Experimental Investigation and Modeling of Inertance Tubes

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Date
2004Author
Schunk, Lothar O.
Publisher
University of Wisconsin-Madison
Metadata
Show full item recordAbstract
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.
Subject
Thesis (M.S.)--University of Wisconsin--Madison, 2004.
Dissertations Academic Mechanical Engineering.
University of Wisconsin--Madison. College of Engineering.
Permanent Link
http://digital.library.wisc.edu/1793/7620Description
Under the supervision of Professor Gregory Nellis; 153pp.
Citation
Schunk, L.O. (2004). Experimental Investigation and Modeling of Inertance Tubes. Master's Thesis, University of Wisconsin-Madison.