are ultimately verified primarily through careful comparison with those quantities that can be easily and reliably measured; specifically the pressure variation along the length of the inertance tube and the mass flow rate into the reservoir. These experimental quantities are shown to be in good agreement with the model's predictions over a range of operating conditions. Design charts are generated with the experimentally verified, distributed component model and are presented for various operating conditions in order to ease the design of inertance tubes for pulse tube refrigerators with kW-level refrigeration power. These design charts enable the designer to select inertance tube geometry that achieves a desired phase shift for a given level of acoustic power.